MDESIGN_bolt_en(VDI2230计算公式)

Calculation of Screws According to VDI 2230, Edition 2003With this program you can carry out predimensioning of the nominal screw diameter (extended version only) as well as the system calculation of cylindrical screw-in joints according to VDI 2230, sheet 1,edition of 2003.The whole calculation process involving force and deformation relations is based on the screw-in joint model. I.e. all dimensions and loads influencing the complete junction from the outside are to be reducedto a screw-in joint and are presumed as known.You can calculate multiscrew joints, such as e.g. circular ring joint flanges. At that, you must take into account, that the angular momentum applied to the perimeter has been considered using the number of screws on the pitch circle and the resultant loads have been considered for each screw separately.In addition, you can take into account centric and eccentric tightenings/loadings.Besides, this calculation program has at its disposal technology files which enable you to read screw dimensions, different strength classes and materials of tightened parts directly into the entry page.All data base tables can be customized to the user (e.g. other standards).Extreme working loads, e.g. corrosion or impact loads can not be taken into account.Calculation BaseThe calculation base of the module Calculation of Screws is founded on VDI 2230, sheet 1, edition of February 2003 "Systematische Berechnung hochbeanspruchter Schraubenverbindungen Zylindrische Einschraubenverbindungen" (System Calculation of High-loaded Screw Joints, Cylindrical Single-screw joints).The fixed tightening force FM of the screw is considered at that as the main selection criterion of the nominal screw diameter.The following DIN standards have been used, too:- DIN EN ISO 4017 Issue of March 2001 Sechskantschrauben mit Gewinde bis Kopf (malehexagon screws threaded to head)- DIN EN ISO 8676 Issue of March 2001 Sechskantschrauben mit Gewinde bis Kopf undmetrischem Feingewinde (male hexagon screwsthreaded to head with metric fine thread)- DIN EN ISO 4014 Issue of March 2001 Sechskantschrauben mit Schaft (male hexagon screwswith body)- DIN EN ISO 8765 Issue of March 2001 Sechskantschrauben mit Schaft und metrischemFeingewinde (male hexagon screws with body andmetric fine thread)- DIN EN ISO 4762 Issue of February 1998 Zylinderschrauben mit Innensechskant (cylindricalscrews with inner hexagon)- DIN EN ISO 4032 Issue of March 2001 Sechskantmuttern, Typ 1 (female hexagon screws,type 1)- DIN EN ISO 8673 Issue of March 2001 Sechskantmuttern, Typ 1, mit metrischem Feingewinde(female hexagon screws, type 1, with metric finethread)- DIN EN ISO 7089 Issue of November 2000 Flache Scheiben, Normale Reihe, Produktklasse A (Flatwashers, standard series, product class A)- DIN EN 20 273 Issue of February 1992 Durchgangslöcher für Schrauben (through holes ofscrews)- DIN 13 T1-10 Issue of November 1999 Metrisches ISO-Gewinde (metric ISO thread)- DIN EN 10269 Issue of November 1999 Stähle und Nickellegierungen für Befestigungselementebei erhöhten Temperaturen (steels and nickel alloys forfastening elements at higher temperature values)- DIN EN ISO 3506-1 Issue of March 1998 Mechanische Eigenschaften von Verbindungselementenaus nichtrost. Stählen (stress-strain properties ofconnectives made of stainless steels)- DIN 267-13 Issue of August 1993 Mechanische Verbindungselemente (mechanicallyconnected elements)- DIN EN ISO 898-1 Issue of November 1999 Mechanische Eigenschaften von Verbindungselementenaus Kohlenstoff –und legiertem Stahl (stress-strainproperties of connectives made of carbon and alloyedsteel)Special returns:- VDI-returns No. 1644, 2001 Schraubenverbindungen (screw joints)LimitationsThe calculation steps are valid for steel screws having the fastening thread with a flank angle of 60°. Service loads can be given as statically or dynamically acting axial forces. In addition, transverse forcesand service moments can be provided, too.All loads effecting the joint and the results connected with them are related only to a single-screw joint.The dimension of the juncture area in the level "screw axis - effect line of the working force" is limited bythe so-called measure G.The elastic flexibility of the tightened parts is presumed as linear variable. I.e., if the axial working force exceeds the separation force, the flexibility increases progressively and there is a loose connection,which can not be calculated by this program.Principally, working temperatures for the screw and the joint parts can be considered as explicitdepending on the material choice in the range of –270°C ≤ T≤ 700°C.Notice:All standard data bank records are stored from +20°C and depending on the chosen material till maximal 600°C!The jar washers can be also taken into account during the calculation. It is presumed then, that on thenut side and on the head side the dimensions and the materials are the same.Calculation of Screws - Formulae Symbols and TermsInputCalculation of Screws – Defining ResultsPredimensioning of the Nominal Screw Diameter, Calculation Process "Entwurf" ("Project")The calculation process "Entwurf" ("Project") enables predimensioning the nominal screw diameter using a minimum of input parameters.The definition of the nominal diameter is carried out depending on a chosen strength class according to the table A7 given in the supplement A of VDI 2230. Strength classes 8.8, 10.9 and 12.9 are there at your disposal.The following table is the calculation basis:Defining the appropriate diameter range is carried out in many sections sketched as follows:1. The next larger force for the given maximal axial force FAO is chosen in the column 1. If an additional maximal transverse force FQ and FA0 < (FQ) / (m Tmin) is specified, FQmax is used only.2. The required minimal preload force ensures, if the following number of steps (strings) continues from the above-named value:- at the fixed value according to FQmax:4 steps at choosing static or dynamic working load- at the fixed value according to FAO:2 steps for dynamically and eccentrically acting axial force1 step for dynamically and centrically or statically and eccentrically acting axial forceno step for static and centrically acting axial force3. The maximal tolerable minimal preload force ensures, if you continue the following number of steps (strings) from this value again:2 steps for tightening the screw using an impact screwdriver1 step for the torque-controlled tightening methodno step for the over-elastic yield-stress-controlled or rotation-angle-controlled tighteningmethod4. The defined value determines after choosing one of three strength classes (columns 2 - 4)the required nominal screw diameter. Besides the diameter, further geometric dimensions dependingon the screw type are shown in the result output. When switching to "Nachrechnung" (Recalculation)the done input values are automatically taken in.Notice:Depending on the working steps shown above the load acting on the juncture can be specified ina range from 250 N up to 630 N!Defining Results of the Calculation Process "Nachrechnung" (Recalculation)Calculation or Identification of the Eccentric Tightening ConditionsBasically, the eccentricity ssym in this program can be taken into account in two ways. At that, the eccentricity can also take on negative values!After specifying the dimensions of the juncture area the eccentricity is defined automatically using the following equation:In addition, the distance from the edge of the separation point of the centroidal axis 0-0 is calculated, too:At the second possibility the parameters ssym and u are to be specified by the user. At that, regulating signs is carried out choosing the appropriate three variants (tension/pressureloading).The distance ssym is positive, if the line of action of the axial working strength and the screw axis lie related to the axis of the deformable members (Axis 0-0) on the same side. If the line of action of the axial working strength and the screw axis lie on the contrary side, the distance ssym is negative.The distance from the edge u, is positive, if the separation point lies relative to the axis 0-0 on the side facing the force, and negative on the appropriate contrary side.Clamping Length lK [mm]For n tightened parts including perhaps jar washers with the thickness hs it is valid at passing screw joints (DSV):For screw-in joints (ESV) with perhaps sink depth ts of the screw-in part is valid:Limit Value G [mm]The limit value G defines the maximal possible juncture dimension in the plane screw axis line of action of the axial working strength at eccentrically tightened joints. It is designated by the length cT.At exceeding the limit value the specified calculation bases are no more valid. Although the program continues calculating you must be aware of a more critical calculation error.For DSV with the smallest plate thickness hmin is valid:At ESV:with counter-bored washer seat in the screw-in partThe main requirement is:bzw.Tightening Factor a A [-]The tightening factor describes the scatter of the assembly pretension load between FMmin and FMmax. Then, depending on the choice of the tightening method it is automatically transferred to the calculation or it is specified by the user by means of "free entering". For more details see also the help text on the input page under Tightening Method!Areal Moment of Inertia in the Juncture IBT [mm^4]Required Minimal Tracking Force Fkerf [N]Defining the required minimal tracking force Fkerf is carried out considering the following main requirements:Minimal Tracking Force of Transmitting a Transverse Force and/or a Torque FKQ [N]At single-screw joints with shear load and FQ as the input value:At multiscrew joints:With the radius of friction ra,we have:Sealing Against a Medium FKP [N]Prevention of an One-sided Separation FKA [N]The required minimal tracking force Fkerf ensures now from the appropriate largest value of the above-mentioned main conditions:Elastic Flexibility of the Screw d S [mm/N]The elastic flexibility of the screw is calculated adding the cylindrical elements taken separately:Notice:If the working temperature is deflecting from the indoor temperature, it is taken into account when calculating with the modulus of elasticity corresponding with the appropriate temperature!Compliance of the Screw Head d SK [mm/N]With the nominal cross-section:Compliance of the Body of Screw d i [mm/N]The compliance of the screw body area is calculated from the sum of the partial lengths. The appropriate cross-section area is considered as follows:body screws with the length l1thinned body screws with the length l2withsmallest suitable body cross-section at "own screw geometry"Compliance of the Free Loaded Thread Part d Gew [mm/N]For body or thinned body screwsFor screws threaded up to headFor screws from "own screw geometry"With the root cross-section:Compliance of the Screw-in Thread Area d GM [mm/N]At DSV with:andAt ESV with the modulus of elasticity EM of the last defined tightened part:andAngle of the Equivalent Deformable Cone j [Grad]Screw-in joints (ESV) with dimensions of the deformable members in the range of:and ,are considered during defining the elastic compliance of the tightened parts as passing screw joints (DSV).For ESV:For DSV:Limit Diameter of the Deformable Cone DAGr [mm]Constant:Cone Height lV [mm]Bush Height lH [mm]Outer Diameter of the Truncated Cone dwi [mm]Starting with the diameter dw of the bearing surface area of the screw head or of the nut the bearing area diameter of the partial deformable cone j is calculated using:Compliance of the Deformable Cone d PV [mm/N]If it is DA≥ DAGr, the deformation model at DSV consists only of two and at ESV only of one equivalent deformable cone.Compliance of the Deformable Bush d PHi [mm/N]If it is DA≤ dw, the deformation model consists only of one deformable bush.Elastic Flexibility of the Centrically Tightened Parts d P [mm/N]If it is dw < DA < DAGr, the equivalent deformable member consists of a cone (or cones) and a bush. Using the above-mentioned partial compliances it is calculated via the appropriate addition of the general compliance to:Notice:If the working temperature is deflecting from the indoor temperature, it is taken into account when calculating using the modulus of elasticity corresponding with the appropriate temperature.The separation, what tightened part belongs to the deformable cone or to the deformable bush,is carried out by program loop automatically.Equivalent Areal Moment of Inertia of a Partial Deformable Cone IBersVi [mm^4]Equivalent Areal Moment of Inertia of an Eccentrically Tightened Partial Deformable Cone IBersVei [mm^4]Equivalent Areal Moment of Inertia of a Partial Deformable Bush IBersHi [mm^4]Elastic Flexibility of Eccentrically Tightened Parts d*p [mm/N]Elastic Flexibility at Eccentric Tightening and Loading d**p [mm/N]Notice:If the working temperature is deflecting from the indoor temperature, it is taken into account when calculating with the modulus of elasticity corresponding with the appropriate temperature.The separation, what tightened part belongs to the deformable cone or to the deformable bush,is carried out by program loop automatically.Force Delivery Factor n [-]If it is not preset by the user in a range of 0 < n≤ 1 the force delivery factor n is defined automatically after the juncture types SV1-SV6 as well as the distances lA, ak and the height h were chosen. At that, the height h, the clamping area between screw head and nut or screw-in section is set by the program automatically.Here, the basis is the table 5.2/1 given in VDI 2230 of Oct. 2001, p. 27. Values lying among the tabular data are defined through linear interpolation.Notice:at centric loading (a = 0), the distance is lA = 0!Force Ratio F [-]Depending on the set type of loading and tightening different force ratios are resulting.In what follows different force ratios are listed:Centrically loaded and centrically tightened, with n = 1Centrically loaded and centrically tightened, with n < 1Centrically loaded and eccentrically tightened, with n = 1Centrically loaded and eccentrically tightened, with n < 1Special case: loading only through an extern working torque MBEccentrically loaded and centrically tightened, with n = 1Eccentrically loaded and centrically tightened, with n < 1Eccentrically loaded and eccentrically tightened, with n = 1Eccentrically loaded and eccentrically tightened, with n < 1Notice:The force ratio is represented in the detail equations without Indices, that is only by F! Shrinkage fz [m m]If there are no trial values to preset, the shrinkage fz can be calculated using this program. But it is presumed, that for a massive contact equal roughness are to be available on the joint surfaces. Besides, the shrinkage values defined by the program make sense only if the limit bearing stress has been not exceeded.The total shrinkage ensures through the appropriate synthesizing on basis of the following table:Notice:for more details see VDI 2230, issue of Oct. 2001, section 5.4.2.1.Preload Force Loss Owing to Shrinkage Fz [N]Owing to shrinkage of a screw joint to the value fz ensures the resulting preload force loss in the working regime to:Preload Force Change Owing to a Working Temperature not Equal to RT D F'Vth [N]Thermally Induced Preload Change D FVth [N]Allowable Assembly Pretension Load FMzul [N]The allowable assembly pretension load is calculated depending on the chosen screw type as follows:For set screws and screws threaded to headDeterminative diameterDeterminative cross-sectionFor screws with compliant bodyDeterminative diameterDeterminative cross-sectionFor screws from "own screw geometry"Choosing "own screw geometry" it is possible to define the screw body area with up to 9 pitch cylinders. At first, the basis is here the smallest diameter dimin of maximal 9 pitch cylinders.The determinative diameter is defined according to the following assumption:If or , thenIf , thenDeterminative cross-sectionFor torsion-free screw-tightening for stability factor proof is valid:Notice:The pure assembly pretension load is available only after the mounting at room temperature was finished. Hence, the values of FMzul are always corresponding with those of the indoortemperature!Minimal Preload Force FVmin [N]If D FVth < 0 you may set D FVth = 0 into the equation. The thermally induced preload change is considered only at D FVth > 0!Axial Force on the Separation Limit FAab [N]At centric loading and tighteningAt an eccentric loadWorking Torque on the Separation Border MBab [Nm]Checking the Linear Loading Process [-]The modulus Calculation of Screws is based on the calculation principles of the linear loading process, which is available in the strict sense only at non-separating joints. If the axial working strength exceeds the separation force, the screw joint starts to separate one-sided. Though the program goes on calculating, a precise definition of the force and deformation action is impossible. You must be aware of a larger calculation error.Hence, the following is valid for the given program in general:Maximal Secondary Screw Force up to the Separation Limit FSAmax [N]For the special case with specifying a secondary working torque MB is valid:Maximal Secondary Plate Force up to the Separation Limit FPAmax [N]Notice:at tensile load (FAO > 0) the secondary plate force FPA is a part of the axial working strength, which unloads the tightened parts. At compression forces (FAO < 0) the tightened parts in thejoint are additionally loaded with FPA!Minimal Required Assembly Pretension Load FMmin [N]If D F'Vth < 0, you may set D F'Vth = 0 into the equation. The preload force change is considered only at D F'Vth > 0!Maximal Tolerable Assembly Pretension Load FMmax [N]The maximal tolerable assembly pretension load is calculated from the equation of the main dimensioning, which is the basis of the screw calculation, as follows:Notice:if the yield-stress-controlled or rotation-angle-controlled tightening method is chosen, the scatter of the assembly pretension load is not defined through tightening but through the yield stress ofthe mounted screws. To design the screw using FMmax is no longer relevant at that. Thetightening factor a A stays not considered, so that the screw is then dimensioned using FMmin! Checking the Allowable Screw dimension [-]The following condition must be fulfilled for a sufficiently dimensioned screw:Defining the Working Load in the Elastic ScopeThis calculation process is to carry out only if the axial working strength FAO and the usage factor of the yield stress n < 100% are preset.Maximal Total Tractive Effort of Screw in the Working Regime FSmax [N]If D FVth > 0, you may set D FVth = 0 into the equation. The thermally induced preload change is considered only at D FVth < 0!Thread Tightening Moment MG [Nmm]Maximal Tensile and Torsional Stress in the Working Regime s zmax, t max [N/mm²]For setscrews and screws threaded up to headDeterminative diameterDeterminative cross-sectionFor screws with the compliant bodyDeterminative diameterDeterminative cross-sectionPolar moment of resistanceFor screws from "own screw geometry"Choosing "own screw geometry" it is possible to define the screw body area with up to 9 pitch cylinders. The basis is here first of all the smallest diameter dimin of maximal 9 pitch cylinders.Standard diameter is determined by following assumption:If or , thenIf , thenDeterminative cross-sectionPolar moment of resistanceComparison Tension in the Operating Regime s redB [N/mm²]With the reduction coefficient:Safety Against Exceeding the Yield Stress SF [-]For torsio-free screw-tightening for stability factor proof is validNotice:if a working temperature of the screw Ts is specified, the appropriate thermal extension limit RpminT is taken as a basic one!Defining the Working Load in the Over-elastic RangeOn the assumption of the over-elastic tightening to be already available at n > 90%, the safety check of the working load is carried out as follows.Preload Force at Over-elastic Tightening FV1 [N]Using the upper value of the strengthening factor according to VDI 2230, p.42:Safety Check in the Over-elastic Range [-]Valid is:Cyclic Load at Dynamic Working LoadLimit Cycle Peak Value of the Screw s a or s ab [N/mm²]For concentric loading and clampingFor eccentric clamping and concentric loading:For concentric or eccentric clamping and eccentric loading, the following applies:Bending resilience for bolted joints with n clamped partsBending resilience of the bolt, in general:Moment of resistance of the stress cross section of the bolt threadAverage bolt load FSm [N]Stress amplitude of the endurance limit s A [N/mm²]The calculation procedure of the fatigue limit is carried out for N≥ 2 · 106 automatically, if not other was specified. Alternating cyclesFor bolt threads rolled before heat treatmentFor bolt threads rolled after heat treatmentSafety margin against fatigue failure SD [-]Depending on the calculation procedure, the following applies:Stress amplitude of the fatigue strength s AZ [N/mm²]For one thing, the calculation procedure within the fatigue strength range is carried out automatically, if the aforecited fatigue limit is not fulfilled or, in the second place, if the "Dynamic strength within the fatigue strength range" was activated by the user. In this case, only the calculation for the fatigue embodiment is performed. Then, the valid area for the number of alternating cycles is applied as follows:For bolt threads rolled before heat treatmentFor bolt threads rolled after heat treatmentSafety at fatigue strength SZ [-]Depending on the calculation procedure, the following applies:Calculation of the head and/or nut bearing area [mm²]Principally, you must distinguish between the head bearing area with or without washer. Besides, the chamfer diameter of the hole can be taken into account, additionally.In general, establishing the maximum inside diameter of the plane bearing area is carried out for:The parameter Da is the inside diameter of the plane nut bearing area (chamfer diameter of the nut). The minimum value corresponds with the nominal thread diameter d!Bearing area of the bolt headBearing area between the washer and the first clamped partWith the outside bearing area diameter for standardized washers:Similar to it, the analysis on the nut side, when selecting bolted joints (DSV), would be: Nut bearing areaBearing area between the washer and the last clamped partFor the outside bearing area diameter of the standardized washers:Maximum surface pressure in the assembly state with utilization of the yield point n < 100% [N/mm²]Depending on the aforecited calculation procedure (bonding technique, with/without washer), the appropriate bearing area is taken into account.Maximum surface pressure under bolt headMaximum surface pressure between the washer and the first clamped partMaximum surface pressure under the nut bearing areaMaximum surface pressure between the washer and the last clamped partMaximum preload FVmax [N]Maximum surface pressure in the working state with utilization of the yield point n < 100% [N/mm²]The calculation of the maximum surface pressure in the working state is omitted, if no any axial working load was specified.In general, the maximum surface pressure in the working state is calculated with the bearing area, similar to that at the assembly state, as follows:If D FVth > 0, in the equation D FVth = 0 is substituted. The thermally induced preload change is taken into account only at D FVth < 0!For joints loaded in compression (FAO < 0), FSAmax = 0 is substituted.Maximum surface pressure with utilization of the yield point n≥ 100% [N/mm²]For tightening beyond the elastic limit or selecting the yield-controlled and angle-controlled tightening, a distinction is no more made between the assembly and the working state when determining the surface pressure, but an appropriate maximum surface pressure is calculated on basis of the aforecited bearing areas.Limiting surface pressure pG [N/mm²]The determined maximum surface pressure may not exceed the limiting surface pressure of the appropriate material. When specifying a working temperature unequal RT, the changed tensile strength is underlying only in the working state or for tightening beyond the elastic limit. The limiting surface pressure for the assembly state is always based on the tensile strength at room temperature.Depending on the specified number and type of material of the clamped parts, the limiting surface pressure of the last defined part is calculated at DSV additionally.The limiting surface pressure is calculated by means of the influencing factor fG as well as the tensile strength of the material as follows:Limiting surface pressure of the washerLimiting surface pressure of the first clamped partLimiting surface pressure of the last clamped part (at DSV)Safety margin against exceeding the limiting surface pressure Sp [-]Depending on the calculation procedure, the following applies:Shearing strength of the thread piece or of the internal thread t BM [N/mm²]Determining the minimum length of engagement is carried out only when selecting "Tapped thread joints (ESV)", because we proceed from the fact, that the standardized nuts are utilized at the least with the strength grades according to the bolts and so they are capable of bearing full load. Thus, a proof of the minimum required length of engagement is omitted.The shearing strength is calculated on basis of the material of the tapped thread component. Because itis intended, that the last defined plate is a component with the internal thread, the material of the last clamped part is considered.Notice:If the working temperature deflects from the room temperature, this fact is taken into account in the appropriate heat-resistance when calculating the temperature.Available effective length of engagement mvorheff [mm]The available length of engagement concerns only the thread turns of bolt and of the internal thread which are completely in engagement.Therefore, the engagement area is reduced by a possible counterbore depth tS (already contained in the clamp length) as well as a thread chamfer for (d - d3) / 2 default.If , thenIf , thenShearing cross section of the internal thread ASGM [mm²]For the pitch diameter of the internal thread:Shearing cross section of the bolt thread ASGS [mm²]Strength ratio Rs [-]。