simdriveline——Analyzing Degrees of Freedom

合集下载

指纹英文

*Corresponding author.Fax:(#39)516443073;e-mail:zkovacs @deis.unibo.itPattern Recognition 32(1999)877—889Fingerprint minutiae extraction from skeletonizedbinary imagesAlessandro Farina,Zsolt M.Kova cs-Vajna *,Alberto LeoneD.E.I.S.,Uni v ersity of Bologna,Viale Risorgimento 2,I-40136Bologna,ItalyReceived 26June 1997,in revised form 25June 1998AbstractFingerprint comparison is usually based on minutiae matching.The minutiae considered in automatic identiﬁcationsystems are normally ridge bifurcations and terminations.In this paper we present a set of algorithms for the extraction of ﬁngerprint minutiae from skeletonized binary images.The goal of the present work is the extraction of the real 40—60minutiae of a ﬁngerprint image from the 2000—3000contained in typical skeletonized and binarized images.Besides classical methodologies for minutiae ﬁltering,a new approach is proposed for bridge cleaning based on ridge positions instead of classical methods based on directional maps.Finally,two novel criteria and related algorithms are introduced for validating the endpoints and bifurcations.Statistical analysis of the results obtained by the proposed approach shows eﬃcient reduction of spurious minutiae.The use of the ﬁngerprint minutiae extraction algorithms has also been considered in a ﬁngerprint identiﬁcation system in terms of timing and false reject or acceptance rates.The presented minutiae extraction algorithm performs correctly in dirty areas and on the background as well,making computationally expensive segmentation algorithms unnecessary.The results are conﬁrmed by visual inspections of validated minutiae of the NIST sdb 4reference ﬁngerprint image database. 1999Pattern Recognition Society.Published by Elsevier Science Ltd.All rights reserved.Keywords :Image processing;Binary image;Post-processing ﬁngerprint;Minutiae;NIST sdb 41.IntroductionResearch in the design of automatic ﬁngerprint identi-ﬁcation systems (AFIS)is currently focusing on ﬁnger-print classiﬁcation into ﬁve classes [1]and on ﬁngerprint matching,whose goal is the identiﬁcation of a person by means of the ﬁngerprints.If the stored image database is huge,the identiﬁcation process needs both the classiﬁca-tion and the matching stages.In this paper we focus ourattention on a part of the matching stage,which is usu-ally based on preprocessing,feature extraction and matching algorithms.There are several useful features in ﬁngerprints,related to ridge topology,called minutiae.The American National Standards Institute has proposed a classiﬁca-tion of minutiae into four main groups:terminations,bifurcations,crossovers and undetermined [2].The most important minutiae types are terminations and bifurca-tions.In a ﬁngerprint identiﬁcation system the ﬁngerprint image is obtained by a sensor or camera and the match-ing process starts with image ﬁltering.The minutiae are extracted and they are compared with those of the0031-3203/99/$—See front matter 1999Pattern Recognition Society.Published by Elsevier Science Ltd.All rights reserved.PII:S 0031-3203(98)00107-1already stored images in order to establish the corres-pondence.The minutiae extraction can be based on gray-scale[3]or binary images.In this paper we focus our attention on a binary image-based technique,where we assume that theﬁnger-print image has been either acquired directly in binary or binarized from a gray-scale image.We assume also that the image has been skeletonized.The problem in this methodology comes from the fact that a minutia in the skeleton image does not always correspond to a mean-ingful point in the real image.In fact,there are more than a thousand apparent ending or bifurcation points,while the real minutiae are less than100.Such a behavior arises as a consequence of under-inking,over-inking,wrinkle, scars and excessively worn prints,and,therefore,spuri-ous minutiae can appear in the skeleton image after pre-processing.In order to simplify or to preserve the reliability of the AFIS and to lower computational costs,post-processing of the skeleton image is necessary to reduce the number of spurious minutiae.Several approaches have been already proposed in the last few years to enhance skeletonized images.The AFIS proposed by Stosz and Alyea[4]uses pore positions coupled to other minutiae extracted from live scanned images:the quality of the valley skeleton isﬁrst improved by analyzing and extracting segments that represent pores(cleaning),then syntactic processing is used to remove undesirable artifacts:two disconnected ridges are connected if their distance is less than a given threshold and endpoint directions are almost the same; wrinkles are detected by analyzing information on neigh-boring branch points.Chen and Kuo[5]adopt a three-step false minutiae identiﬁcation process:(i)ridge breaks are repaired some-how using the ridge directions close to the minutiae;(ii) minutiae associated with short ridges are dropped;(iii) crowded minutiae in a noisy region are dropped.Malles-wara’s methods[6]are used to eliminate those false minutiae which are caused by noise or imperfect image processing.A post-processing algorithm applied to binarized and not thinned images is proposed by Fitz and Green[7]. These techniques are employed to remove small holes, breaks and lines in and along the ridges and they are implemented by convolving morphological operators with the image.Spikes caused by the skeletonizing process can be removed by the adaptive morphologicalﬁlter proposed by Ratha et al.[8].Minutiae are detected by counting the BLACK neighbors in a3;3window.False endpoints and bifurcations are removed by means of three heuristic criteria:(i)two endpoints with the same orientation and whose distance is below a threshold are deleted(ridge break elimination);(ii)an endpoint connected to a bifur-cation and below a certain threshold distance is removed (spike elimination);(iii)minutiae below a certain distance from the boundary of the foreground region are cancelled (boundary eﬀect treatment).The duality between valley image and ridge image has been exploited by Hung[9]considering that bifurcations and bridges in one of the two images correspond to endings and breaks,respectively,in the dual image. Therefore,the same algorithm can be applied both to valley and ridge images to remove ridge breaks and bridges.A graph is deﬁned for both images by assigning a vertex to each endpoint and bifurcation and by assign-ing an edge to each ridge.Each edge is characterized by the length of the corresponding ridge,while the degree of a vertex is given by the number of converging edges. Spurs,holes,bridges and breaks are then removed by considering some property of the ridge graph.The same algorithm can be mostly applied to the valley graph to remove ridge breaks,crossovers and other particular conﬁgurations.Xiao and Raafat[10]assume thatﬁngerprints have already been pre-processed and skeletonized.They pro-pose a post-processing based on a combined statistical and structural approach.Fingerprint minutiae are char-acterized by a set of attributes like the ridge length,the direction for endpoints and bifurcations,the angle be-tween two minutiae.Moreover,each endpoint or bifurca-tion is also characterized by the number of‘‘facing’’minutiae in its neighborhood.The neighborhood area depends on the local distance between ridges.Finally,the number of‘‘connected’’minutiae is evaluated.The post-processing algorithm connects facing endpoints,removes bifurcations facing with endpoints or other bifurcations and then connects the newly generated endpoints,and ﬁnally removes spurs,bridges,triangle structures and ladder structures.Unfortunately,it is not possible to assign a‘‘global’’ridge distance to the whole image, because it varies up to300%of its local value in a typical ﬁngerprint.Several methodologies of the local ridge distance map computation may be found in the liter-ature[11].The algorithm proposed in this paper works on the skeleton image obtained from a binarized version of the ﬁngerprint image.Standard algorithms are used to re-move close minutiae in noisy areas.Ridge repair is per-formed on the base of the directions of the two ridge pieces to be connected and the direction of the segment which should rebuild the broken ridge,while previous works suggested the use of structural and statistical con-siderations[10]or analysis of the distance between the two broken ridges[8].The novel approach proposed to remove bridges is based on the ridge positions instead of evaluating CPU-consuming direction maps[9].Short ridges are removed on the basis of the relationship be-tween ridge length and average distance between ridges, instead of considering the average ridge length.Island ﬁltering(already proposed in the literature)is performed878 A.Farina et al./Pattern Recognition32(1999)877—889Fig.1.Generic structure of an automatic ﬁngerprint identiﬁcation system and detail of the ‘‘Minutiae Extraction’’block.in a more eﬃcient way,since it is not based on a graph construction to detect closed paths.Finally,two new topological validation algorithms are presented to clas-sify reliable endpoints and bifurcations:they are removed if topological requirements are not satisﬁed,they are classiﬁed as less reliable minutiae if requirements are not fully satisﬁed,else they are considered as highly reliable minutiae.Less reliable minutiae can be taken into ac-count if the number of highly reliable minutiae cannot guarantee the required conﬁdence level of the identiﬁca-tion.Simulation results demonstrate the eﬀectiveness of the proposed algorithm and display a sort of implicit segmentation that removes all minutiae related to re-gions outside the ﬁngerprint.2.The Proposed AlgorithmThe minutiae extraction methodology proposed in this work is suitable for an AFIS like the one sketched in Fig.1.We assume that the skeleton image has been deﬁned and a local ridge distance map has been derived.The local ridge distance map deﬁnes the average ridge distance in each region of the image [11].This is neces-sary because the ridge distance varies over the image and it is one of the most important reference parameters in the image both for ﬁlter design and minutiae extraction.The algorithm performs the following steps,according to the sequence detailed in Fig.1.2.1.Pixel codi ﬁcationThe codiﬁcation stage performs minutiae classiﬁcation and removal of unclassiﬁed conﬁgurations.The skeleton image is processed in order to obtain a codiﬁed imagewhere the value of each pixel represents the number of outgoing branches in the corresponding pixel of the skel-eton image [3].2.2.Pre-ﬁlteringLow-quality areas are often present in the original scanned ﬁngerprint image.Binarizing and thinning algo-rithms usually produce a large number of spurious high-density minutiae in these sections of the ﬁngerprint with obvious diﬃculties for the identiﬁcation algorithms.Pre-ﬁltering is necessary to remove as many as possible spurious minutiae without reducing,if possible,the num-ber of details useful for the identiﬁcation.A ﬁrst pre-ﬁltering has already been performed in the codiﬁcation phase,removing isolated points and blobs.The pre-ﬁltering algorithm scans the codiﬁed image in the usual way (row by row from top-left to bottom-right)and acts according to the type of the minutia conﬁgura-tion.At this phase an endpoint next to another minutia is deleted.Adjacent bifurcations are removed and those where one or more crosses are detected in their neighbor-hood.Also,crosses are removed if another cross is detec-ted in their neighborhood.2.3.Skeleton enhancementSkeleton enhancement allows for:ridge repair by con-necting endpoints identiﬁed as ridge breaks,elimination of bridges,spurs and short ridges.Ridge breaks are caused by insuﬃcient ink,wrinkle and scars.Two facing endpoints can be connected,repairing the ridge,if they are assumed to belong to the same ridge.The ridge repair algorithm works in three steps:search of facing end-points,best endpoint selection and ridge reconstruction.A.Farina et al./Pattern Recognition 32(1999)877—889879Fig.3.Spur and processedslide.Fig.2.Bridge and processed slide.2.4.Minutiae in v alidationMinutiae originated by bridges and spurs are invali-dated,once these conﬁgurations have been recognized.Close minutiae are also removed.2.4.1.Elimination of bridges and spursBridges and spurs give rise to false minutiae and they must be removed as in the examples shown in Figs 2a and 3a.It is important to apply this algorithm before the close minutiae are searched for,in order to keep as many as possible valid minutiae.A novel method is proposed to detect and clear bridges and spurs.In previous works,bridges and spurs are detected using a local dominant directional map [9].The novel algorithm,proposed in this work,uses a visual consideration:bifurcations found when these two spurious patterns are detected,are diﬀer-ent from real bifurcations.In these ‘‘spurious’’bifurca-tions only two branches are aligned while the direction of the third branch is generally diﬀerent.In bridges,the third branch is almost orthogonal to the other two.The absolute value of the scalar product between branch unit vectors is used to estimate the alignment or orthogonality of the two branches.In this implemen-tation one orthogonality threshold @Qand two align-ment thresholds @Q and @Qhave been used.Twodirections are considered to be orthogonal if the absolute value of the scalar product is lower than @Q"0.55,i.e.when the angle is greater than 56°.Two directions are considered to be aligned if the absolute value of the scalar product is greater than @Q(in step 1e ofthe algorithm)or @Q (in step 2a). @Q"0.85and@Q"0.80(corresponding to an angle less than 32°and 37°,respectively).Algorithm.Elimination of bridges and spurs For each bifurcation:(1)if there are at least N JP" points in each branch,where is the local ridge distance in pixels:(a)estimate the direction of each branch by linearregression using at least N JPpoints;880 A.Farina et al./Pattern Recognition 32(1999)877—889Fig.4.Islands caused by largeridges.Fig.5.Three bifurcations belonging to anisland.mon bifurcation topology.(b)if two branches are aligned and the third is almostorthogonal:search for another minutia along the orthogonal branch in the ﬁrst N @Q"5 /6points;(c)if another minutia is found:remove the bridge or spur;(d)if two branches are aligned,but the third is notorthogonal:search for an endpoint in the ﬁrst N @Q"3 /2points;(e)if the endpoint is found:remove the spur;(2)if only two branches contain at least N JP points:(a)if these two branches are aligned:search along thethird one and remove this short bridge or spur.2.4.2.Elimination of close minutiaeThe algorithm ﬁrst removes the close endpoints and then the other close minutiae.Any endpoint found in a small square area is removed.The minimum acceptable distance between two endpoints is given by N AC" /2pixels,where is the local ridge distance.The search region is a square of side 2N AC#1centered on the cur-rent endpoint.There are less than 100minutiae in a good quality rolled ﬁngerprint image and their relative distance is rarely less than the local ridge distance,therefore too close minutiae on the same branch are removed.2.5.Topological v alidationThe topological validation algorithms are based on neighboring ridge topology:Island removal :Bifurcations belonging to a short closed path are invalidated.Bifurcation and endpoint validation :Neighboring ridge layout is considered to verify the existence of the correct pattern.These two novel algorithms will introduce re-liable and less reliable minutiae codes.2.5.1.Island eliminationClosed paths are commonly referred to as islands.Even if this particular minutia can occur in a common ﬁngerprint,islands are often generated in the skeleton image by noisy areas and where large irregular ridges are thinned as shown in Fig.4,giving rise to false minutiae.The term island is usually employed for two facing bifurcations which form a closed path.It may be noted that this is the most frequent situation only in high-quality images.We also experienced closed paths gener-ated by the interaction of three or more bifurcations and crosses,as the example of Fig. 5.An island can be generated also by a single bifurcation where two branches ﬂow into one another.2.5.2.Bifurcation v alidationFig.6shows the topology of a typical valid bifurcation.In fact,with the exception of bifurcations located nearA.Farina et al./Pattern Recognition 32(1999)877—889881Fig.8.Reliabilitydetermination.Fig.7.Bifurcationvalidation.mon endpoint topology.the core or delta of the ﬁngerprint,ridges near the bifur-cation run parallel to the outgoing branches.Diﬀerent bifurcation structures can be evidenced in the ﬁngerprint margins or in textured areas.Therefore,the above prop-erty is suitable for removing isolated bifurcations in meaningless areas.The proposed validation algorithm can be divided into two phases:the ﬁrst is necessary to distinguish between a valid and an invalid bifurcation,the second is required to ﬁnd a reliable bifurcation.The ﬁrst phase checks the existence of lateral ridges for each branch departing from the bifurcation (Fig.7).The second phase checks the geometrical properties around the bifurcation (Fig.8).Algorithm.Bifurcation validation For each valid bifurcation:(1)compute the three branch directions on N @T"3 /2points;(2)if a minutia is found within N @T" points:invali-date this bifurcation and go further;(3)move along each branch for N @T" /2points andverify that a lateral edge is present within N @T"3 /2points (see Fig.7);(4)if a lateral ridge is not found:invalidate this bifurca-tion and go further;(5)if lateral ridges are found:mark the bifurcation asa less reliable bifurcation;(6)deﬁne a rectangular area ABCD (see Fig.8)with:AB "3 /2,AD "4 ;(7)move along the lateral ridges (see Fig.8)from the leftintersections with the rectangle P0and P1to the right intersections P2and P3;(8)if an endpoint is found:invalidate this bifurcation andgo further;(9)if P2and P3are reached:mark the bifurcation asreliable .2.5.3.Endpoint v alidationThe distance between two adjacent ridges remains almost constant where no other minutiae exist in the valley between the two ridges.The same consideration applies to the dual representation of the ﬁngerprint ana-lyzing the valley behavior.This regularity is perturbed by the presence of an endpoint when a ridge is interrupted or by its dual structure,a bifurcation,when a valley is ended.Fig.9shows the typical ridge behavior around an endpoint:neighbor ridges close each other up when the ridge between them is interrupted.It can be noted how the distance between adjacent ridges remains almost con-stant.The proposed endpoint validation algorithm is based on this visual consideration and removes most of the882 A.Farina et al./Pattern Recognition 32(1999)877—889Fig.10.Rectangular area.Table1Reduction of the number of minutiae(average and standard deviation)after application of the proposed algorithm Preliminary Initial Final Reduction processing factorGLGX GLGX DGL DGLNo processing2933111449(29)1798.33% Segmentation184570347(29)1797.45% Segmentationandﬁltering72236370(54)1590.30%spurious endpoints and those originated byﬁngerprint borders.Algorithm.Endpoint validationFor each valid endpoint:(1)evaluate the endpoint direction deﬁned as the direc-tion of the broken ridge over N P" points;(2)if the direction cannot be evaluated for the existenceof a minutia within N P points:invalidate the end-point and go further;(3)move along the endpoint ridge for N CT " /2points;(4)search orthogonally to the endpoint ridge directionfor the neighboring ridges;(5)if within N CT "3 /2points the ridges are not inter-cepted:invalidate the endpoint and go further; (6)deﬁne a rectangular area ABCD(see Fig.10)with:AB"3 /2,AD"3 ,(7)lateral ridges are scanned from P0and P1to the exitfrom the rectangle(points P2and P3)or a minutia occurrence;(8)if a lateral ridge crosses the rectangle in DC or AB,while the other crosses the rectangle in BC:mark the endpoint as a less reliable endpoint;(9)if a minutia is found:invalidate the endpoint and gofurther;(10)if both lateral ridges cross the rectangle in BC:(a)if the lateral ridges are not convergent(as deﬁnedin Section2.5.4):mark the endpoint as a less reliable endpoint else mark the endpoint as a highly reliable endpoint;(b)if a ridge is detected between P2and P3:invali-date the endpoint.2.5.4.Ridge con v ergenceThe points of lateral ridges contained in the rectangle ABCD are used to estimate their directions.If u and u are the unit vectors of the estimate directions,the degree of convergence is estimated by the vertical com-ponent of the vector product:C"(u u ))k(1) where k is the unit vector of the axis normal to the image teral ridges are considered convergent if the coeﬃcient C* CN"0.085corresponding to an angle of 4°.If the ridges are almost parallel,we have C:0,while C(0for divergent ridges.If an endpoint does not verify the convergence condi-tion it is marked as less reliable but it is not invalidated since lateral ridges of valid endpoints can be almost parallel and characterized by very slow convergence.3.ResultsThe proposed minutiae extraction procedure has been tested on500ﬁngerprint images from the NIS¹Special Database4[12](ﬁgs—0data).Fingerprint images are stored as512;512pi xel8-bit gray-scale images.The database is organized to guarantee the existence of sev-eral diﬀerentﬁngerprint topologies and diﬀerent quality images.3.1.Statistical resultsThe performance evaluation of this kind of algorithm is not a well-deﬁned task.However,qualitative consider-ations can be based on a contextual visual check. The goal of post-processing is to minimize the number of spurious minutiae and to maximize the amount of reliable minutiae to allow reliableﬁngerprint matching. Statistical analysis has been carried out on three diﬀerent initial image conditions:(i)raw image;(ii)seg-mented image:boundary areas without information have been removed,then images have been binarized andA.Farina et al./Pattern Recognition32(1999)877—889883Table 2Minutiae average number and relative reduction AlgorithmEnd.Bif.Endpoint Bifurcation Total reductionreductionreductionPre-ﬁltering 379266Ridge breaks 31126617.940.0010.54Bridge and spur 26412415.1153.3832.76Short ridge 21712417.800.0012.11Close endpoint 17012421.660.0013.78Close minutiae 1416717.0645.9729.25Island141550.0017.915.77Validate bif.14134(10)0.0038.18(56.36)10.71(15.82)Validate ep.36(6)34(10)74.47(78.72)0.0060.00(67.27)Table 3Total execution time (s)Execution timePreventive AverageStandard action deviation No action 1.7060.137Segmentation 1.6610.121Segmentation 1.4970.087and ﬁlteringTable 4Algorithm execution time (segmented and ﬁltered images)AlgorithmExecution Standard Normalized time deviation exec.time Codiﬁcation 0.0510.0090.000087Pre-ﬁltering 0.0400.0090.000068Ridge breaks 0.0890.0290.000247Bridge and 0.3420.0330.001702spursShort ridges 0.1580.0110.000712Close endpoint 0.1470.0100.000800Close minutiae 0.1530.0100.000613Island 0.1600.0140.002692Bif.valid.0.1780.0130.003624Endp.valid.0.1790.0140.001403thinned;(iii)segmented and ﬁltered image:segmented image has also been improved by non-linear enhance-ment [13].The minutiae extraction algorithms applied to the three diﬀerent sets of test images produce the results shown in each row of Table 1,where the average and the standard deviation of the number of minutiae in the original images are shown in columns 2and 3,respective-ly,while average and standard deviation estimated after the application of the proposed algorithm are shown in columns 4and 5.Column 5also reports the average number of less reliable minutiae (between round brackets).The last column reports the percentage of minutiae removed by the algorithm.Obviously,segmented and ﬁltered images contain a lower initial number of spurious minutiae,because the image quality is higher.Even for this class of images,the number of minutiae is reduced by an order of magnitude.It must also be noted how the standard deviation is reduced.Therefore,the number of valid minutiae is ‘‘more uniform’’in the post-processed image set,which displays the real minutiae distribution in ﬁngerprints.Better results are obtained for raw and segmented-only images.It should be noted how a lower number of minutiae have been validated in these lower-quality im-ages.This,together with the visual check,highlights an implicit segmentation property of the proposed algo-rithms.Furthermore,the algorithms eliminate minutiae located in noisy inner ﬁngerprint image regions.Table 2gives the statistics related to segmented and ﬁltered images,reporting outcome of application of each step of the proposed algorithm in each row:columns 2and 3show the average number of endpoints and bifurcations after application of the algorithm speciﬁed in column 1.The number of less reliable minutiae is reported in brackets.The last three columns show the endpoint,bifurcation and total reduction factors after application of each algorithm (numbers in brackets show the reduction factors,including less reliable minutiae).The algorithm which most reduces the endpoint num-ber is the topological endpoint validation,since it takes into account image boundaries.For the bifurcation num-ber,bridge and spur elimination and close minutia elim-ination are the most eﬀective.This is due to low-quality image areas where the minutiae density is very high.884 A.Farina et al./Pattern Recognition 32(1999)877—889Fig.11.Skeleton with minutiae points marked:(a)before post-processing;(b)afterpost-processing.Fig.12.Extracted minutiae points superimposed on the gray-level image.False minutiae are marked by a square.The statistics of raw images or segmented-only images display a major impact of the algorithms on close minu-tiae and topological validation.This is due to the higher number of spurious minutiae that are present in the raw or segmented-only images.This result also shows that the proposed algorithm performs an implicit image segmen-tation,since the ﬁnal number of minutiae obtained from raw images turns out to be comparable to that obtained from high-quality pre-processed images.3.2.Algorithm performanceThe algorithms have been executed on a S ºN SPARC -station 20with total execution time depending on the initial image treatment as shown in Table 3.For each algorithm the following statistics have been evaluated on the 500test images:average execution time;standard deviation of the execution time.The execution times of each step of the extraction procedure (relative to segmented and ﬁltered images)are reported in Table 4.The normalized average execution time is also reported in column 4.Normalization is obtained by dividing the execution time by the number of minutiae processed by the corresponding algorithm.The bridge and spur elimination algorithms are the most CPU-expensive but this is due to the order of application of the diﬀerent algorithms.If normalized times are considered the island elimination and the bifur-cation topological validation turn out to be computa-tionally more intensive.The sequence of the diﬀerent sub-algorithms has been adjusted to optimize the ﬁnal result.However,since the most CPU-expensive steps are performed when the number of minutiae has already been signiﬁcantly reduced,execution times appear to be almost equally distributed among the diﬀerent procedures.3.3.Minutiae extraction algorithms in an AFISThe eﬀect of the minutiae extraction algorithm set has been investigated in terms of false acceptance and false reject rates.The AFIS where the algorithms are applied has the structure reported in Fig.1.The last operation,before the answer is generated,is a validation stage where the ﬁngerprint regions are checked between matching minutiae.This ﬁnal inter-minutiae check is very strict and it is able to discard the matchings where a number of false minutiae generate a valid matching conﬁguration.Thanks to this stage,the false acceptance rate does not increase if the minutiae are not completely ﬁltered.The false reject rate does not increase by adding false points to the correct minutiae.These considerations have beenA.Farina et al./Pattern Recognition 32(1999)877—889885。

Evidence for a massive BH in the S0 galaxy NGC 4342

Subject headings: black hole physics — galaxies: elliptical and lenticular, cD — galaxies: individual (NGC 4342) — galaxies: kinematics and dynamics — galaxies: nuclei — galaxies: structure.
–3– 1. Introduction
Several lines of evidence suggest that active galactic nuclei (AGNs) are powered by accretion onto a super-massive black hole (BH) (Lynden-Bell 1969; Rees 1984). The much higher volume-number density of AGNs observed at redshift z ≈ 2 than at z = 0, suggests that many quiescent (or ‘normal’) galaxies today must have gone through an active phase in the past, and therefore harbor a massive BH as well. Such a BH will signiﬁcantly inﬂuence the dynamics of the galaxy inside a radius of inﬂuence, rBH = GMBH /σ 2 , where σ is a characteristic velocity dispersion of the stars in the center. In particular, hydrostatic equilibrium requires that the rms velocities of the stars surrounding a massive BH follow an r −1/2 power-law (Bahcall & Wolf 1976; Young 1980). Since the late 70s, combined imaging and spectroscopy of the central regions of galaxies has suggested that massive BHs should be present in a number of early-type galaxies (see Kormendy & Richstone 1995 for a review). Conclusive dynamical evidence for the presence of a central BH requires that a model with a BH can ﬁt all observations (photometric and kinematic), and that no model without a BH can provide an equally good ﬁt. Such conclusive evidence can only be inferred from observations that probe well inside the radius where the BH dominates the dynamics. Up to a few years ago, most claimed BH detections were based on observations with spatial resolutions of similar size as the radii of inﬂuence of the inferred BH masses (Rix 1993). This, together with the limited amount of freedom in the models used to interpret the data, has hampered an unambiguous proof for the presence of these BHs (i.e., the observed kinematics could not be confronted with all possible dynamical conﬁgurations without a BH). Often spherical models were used even when the observed ﬂattening was signiﬁcant. If the models were axisymmetric, the distribution function (hereafter DF) was often assumed to depend only on the two classical integrals of motion, energy and vertical angular momentum; f = f (E, Lz ). This implies that the velocity dispersions in the radial and vertical directions are equal (i.e., σR = σz ). It is well-known that strong radial anisotropy in the center of a galaxy results in a high central velocity dispersion, mimicking the presence of a massive BH (cf. Binney & Mamon 1982). Conclusive evidence for a BH therefore requires that one can rule out radial anisotropy as the cause of the high velocity dispersions measured, and models must thus be suﬃciently general. Recently two major breakthroughs have initiated a new era in the search for massive BHs in normal galaxies. First of all, we can now obtain kinematics at much higher spatial resolution (down to FWHM ∼ 0.1′′ ), using specially-designed spectrographs, such as the Subarcsecond Imaging Spectrograph (SIS) on the Canada-France Hawaii Telescope, or the Faint Object Spectrograph (FOS) and STIS aboard the HST. This allows us to probe the gravitational potential much closer to the center, where the BH dominates the dynamics. Not only has this improved the evidence for massive BHs in several old BH-candidate galaxies (M31, Ford et al. 1998; M32, van der Marel et al. 1997, 1998; M87, Harms et al. 1994, Macchetto et al. 1997; NGC 3115, Kormendy et al. 1996a; NGC 4594, Kormendy et al. 1996b), but it has also provided new cases (M84, Bower et al. 1998; NGC 3377, Kormendy et al. 1998; NGC 3379, Gebhardt et al. 1998; NGC 4261, Ferrarese, Ford & Jaﬀe 1996; NGC 4486B, Kormendy et al. 1997; NGC 6251, Ferrarese, Ford & Jaﬀe 1998; and NGC 7052, van der Marel & van den Bosch 1998). Secondly, the revolutionary increase in computer power has made it possible to investigate a large number of fully general,

CALPHAD软件介绍

Abstract
The phase-ﬁeld method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-ﬁeld modeling technique. The concept of diffuse interfaces, the phase-ﬁeld variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-ﬁeld equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-ﬁeld models, different model formulations are exploited, depending on which is most common or most illustrative. c 2007 Elsevier Ltd. All rights reserved.

SimMechanics Getting Started Guide

Trademarks MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See /trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.
SimMechanic2012b
How to Contact MathWorks

Web
comp.soft-sys.matlab
Newsgroup
/contact_TS.html Technical Support
Required and Related Products . . . . . . . . . . . . . . . . . . . . . 1-3 Required Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
suggest@ bugs@ doc@ service@ info@
Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information

Simapck_fembs_8903

6.4 6.5 6.6 6.7 6.8 6.9
Using I-DEAS . . . . . . . . . . . . . . . . . . . . . . . . 6.4 -53 Using PERMAS . . . . . . . . . . . . . . . . . . . . . . . 6.5 -58 Geometric Stiﬀness using NASTRAN - (MSC) . . . . . . . 6.6 -60 Geometric Stiﬀness using ANSYS . . . . . . . . . . . . . . 6.8 -62 Geometric Stiﬀness using ABAQUS . . . . . . . . . . . . . 6.8 -63 Geometric Stiﬀness using PERMAS . . . . . . . . . . . . . 6.0 -64 7.0 -67
FEMBS:0.0 -5
8 Notes on Usage 9 Known Bugs A Static Condensation B Dynamic Condensation
8.0 -69 .0 -71 A.0 -73 B.0 -77
FEMBS:0.0 -6
CONTENTS
FEMBS:1.
FEMBS:1.1
6.3
Using ABAQUS . . . . . . . . . . . . . . . . . . . . . . . 6.3 -49 Superelement interface via FIL ﬁles . . . . . . . . . . . . . 6.3 -49 Superelement interface via ODB ﬁles . . . . . . . . . . . . 6.3 -50 Notes on usage with the interface via ODB ﬁles . . . . . . 6.3 -52

皮带卸料机电气控制系统设计英文翻译原文

High Fidelity Simulation Modeling ofautomatic conveying systemYukun Liu, Lijie GaoLogistics Department of Automation School Beijing University of Posts and TelecommunicationsBeijing, China{ lyktsh2006, glj456}@Gang Tan, Hao WangGuiyang Potevio Logistics Tech Ltd.Guiyang, China putiantangang@ Wh539@Abstract —Automatic conve ing s stem was used widel in Distribution Center. The paper discusses the high-fidelit ysimulation methods on Automatic convey ing sy stem, analy zed automatic convey ing sy stem high-fidelity simulation levels of classification, reference standards and key points. An evaluation for simulation value and cost of each model is implemented. A high fidelity Simulation Modeling of a cold DC Automatic convey ing sy stem, which simulate the storage operations of cold distribution center.Keywords- automatic conveying system; simulation modeling; high-fidelity simulation; AutoModI.I NTRODUCTION Distribution Center automatic conveying system is a criticalequipment to connect external input and output and automated storage. Automated conveying system can greatly enhance the efficiency of storage operations and reduce costs. The utilization of automation equipment directly related to the distribution center's operational efficiency. And the efficiency of automatic conveying system directly affects the efficiency of distribution center storage operations.Three-dimensional simulation technology can carry out simulation research of the logistics distribution center. High-fidelity physics simulation model can simulate and reproduce the operation of the logistics distribution center. High-fidelity physics simulation model demands high simulation accuracy and ensure the credibility of the simulation. If simulation accuracy is not enough precise and accurate, the physics model would be difficult to achieve a high fidelity display of processes and details of the action. Engineering analyze the physical distribution center of high fidelity simulation results, can be very intuitive understanding of system operation and found the system inadequate to help improve the system parameters, modify and develop logistics and distribution center design. Research on the influencing factors of simulation credibility, people mostly focused on the logical flow of the simulation fine condition, while three-dimensional simulation of high-fidelity physics research is less. This article first analyzes the level of physical fidelity simulation and the key point of automatic conveying systems high-fidelity simulation. And then research a cold distribution center automation conveyor system module, with AutoMod 3D simulation software, build a high-fidelity three-dimensional simulationmodel, which was used to demonstrate and validate realistic automatic transmission equipment, dynamic process. II.A NALYSIS OF HIGH P HYSICAL FIDELITY SIMULATIONA.Division-level of high physical fidelity simulationFidelity of a simulation object is an external side or the overall level of state and behavior of reproduction [1]. Fidelity is used to measure the simulation degree on behalf of the real world, and is the key point to verify the model. However, fidelity is difficult to quantitative research and application. A typical application is to divide fidelity into high, medium and low grade. We can use the seven concepts to define and describe the model or simulation fidelity. The seven concepts are the details, decomposition level, accuracy / error, sensitivity, accuracy, timing and loading [2].According to the general characteristics of the logistics system, we can choose the physical model of fidelity, input data modeling approach, workflow simplification simulation of the three perspectives to examine fidelity [3]. Physical model fidelity is the visual effect which the model gives. We can divide physical simulation fidelity into high, medium and low levels, which expresses the simulation model difference between the performance and the operational details.Table I shows the simulation physical fidelity reference distinction standards of the high, medium and low levels.TABLE I.S IMULATION PHYSICAL F IDELITY D IVISION -LEVEL OF H IGH , MEDIUM AND LOW -LEVELLow-level Medium-level High-levelOnly completed the processes’ key actions and other actions were completed by the logic model, three-dimensional characteristics of delivery systemsdo not described.Completed the processes’ key actions and some actions details,and other actions were completed by the logic model,described some three-dimensional characteristics of conveying systems. Completed theprocesses’ key actions and most even all actions details,the remaining action details is completed by the logical model, described some three-dimensionalcharacteristics of conveying systems.criteria among high, medium and low levels, only through different visual effects between people to distinguish showedThis work is supported by the Key Projects of Guizhou Science and Technology Department. ([2007]6017)978-1-4244-7161-4/10/$26.00 ©2010 IEEEby a simulation model of the real system. Meanwhile, the three levels are needed to ensure the credibility of the simulation model, which called for strict accordance with the actual system to simulate the processes.First, high physical fidelity simulation makes high simulation accuracy requirements.High physical fidelity generally requires higher input data accuracy and the higher degree of operating processes. With the help of higher input data accuracy and the higher degree of operating processes, we have the precondition of high physical fidelity simulation. Also realized that the physical model fidelity, input data modeling approach, three aspects of workflow simplification of the high degree of unity, to achieve high quality simulation model.Distribution Center high physics fidelity simulation of automatic conveying system, we need to complete number of key actions and most of the action details of the automatic conveying system. Automatic conveying system is a mechanical device, the operation actions are fixed, which also provided the conditions for the high physics fidelity simulation. High physics fidelity simulation is better to reflect the credibility of the simulation model and demonstrates the actual operation process of automatic transmission system.B.Key point of automatic conveying system high physicalfidelity simulationFigure 1 illustrates a simple automatic conveying system processes. Automatic conveying system needs to complete the shape and weight test of pallet, and pallet angle shift operation. After shape and weight test of pallet, the unqualified pallet can return back along the original path, or along the other path. Pallet rectangular turn, generally requires two directions by setting the height difference between the transmission line, completes the shift operation by vertical lifting equipment.Figure 1. Automatic conveying system basic operating proceduresAutomatic conveying systems and other automation equipment used in distribution center, the complexity of its operations is also increasing, and their operating procedure is more complex than the figure 1. However, for the high-fidelity simulation in terms of physics, it only increase operating procedures, and modeling is more complex. It Will not affect the effect of high fidelity simulation.Automatic conveying system with high physics fidelity simulation, we should pay attention to several key points as followed.•First, high physical fidelity simulation of automatic conveying system, we need to characterize and expressthe typical three-dimensional features of automaticconveying system.The automatic conveying systemfrequently used in distribution center includes stickconveyor, chain conveyor and belt conveyor etc. At thecross-shift position in the automatic conveying system,two automatic conveying systems usually were usedtogether. High physical fidelity simulation ofautomatic conveying system must characterize andexpress the typical three-dimensional features ofdifferent automatic conveying system.Fortunately,now the popular three-dimensional logistics simulationsoftware can easily characterize and express the three-dimensional characteristics of commonly usedautomatic conveying system.•Crossroads cross-cutting issues require high accurate simulation based on actual operating strategy.Crossedautomatic conveying system, generally achievedthrough the vertical lifting device to shift functions.Itssimulation consists of two main aspects,First, set thepriority of input side.When contention occurs we needto arrange the work strategy according to priority.Second, the intersection lifting mechanism is occupied,we should mark and lock it.We need to carry outappropriate design the mark and lock methodaccording to the different simulation software features.•We need to design separately the active and passive forward logic of automatic conveying system.Ingeneral, pallets are active go along, but when the passconditions are not met, the pallets will enter thewaiting list. Like lifting device at the intersection isoccupied or other pass conditions are not met. At thispoint we need to design a good passive forward logic,when the pass conditions are met; we can quickly wakeup the pallet in waiting list to move on.•We need to analyze the type of the delivery system sub-module and simulate separately the automaticconveying system relative motion and absolute motion.In particular, a detailed description of the details of theaction between the sub-modules is needed.On therelative motion, we should strictly describe the actionbetween different conveying devices, showing obviouseffects of the action.Such as vertical lifting motion,translational motion, and chain conveyors. However,on the absolute motion, we do not need to describe theabsolute action. Such as the stick rotation of the stickconveying system.III.E XAMPLE OF HIGH-FIDELITY MODELING BASED ONAUTOMODA high physical fidelity simulation model of automatic conveying system of a cold distribution center was established. As processes are complex, the automatic conveying system of cold distribution center was more complex.Figure 2 shows the work flow of the automatic conveying system of cold distribution center. There are chain conveying system and stick conveying system used in the cold distribution center. Storage processes as follows: The pallet needs to pass a closed low-temperature zone on the chain conveying system. When the pallet will enter or exit the low-temperature zone, the door will open quickly, and then the pallet can pass. After shape and weight test of pallet, the unqualified pallet can return back along the original path, or along the other path.Qualify pallet goes along, and requests to open the door. After the door open, the chain moves to the pallet direction, then pallet gets on the chain conveying system. The chain conveying system delivers pallet back, and then the door goes down and closes. Low-temperature zone can store two pallets temporarily. When the second pallet enter low-temperature zone, then the door rise and open. With the help of vertical lifting equipment, pallet was sent into stick conveying system. Then pallet goes along on the stick conveying system. After the second pallet exits, the door goes down and be closed.Figure 2. Work flow chart of the cold distribution center automaticconveying systemAutoMod 3D simulation software can complete simulation analysis, evaluation and optimization design of the manufacturing system, storage system, distribution centers internal logistics. The Conveyor subsystem of AutoMod is designed to simulate automatic conveying system. Conveyor can display three-dimensional characteristics of different automatic conveying system. The kinematics subsystem of AutoMod can simulate the details of action. So, with the help of kinematics, we can describe and simulate the door action, the move action of chain conveying system and the lift action of vertical lifting equipment.According to the systems features, we can realistically simulate the automatic conveying system of cold distribution center. High physical fidelity simulation model of automatic conveying system of the cold distribution center, we need to pay attention to details as follows.•As automatic conveying system of the cold distribution center needs to complete in and out operations indifferent time .The automatic conveying system can dotwo-way movement.•When pallet passes the low-temperature zone, we should determine the open and close conditions.Notethat the enter door and exit door cannot open at thesame time.Figure 3. Simulation logic chart of cold distribution center automaticconveying systemFigure 3 is simulation logic chart of cold distribution center automatic conveying system. The basic simulation modeling idea is as follows. Use Conveyor subsystem to simulate the chain conveying system and stick conveying system. To solve the two-way movement problem, set two path of the two opposite together, and set different control points, meet the needs of actual control logic. Use Kinematics subsystem to simulate the lifting equipment and door. We should pay attention to set the control points accurately and meet the need of realistic simulation.The chain conveying system was simulated by Convey and Kinematics subsystem. We should set the same speed of chain conveying system in different subsystem. Figure 4 is the simulation model run chart of cold distribution center automatic conveying system.Figure 4. Simulation model run chart of cold distribution center automaticconveying systemIV.CONCLUSIONHigh fidelity simulation model, for the simulation analysts, the simulation model can be used as a method of model verification.If the model is not enough credible and accurate, three-dimensional animation will have errors. For the engineers and designers, high fidelity simulation model can simulate the whole Work process, and display the running condition of key part. The high fidelity simulation model can help them to design and improve the plan of distribution center.Although high fidelity simulation could help the engineers and designers to design and improve the plan, the higher fidelity also needs the higher cost of model development work. Especially for the whole distribution center, how to accurately grasp the balance between simulation accuracy and simulation cost is very difficult. This article mainly analyzes the level of physical fidelity simulation and the key point of automatic conveying systems high physical fidelity simulation, and simulates the automatic conveying system of a cold distribution center.R EFERENCES[1]Sun Yafeng, Wang Chaoyang, Huang Zhiping, Research on simulationcredibility, Electronic Measurement Technology. vol. 32(11), 2009, pp.8–11.[2]Liu Feil, Yang Ming. Research on Distributed Simulation’s Fidelity.Computer Simulation. vol. 22(6), 2005, pp. 49–52.[3]Liu Yukun, Fu Yu, Zhou Xiaoguang, Effect of Different ModelingFidelity Levels on Simulation Evaluation of Operation Efficiencies of Distribution Centers, J ournal of System Simulation. vol. 21(11), 2009, pp. 6705–6709.[4]David C Gross㧚Report from the Fidelity Implementation Study Group [C]//Proceedings of 1999 Spring Simulation Interoperability Workshop. Orlando 㧘FL㧘USA:SISO, 1999:99S-SIW-167.[5]Jerry Banks. Getting Started with AutoMod[M]. Brooks Automation㧘2004.[6]Xu Gengbao, Zeng Lianzhi. Dependability Problem on Modeling &Simulation, Computer Simulation. vol. 20(8),2003, pp.36–38.[7]MengJianjun, Wang Xiaoyu, Kong Qingde. The Research and Realization of the Simulation Softw are about the CargoFlow System at the Communication Automation Field, Computer Simulation. vol.20(8),2003, pp.106–108,135.。

Physics of thick polymers

arX iv:c ond-ma t/58446v1[c ond-m at.s oft]19A ug2005Physics of Thick PolymersDavide Marenduzzo 1,Alessandro Flammini 2,Antonio Trovato 2,Jayanth R.Banavar 3and Amos Maritan 21Department of Physics,Theoretical Physics,University of Oxford,1Keble Road,Oxford OX13NP,England 2INFM and Dipartimento di Fisica “G.Galilei”,Universit `di Padova,Via Marzolo 8,35131Padova,Italy 3Department of Physics,104Davey Laboratory,The Pennsylvania State University,University Park,Pennsylvania 16802,USA Correspondence:Davide Marenduzzo,Department of Physics,Oxford University,1Keble Road,Oxford OX13NP,United Kingdom,F AX:+441865273947—e-mail:d.Marenduzzo1@Authors’e-mail addresses:Davide Marenduzzo:davide@Alessandro Flammini:ﬂammini@shannon.sissa.itAntonio Trovato:trovato@pd.infn.itJayanth R.Banavar:jayanth@Amos Maritan:maritan@shannon.sissa.itWe present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers.The concept of the thickness of sucha polymer,viewed as a tube,is encapsulated by a special three body interaction and impacts onthe behaviour both locally and non-locally.When thick polymers undergo compaction due to anattractive self-interaction,weﬁnd a new type of phase transition between a compact phase and aswollen phase at zero temperature on increasing the thickness.In the vicinity of this transition,short tubes form spaceﬁlling helices and sheets as observed in protein native state structures.Uponincreasing the chain length,or the number of chains,we numericallyﬁnd a crossover from secondarystructure motifs to a quite distinct class of structures akin to the semi-crystalline phase of polymersor amyloidﬁbers in polypeptides.I.INTRODUCTIONTheoretical studies of polymer chains have a long history.Our focus,in this paper,is the study of a class of polymers characterized by a non-zero thickness and that can be viewed as tubes similar to garden hoses orﬂexible strands of spaghetti. Examples of such polymers abound and include vital biomolecules such as proteins and DNA.Classic polymers are diﬀerent from proteins on several counts.First,proteins are often very short chains made up of around a100or so aminoacids.Second,the aminoacid speciﬁcity plays a key role in the choice of its native state or ground state structure.One can imagine that the behavior of short chain molecules ought to be non-universal with the details mattering a great deal.To quote from Flory[1],“Synthetic analogs of globular proteins are unknown.The capability of adopting a dense globular conﬁguration stabilized by self-interactions and of transforming reversibly to the random coil are peculiar to the chain molecules of globular proteins alone”.In spite of the diﬃculties mentioned above,a study of the experimental data on proteins reveal an astonishing simplicity. All small globular proteins adopt,as their native conformations,structures made up of simple motifs such as helices,hairpins and sheets connected together by tight turns[2,3].Furthermore,the total number of distinct native state folds total just a few thousand in all instead of the vastly larger number that one would expect for a conventional chain molecule of this length[4]. The structures areﬂexible and allow for a dizzying array of tasks that enzymes perform.One might ask where these common attributes of proteins originate from.Recent work has shown that the concept of a thick polymer might be useful for bridging the gap between polymer physics and the biomolecular phase[5–11].Here we study a thick polymer through numerical simulations and approximate meanﬁeld theory to understand its phase behavior.Our work is somewhat limited in scope because we do not consider certain features such as twist rigidity,which are essential for understanding DNA elasticity[12,13].It has been suggested that the eﬀects of twist rigidity are not important for proteins[14].Furthermore,as we shall demonstrate,the notion of thickness is suﬃcient to interpolate between the conventional compact polymer phase and the phase employed by nature to house protein native state structures.While non-universal behavior is expected for short chains,short chains with the right thickness exhibit very novelﬁnite size eﬀects with some quite robust features independent of the details.Our results are in excellent accord with experiments carried out on proteins over several decades and provide a framework for understanding the common character of proteins.The simplest paradigm of a polymer consists of spheres tethered together to form a chain.In the continuum limit,such a model is described by the classic Edwards model[15]which captures self-avoidance by means of singular delta-function interactions.However,such a singular interaction does not admit a description of a chain of non-zero thickness and,indeed, one must renormalize it to analyze such a continuum model.Furthermore,the Edwards model is dynamically unable to preserve the knotting number of a closed chain.Indeed this result arises because the penalty for chain crossing isﬁnite and thus crossing is not entirely forbidden.The simple model of tethered spheres is merely a starting point and it has been modiﬁed to take into account local bending energies[16]and other features that are known to play a role in experiments.Here,we take a fresh look at the very basis of the description of a polymer chain.We suggest that a model of an isotropic sphere as the basic tethered unit leaves out a crucial feature–the inherent anisotropy associated with each unit arising from a special direction deﬁned by the neighbouring units along the chain.Physically,we argue that this anisotropy can be captured by considering a chain made up of tethered coins or discs,which in turn leads to a tube picture of the chain.From a theoretical point of view,the model of tethered coins has the non-trivial advantage of lending itself,in a natural and singularity-free manner,to a continuum description.The singular potential is avoided because one can imagine stacking together thinner and thinner coins closer and closer together while maintaining the coin radius constant to obtain a tube of non-zero thickness[17].One may rationalize the description of a generic polymer such as a polyethylene chain by a thick tube.Polyethylene chains have a Kuhn length around1nm and an approximate hard core diameter of a united atom of methylene around0.35nm[18]. The picture of a tube of non-zero thickness is thus a physically motivated description of such a chain and can serve as an alternative to the model of aﬂexible line with aδ-function hard core self-avoidance interaction.Indeed,the key diﬀerence in the two cases is in the nature of self-avoidance.One elegant way of describing the self-avoidance of a tube is by means of a three body potential,which enforces the constraint that a suitable length,constructed in terms of the positions of any triplet of points sitting on the axis of the tube,is greater than the tube thickness.As explained in Section III,this length associated with a triplet of points is the radius of the circle through them[19].This length is the local radius of curvature when the three points tend to a single point on the curve,but non-local triplets play a signiﬁcant role as well.The allowed conﬁgurations of a simple system of unthetered hard spheres are those in which one considers all pairs of spheres and for each pair,one ensures that the sphere centers are no closer than a sphere diameter.Such a rule ensures that the spheres are non-overlapping.The generalization of this to the chain context is to consider all triplets along the axis of the tube.Self-avoiding conformations of aﬂexible tube are obtained by drawing circles through each of the triplets and ensuring that none of the radii is less than the tube radius.A tube description is useful for the understanding of proteins–the backbone of a protein,when viewed as a tube,has an intrinsic non-zero thickness in order to accommodate the steric constraints imposed by the atoms of the side chains(for a sketch,see Fig.1).Our model is characterized by two parameters other than the length of the tube,its thickness R0and the range of the attractive potential R1.When these two lengths are comparable,weﬁnd that the ground state conﬁgurations of a short tube closely resemble the secondary motifs of folded proteins.We will demonstrate that these conﬁgurations change to amyloid-like structures upon increasing the tube length.We will present detailed studies of the phase diagram and will discuss similarities and diﬀerences with those obtained with previously studied polymer models.Through an extensive statistical analysis of triplet radii in known ground states of proteins,we found that the average thickness of a protein is0.27nm[8]. Consequently,the typical values of R0and of R1are matched in native structures of proteins,where R1≃0.55nm,when intra-chain hydrogen bonding is considered.There are several new features,both at local and non-local levels,that are characteristic of a tube.First,there is a constraint on the local radius of curvature which forbids the radius from being smaller than the tube thickness.This constraint is diﬀerent from the bending rigidity potential energy[16]which is usually taken to be of the formκ(1−cos(θ))whereκis a positive coupling,andθthe angle between successive links–as the temperature is lowered the chain becomes straighter.In contrast, the local radius constraint in a tube is a rigid constraint which is independent of temperature.In addition,the tube imposes a non-local constraint which,physically,reﬂects the fact that diﬀerent segments of a tube cannot approach each other closer than a threshold distance governed by the tube thickness.This is captured by imposing that no three-body radius(of any non-local triplets)can be smaller than the tube thickness.In order to best avail of the attractive interactions between diﬀerent parts of a tube,the relative orientation of neighbouring segments becomes important reﬂecting the inherent anisotropy associated with a tube[20,21].These new features lead to a phase diagram in which one can distinguish between three classes of tube thickness.In the thin tube regime,one obtains two distinct phase transitions on lowering the temperature from the swollen phase.First one enters an isotropic collapsed phase which is supplanted by an oriented nematic-like phase after the second phase transition. For intermediate thickness,there is only one phase transition to an oriented,compact phase while,for larger tube sizes,one simply obtains the swollen phase.Our studies of short tubes in the intermediate thickness regime show several unusual characteristics.First,the number of ground state structures is much smaller than the corresponding number for chains of spheres:the energy landscape is vastly simpler.Second,the resulting structures are marginally compact(the eﬀects of attractive self-interactions have just set in) and,because of their proximity to a phase transition,are sensitive to the right types of perturbations.Strikingly,weﬁnd that the resulting structures are predominantly space-ﬁlling helices(with a speciﬁc pitch to radius ratio)and nearly planar zig-zag hairpin and sheets.These structures are found to be quantitatively akin to the building blocks of protein structures.Our results indicate the presence of a previously unstudied phase of matter,associated with short tubes of intermediate thickness,which has many attendant advantages exploited by nature in housing biomolecular structures.Our results show that the tube picture provides a uniﬁed framework for understanding the common character of small globular proteins.Upon increasing the length of the polymer,or the number of polymer chains,we observe,in computer simulations,a crossover to semi-crystalline structures with diﬀerent portions of the backbone chain lying parallel to one another.Signiﬁcantly,this low temperature anisotropic phase of tubes provides a simple rationalization for the formation of amyloid in misfolded proteins(leading to deadly diseases, including Alzheimer’s and the Mad Cow disease[30])and the formation of semicrystalline polymer.There are some remarkable diﬀerences between the behavior of our model and that of a stiﬀchain as embodied by the semiﬂexible chain model[31–33].The phase diagrams of a self-interacting tube and a semiﬂexible chain both display three phases:a swollen phase,an isotropic collapsed phase,and an anisotropic globular phase(semi-crystalline phase).However, the phase boundaries look rather diﬀerent.In particular,there is a zero-temperatureﬁrst order phase transition in the thick polymer case which is observed on increasing the thickness,which has no counterpart in the stiﬀpolymer phase diagram. Moreover,the thickness acts as a constraint on viable conﬁgurations,while the bending rigidity acts as an energetic penalty. Technically,this leads to the swollen phases being somewhat diﬀerent in that in the continuum limit the typical tube centerlines are smoother than the semiﬂexible chain backbones.Also short tubes of intermediate thickness yield helices and almost planar zig-zag conformations,a feature absent in the semi-ﬂexible chain model.Our paper is organized as follows.Section II presents a brief review of the Edwards model.Section III presents the tube picture of a polymer chain and its advantages.Section IV deals with studies of the ground states of short chains subject to self-attraction and underscores the qualitative diﬀerences between chains of spheres(with or without bending energies)and short tubes.We review work which shows that the latter describes a novel phase used by nature to house biomolecular structures.Section V presents an attack on deducing the phase diagram of tubes using several complementary techniques.Some of the technical details are relegated to an appendix.We conclude with a brief summary in Section VI.II.EDW ARDS MODEL OF A POLYMER CHAINField theory models have proved to be useful for carrying out analytic calculations of the scaling behavior of polymers.The standard model is that due to Edwards–the polymer is described by a continuous curve, r(s),with an eﬀective energy given byH({ r})=16 L0L0δ( r(s)− r(s′))dsds′++v32b2k( r1− r k)2}(2)for large k.Consider now a‘coarse-grained’chain made up of n pieces of such k-step chains.Let the i-th piece start at the position r(i−1)k and end at r ik for each i=1,2,...,n.It then follows that the probability of obtaining this conﬁguration of the chain is given byP( r0, r1,..., r n)∝exp{−drepulsive part which becomes larger as r decreases.In order to take the continuum limit,the bead density along the chain must increase,because the tethering u potential constrains successive beads to lie closer to each other as b→0.As b decreases,the number of bead-pairs within the repulsive region of the V potential increases and,in the continuum limit,the chain would have an inﬁnite energy and an inﬁnite rigidity.As b→0,this unphysical consequence can be avoided by simultaneously shrinking the size of the repulsive region of the interaction potential V in eq.(5)leading to singularδ-function potentials in the continuum limit as in eq.(1).Furthermore,there does not exist,to our knowledge,a continuum formulation of closed polymers which allows one to carry out studies within a given knot class,i.e.with aﬁxed number of knots.Indeed,a drawback of any formulation using two-body potentials,such as eq.(1)),is that the self-intersection of the chain is allowed albeit with some energetic penalty and thus one can change,at will,the topology of the polymer.This is not what happens in realistic situations.Furthermore,there are interesting physical problems pertaining to the estimation of entropic exponents and weights of polymer conﬁgurations within a given topology[41,42].While such calculations can be carried out numerically,at present,there is no simple analytic formulation of this problem.A simple discrete model of spheres tethered together in a chain would lead,in the continuum limit,to the Edwards model. As the distance between successive spheres shrinks,so must the radius of the spheres and in the limit one obtains a string of inﬁnitesimal thickness.So how would one describe mathematically a string of non-zero thickness analogous to a tube or a garden hose or a spaghetto?Is there a way to avoid a singular interaction potential?More important,is the physics of thick strings qualitatively diﬀerent from that predicted by the Edwards model?Our focus,in this paper,is on answering these questions.III.TUBE PICTURE OF A POLYMER CHAINIn this section,we provide a brief description of how one might describe a tube of non-zero thickness.Let us consider the general case when the interacting particles(monomers)are restricted to lie in D-dimensional manifolds such as a string(D=1) or a surface(D=2)embedded in d-dimensional space.Examples of such systems include strings and random surfaces and are widely studied in many branches of science[43,44].The interaction(tethering)potential leading to the system being restricted in the form of a manifold or bending rigidity terms are not our concern here–there are many satisfactory ways to construct such a potential for strings and surfaces.Our focus is on the self-interaction not captured by the tethering potential.This self-interaction between the monomers are meant to be eﬀective interactions resulting from the elimination of theﬁner degrees of freedom.We will argue that the basic interacting unit must have at least D+2monomers in order to deﬁne a meaningful characteristic length associated with this interaction.Such a basic many-body interacting unit is necessary for a continuum approach to these classes of problems.Note that for unconstrained particles,D=0and pair-wise interactions suﬃce.Consider a D=1system of a string in d=3.In order to account for steric interactions,that prevent the string from intersecting with itself,one might postulate a pairwise potential which becomes large when two of the constituent particles are near each other.However,given two nearby particles,it is impossible to distinguish whether they are from distinct parts of the string or whether they are close by simply because of the string connectedness.As one approaches the continuum limit by increasing the density of particles along the string and shrinking the distance between them,the energy contribution from the latter category of pairs,which are close to each other essentially because of the tethering potential,vastly exceeds the contribution from particles that are genuinely responsible for a self-intersection.There is no inherent small-distance cutoﬀin the theory and regularization procedures are needed that re-introduce such a length scale in order to avoid inﬁnities.The requirements for a well-founded theory are that one ought to be able to take a continuum limit on increasing the density of particles,that self-interactions be properly taken into account and that there be a characteristic microscopic length other than the spacing between neighboring particles along the string.As explained above,a pairwise potential is not equal to the task.Let us consider a three-body potential characterizing the interaction between three particles,which lie on the corners of a triangle.Let the sides of the triangle have magnitudes r1,r2and r3.In order to specify a triangle uniquely,one needs three attributes.The potential of interaction can therefore depend on three independent length scales,which are invariant under translation,rotation and permutation of the three particles.One may choose these length scales to be the perimeter,P,of the triangle,the ratio of the area,A,of the triangle to its perimeter,P,andﬁnally r1r2r3/A.Theﬁrst two lengths do not cure the problems alluded to before–they both vanish when the particles approach each other either from the same region or diﬀerent regions of the string.The third length scale is proportional to R,the radius of a circle drawn through the three particles and has proved to be valuable for the study of knots[5].If one considers the minimum over all triplets of this quantity,that is just the‘thickness’[19]of the continuum curve we are considering–the thick curve may be thought of as a tube or a thick polymer.The key result is that the description of the eﬀective self-interactions of a string,which satisﬁes all the requirements of a well-founded theory will involve a three bodypotential,V3(R),among all triplets of particles in the string.In this case,the continuum limit can be taken safely,self-avoidance is respected and a cut-oﬀscale naturally arises through the functional form of V3,in this case a hard-core form.One may illustrate the diﬀerence between the approach to the continuum limit in the chain of spheres model and the tube model in the following manner.Considerﬁrst a self-avoiding chain made up of spheres tethered together with the distance between successive spheres equal to the bond length b.Let R hc represent the hard core radius of the sphere.Physically,b is expected to be of the order of2R hc.For a chain of length N,one may,from general considerations,write the radius of gyration as R g(N,b,R hc)=R hc F s(N/R hc,b/R hc).In order to take the continuum limit,one must let b approach0.But this automatically constrains R hc to go to zero as well,while maintaining the ratio of b/R hc at some suitable non-zero value.This immediately poses a problem because,in order for one to obtain the well-known result that R g scales as Nν,there is no other non-zero length scale in the problem.The cure for this,of course,is to use renormalization procedures by introducing an artiﬁcial cutoﬀfollowed by a demonstration that the answers do not depend on the cut-oﬀ.This problem is nicely avoided in a tube description within which R g(N,b,R0)=R0F t(N/R0,b/R0),where R0is the tube thickness.The only constraint on b now is that it is less than or at most comparable to R0.Thus,the continuum limit canbe safely taken by letting b go to0and obtaining R g=R0F t(N/R0,0)∼R1−ν0Nν.In other words,the nonzero thickness(asembodied in a suitable three body potential)of a tube provides a suitable cut-oﬀlength scale and avoids the singularity implicit in the conventional Edwards model and the absolute need for the use of renormalization techniques[39],allowing for theﬁrst time analytic studies of polymers withﬁxed knotting numbers.In the continuum limit,the many-body potential replaces the pairwise self-interaction potential and ought not to be thought of as a higher order correction[45].Nevertheless,for discrete models of a thick tube,two-body interactions do not suﬀer from the problem described above and can coexist with three-body terms which model the non-zero thickness of the curve approximately.Consider the Hamiltonian for a string of the formH chain= i u(r i,i+1)+ i<j V2(r i,j)+ i<j<k V3(r i,j,k),(6)where,as before u is a generic tethering potential,V2is a pairwise potential and V3is a three-body potential.In most of our simulations,we have chosen u to constrain r i,i+1to be constant.The pair potential is taken to beV2(r i,j)= ∞if r i,j<2R h.c.−1if2R h.c.<r i,j<R10if R1<r i,j(7)where R1,the range of the attractive interaction is taken to be1.6units(measured in units of the bond length or theﬁxed distance between successive beads,which is chosen to be1)in our simulations and R h.c.is the hard core radius,which we take to be0.55in our calculations.These values have been selected in order to mimic values typical of a protein backbone(see Introduction).We veriﬁed that small changes in the attraction range do not change the results shown here appreciably(see Fig.4).A Lennard-Jones potential for the two-body interaction energy,with an equilibrium distance slightly larger than the neighbouring site distance,is also expected to give qualitatively similar results,provided the potential is truncated in order to eliminate the unphysical eﬀects of a long range tail.The three body potential[19,47],V3,disallows conformations for which R0>min i=j=k r i,j,k,where r i,j,k is the radius of the circle going through the centers of the beads i,j and k(Fig.2).This three body constraint leads,in the continuum limit,to a tube of radius R0,whose axis is given by the string deﬁned by r i(see Fig.2).This can be simply proved by noting that the quantity min i=j=k r i,j,k is the thickness of the maximally inﬂated tube with centerline{ r i}i=1,...,N[19].If the maximally inﬂated tube has a thickness greater than R0,then this means that the discrete curve under analysis is a viable centerline for a tube of thickness R0.For the discrete case,the three-body constraint is not as severe as in the continuum limit–we will show that discreteness can play a vital role in producing planar structures for short tubes subject to self-attraction.In the remaining sections,we will demonstrate,using various complementary techniques,that a rich variety of new phases is obtained for a tube subject to self-attraction,which allow a bridging of conventional polymer phases to a novel phase used by nature for housing biomolecular structures.IV.GROUND STATES OF SHORT CHAINSOur focus,in this section,is to discuss the ground state structures of short chains subject to self-attraction.Strikingly, marginally compact tube structures have helical,hairpin and sheet conﬁgurations which are the building blocks of proteinnative state structures.We will consider the structures adopted by a tube and by a chain of spheres in order to understand the common features of both classes and underscore the qualitatively new features introduced on incorporating the intrinsic local anisotropy of a chain.We will also assess the nature of the structures adopted by a stiﬀchain,or equivalently a semiﬂexible polymer,subject to compaction.This analysis demonstrates that,at least,within the parameter range we have explored,there is less secondary structure content in short semiﬂexible chains in clear contrast to the marginally compact phase obtained for a tube.Hard spheres are the simplest basic entities for modelling matter.In spite of their simplicity,hard spheres exhibit an entropy-driven phase transition between aﬂuid phase at low packing fractions and a crystalline phase at high packing fractions. The favored crystalline structure is that of a face-centered-cubic crystal which allows for the most eﬃcient packing.In two dimensions,hard disks would prefer to pack most eﬃciently in a triangular lattice.Let us now consider a chain molecule made up of tethered hard spheres(in three dimensions)or tethered disks(in two dimensions).For simplicity,let us restrict ourselves to the simplest case in which the tethering constraints for compact conformations are not frustrating and lead to the same ground state as in the untethered case.This greatly simpliﬁes the analysis of the ground state conformations of compact chains because one can carry out the analysis for unconstrained,untethered objectsﬁrst and imagine placing the tethers through the resulting ground state structure(s).The systems that we will study(without and with the three body tube constraint,and with the stiﬀness term)are all subject to the same attractive potential energy of interaction.They consist of a chain of spheres subject to a pair-wise attractive potential–a pair of spheres,at r i and r j,have an interaction given by eq.7.There is an additional constraint for the tube case which forbids any of the three-body radii associated with the spheres of the chain from being smaller than the tube thickness R0(potential V3in eq.(6)).Finally,for a chain of spheres with a non-zero stiﬀness[31,32],we complement the two body potential in Eq.7with a bending-rigidity term of the form:H b=−κ i r i,i+1· r i+1,i+2,(8)withκa constant,the chain stiﬀness,and with r i,i+1= r i+1− r i.We will point out similarities and diﬀerences between these three cases.A.Geometry of chains of spheresWe begin with an analysis of the chain without the three-body constraint.In this case,R h.c,the hard-core radius is held ﬁxed at a value of0.5and we will consider the nature of the ground state structures on varying R1,the range of the attractive interaction.Recall that while our focus is on chains of spheres(or disks),the tethering constraint does not play a role for the selection of compact conformations.The role of the tethering constraint here is simply to enhance the degeneracy of the ground state.This is because there is an exponential(as a function of the length)number of ways in which one might accomodate the tether through a packed conﬁguration of beads.A well-known example is provided by Hamiltonian walks,which are the ensemble of conﬁgurations of chainsﬁlling a aﬁnite sized square lattice[48].For simplicity,here we will consider just the degeneracy of the underlying conformation of spheres without taking into account this extra degeneracy.Two-dimensional caseIn d=2it is well known that there is a unique way of packing hard disks so that the packing is most eﬃcient.This optimal packing is performed by placing the centers of the disks on a triangular lattice,whose lattice parameter equals the disk diameter.Each disk is then surrounded by six nearest neighbors.This is indeed the ground state structure of tethered disks when R1=2R hc.Let usﬁrst discuss the nature of the ground state structures for arbitrary values of the attraction range R1in the thermodynamic limit.Finite size eﬀects are less relevant here and will be considered carefully for the tube and semi-ﬂexible chains considered later on in this Section,and,for the two-dimesnional case,will be brieﬂy discussed at the end of this sub-section.When the number of disks or spheres becomes large,one expects the ground state to be a translationally invariant lattice. When R1<2R hc,the disks are unable to avail of the attractive interaction and one obtains a swollen phase–all conformations of the chain which do not violate the hard disk constraint are equally likely.We now turn to an analysis of the compact conformations that one obtains when R1>2R hc.Figure3shows a sketch of the winning lattice structures as a function of R1in the compact phase(the lattice consideredare all Bravais two-dimensional lattices,deﬁned by the angle between two unit vectors).The ground state is non-degenerate at√R1=2R hc=1,but on increasing R1,the degeneracy goes up(see shaded region in theﬁgure)until a value of R1=。

FMX570英文操作手册

silometer FMX 570Level MeasurementOperating InstructionsBA 119F/00/en/06.03 Software Version 1.xFMX 570Hauser+Endress The Power of Know HowLevel Measurement at a Glance*Can be performed in reverse orderFunctionMatrix Action1Reset transmitterV9H5q Enter 671: »+« and »-« keys, ⇒ changes digit Press »E« to register entry-Omit if commissioned as in Section 4.12»Empty« calibration*V0H1q Fill vessel 0…40% full (probe covered)Enter level in %, m, ft, etc.Press »E« to register entry3»Full« calibration*V0H2q Fill vessel 60…100% full Enter level in %, m, ft, etc.Press »E« to register entry40/4 mA signal V0H3V0H5V0H6q Enter 0 for 0…20 mA signal, 1 for 4…20 mA signal Press »E« to register entryq Enter level for 0/4 mA signal (if not 0)Press »E« to register entryq Enter level for 20 mA signal (if not 100)Press »E« to register entrySilometer FMX 570Measurement at a GlanceSilometer FMX 570Selects vertical matrix positionSelects horizontal matrix position Select position V0H0Selects next digit Move decimal pointIncreases value of digitDecreases value of digit Registers entry100VH00V H+EFMX 570mMeasured value Bar chartMatrix selectionParameter entryAlarm relay lit: faultMatrix position Test sockets for 0/4…20 mA output++See also »Controls«, Chapter 3Measurement at a Glance Silometer FMX 5701Table of ContentsMeasurement at a GlanceNotes on Safety . . . . . . . . . . . . 31Introduction . . . . . . . . . . . . . 51.1Application . . . . . . . . . . . . . . . 61.2Measuring principle . . . . . . . . . . . 72Installation . . . . . . . . . . . . . . 82.1Probes and sensors . . . . . . . . . . . 82.2Silometer installation . . . . . . . . . . . 92.3Transmitter wiring . . . . . . . . . . . . 112.4Sensor connection . . . . . . . . . . . . 132.5Technical data: Silometer FMX 570 transmitter . 143Controls . . . . . . . . . . . . . . . 153.1Commutec operating matrix . . . . . . . . 153.2Configuration and display . . . . . . . . . 164Calibration and Operation . . . . . . . 174.1Commissioning . . . . . . . . . . . . . 174.2Calibration for level measurement . . . . . . 184.3Calibration for linear volume or weightmeasurement . . . . . . . . . . . . . . 194.4 »Dry calibration« for open vessels . . . . . 204.5Level offset value . . . . . . . . . . . . 224.6Measured value display . . . . . . . . . 234.7Locking the parameter matrix . . . . . . . 235Linearization . . . . . . . . . . . . . 245.1Linearization for a horizontal cylindrical tank . 255.2Linearization for a tank with conical outlet . . 265.3Other modes . . . . . . . . . . . . . . 296Analogue Outputs . . . . . . . . . . 306.1Analogue output settings . . . . . . . . . 317Trouble-Shooting . . . . . . . . . . . 337.1Trouble-shooting tables . . . . . . . . . 337.2Simulated operating mode . . . . . . . . 357.3Exchanging transmitters, probes and electronicinserts . . . . . . . . . . . . . . . . 367.4Repairs . . . . . . . . . . . . . . . . 378Quick programming guide . . . . . . . 388.1Level measurement . . . . . . . . . . . 388.2Continuous volume measurement (linearization)39Index . . . . . . . . . . . . . . . . 40 Operating matrixSilometer FMX 570Table of Contents2Notes on SafetyThe Silometer FMX 570 is a level measurement transmitter which can be used with avariety of probes and sensors. It must be installed by qualified personnel according tothe instructions in this manual.Certificates The Silometer FMX 570 transmitter is available with certificate. The Table below indicatesthe combinations available and conditions for installation. Full details can be taken fromthe certificates. Please note that where quoted technical data differs from that listed inSection 2.5, that in the certificate applies.Certificate Instruments NotesTÜV 00 ATEX 1640Silometer FMC 671 Z/676 Z II (1) GD,[EEx ia] IIC/IIB,install outside Ex-areaPTB 98 ATEX 2215 X DC 12 TE, DC .. TE .,DC .. E ., DC ..Capacitance probes11500 Z(M), 11961 (Z),21561 (Z)with electronic insertEC 16/17/27/37/47 Z,FEC 12,HTC 16/17/27 Z, HTC 10 E,HMC 37/47 Z II 1/2 G, II 2 G, EEx ia IIC/IIB T6PTB 98 ATEX 2215 X DC 12 TE, DC .. TE .,DC .. E ., DC ..Capacitance probes11500 Z(M), 11961 Z,21561 Zwith electronic insertEC 17/37/47 Z, FEC 12II 1 G,EEx ia IIC/IIB T6PTB 98 ATEX 2094DB 50, DB 50 L,DB 51, DB 52, DB 53II 1/2 G, II 2 G, EEx ia IIC T4…T6DIBt No. Z-65.11-29Silometer FMX 570,DB 50 (52)with electronic insertFEB 17 / FEB (17) P Continuous level measurementfor overspill protection in stationary vessels(for storage of non-combustible, water-polluting liquids)Silometer FMX 570Notes on Safety3Safety conventionsIn order to highlight safety-relevant or alternate operation procedures in the manual the following conventions have been used, each indicated by a corresponding icon in the margin.Note!•A note highlights actions or procedures which, if not performed correctly, may indirectly affect operation or may lead to an instrument response which is not planned.Caution!•Caution indicates actions or procedures which, if not performed correctly, may lead to personal injury or incorrect functioning of the instrument.Warning!•A warning indicates actions or procedures which, if not performed correctly, willlead to personal injury, a safety hazard or destruction of the instrument.Notes on Safety Silometer FMX 5704Silometer FMX 570Chapter 1: Introduction 1IntroductionThe front cover contains short instructions for continuous level measurement with theQuick Operating Guides default parameters.Users unfamiliar with the Silometer FMX 570 must read the operating instructions, whichIn this manualare structured as follows:•Chapter 1: Introduction;contains general information including application, measurementprinciple and functional description.•Chapter 2: Installation;contains hardware configuration, installation instructions.connection diagrams and technical data for the plug-in card.•Chapter 3: Controls;describes the front panel keys and operating matrix.•Chapter 4: Calibration and Operation;tells you how to commission the Silometer for level measurement.•Chapter 5:Linearization;tells you how to calibrate the Silometer to measure volume in ahorizontal cylindrical tank or a tank with a conical outlet.•Chapter 6: Analogue Outputs;describes in detail the setting of the 0/4…20 mA signal line.•Chapter 7: Trouble-Shooting;contains a description of the self-checking system with errormessages, the simulation feature as well as instructions forconfiguration on replacement of the transmitter, probe or electronicinsert.•Chapter 8:Short Operating Guidecontains a flowcharts for level and volume measurements•Chapter 9: Index;lists key words to help you find information quickly.•Chapter 10:Operating Matrixcontains the operating matrix, the default parameters and a table toenter your operating parameters,Further documentation Installation of the probes, electronic inserts and accessories are described in thedocumentation accompanying these articles - see text for references. When installingprobes in explosion hazardous areas the instructions included in the accompanyingprobe certification must also be observed.51.1ApplicationThe Silometer FM X 570 is designed for level measurement with a capacitance or hydrostatic pressure probe in safe or explosion hazardous areas. It possesses an intrinsically-safe sensor circuit conforming to EEx ia IIC and IIB. A list of certificated combinations is to be found in »Notes on Safety« preceding this chapter. A working system for level measurement comprises:•Silometer FMX 570 transmitter,•Capacitance, Multicap or Deltapilot S probe •Electronic insertSilometer functionThe capacitance or pressure measured by the sensor is converted into a frequency signal by the electronic insert located in its head. The Silometer FMX 570 supplies the power and receives a level-proportional frequency signal over a two-core cable. The signal is then processed to provide a level or volume measurement.Fail-safe operationIf a fault condition is detected, e.g. a break in sensor - transmitter cable, the analogue signal switches to -10 % or +110 % level or holds the last measured value. In addition,the alarm relay de-energises.211FMX 570mA10/4...20 mA,0/2...10V outputSilometer FMX 570transmitterLiquidsBulk solidsChannel 1Ex non-Exor orBA119Y01Fig. 1.1:Standard application showing Silometer FMX 570 controllinglevel measurement Capacitance probeDeltapilotfrequencyanalogdigitalcurrent voltagesens. [Hz/pF]offset [Hz]offset [pF] sens. [pF/cm]range upper limitV2range lower limitV1frequencyelectronic-insertelectronic-insertcapacit./ pressure volumeV2V1levelvolume H2H1level cap./press.level zero point shiftBA119E08Fig. 1.2Signal processing in theSilometer FMX 570Chapter 1: Introduction Silometer FMX 57061.2Measuring principleThe Silometer FMX 570 measures level on the basis of the capacitance and hydrostaticmea surement principles. In both ca ses the mea sured va lue is processed by the electronic insert and passed on as a frequency signal.The probe and vessel form the two plates of a ca pa citor, the tota l ca pa cita nce of which ca n then be ca lcula ted from the formula :C tot =C 1+ 2πε0εr x LpF (1)--------------------------------ln (D/d)wherebyC tot =total capacitanceC 1=capacitance or feed through ε0=dielectric constant of airεr =rel. dielectric constant of productD=diameter of vessel d=diameter of probe L=length of probe immersed inproduct in metersIf the product conducts, the capacitance is determined by the thickness a nd properties of the insul a ting m a teri a l surrounding the probe. Equ ation (1)applies, whereby the variable D is now the diameter of the probe with insulation. In this ca se the ca pa cita nce va ries by a pprox.300 pF/m.Measurement is independent of dielectric constant and not affected by changes in this variable.In an open vessel, the level is derived from the hydrosta tic pressure exerted by a column of liquid on a probe placed at its foot. The pressure exerted is:p 1=ρ x g x h(2)whereby p 1 =hydrost a tic pressureρ =density of the liquidg =acceleration due to gravity h =height of the liquid column.Assuming a constant density, the level of the liquid ca n be ca lcula ted from the pressure measured by the Deltapilot.BA119Y05dLDC 1Fig. 1.3Capacitance measurement principleBA119E06dConductingproductLD Fig. 1.4Measurement in conducting mediaBA119Y07p 1 = ρ x g x hhatmospheric pressurep 1Fig. 1.5Hydrostatic measurement principleCapacitance measurementHydrostatic measurementMeasurement in conducting mediaSilometer FMX 570Chapter 1: Introduction72InstallationThis Chapter describes:•The probes for use with the Silometer FMX 570•Silometer installation in a rack or Monorack housing •Transmitter wiring •Sensor connection.•Technical data.Warning!•The Silometer FMX 570 transmitter must be installed outside explosion hazardous areas.2.1Probes and sensorsTable 2.1 lists the probes most frequently used with the Silometer FMX 570 transmitter.In addition to those listed, all probes which can be used with an EC 37 Z or EC 47 Z electronic insert can be connected to the transmitter. Installation hints can be taken from the appropriate Technical Information Sheet.Sensor constantsDeltapilot S sensors and EC 37 Z/47 Z inserts for capacitance probes are supplied with the sensor constants zero frequency »fo« and sensitivity »∆f« or »S«. For Deltapilot S sensors the constants are printed on a label stuck inside the sensor head, for inserts they are printed on the name plate, see Fig. 7.1, Section 7.3.Note these constants and enter them into fields V3H5 and V3H6 during commissioning,Section 4.1. This dispenses with the need for a recalibration of the transmitter on replacement of the sensor or insert.Principle ProbeTI sheet Insert Capacitance,Multicap11 500 ZTI 161F Multicap DC 11TI 169F Multicap DC 16TI 096F Multicap DC 21TI 208F Multicap DC 26TI 209F Multicap TA TI 239F Multicap TE TI 240F Multicap E TI 242F Multicap A TI 243F EC 37 Z EC 47 Z FEC 12Hydrostatic pressure Deltapilot S TI 031F DB 50 (53)TI 257PFEB 17 (P)Table 2.1:Selection of probes suitable foruse with the Silometer FMX 570Cell type Electronic insert FEB 17/FEB 17 P Rangef 0∆f Rangef 0∆f 0.1 bar BA 0…100 mbar 20010DA -100…100 mbar 20050.4 bar BB 0…400 mbar 200 2.5DB -400…400 mbar2001.251.2 bar BC 0…1200 mbar 2000.833DC -900…1200 mbar 2000.4764.0 barBD 0…4000 mbar2000.25DD -900…4000 mbar 2000.204Table 2.2:Measuring ranges and sensorconstants of the Deltapilot S DB 5xSilometer FMX 570Chapter 2: Installation82.2Silometer installationThere are three possibilities for installing Silometer transmitters:•Standard 19" rack with space for 12 7HP cards,•Field housing with space for up to 6 7HP cards,•Monorack housings for single transmitters.Rack installationA Racksyst system can be ordered fully wired, in which case the sensors and the external power supply only need to be wired. Planning hints can be found in Publication SD 041/00/e, »Racksyst Assembly Racks« .For non-Racksyst installations and for installations including non-Racksyst cards, fill the rack as follows (see also Fig. 2.1):Rack arrangementStep Procedure1Allocate the power supply (NT 470) at the rightmost position.-If two NT 470s are used, install a 2 HP dummy panel between them.2Install non-intrinsically safe transmitters next to the power supply.-Install a 2 HP dummy panel between all foreign transmitters and betweenRacksyst cards and foreign transmitters 3Install intrinsically safe transmitters to the left of the rack.-Install foreign cards first.-Install dummy panels between all foreign transmitters and between Racksystcards and foreign transmitters in accordance with the instructions on the Ex-Certificate.-No spacer is required between Racksyst cards.Racksyst field housingInstructions for installing Commutec transmitters in the Racksyst field housing with half 19" rack are to be found in Publication PI 003.•Check that the field housing is not installed in direct sunlight.-If appropriate fit a protective sun cover.•The maximum permissible ambient temperature for the field housing varies between +50…+60 °C according to the power consumption of the cards (0…20 W)BA119E09Non-E+H (Ex)i devices E+H (Ex)i devicesE+H devicesNon-E+H devices NT power supplySpacing betweennon-E+H (Ex)i devices as per certificate2 HP dummy panel between E+H and non-E+H devicesFig. 2.1:Recommended arrangement for Racksyst rack assembliesChapter 2: Installation Silometer FMX 5709Monorack housing The Silometer FMX 570 transmitter and Monorack housing are supplied separately. Thesystem must be assembled as shown in Fig. 2.2 before use.•The Monorack is prepared for wall-mounting, degree of protection IP 40.•The site must be chosen such that the operating temperature of-20°C…+60°C for one Monorack and -20°C…+50°C for Monorack banks isnot exceeded.Full details of the Monorack installation procedure can be taken from the manual suppliedwith it.Monorack protective housing If the Silometer FMX 570 transmitter and Monorack housing are to be mounted at an exposed site, then it is recommended that they be installed in the protective housing, degree of protection IP 55, which is available as an accessory.•The protective housing accomodates two Silometer FMX 570 transmitters.•The permissible ambient temperature is -20°C…+50°C for one Monorack and-20°C…+40°C for two.Dimensions and instructions for installation are to be found in the Technical Information sheet TI 099/00/e.BA119E10 Plug-in cardMonorackhousingMonorack base(terminal block)RetainingscrewsRetainingflapFig. 2.2:Assembly and disassembly ofthe Monorack housingPowerpackFig. 2.3:Monorack protective housingBA119E60Silometer FMX 570Chapter 2: Installation 102.3Transmitter wiringWarning!•Make electrical connections with the power supply switched off!•When wiring up probes and sensors in explosion hazardous areas, observe the instructions on the certificate and other appropriate regulations.Rack wiringFig. 2.4 is a pin assignment diagram for the Silometer FMX 570.•Terminals z 30, b 14 and d 14 are connected internally•Inputs d2, d4 are electrically isolated from the circuit and each other.•The circuit zero of the unit ( ⊥ ) is connected to the negative terminal of the supply voltage.Note!•Two indexing pins, at positions 2 and 9 in the rack connector ensure that Silometer FMX 570 transmitters only can be inserted at these points. The pins must be inserted if the rack is not custom built by Endress+Hauser.Analogue outputsThe negative terminal of the current output, of the voltage output and of the supply voltage are connected to the circuit zero of the Silometer FMX 570 module.•Any number of measurement and control units can be connected in parallel to the voltage output, provided that all potentials are related to negative terminal of the 24 V supply (R L ≥ 10 kOhm).-There is no limit to the number of floating devices, apart from that imposed by considerations of maximum or minimum load.•Only one non-floating device can be connected to each of the currentoutputs.d b z +246821+-EC 47 Zd2d432+-FEB 17 (P)d2d421+-EC 37 Z d2d4L L+20 V...30 Vz30d32++d12d140/4...20 mA ++b12b140/2...10 Vr z26d28z28u a1012 + +141632 L+1820222426 r 28 u a 30 -L Analogue outputsAlarm relayPower supplyLevel,volumeBA119Y11Alarm relay FMX 570Non-Ex- area InputDC supplyDeltapilot S Ex-areaCurrent VoltageCapacitance/Multicap probe Capacitance/Multicap probeInputFig. 2.4:Pin assignment diagram forSilometer FMX 570Chapter 2: Installation Silometer FMX 57011Monorack wiringFig. 2.5 shows the layout in the base of the Monorack II housing, the pin assignments correspond to those in Fig. 2.4. When connecting together several Monoracks, follow the instructions supplied with the housing.•Set the jumper to position "Racksyst I"•Insert the coding pins supplied at positions 2 and 9 in the female connector at the base of the housing.•The pin assignments printed in black are valid for the Silometer FMX 570.Note!If you are installing the Silometer FMX in a Monorack I housing, please note that there is no jumper switch. In addition, for the 24 VDC version, the dummy card in the power control slot must be replaced by the 24 V card supplied.PC boardslotBA119E14PowerOutputs see Fig. 2.4Input, d2, d4Insert coding pins for Z-version at Positions 2 and 9Hole for mounting screwHole for mounting screwJumper positioned for Racksyst I cardFig. 2.5:Layout of Monorack terminalblocksSilometer FMX 570Chapter 2: Installation122.4Sensor connectionThe Silometer FMX 570 can be operated with a variety of sensor types, each requiring a different electronic insert, e.g.:•EC 37 Z or EC 47 Z for capacitance and Multicap probes •EB 17 Z or EB 27 Z for DeltapilotsSensor cableUse commercial 2-core installation cable, max. line resistance 25 Ω/core, for the sensor/transmitter cable. If electromagnetic interference is to be expected, we recommend•that the PFM negative line be grounded at the sensor (check Ex-regulations)•in case of heavy interference, that shielded cable be used, grounded at both ends.EC 37 Z and EC 47 ZThe electronic inserts EC 37 Z and EC 47 Z have two measuring ranges which can be selected by inserting a bridge between terminals 4 and 5 of the insert, see Fig 2.6. Full instructions on the selection of the insert are to be found in Publication E 07.80.06/1c.•Note the zero frequency f o ____ and sensitivity S_____on the insert.FEB 17 (P)The FEB 17 (P) electronic insert can be used with Deltapilot S sensors to measure level and volume in open vessels.•Note the zero frequency f o _____ and sensitivity ∆f _____ of the probe (see Table 2.2 on page 8)BA119E15Insert bridge for Range II (standard) Remove for Range I Ground connectionFMX 570 inputFig. 2.6:Connection diagram for electronic inserts EC 37 Z/EC 47 ZFEB 17/FEB 17 P1234BA119Y18FMX 570 inputFig. 2.7:Connection diagram for electronic insert FEB 17 (P)Chapter 2: Installation Silometer FMX 570132.5Technical data: Silometer FMX 570 transmitterConstruction•Design: 19", 7 HP , plug-in card•Front panel:black synthetic with blue field inlay, grip and markings,Protection: IP 20 (DIN 40050)•Dimensions:see diagram•Weight:approx. 0.3 kg/11 oz•Operating temperature:-0 °C...+70 °C/+32 °F ..158 °F Storage temperature: -20 °C...+85 °C/-4 °F ...185 °FElectrical connection •Multipoint plug: conforming to DIN 41612, Part 3, Type F (28-pole)Coding pins in positions 2 and 9•Power supply:24 V DC (+6 V …-4 V); residual ripple 2 V , within tolerance •Supply current: approx. 90 mA, max. 125 mA•Signal inputs:Electrically isolated from the rest of the circuitry.Protection [EEx ia] IIC or IIB •Probes:Capitance probes, impedance probes with EC 37 Z or EC 47 Z electronic insertDeltapilot S with electronic insert FEB 17 / FEB 17 P•Electromagnetic Interference Emission to EN 61326, Electrical Equipment Class A compatibility:Interference Immunity to EN 61326Outputs•Analogue output:0...20 mA/4...20 mA selectable, R L max. 500 Ω0...10 V/2...10 V selectable, R L min. 10 k Ω•Alarm relayrelay with a potential-free change-over contact Max. switching capacity:2.5 A, 250 VAC, 300 VA at cos ϕ > 0.7 or 100 VDC, 90 W Certificates •Silometer FMX 570Intrinsically safe circuit to [EEx ia] IIC and IIB (PTB certification in preparation)see also »Safety Notes«.Fig. 2.8Silometer FMX 570 plug-in cardSilometer FMX 570Chapter 2: Installation143ControlsThis Chapter describes how the Silometer FMX 570 transmitters are operated. It is divided into the following sections:•Commutec operating matrix•Configuration and display: Silometer FMX 5703.1Commutec operating matrixAll functions, including the analogue outputs and relay switch points are configured via the operating matrix, see Fig. 3.1:•Each field in the matrix is accessed by a vertical (V) and horizontal (H)position which can be entered at the front panel of the FMX 570 with the V and H keys•The parameters are entered with the plus, minus, arrow and enter keys.Parameter at current matrix positionPressed together Move to V0H0Move H0 …H9, H0Move V0…V9, V0BA119E25Current matrix positionFig. 3.1:Silometer FMX 570 displayParameter matrix operation with function of V and H keys.The complete matrix has 10 x 10fields, although not all are usedSilometer FMX 570Chapter 3: Controls153.2Configuration and displayFig. 3.1 shows the LC-display with matrix of the Silometer FMX 570, Fig. 3.2 its front panel.Table 3.1 below describes the function of the operating keys.•Changes are not possible if the matrix has been locked (Section 4.7).•Non-flashing parameters are either read-only indications or locked entry fields.100VH 00V H+EFMX 570mMeasured value display with 10-step bar chart showingpercentage 0/4 …20 mA signalParameter entry keysAlarm relay LED• Lights on fault condition, relay de-energises • Flashes on warning, relay remains energisedMatrix selection keysMatrix position indicatorBA119E23Test sockets for0/4…20 mA current outputFig. 3.2:Front panel of theSilometer FMX 570 transmitterKeysFunctionMatrix selection•Press V to select the vertical position.•Press H to select the horizontal position•Press simultaneously to select the measured value field, V0H0Parameter entry•Select the digit to be changed.The digit at the extreme left is selected and flashes.•Move to the next digit by pressing »⇒« again. When the last digit is reached »⇒« selects the leftmost digit again.•To change the position of the decimal point , press down both »⇒« and »+«. The decimal point moves 1 space to the right.•Increases the value of the flashing digit•Decreases the value of the flashing digit•To enter a negative number decrease the leftmost digit until a minus sign appears in front of it•Press »E« to register entry.•Unregistered entries remain ineffective and the instrument will operate with the old value.++Table 3.1:Silometer FMX 570Parameter entry and display keysChapter 3: Controls Silometer FMX 57016Chapter 4: Calibration and Operation Silometer FMX 570 4Calibration and OperationThis chapter is concerned with the basic settings of the Silometer FMX 570 which allowit to operate for continuous level measurement. The principle sections describe:•Commissioning•Calibration for level measurement•Calibration for linear volume or weight measurement•Dry calibration for Deltapilot probes•Level offset•Display of measured values•Locking the parameter matrix.The linearization for volume or weight measurements is described in Chapter 5, thesetting of the analogue outputs in Chapter 6 and the controls in Chapter 3.When configuring, note your parameters in the Table in the rear cover.Note your settings!•If the transmitter is ever replaced, these parameters can be entered at thefront panel. The transmitter will then measure correctly without the need foranother calibration.4.1CommissioningIf programming the module for the first time, reset the module to the factory basedparameters, see Table in back cover. Then enter the probe constants fo and S (∆f). Thisensures that the EC 37 Z/EC 47 Z electronic insert or Deltapilot can be replaced withoutthe need for recalibration, see Section 7.3.Step Matrix Entry Significance1V9H5 e.g. 672 Enter any number 670…679 to reset transmitter2-»E«Register change3V3H5 e.g. 475.3 Enter zero frequency f o (offset) of electronic insert or sensor4-»E«Register change5V3H6 e.g. 0.652 Enter sensitivity, S or ∆f, of electronic insert or sensor6-»E«Register changeThe operating mode is set at V8H0. Since the default value corresponds to levelOperating mode measurement, this step can be omitted if the transmitter has been reset.For a recalibration without reset check that mode 1, is on display:•1 = continuous level measurement, Sections 4.2, 4.3, 4.4.•6 = simulation, see Chapter 7, Section 7.2.Step Matrix Entry Significance1V8H0 e.g. 1Mode 1, continuous level measurement2-»E«Register entry17。

2014.9.1翻译E2412-04

利用红外光谱对物质分子进行的分析和鉴定。

将一束不同波长的红外射线照射到物质的分子上，某些特定波长的红外射线被吸收，形成这一分子的红外吸收光谱。

每种分子都有由其组成和结构决定的独有的红外吸收光谱，据此可以对分子进行结构分析和鉴定。

红外吸收光谱是由分子不停地作振动和转动运动而产生的，分子振动是指分子中各原子在平衡位置附近作相对运动，多原子分子可组成多种振动图形。

当分子中各原子以同一频率、同一相位在平衡位置附近作简谐振动时，这种振动方式称简正振动（例如伸缩振动和变角振动）。

分子振动的能量与红外射线的光量子能量正好对应，因此当分子的振动状态改变时，就可以发射红外光谱，也可以因红外辐射激发分子而振动而产生红外吸收光谱。

分子的振动和转动的能量不是连续而是量子化的。

但由于在分子的振动跃迁过程中也常常伴随转动跃迁，使振动光谱呈带状。

所以分子的红外光谱属带状光谱。

分子越大，红外谱带也越多。

红外光谱仪的种类有：①棱镜和光栅光谱仪。

属于色散型，它的单色器为棱镜或光栅，属单通道测量。

②傅里叶变换红外光谱仪。

它是非色散型的，其核心部分是一台双光束干涉仪。

当仪器中的动镜移动时，经过干涉仪的两束相干光间的光程差就改变，探测器所测得的光强也随之变化，从而得到干涉图。

经过傅里叶变换的数学运算后，就可得到入射光的光谱。

这种仪器的优点：①多通道测量，使信噪比提高。

②光通量高，提高了仪器的灵敏度。

③波数值的精确度可达0.01厘米-1。

④增加动镜移动距离，可使分辨本领提高。

⑤工作波段可从可见区延伸到毫米区，可以实现远红外光谱的测定。

红外光谱分析可用于研究分子的结构和化学键，也可以作为表征和鉴别化学物种的方法。

红外光谱具有高度特征性，可以采用与标准化合物的红外光谱对比的方法来做分析鉴定。

已有几种汇集成册的标准红外光谱集出版，可将这些图谱贮存在计算机中，用以对比和检索，进行分析鉴定。

利用化学键的特征波数来鉴别化合物的类型，并可用于定量测定。

SIMDRIVE_3D_V6_Whats_New

V5
Seite 3 Datum: 15.01.2013
SIMDRIVE3D-Version 6
Main Menu
NEW V5
New arrangement of the main menu for an easier orientation: View has been moved to the menu of the model window Setup options have been moved to the first level Headers for a better overview and comprehensibility
Stärken der flexiblen Körper:
Jedes System bestehend aus Masse und Steifigkeit kann modelliert und frei im Raum positioniert werden. Flexible Lagerung drehender Systeme und die Auswertung der dabei auftretenden Kräfte ist möglich. Jeder Massepunkt kann bezüglich Position, Geschwindigkeit und Beschleunigung ausgewertet werden. Mittels der Verbinder können die Kräfte und Momente ausgewertet werden.
Merging of surfaces
Overlay function
Seite 12
Datum: 15.01.2013

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Analyzing Degrees of Freedom自由度分析关于动力传动系统的自由度与约束识别旋转自由度是非常重要的建设和分析一个传动系统，尤其是许多制约因素和外部复杂的驱动系统。

Simulink作为传动系统自由度的代表，包括纯Simulink的状况。

如需要更多的有关传动系统驱动，参见本章简单模型与转矩和动作动作动力传动系统。

参见Findingand Using Driveline States下面是更多的情况和它们是如何相关的自由度。

本节讨论如何识别传动系统自由度，考虑到制约因素，并从中提取一个完整的传动系统图中的真实或独立的自由度。

它包括以下基本步骤：•传动系统图中的基本要素：连接线动态因素和内部约束力矩约束•传感器和执行器：进口和出口，并从信息到您的传动系统终止件自由度有了这些，你可以枚举所有的自由度任何传动系统。

本节讲一个如何做到这一点的例子。

识别自由度在SimDriveline模型中，所有的机械运动是旋转。

因为绝对的角度是不会用在SimDriveline软件，它是最简单的识别传动系统的自由程度（自由度）的一角速度。

（有些块使用两轴传动系统相对角度来确定内部动力传动系统的动态因素所产生的力矩。

）一个自由度是一个单一的，不同的角速度。

每个自由度对扭矩上作出了响应从而组成该传动系统。

结合牛顿的旋转运动方程组确定的角运动。

在基本条件下，是机械自由度旋转惯性特性。

这是一贯的，易于识别一个SimDriveline自由度作为传动系统轴（理想化的驱动轴与连接惯性），因为惯性是严格的联系到它们的理想轴。

因此，为了识别和计数传动系统自由度，你需要首先找一个SimDriveline与物理模型传动系统连接，然后才考虑它的组成部分。

传动系统块修改自由度为代表的连接线代表：•相对轴之间的传动链施加扭矩•添加轴之间的传动系的限制•施加外部轴驱动力矩和运动基本自由度该传动系统运动的基本单位是自由度（自由度）由一个完整的传动系统连接线代表。

这种线代表无质量和完美的理想化刚性驱动轴。

旋转与旋转惯性机构，由惯性块代表，是严格联系到这些线路和旋转的轴。

轴传动系的基本自由度一个传动系连接线通过传动系统连接器端口固定，代表一个理想化的轴传动系统。

连接线强制约束这两个连接的传动系统部件旋转角速度相同。

你通过一个运动传感器块衡量一轴角速度。

对于单一轴SimDriveline分析，只有角速度是重要的。

国内未定义一个轴的绝对角速度。

通过运动传感器测量轴传动系运动定义相对和绝对角相对角度，有时需要计算之间的轴对内部产生的力矩（see Connected Degrees of Freedom following）。

要确定一个相对角度，模块集成了对轴的相对角速度，并增加了初步的结果，相对角度，您指定的情况下在需要的地方。

只有当你通过一个运动传感器块测量它的运动，您可以定义为一个单一轴的绝对旋转角度。

该传感器通过集成的轴角速度和添加一个任意角度绝对参照定义了绝对角度，该角度为您在运动传感器提供的绝对角度输入。

轴传动系的硬性旋转惯性相对于本身，一个传动系统连接线代表一个单一的自由度。

这个自由度可以不受任何力矩，因为它缺乏转动惯量。

其他基本要素需要建立一个正常运作传动系统模型是一个或多个惯性块。

在实际的机械系统，旋转机构同时携带惯性和自由度。

SimDriveline旋转机构硬性附加到一个轴传动系统。

它是采取简单的观点相等于一点（简化），传动系统轴是基本自由度和机构进行唯一的惯性。

你用连接线的分支对传动系统连接线的附加惯性。

所附的惯性受到任何扭矩是由连接线传递的，其中规定的一切附加到一个单一行必须以同样的速度旋转约束传播。

轴传动系分枝规则和约束您可以分支传动系统连接线。

你只能连接任何一个分支传动系统连接线的结尾处到传动系统连接器端口。

所有传动系统连接到一个分支线的两端设置在同一部件旋转角速度。

一条割不断的设置，分支连接线代表一个单自由度。

支连接线和角速度约束自由度的连接你可以通过内部动力元素连接两个代表独立的自由度的两个独立的轴传动系统。

一个动态元素生成一个从相对角度/或两轴运动的相对的扭矩。

这种相对扭矩表现在两轴之间，这仍然是独立的自由度和扭矩传输（具有同等规模和在基轴和从动轴上异号），以各自的附加惯性。

动态生成元素和内部转矩该库包含代表传动系元素产生内部扭矩的动态元素块。

（See Dynamic Elements in the block reference chapter。

）单一的相对扭矩应用与正信号的（F）的从动轴和负信号的基轴（乙）。

•Hard Stop和Torsional Spring-Damper产生弹簧般的扭矩和阻尼作用于轴传动系统连接到它们。

这些力矩是两个轴的相对角度和角速度的一小部分。

•变矩器生成一种粘性传动系统扭矩作用于轴连接到它。

这扭矩是相对的两轴角速度的一小部分。

在正常操作（前进潮流），叶轮（一）相当于泵轮（B）和涡轮（T）的导轮（F）之间。

离合器和有条件的连接离合器是有条件的或动态的约束。

一个离合器，如果没有锁止，也连接两个轴传动系统，可以不使用他们一个相对的扭矩，使两轴独立。

解除锁定离合器要么是完全未介入，根本没有施加扭矩，或参与，施加作为两个连接轴的相对速度的功能动摩擦。

可控离合器摩擦块模型，如离合器。

如果离合器锁止，只适用两连接轴的之间的静摩擦力，两轴不再是独立的。

相反，他们作为一个单一的坐标轴，以同样的速度旋转。

See Constrained Degrees of Freedom following.自由度的约束轴传动系的某些元件在这样一种方式的连接以消除他们的自由运动。

这些因素对所连接轴的运动限制。

一个约束轴不独立与其他轴，不计入总网或独立运动的传动系统。

这些限制消除系统的独立自由度。

并非所有的限制都是独立的。

截止到分支回路内连接线形成一些限制。

有效的或独立的限制数量是由若干块所引起的限制减去独立传动系统连接线封闭循环的数目。

除离合器，传动系的限制是无条件的或静态的限制，即在模拟不变。

离合器施加条件或动态限制。

锁定轴传动系传动系统的连接线连接到一个Housing block冻结相应的传动系统轴运动。

它不能移动，它的角速度在模拟过程中限制为零。

这样轴没有关联的独立的自由度。

通过离合器锁止两轴传动系统锁定的离合器，只要锁定的条件长期有效，限制了两个连接传动系统轴旋转起来。

这两个轴各有不同，但只有一个代表一个独立的自由度。

另一个是独立的。

See Controllable Friction Clutch for more details.未锁好的离合器，即使它继续采用一种相对轴之间的动摩擦力矩，不再规定一个制约因素。

相反，它作为一个动态元素。

See Connected Degrees of Freedom preceding.轴与齿轮传动系统耦合两个或两个以上齿轮传动系统耦合轴施加的限制减少了传动系统的独立自由度。

这些限制的性质取决于所使用的齿轮。

两个连接轴与齿轮块施加一个这样的限制，减少两轴到一个独立的自由度。

多轴齿轮施加多个约束。

例如，行星齿轮轴规定在三个轴上施加两个约束，减少了一个独立的自由度轴。

（此数不包括第四，内部自由度，行星轮，这是没有连接到一轴）封闭循环，有效的约束和约束一致性实际约束计数来确定的自由度数是有效的或独立的限制。

当连接线形成闭合回路，你必须特别小心数传动系统的限制。

对在一个闭合回路中通过绘制一些多余的制约因素来减少有效约束计数独立的制约因素=从块数限制数- 独立闭环数您可以通过计算基本回路独立循环的数目可靠地计算独立闭环数。

根本没有subloops 循环。

你可以跟踪一个只有一个基本循环的路径。

通过只计算基本循环，可避免过高的重叠的循环。

例如，这张图清楚地有两个独立的回路。

在此图中，你可以得出三个循环：两个内部循环，左，右，和外循环。

外循环包括内部循环。

在此图中有两个独立的回路图，因为只有两个是完整的。

最外层循环是不是完整。

一致性约束一个封闭的循环冗余使得它包含一个内部的限制，只要线的分支的所有限制角速度在整个环中相等。

（See Driveline Axis Branching Rules and Constraints preceding.)没有直接的线路连接的角速度也必须是一致的，举个例子，他们是通过齿轮传递。

自由动作，遥感，和终止度你可以使用只有一个传动系统连接器端口（SimDriveline块）产生和/或终止自由度（自由度），因为他们可以结束传动系统的连接线。

这些模块包括：∙Driveline Environment∙Inertia∙Housing∙传感技术（see Sensors & Actuators），除了扭矩传感器∙汽车零部件（see Vehicle Components），如轮胎和发动机在一个子系统中使用的传感器和执行器。

终止一个连接线实际上并不产生或减少自由度，但它限制了自由度。

如果终止是一个执行机构，终止可以修改传动系统的自由度。

另一方面，传感器不会对传动系统自由度产生影响。

方向性，动作，和传感传动系统的连接线有没有内在的方向性。

该运动的方向和转矩流取决于你模拟时传动系统动态。

相反，Simulink的端口>和信号线具有固有的方向性。

虽然传动系统连接线无方向性，当您向图中附加驱动器块时方向性是隐式的引入到一个传动系统模型（见本章简单传感器和执行器的模型），因为这些块的接口通过其他的Simulink与纯SimDriveline块互通。

执行器的对传动系统的影响，取决于Simulink的输入信号。

从动力传动系统仿真结果的动作决定了由传感器模块输出的Simulink的输出信号。

关于自由度驱动力矩的影响转矩驱动器连接到传动系统适用于由Simulink的输入信号到指定的扭矩传动系统。

这样的驱动没有对系统自由度数产生影响。

该传动系统轴的扭矩传递到他们的连接惯性，而传动系统对所施加扭矩自由的回应。

该动作是结合传动系统加速度（施加扭矩的结果）进行仿真，以获取传动系统速度。

关于自由度运动驱动的影响连接一个运动器到轴传动系统删除该轴扭矩的自由回应，而不是在指定的驱动器的Simulink的输入信号模拟轴运动。

运动驱动，不像扭矩驱动，从系统中删除一个独立的自由度。

自由度的独立计数要确定在传动系统中若干独立自由度，1．在你的的模型图中SimDriveline部分计数所有的连续、不间断的动力传动系统的连接线。

这些线路总数记为N CL。

这些线连接两个传动系统连接端口或终止传动系统连接器端口，如前面讨论的Fundamental Degrees of Freedom and Actuating, Sensing, and Terminating Degrees of Freedom 2．计数模块的所有限制，从他们所施加的限制连接轴传动系统。