vdi2230

nullOverview of VDI 2230Overview of VDI 2230An Introduction to the Calculation Method for Determining the Stress in a Bolted JointImportant NoteImportant NoteThis summary of the VDI 2230 Standard is intended to provide a basic understanding of the method. Readers who wish to put the standard to use are urged to refer to the complete standard that contains all information, figures, etc.DefinitionsDefinitionsCovers high-duty bolted joints with constant or alternating loads Bolted joints are separable joints between two or more components using one or more bolts Joint must fulfill its function and withstand working loadAim of CalculationAim of CalculationDetermine bolt dimension allowing for: Strength grade of the bolt Reduction of preload by working load Reduction of preload by embedding Scatter of preload during tightening Fatigue strength under an alternating load Compressive stress on clamped parts1. Range of Validity1. Range of ValiditySteel Bolts M4 to M39 Room Temperature2. Choice of Calculation Approach2. Choice of Calculation ApproachDependent upon geometry Cylindrical single bolted joint Beam connection Circular plate Rotation of flanges Flanged joint with plane bearing faceCylindrical Single Bolted JointCylindrical Single Bolted JointAxial force, FA Transverse force, FQ Bending moment, MBBeam Geometry, Ex. 1Beam Geometry, Ex. 1Axial force, FA Transverse force, FQ Moment of the plane of the beam, MZBeam Geometry, Ex. 2Beam Geometry, Ex. 2Axial force, FA Transverse force, FQ Moment of the plane of the beam, MZRotation of FlangesRotation of FlangesAxial force, FA (pipe force) Bending moment, MB Internal pressure, pFlanged Joint with Plane Bearing Face, Ex. 1Flanged Joint with Plane Bearing Face, Ex. 1Axial force, FA (pipe force) Torsional moment, MT Moment, MBFlanged Joint with Plane Bearing Face, Ex. 2Flanged Joint with Plane Bearing Face, Ex. 2Axial force, FA (pipe force) Transverse force, FQ Torsional moment, MT Moment, MBFlanged Joint with Plane Bearing Face, Ex. 3Flanged Joint with Plane Bearing Face, Ex. 3Axial force, FA (pipe force) Transverse force, FQ Torsional moment, MT Moment, MB3. Analysis of Force and Deformation3. Analysis of Force and DeformationOptimized by means of thorough and exact consideration of forces and deformations including: Elastic resilience of bolt and parts Load and deformation ratio for parts in assembled state and operating state4. Calculation Steps4. Calculation StepsBegins with external working load, FB Working load and elastic deformations may cause: Axial force, FA Transverse force, FQ Bending Moment, MB Torque moment, MTDetermining Bolt DimensionsDetermining Bolt DimensionsOnce working load conditions are known allow for: Loss of preload to embedding Assembly preload reduced by proportion of axial bolt force Necessary minimum clamp load in the joint Preload scatter due to assembly methodCalculation Step R1Calculation Step R1Estimation of bolt diameter, d Estimation of clamping length ratio, lK/d Estimation of mean surface pressure under bolt head or nut area, pG If pG is exceeded, joint must be modified and lK/d re-determinedCalculation Step R2Calculation Step R2Determination of tightening factor, aA, allowing for: Assembly method State of lubrication Surface conditionCalculation Step R3Calculation Step R3Determination of required average clamping load, Fkerf, as either: Clamping force on the opening edge with eccentrically acting axial force, FA Or Clamping force to absorb moment MT or transverse force component, FQCalculation Step R4Calculation Step R4Determination of load factor, F, including: Determination of elastic resilience of bolt, dS Evaluation of the position of load introduction, n*lK Determination of elastic resilience of clamped parts, dP Calculation of required substitutional cross-section, AersCalculation Step R5Calculation Step R5Determination of loss of preload, FZ, due to embedding Determination of total embeddingCalculation Step R6Calculation Step R6Determination of bolt size and grade For tightening within the elastic range, select bolt for which initial clamping load is equal to or greater than maximum initial clamping load due to scatter in assembly process For tightening to yield, select bolt for which 90% of initial clamping load is equal to or greater than minimum initial clamping load due to scatter in assembly processCalculation Step R7Calculation Step R7If changes in bolt or clamping length ratio, lK/d, are necessary, repeat Steps R4 through R6Calculation Step R8Calculation Step R8Check that maximum permissible bolt force is not exceededCalculation Step R9Calculation Step R9Determine alternating stress endurance of bolt Allow for bending stress in eccentric load applications Obtain approximate value for permissible stress deviation from tables If not satisfactory, use bolt with larger diameter or greater endurance limit Consider bending stress for eccentric loadingCalculation Step R10Calculation Step R10Check surface pressure under bolt head and nut bearing area Allow for chamfering of hole in determining bearing area Tables provide recommendations for maximum allowable surface pressure If using tightening to or beyond yield, modify calculation5. Influencing Factors5. Influencing FactorsAllow for factors depending upon: Material and surface design of clamped parts Shape of selected bolts and nuts Assembly conditionsStrength of the BoltStrength of the BoltStress caused by: Torsional and axial stresses during tightening Working load Should not exceed yield loadMinimum Thread EngagementMinimum Thread EngagementDepends upon: Thread form, pitch, tolerance, and diameter Form of the nut (wrenching width) Bolt hole Strength and ductility of bolt and nut materials Type of stress (tensile, torsional, bending) Friction coefficients Number of tighteningsThread Shear StrengthThread Shear StrengthBolt-Nut Strength Matching Number for strength grade of nut is equivalent to first number of strength grade of boltCalculation of Required Nut HeightCalculation of Required Nut HeightAllows for geometry and mechanical properties of joint elements Predicts type of failure caused by overloading Considers: Dimensional values (tensile cross-section of bolt thread, thread engagement length, etc.) Thread form & nut form Bolt clearance holeBolt Head HeightBolt Head HeightEnsures that failure will occur in free loaded thread section or in the shank Highest tensile stress in thread < Highest tensile stress in bolt headSurface Pressure at Bolt Head & Nut Bearing AreasSurface Pressure at Bolt Head & Nut Bearing AreasCalculation determines surface pressure capable of causing creep resulting in loss of preload Surface pressure due to maximum load should not exceed compressive yield point of clamped material Tightening Factor, Alpha ATightening Factor, Alpha AAllowance must be made for torsional stress caused by pitch and thread friction, and axial tensile stress Scatter in friction coefficients and errors in method of controlling preload create uncertainty in level of tensile and torsional stress Tightening factor, aA, reflects amount of required “over-design”Fatigue StrengthFatigue StrengthDesign modifications to improve endurance limit of joint Increase preload Reduce pitch of screw thread Reduction of modulus of nut material elasticity Increase thread engagementFatigue Strength -ContinuedFatigue Strength -ContinuedDesign modifications to improve endurance limit of joint Change form of nut Reduce strength of nut material Increase elastic resilience of bolt, lower elastic resilience of parts Shift introduction of load toward interfaceEmbeddingEmbeddingCaused by flattening of surface irregularities Affects forces in joint Reduces elastic deformation and preloadSelf-Loosening and PreventionSelf-Loosening and PreventionPreload drops due to: Relaxation as a result of embedment or creep Rotational loosening due to relative movements between mating surfaces6. Calculation Examples6. Calculation ExamplesEx. 1, Concentric Clamping and Concentric Loading Ex. 2, Transverse Shearing Force Ex. 3, Torsional Shearing Load Ex. 4, Eccentric Clamping and Eccentric Loading Ex. 5, Eccentric Clamping and Loading