Effect of the geometry of workpiece on polishing velocity in free annular polishing
lathe 部分翻译
The purpose of a lathe is to rotate a part against a tool whose position it controls. It isuseful for fabricating parts and/or features that have a circular cross section. The s pindleis the part of the lathe that rotates. Various workholding attachments such as three jawchucks, collets, and centers can be held in the spindle. The spindle is driven by a n electric motor through a system of belt drives and/or gear trains. Spindle speed i s controlled byvarying the geometry of the drive train.The tailstock can be used to support the end of the workpiece with a center, or to holdtools for drilling, reaming, threading, or cutting tapers. It can be adjusted in positionalong the ways to accommodate different length workpieces. The ram can be fed a longthe axis of rotation with the tailstock handwheel.该车床的目的是旋转一个它所控制（夹持）工件的一部分。
全国职称英语考试理工类AB级课堂笔记：概括大意与完成句子第2讲（6）
⽂章主题分析：Global Warming来源：考试⼤Smoke is clouding our view of global warming, protecting the planet from perhaps three- quarters of the greenhouse(温室)effect．cloud v.使不清晰, 使多云，使阴暗;来源：考试⼤The sky clouded over.天空中云层密布(clear up v. 放晴)in the clouds 空想的; 想象的；不真实的；不切实际的来源：考试⼤被选择项分析：A Atmospheric ScientistsB The Calculations Made at the Berlin WorkshopC The Previous Calculations of the Effect of AerosolsD The Scientists’AgreementE The Authoritative ConclusionF Greenhouse Gases分析：B和C中⼀定会有答案出现。
来源：考试⼤E．分析：该段结构“这是⼀个具有很⼤影响的⼀个结论，在。
地⽅达成的，由。
科学家达成”（注意借助各句⼦主⼲内容判断句⼦⼤意），所以判断E（段落中提到的科学家仅仅是为了给提到的结论增加权威性）是答案。
同时可以判断A是⼲扰项可以被排除掉。
（A Atmospheric Scientists）B The Calculations Made at the Berlin WorkshopC The Previous Calculations of the Effect of AerosolsD The Scientists’Agreement来源：考试⼤F Greenhouse Gases24 Paragraph 33 IPCC scientists have suspected for a decade that aerosols(浮质)of smoke and other particles from burning rainforest，crop waste and fossil fuels are blocking sunlight and counteracting the warming effect of carbon dioxide(⼆氧化物)emissions．Until now，they reckoned that aerosols reduced greenhouse warming by perhaps a quarter, cutting increases by 0．2。
模具专业英语翻译
单词翻译：PlasticsCompression Molding for PlasticsTransfer Molding and Injection MoldingPressure Die Casting DiesForging DieFundamental of Chip-type Machining ProcessesFundamental of T urning and Boring on LatheMillingElectrodischarge Machines翻译划线的部分T urning is the process of machining external cylindrical and conical surfaces. It is usually performed on a lathe.The depth of cut (DOC), d, represents the third dimension.As the plastic is fed to the rotating screw, it passes through thre e zones as shown: feed, compression, and metering（定量）.句子翻译The molds used for compression molding are classified into four basic types, namely, positive molds, landed positive molds, flash-type molds, and semipositive molds.In order to harden and eject thermoplastic parts from the mold, cooling would be necessary.There are seven basic chip formation processes: shaping, turning, milling, drilling, sawing, broaching, and grinding (abrasive machining).In the injection mold, The screw（螺杆）acts as a combination injecting and plasticizing unit .The physcal composition of the workpiece greatly influences the selection of the machining method, the tool composition and geometry, and the rate of material removal.The clamping force that a machine is capable of exerting is part of the size designation and is measured in tons.Proper selection of the die material and of the die manufacturing technique determines, to a large extent, the useful life of forging dies.In compression molding the plastic material as powder or performs is placed into a heated steel mold cavity.The guide pins, or posts, are mounted in the lower shoe.Plastic often contain other added materials called fillers.When applying the electrical discharge machining process, the material is eroded as a result of electrical discharge between tool and work.Parts made by transfer molding have greater strengths, more uniform densities, closer dimensional tolerances, and the parting line requires less cleaning as compared with parts made by compression molding.The die blocks contain the movement mechanisms of the die and the inserts incorporating the casting form so that the assembly can be mounted between the tie bars of the machine.In the early dawn civilization mankind discovered that a heated piece of metal was more easily hammered into different shapes.The tools necessary to produce a given forging cannot be made until the shape of the final forging has been determined.Solid models eliminate most of the problems of the wire frame.1.This process of annealing consists of heating the steel to an elevated temperature fora definite period of time and, usually, cooling it slowly.The pattern is a replica of the part being made but has slightly larger dimensions to allow for shrinkage during solidification and cooling of the casting.This type of mold is widely used because it is comparatively easy to construct and it controls thickness and density within close limits..1.If the surface is unusually hard, the cutting speed on the first roughing cut should bereduced accordinglyWelding is a process in which two materials, usually metals, are permanently jointed together through localized coalescence, resulting from a suitable combination of temperature, pressure and metallurgical conditions.汉译英传递模注射模自由锻Smith forging切削加工过程段落翻译After the feed zone, the screw flight depth is gradually reduced, forcing the plastic to compress. The work is converted to heat by shearing the plastics, making ita semifluid（半流体）mass.In the metering zone, additional heat is applied by conduction from the barrel surface. As the chamber in front of the screw becomes filled, it force the screw back, tripping a limit switch that activates a hydraulic cylinder that force the screw forward and injects the fluid plastic into the close mold.Gas tungsten arc welding is performed with the heat from an electric arc discharged between the workpiece and a nonconsumable（不熔化）electrode made of tungsten.This process, like GNA W(gas metal arc welding), is gas-shielded arc welding, where an atmosphere of inert gas is maintained around the arc and no flux（熔剂）is used.The process is often called tungsten inert（惰性）gas welding.。
冲压模具成型外文翻译参考文献
冲压模具成型外文翻译参考文献(文档含中英文对照即英文原文和中文翻译)4 Sheet metal forming and blanking4.1 Principles of die manufacture4.1.1 Classification of diesIn metalforming,the geometry of the workpiece is established entirely or partially by the geometry of the die.In contrast to machining processes,ignificantly greater forces are necessary in forming.Due to the complexity of the parts,forming is often not carried out in a single operation.Depending on the geometry of the part,production is carried out in several operational steps via one or several production processes such as forming or blanking.One operation can also include several processes simultaneously(cf.Sect.2.1.4).During the design phase,the necessary manufacturing methods as well as the sequence and number of production steps are established in a processing plan(Fig.4.1.1).In this plan,theavailability of machines,the planned production volumes of the part and other boundary conditions are taken into account.The aim is to minimize the number of dies to be used while keeping up a high level of operational reliability.The parts are greatly simplified right from their design stage by close collaboration between the Part Design and Production Departments in order to enable several forming and related blanking processes to be carried out in one forming station.Obviously,the more operations which are integrated into a single die,the more complex the structure of the die becomes.The consequences are higher costs,a decrease in output and a lower reliability.Fig.4.1.1 Production steps for the manufacture of an oil sumpTypes of diesThe type of die and the closely related transportation of the part between dies is determined in accordance with the forming procedure,the size of the part in question and the production volume of parts to be produced.The production of large sheet metal parts is carried out almost exclusively using single sets of dies.Typical parts can be found in automotive manufacture,the domestic appliance industry and radiator production.Suitable transfer systems,for example vacuum suction systems,allow the installation of double-action dies in a sufficiently large mounting area.In this way,for example,the right and left doors of a car can be formed jointly in one working stroke(cf.Fig.4.4.34).Large size single dies are installed in large presses.The transportation of the parts from oneforming station to another is carried out mechanically.In a press line with single presses installed one behind the other,feeders or robots can be used(cf.Fig.4.4.20 to 4.4.22),whilst in large-panel transfer presses,systems equipped with gripper rails(cf.Fig.4.4.29)or crossbar suction systems(cf.Fig.4.4.34)are used to transfer the parts.Transfer dies are used for the production of high volumes of smaller and medium size parts(Fig.4.1.2).They consist of several single dies,which are mounted on a common base plate.The sheet metal is fed through mostly in blank form and also transported individually from die to die.If this part transportation is automated,the press is called a transfer press.The largest transfer dies are used together with single dies in large-panel transfer presses(cf.Fig.4.4.32).In progressive dies,also known as progressive blanking dies,sheet metal parts are blanked in several stages;generally speaking no actual forming operation takes place.The sheet metal is fed from a coil or in the form of metal ing an appropriate arrangement of the blanks within the available width of the sheet metal,an optimal material usage is ensured(cf.Fig.4.5.2 to 4.5.5). The workpiece remains fixed to the strip skeleton up until the laFig.4.1.2 Transfer die set for the production of an automatic transmission for an automotive application-st operation.The parts are transferred when the entire strip is shifted further in the work flow direction after the blanking operation.The length of the shift is equal to the center line spacing of the dies and it is also called the step width.Side shears,very precise feeding devices or pilot pins ensure feed-related part accuracy.In the final production operation,the finished part,i.e.the last part in the sequence,is disconnected from the skeleton.A field of application for progressive blanking tools is,for example,in the production of metal rotors or stator blanks for electric motors(cf.Fig.4.6.11 and 4.6.20).In progressive compound dies smaller formed parts are produced in several sequential operations.In contrast to progressive dies,not only blanking but also forming operations areperformed.However, the workpiece also remains in the skeleton up to the last operation(Fig.4.1.3 and cf.Fig.4.7.2).Due to the height of the parts,the metal strip must be raised up,generally using lifting edges or similar lifting devices in order to allow the strip metal to be transported mechanically.Pressed metal parts which cannot be produced within a metal strip because of their geometrical dimensions are alternatively produced on transfer sets.Fig.4.1.3 Reinforcing part of a car produced in a strip by a compound die setNext to the dies already mentioned,a series of special dies are available for special individual applications.These dies are,as a rule,used separately.Special operations make it possible,however,for special dies to be integrated into an operational Sequence.Thus,for example,in flanging dies several metal parts can be joined together positively through the bending of certain metal sections(Fig.4.1.4and cf.Fig.2.1.34).During this operation reinforcing parts,glue or other components can be introduced.Other special dies locate special connecting elements directly into the press.Sorting and positioning elements,for example,bring stamping nuts synchronised with the press cycles into the correct position so that the punch heads can join them with the sheet metal part(Fig.4.1.5).If there is sufficient space available,forming and blanking operations can be carried out on the same die.Further examples include bending,collar-forming,stamping,fine blanking,wobble blanking and welding operations(cf.Fig.4.7.14 and4.7.15).Fig.4.1.4 A hemming dieFig.4.1.5 A pressed part with an integrated punched nut4.1.2 Die developmentTraditionally the business of die engineering has been influenced by the automotive industry.The following observations about the die development are mostly related to body panel die construction.Essential statements are,however,made in a fundamental context,so that they are applicable to all areas involved with the production of sheet-metal forming and blanking dies.Timing cycle for a mass produced car body panelUntil the end of the 1980s some car models were still being produced for six to eight years more or less unchanged or in slightly modified form.Today,however,production time cycles are set for only five years or less(Fig.4.1.6).Following the new different model policy,the demands ondie makers have also changed prehensive contracts of much greater scope such as Simultaneous Engineering(SE)contracts are becoming increasingly common.As a result,the die maker is often involved at the initial development phase of the metal part as well as in the planning phase for the production process.Therefore,a muchbroader involvement is established well before the actual die development is initiated.Fig.4.1.6 Time schedule for a mass produced car body panelThe timetable of an SE projectWithin the context of the production process for car body panels,only a minimal amount of time is allocated to allow for the manufacture of the dies.With large scale dies there is a run-up period of about 10 months in which design and die try-out are included.In complex SE projects,which have to be completed in 1.5 to 2 years,parallel tasks must be carried out.Furthermore,additional resources must be provided before and after delivery of the dies.These short periods call for pre-cise planning,specific know-how,available capacity and the use of the latest technological and communications systems.The timetable shows the individual activities during the manufacturing of the dies for the production of the sheet metal parts(Fig.4.1.7).The time phases for large scale dies are more or less similar so that this timetable can be considered to be valid in general.Data record and part drawingThe data record and the part drawing serve as the basis for all subsequent processing steps.They describe all the details of the parts to be produced. The information given in theFig.4.1.7 Timetable for an SE projectpart drawing includes: part identification,part numbering,sheet metal thickness,sheet metal quality,tolerances of the finished part etc.(cf.Fig.4.7.17).To avoid the production of physical models(master patterns),the CAD data should describe the geometry of the part completely by means of line,surface or volume models.As a general rule,high quality surface data with a completely filleted and closed surface geometry must be made available to all the participants in a project as early as possible.Process plan and draw developmentThe process plan,which means the operational sequence to be followed in the production of the sheet metal component,is developed from the data record of the finished part(cf.Fig.4.1.1).Already at this point in time,various boundary conditions must be taken into account:the sheet metal material,the press to be used,transfer of the parts into the press,the transportation of scrap materials,the undercuts as well as thesliding pin installations and their adjustment.The draw development,i.e.the computer aided design and layout of the blank holder area of the part in the first forming stage–if need bealso the second stage–,requires a process planner with considerable experience(Fig.4.1.8).In order to recognize and avoid problems in areas which are difficult to draw,it is necessary to manufacture a physical analysis model of the draw development.With this model,theforming conditions of the drawn part can be reviewed and final modifications introduced,which are eventually incorporated into the data record(Fig.4.1.9).This process is being replaced to some extent by intelligent simulation methods,through which the potential defects of the formed component can be predicted and analysed interactively on the computer display.Die designAfter release of the process plan and draw development and the press,the design of the die can be started.As a rule,at this stage,the standards and manufacturing specifications required by the client must be considered.Thus,it is possible to obtain a unified die design and to consider the particular requests of the customer related to warehousing of standard,replacement and wear parts.Many dies need to be designed so that they can be installed in different types of presses.Dies are frequently installed both in a production press as well as in two different separate back-up presses.In this context,the layout of the die clamping elements,pressure pins and scrap disposal channels on different presses must be taken into account.Furthermore,it must be noted that drawing dies working in a single-action press may be installed in a double-action press(cf.Sect.3.1.3 and Fig.4.1.16).Fig.4.1.8 CAD data record for a draw developmentIn the design and sizing of the die,it is particularly important to consider the freedom of movement of the gripper rail and the crossbar transfer elements(cf.Sect.4.1.6).These describe the relative movements between the components of the press transfer system and the die components during a complete press working stroke.The lifting movement of the press slide,the opening and closing movements of the gripper rails and the lengthwise movement of the whole transfer are all superimposed.The dies are designed so that collisions are avoided and a minimum clearance of about 20 mm is set between all the moving parts.4 金属板料的成形及冲裁4. 模具制造原理4.1.1模具的分类在金属成形的过程中，工件的几何形状完全或部分建立在模具几何形状的基础上的。
夹具设计英文文献
夹具设计英文文献In the realm of manufacturing, fixture design is acritical component that ensures precision and efficiency inthe production process. It involves creating devices that securely hold workpieces in place during machining operations.The design process begins with a thorough understandingof the workpiece's geometry and the specific machining requirements. This understanding guides the selection of materials, the determination of size, and the configurationof the fixture's components.Innovative fixture designs often incorporate adjustable features to accommodate a variety of workpieces, thereby enhancing the flexibility of the manufacturing setup. This adaptability is key to reducing production time andminimizing costs.Safety is paramount in fixture design, with mechanisms ensuring that both the operator and the workpiece areprotected from potential hazards. Ergonomic considerationsalso play a role, with the fixture's design facilitating ease of use for the operator.Advancements in technology have led to the integration of computer-aided design (CAD) and simulation software infixture design. These tools allow designers to virtually test and optimize fixture performance before physical prototyping.Sustainability is becoming an increasingly important aspect of fixture design, with a focus on using recyclable materials and minimizing waste throughout the manufacturing process.The future of fixture design looks towards automation and robotics, where fixtures can dynamically adjust to different workpieces, further streamlining the production line and reducing the need for manual intervention.In conclusion, fixture design is a multifaceteddiscipline that requires a deep understanding of materials, mechanics, and manufacturing processes. As technology continues to evolve, so too will the sophistication and capabilities of fixtures in the industry.。
简述旋压成型的工艺流程
简述旋压成型的工艺流程Rotary forming is a metal forming process that utilizes a rotating tool to shape the workpiece. 旋压成型是一种利用旋转工具对工件进行成型的金属成型工艺。
This process is commonly used in the production of cylindrical and conical parts such as tubes, pipes, and containers. 这种工艺通常用于生产圆柱形和锥形零件，如管道和容器。
The tool exerts pressure on the workpiece as it rotates, causing the material to deform and take on the desired shape. 工具在旋转时对工件施加压力，使材料变形并呈现出所需的形状。
One of the key steps in the rotary forming process is the preparation of the workpiece. 旋压成型工艺中的一个关键步骤是对工件的准备。
The workpiece is typically a flat sheet or plate of metal, which is loaded into the rotary forming machine. 工件通常是一张金属平板或板材，它被装载到旋压成型机器中。
The machine then begins to rotate the tool and apply pressure to the workpiece, gradually forming it into the desired shape. 机器随后开始旋转工具并对工件施加压力，逐渐将其成型为所需的形状。
abaqus切削热传导公式
abaqus切削热传导公式English Answer:Heat Transfer in Cutting with Abaqus.Heat transfer plays a crucial role in cutting operations, affecting the temperature distribution, tool wear, and workpiece quality. Abaqus offers comprehensive capabilities for modeling heat transfer in cutting simulations, enabling engineers to accurately predict thermal effects and optimize cutting parameters.Heat Transfer Mechanisms in Cutting.During cutting, heat is generated due to friction between the tool and workpiece, plastic deformation of the material, and chip formation. Heat transfer occurs through various mechanisms, including:Convection: Heat transfer between the tool, workpiece,and surrounding environment.Conduction: Heat transfer within the tool, workpiece, and chips.Radiation: Heat transfer through electromagnetic waves.Heat Transfer Modeling in Abaqus.Abaqus provides several methods for modeling heat transfer in cutting simulations:Element-based Heat Transfer: Heat transfer is solved within each element, considering conduction, convection,and radiation.Surface-based Heat Transfer: Heat transfer is applied as boundary conditions on surfaces, such as contactsurfaces between the tool and workpiece.User Subroutines: Custom heat transfer models can be implemented through user subroutines.Governing Equations.The heat transfer analysis in Abaqus is based on the following governing equations:Conservation of Energy: The rate of heat transfer into a control volume minus the rate of heat transfer out of the control volume equals the rate of change of energy within the control volume.Conduction: Fourier's law describes heat conduction as a function of temperature gradient.Convection: Newton's law of cooling describes heat convection as a function of surface temperature and surrounding environment temperature.Radiation: Stefan-Boltzmann law describes heat radiation as a function of surface temperature and emissivity.Material Properties.Accurate material properties are essential for reliable heat transfer simulations. Abaqus requires the following thermal properties:Thermal Conductivity: The ability of a material to conduct heat.Specific Heat Capacity: The amount of heat required to raise the temperature of a unit mass of material by one degree.Density: The mass per unit volume of a material.Boundary Conditions.Appropriate boundary conditions are necessary to define the temperature or heat flux at the simulation boundaries. Common boundary conditions include:Convection Boundary Conditions: Prescribed heattransfer coefficient and reference temperature.Radiation Boundary Conditions: Prescribed surface emissivity and surrounding environment temperature.Temperature Boundary Conditions: Prescribed temperature values on surfaces.Simulation Workflow.The typical workflow for heat transfer modeling in Abaqus involves:1. Defining the geometry and mesh of the model.2. Assigning material properties.3. Applying boundary conditions.4. Specifying heat transfer settings.5. Running the simulation.6. Post-processing the results to analyze temperature distribution, heat flux, and other thermal effects.Benefits of Heat Transfer Modeling in Cutting.Incorporating heat transfer into cutting simulations provides valuable insights into:Temperature Distribution: Predicting the temperature distribution within the tool, workpiece, and chips.Tool Wear: Assessing the impact of heat on tool wear and life expectancy.Workpiece Quality: Evaluating the effects of heat on workpiece surface finish, distortion, and residual stresses.Cutting Parameters Optimization: Identifying optimal cutting parameters to minimize heat generation and improve productivity.中文回答：Abaqus 中切削热传导公式。
机加工精度要求 英文
机加工精度要求英文Machining accuracy is a crucial aspect in the manufacturing industry, as it directly affects the quality, performance, and durability of the final product. The precision with which a part is machined determines its fitness for use and its ability to meet design specifications. Therefore, it is essential to understand and control machining accuracy to ensure the consistency and reliability of manufactured components.Machining accuracy requirements vary depending on the application and the type of material being machined. For example, high-precision machining is required for components in the aerospace, medical, and automotive industries, where parts must meet strict tolerances and performance standards. On the other hand, lower precision may be acceptable for certain applications where the parts do not require as much accuracy.To achieve the desired machining accuracy, it isnecessary to consider several factors, including machinetool precision, cutting tool selection, workpiece material, and machining processes. Machine tool precision is influenced by factors such as machine rigidity, thermal stability, and vibration control. Cutting tool selection involves choosing the appropriate tool material, geometry, and coating to match the workpiece material and machining conditions. Workpiece material properties, such as hardness, ductility, and thermal conductivity, also affect machining accuracy.Machining processes, such as turning, milling, drilling, and grinding, each have their own unique challenges and considerations. For example, turning is typically used for cylindrical parts and requires precise control of feed rate, spindle speed, and cutting depth to achieve the desired surface finish and dimensional accuracy. Milling, on the other hand, is suitable for flat and contoured surfaces and requires careful selection of cutting conditions to avoid tool wear and maintain dimensional stability.To ensure machining accuracy, it is important toimplement quality control measures throughout the manufacturing process. This includes regular machine tool maintenance and calibration, inspection of workpieces before and after machining, and the use of precision measuring equipment. Additionally, it is beneficial to employ advanced machining technologies, such as CNC machining and additive manufacturing, which provide greater control and repeatability.In conclusion, machining accuracy requirements are critical for ensuring the quality and performance of manufactured components. By considering machine tool precision, cutting tool selection, workpiece material, and machining processes, as well as implementing qualitycontrol measures, manufacturers can achieve the desired machining accuracy and produce reliable parts that meet design specifications.。
2A12厚板铝合金淬火过程有限元建模研究
2A12厚板铝合金淬火过程有限元建模研究冯潇;张磊;李兆光;刘长勇【摘要】淬火残余应力可能造成工件淬后裂纹、削弱其疲劳强度以及造成其体积和形状的变化.在需要进行淬火处理的厚板结构铝合金零件中,这一情况尤为显著.因此,对厚板铝合金淬火过程进行有限元模拟,预测其淬后残余应力大小及分布,具有十分重要的意义.本文运用ABAQUS/Standard软件建立了2A12厚板铝合金的淬火过程有限元模型,并用反传热算法确定了以聚乙撑二醇(PAG)溶液作为淬火介质时的换热边界条件.为了验证模拟结果的可靠性,应用X射线法对厚板淬火残余应力进行了测量.模拟结果与实测数据具有较好的一致性,表明本文建立的有限元模型具有较高的精度.%Quenching residual stresses may induce quench crack and fatigue strength reducing, and cause distortion and dimensional variation. This phenomenon is particularly obvious in aluminum parts with block structure. Thus, it's important to conduct quenching simulation of aluminum blocks in order to predict the magnitude and distribution of quenching residual stress. In this study, finite element model of aluminum alloy 2A12 blocks were developed by using commercial finite element code ABAQUS/Standard software. Heat transfer boundary condition had also been investigated through inverse heat transfer method while PAG solution was used as quenching medium. The agreement between simulation results and experimental data proves the reliability of the finite element model developed in this study.【期刊名称】《新技术新工艺》【年(卷),期】2012(000)010【总页数】4页(P57-60)【关键词】淬火;有限元;2A12铝合金;残余应力【作者】冯潇;张磊;李兆光;刘长勇【作者单位】清华大学机械工程系,北京100084;清华大学机械工程系,北京100084;北京控制工程研究所,北京100190;清华大学机械工程系,北京100084【正文语种】中文【中图分类】TG156.352×××系列铝合金在淬火时效之后具有很高的强度，被广泛应用于航空航天领域。
学生对反函数概念的理解
从上述图表中可以看出，５０％以上的高一学生对反函数概念定义的回答还处于水平一（前结构水平），高二学生在四个水平上的分布相对来说是比较均匀的，高三大部分学生处在水平二（单结构水平）和水平三（多结构水平）上。
让人感到意外的是，对反函数概念定义的回答达到水平四（关联水平）的高二学生远远多于高三学生，水平四上的高一和高三学生人数百分比是相当的。
ｖｉｎｎｅｒ的关于定义与概念表象关系的理论，在这里或许能够作为一个很好的解释：学生在学习过程中不断建构反函数概念的表象，而反函数概念的定义在建构中起到了“协助”作用，是概念形成的脚手架，随着概念表象建构得越来越准确，直到反函数概念大厦筑成之后，他们再次看到“反函数”一词时的反应一般就不再拘泥于定义的形式，而是有了自己完善的理解。
在本研究后面的分析中我们也将会看到，事实上，高三学生在解答题目的表现上确实是好于其他两个年级的。
图２显示了三个年级所有学生对反函数概念定义回答水平的比较。
塑墼堡垒重墨旦查查！塑！！趣一从上述图表中可以看出，学生对反函数概念定义的回答一般可以达到水平二和水平三：由于高一有一半以上学生的回答还处于水平一，所以，尽管高二、高从表２中可以看出，就年级来讲，学生呈现出的各种理解的总频数高二年级为１０８次，比学生数高出９２．９％；高三年级为６１次，比学生数高出４５．２％；高一年级为６５次，比学生数高出２２．２％。
就总体来讲，学生呈现出的各种理解的总频数为２３４次，比学生数高出５３．９％。
比学生数高出的百分比越大，说明有些学生回答中呈现出的概念表象越多，从而可以说明学生对反函数概念定义各个侧面的理解越全面。
以上数据表明对反函数概念定义理解的全面程度从高到低依次为高二年级、高三年级和高一年级。
从上述图表中学生呈现出的各种理解来看，高一年级学生的“无／错表象”在各种理解中是最高的，达４４．６％，而高二和高三年级学生的“无／错表象”一类在各种理解中仅分别占１２．Ｏ％和１１．５％。
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298CHINESE OPTICS LETTERS/Vol.5,No.5/May10,2007Effect of the geometry of workpiece on polishing velocityin free annular polishingQuantang Fan(),Jianqiang Zhu(),and Bao’an Zhang() Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,Shanghai201800Received November27,2006Base on Coulomb friction model,the workpieces with different geometry rotating in free annular polishingare simulated.From simulation,the following conclusions are drawn.The angular velocity of workpiece ishigher than that of polishing pad if the ring rotates uncontrolled in free annular polishing.The circularworkpiece can synchronize with polishing pad through controlling the rotation of ring,which depends onthe radii of ring and workpiece,the friction coefficients of polishing pad-workpiece and ring-workpiece,and the angular velocity of polishing pad.The workpiece with sharp corner cannot contact with the ringcontiguously,which causes the contact state changing and the angular velocity of workpiece fluctuatingceaselessly,and this type of workpiece should be controlled with clamp to rotate synchronistically with thepolishing pad.OCIS codes:000.4430,220.5450.Chemical mechanical polishing(CMP)is one of the most effective planarization technologies in integrated circuit (IC)industry and optics industry.During the CMP pro-cess,two important factors that affect the processing quality and the productivity are pressure and relative velocity,which are expressed by Preston[1]firstly.No matter plane or spherical polishing,the dense and un-repeated traces in workpiece surface are required in or-der to obtain fine finishing surface.Several researchers have worked on the relative velocity and traces of work-piece and polishing pad.They concentrated on several aspects:1)only the relative velocity,which is deduced mathematically from the geometry relationship between workpiece and polishing pad[2−5];2)the relative veloc-ity and the trajectory of the random point on workpiece moving on polishing pad[6−9];3)the relative velocity and the torque deduced from geometry relationship between workpiece and polishing pad with considering the fric-tion between workpiece and polishing pad[1,10−12],even the eccentricity of the workpiece[12,13].Preston studied the rotational motion of an infinitely narrow driven ring with fixed parallel axes and gave a new solution[1].Cooke et al.described the annular lapping machine and the cor-responding theory and practice[2].However,the geometry of workpiece should be consid-ered,as well as the relative velocity between workpiece and polishing pad in free polishing,because the geome-try of workpiece will affect the friction force and relative motion between the polishing pad and workpiece,which is also one of the reasons that the optical polishing needs the experienced and skilled technician to treat different geometries of workpiece in practice.In this paper,we will analyze the geometry difference of workpiece in annular polishing with simulating the change of relative velocity between workpiece and polishing pad by Coulomb fric-tion model.To simplify the polishing process,we make the follow-ing assumptions.1)The effect of abrasive particles and slurry fluid is ignored;2)during the polishing process, the workpiece contacts entirely with the polishing pad;3)the workpiece,polishing pad,and ring are taken as rigid continuum and they have no distortion;4)the sur-face of the polishing pad,contacting with the workpiece,is plane;5)the frictional coefficient of workpiece to pol-ishing pad is constant.We begin with just considering the workpiece rotat-ing uniformly on polishing pad.Taking a circle centered at O2with random radius r on workpiece,as shown inFig.1.A line passes through the center O1of polishingpad and makes a joint angleθwith O1O2,which inter-sects with circle O2at points C and D.The workpiece issubjected to two frictional torques in positive and nega-tive directions simultaneously.The left part of workpiece is subjected to anti-clockwise frictional torque,and the right part to clockwise torque.The point C is in the left side of the workpiece and point D in the right side.The velocity of point C isv C=(v2C t+v2C n)1/2,(1)where the tangent velocity is v C t=l O1Cω1cosαC+ l O2Cωw and the normal velocity v C n=ρCω1sinαC.In a similar way,the velocity of point D isv D=(v2D t+v2D n)1/2,(2)where the tangent velocity v D t=l O1Dω1cosαD+l O2Dωw and the normal velocity v D n=ρDω1sinαD.l O1CandFig.1.Velocity analysis of workpiece motion.1671-7694/2007/050298-03c 2007Chinese Optics LettersMay10,2007/Vol.5,No.5/CHINESE OPTICS LETTERS299l O 1D are the distances of points C and D to O1,respec-tively;αC andαD are the acute angles between direction of friction force and velocity direction of the two points C and D,respectively;ω1andωw are the angle velocitiesof polishing pad and workpiece,respectively;l O2C andl O 2D are the distances of points C and D to the centerof workpiece.The eccentricity e is the distance between polishing pad center O1and workpiece center O2.From the geometry relationship,we getcosαC=e2−l2O1C−r22l O1Cr,(3)cosαD=e2−l2O1D−r22l O1Dr.(4)From the above,the velocity and direction are different in all points.Consequently,the friction force which spurs the workpiece rotating on the polishing pad and its direc-tion are different too.The force torques come to balance when the angular velocity of workpiece reaches a given value.Then the rotation of workpiece comes into steady state,and the angular velocity of workpiece becomes uniform.In a similar way,we can also calculate the angular velocity of ringωr.When the workpiece rotates,it will contact with the inside surface of the ring,so the different angular velocities of workpiece and ring will change,until they reach the same value.However,the contact states are different for workpieces with different geometries.The contact states are shown in Fig.2.In Fig.2(a),the circular workpiece will contact linearly and continuously with the ring when it rotates on polishing pad and within the ring,and the contact point is rela-tively fixed.In Fig.2(b),only the corners of the square workpiece contact with the ring when it rotates,and the four corners do not contact with the inside surface of the ring simultaneously,consequently there are only one or two corners at a same time.The unstable contact state makes the contact discontinuity,which causes the angular velocity of workpiece changing with time.The discontinuous contact will cause the workpiece and ring colliding.The non-zero collision causes an instantaneous change in the velocity of workpiece,which will be dis-cussed in the following simulation.In order to analyze the motions of workpieces with different geometries in free annular polishing,the dy-namic analysis software,MSC.ADAMS,is used to sim-ulate the polishing process.In the simulation,the posi-tions of the workpieces placed are shown in Fig.2.Some parameters used are the same as those in Ref.[10],as listed in Table 1.Fig.2.Contact states of(a)circular and(b)square work-pieces.Table1.Simulation Parameters inFree Annular PolishingParameter ValueCircular Workpiece Sizeφ40×5(mm)Square Workpiece Size35.445×35.445(mm) Annular Velocity of Polishing Pad16rpm(1.67552rad/s) K8Glass Elastic Modulus5950N/mm2K8Glass Poisson Coefficient0.211K8Glass Density2.52×10−6kg/mm3 Pitch Elastic Modulus2500N/mm2Pitch Poisson Coefficient0.4Pitch Glass Density1.05×10−6kg/mm3In the simulation,the material of polishing pad is pitch, and the material of ring and workpiece is K8glass.So the friction coefficient between the polishing pad and work-piece is different from that between ring and workpiece. The polishing pad connects with ground by revolute joint to ensure that the polishing pad only rotates.The ring connects with ground by cylindrical joint to ensure that the ring not only rotates but also presses on polishing pad by its own dead weight,which causes the friction between polishing pad and ring.The ring contacts with polish-ing pad by solid-solid contact,and the friction model is Coulomb friction.The workpiece is put on the polish-ing pad and within the ring,and contacts with them by solid-solid contacts.All friction coefficients are default. Every workpiece state is simulated for three conditions: the first one is the ring rotates freely;the second one is the angular velocity of ring is set at1.67552rad/s to equal that of polishing pad;the last one is the angular velocity of ring is set by equation.All simulations are operated for5s.The simulation results are shown in Fig.3.From Fig.3(a),we can known that the circular work-piece does not rotate steadily when the angular veloc-ity of polishing pad is1.67552rad/s and the ring ro-tates freely.The angular velocity of circular workpiece is higher than2.5rad/s.And the angular velocity of ring is also higher than that of polishing pad.While the uniform removal of workpiece surface comes from the angular velocity synchronization between polishing pad and workpiece[2].If we set the angular velocity of ring at 1.67552rad/s,the circular workpiece gets a much higher angular velocity.That is,we should lower the angular velocity of circular workpiece through controlling the an-gular velocity of ring.From the angular velocity syn-chronization between polishing pad and workpiece and considering the friction between them,we getωw=(1−μw)ω1,(5) whereμw is the friction coefficient between polishing pad and workpiece.At the same time,the workpiece contacts with the ring at a point.The linear velocity of workpiece should equal that of the ring at the contact point.Con-sidering the friction,too,we getr wωw=(1−μr)r rωr,(6) whereμr is the friction coefficient between ring and300CHINESE OPTICS LETTERS/Vol.5,No.5/May10,2007Fig.3.Simulations of workpieces with different geometries in annular polishing.(a)Circular workpiece,the ring rotates freely;(b)circular workpiece,the ring rotates with angular velocity of0.60928rad/s;(c)square workpiece,the ring ro-tates freely.workpiece,r r is the inside radius of ring.We can calcu-late the angular velocity of ring from Eqs.(5)and(6),ωr=r w(1−μw)ω1(1−μr)r r.(7)In order to validate the angular velocity of ring,we sim-ulate the circular workpiece in the free annular polishing with the calculated annular velocity of ring(Fig.3(b)), and in the simulation the materials of ring and workpiece are the same,so their friction coefficients are the same. From Fig.3(b),the angular velocity of workpiece agrees with that of polishing pad well enough.The angular ve-locity of workpiece is very smooth compared with that of Fig.3(a).That is,the annular velocity of ring should be controlled by Eq.(7)to synchronize the angular veloci-ties of polishing pad and workpiece.For square workpiece,the four corners contact with the inside surface of the ring periodically when the work-piece rotates on the polishing pad and within the ring in free annular polishing simulation(Fig.3(c)).The al-ternative contact of four corners of the workpiece causes the angular velocity of workpiece fluctuating between the maximum and minimum values ceaselessly.The angular velocity of ring also changes when the four corners of the workpiece contact with the ring periodically.And the an-gular velocity of workpiece cannot be controlled through controlling the angular velocity of ring,which needs to be controlled with the clamp.From the above annular polishing simulation,we can draw the following conclusions.1)The angular velocity of workpiece is more than that of polishing pad if the ring rotates freely in free annular polishing.2)The workpiece can synchronize with the polishing pad through control-ling the angular velocity of ring by Eq.(7).The angular velocity of ring depends on the radii of ring and work-piece,the friction coefficients of polishing pad-workpiece and ring-workpiece,and the angular velocity of polishing pad.3)The workpiece with sharp corner cannot con-tact with the ring contiguously,which causes the con-tact state changing and the angular velocity of work-piece fluctuating ceaselessly.So this type of workpiece cannot be controlled like circular workpiece.This type of workpiece can synchronize with the polishing pad with a clamp,where the clamp is fixed on the work ring,or floating on the work ring and the angular velocity of workpiece is controlled independently.Q.Fan’s e-mail address is qtfan@. References1.F.W.Preston,J.Soc.Glass Technol.11,214(1927).2.F.Cooke,N.Brown,and E.Prochnow,Opt.Eng.15,407(1976).3.D.-Z.Chen and B.-S.Lee,J.Electrochem.Soc.146,744(1999).4.P.-L.Tso,Y.-Y.Wang,and M.-J.Tsai,Journal of Mate-rials Processing Technology116,194(2001).5.W.D.Dong,E.S.Putilin,and Ya.V.Rudin,J.Opt.Technol.70,573(2003).6.J.Su,D.Guo,R.Kang,Z.Jin,and X.Li,China Me-chanical Engineering(in Chinese)16,815(2005).7.Y.Jin,Equipment for Electronic Products Manufactur-ing(in Chinese)(9)37(2005).8.X.Shi,M.Tong,and J.Ren,Aviation Precision Manu-facturing Technology34,(2)1(1998).9.X.Shi,M.Tong,X.Yuan,and J.Ren,Aviation PrecisionManufacturing Technology34,(3)5(1998).10.V.V.Travin,J.Opt.Technol.72,266(2005).11.J.Yang,C.Ren,C.Wang,and L.Wang,Opt.Technol.(in Chinese)24,(5)39(1998).12.X.Yang,W.Zhang,Z.Hu,and X.Hu,Opt.Technique(in Chinese)29,480(2003).13.H.Zhang,H.Gao,and M.Wu,Optics and PrecisionEngineering(in Chinese)6,77(1998).。