Advanced Fixture Design Method and Its Application

344 Pages·2021·12.192 MB·English

by  Guohua Qin

Guohua Qin
Advanced Fixture
Design Method and
Its Application
Advanced Fixture Design Method and Its
Application
Guohua Qin
Advanced Fixture Design
Method and Its Application
GuohuaQin
NanchangHangkongUniversity
Nanchang,Jiangxi,China
ISBN978-981-33-4492-1 ISBN978-981-33-4493-8 (eBook)
https://doi.org/10.1007/978-981-33-4493-8
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Preface
Manufacturingtechnologyisthefoundationandkeytothedevelopmentofallindus-
tries. But in the manufacturing technology, fixtures are one kind of indispensable
technicalequipmentthatcandirectlyinfluencethemachiningaccuracy,production
efficiencyandmanufacturingcost.Therefore,fixturedesignplaysanimportantrole
inproductiontechnologypreparationaswellasproductdesignandmanufacturing.
Fixture design is an important and complex technical work. In the traditional
fixturedesignmethod,thedeterminationoffixturinglayout,theselectionoffixture
elementsandtheassemblyoffixtureelementsareallcompletedbyfixturedesigners.
Thetraditionaldesignmethodnotonlyrequiresmoremanpowerandalongerdesign
cycle,butalsoreliesontherichexperienceofdesigners.Withthewideapplication
of computer technology in the manufacturing field, a new fixture design method
is formed by using the integration of the computer with advanced manufacturing
technologiesincludingthefeaturetechnology,grouptechnologyandartificialintel-
ligence.Thisistheso-calledcomputer-aidedfixturedesigntechnology.Inthepast,
thekeytodevelopthecomputer-aidedfixturedesignsystemistocollectandexpress
the knowledge from the experience of the fixture designers. However, it is either
impossibleorunrealistictofullyexpressallfixturedesignknowledge.
Combined with kinematics, contact mechanics, elastic mechanics, mathemat-
icalmodelingtechnologyandoptimizationtechnology,theadvancedfixturedesign
method is systematically proposed. The essence of the proposed design method is
to iteratively analyze the fixturing performance for the new fixturing layout until
itissatisfied.Theestablishedanalysismodeloffixturingperformanceincludesthe
locatingdetermination,theworkpiecestability,theclampingreasonability,thework-
piece attachment/detachment, and the locating accuracy. By discretizing the value
range of design variables, some planning algorithms are suggested including the
selection algorithm of locating datum, the planning algorithm of clamping force,
andsoforth.
In the proposed advanced fixture design method, the continuous fixture design
problem is transformed into a discrete problem so that it can be easily realized by
programming.Accordingly,itcanenrichanddevelopthebasictheoryofcomputer-
aidedfixturedesignandchangetheempiricalmethodoffixturedesign.Thecombi-
nation of theoretical analysis and mathematical modeling technology can resolve
v
vi Preface
thekeyproblemsintheprocessoffixturedesign,whichwillplayacertainrolein
promoting the progress of manufacturing technology, improving the precision and
levelofproductmanufacturing,andmeetingthehigherandhigherrequirementsof
themechanicalmanufacturingindustry.
Thecontentscoveredinthisbookincludemajorresearchoutcomesofnumerous
research projects sponsored by the National Natural Science Foundation of China
(51765047; 51465045; 51165039), Major Discipline Academic and Technical
LeaderTrainingPlanProjectofJiangxiProvince(20172BCB22013),Aeronautical
ScienceFoundationofChina(2006ZE56006;2010ZE56014),NaturalScienceFoun-
dationofJiangxiProvince(2009GZC0104),KeyProjectofScienceandTechnology
SupportPlanofJiangxiProvince(2010BGB00300),andChinaPostdoctoralScience
Foundation (20070411142). Moreover, several postgraduate students participated
in relevant research work, including Haichao Ye, Huaping Huang, Meidan Zhou,
XiyuanGuo,YueCui,HuaminWang,ZikunWang,ShuoSun,XuiangZhao,Yuanjun
Hou,ZheHuang,JiameiLi,XiupingDai,WeidaLou,FengLin,JianpengQiu,etc.
Iherebyexpressmysinceregratitudetothem.
Nanchang,China GuohuaQin
September2020
Contents
1 Introduction .................................................. 1
1.1 FixturingMethod ........................................ 1
1.1.1 AlignmentFixturing .............................. 2
1.1.2 FixtureFixturing ................................. 3
1.2 FixtureStructure ......................................... 4
1.2.1 TypesofFixtures ................................. 4
1.2.2 ConfigurationofFixtures .......................... 11
1.3 FixtureDesign ........................................... 13
References .................................................... 16
2 AnalysisofLocatingDetermination ............................. 17
2.1 ModelofTheoreticalDOF ................................. 17
2.1.1 RelationshipBetweenMachiningRequirements
andDOFs ....................................... 18
2.1.2 EstablishmentofTheoreticalDOFModel ............ 19
2.1.3 UndeterminedCoefficientMethod ................... 23
2.1.4 SolvingRankMethod ............................. 25
2.2 DOFLevelModelofPositionSizes ......................... 28
2.2.1 PositionSizeofPlaneRelativetoPlane .............. 28
2.2.2 PositionSizeofLineRelativetoPlane ............... 30
2.2.3 PositionSizeofPlaneRelativetoLine ............... 31
2.2.4 PositionSizeofLineRelativetoLine ................ 33
2.3 DOFLevelModelofOrientations .......................... 36
2.3.1 RelationBetweenParallelismToleranceandDOFs .... 36
2.3.2 RelationBetweenPerpendicularity/Inclination
ToleranceandDOFs .............................. 44
2.4 DOFLevelModelofLocations ............................ 52
2.4.1 RelationBetweenCoaxialityToleranceandDOFs ..... 52
2.4.2 RelationBetweenSymmetryToleranceandDOFs ..... 53
2.4.3 RelationBetweenPositionToleranceandDOFs ....... 57
2.4.4 RelationBetweenRunoutToleranceandDOFs ........ 61
2.5 ModelofLocatingPointLayout ............................ 63
vii
viii Contents
2.5.1 EstablishmentofLocatingPointLayoutModel ....... 64
2.5.2 SolutionofLocatingPointLayoutModel ............ 67
2.6 JudgmentCriteriaofLocatingDetermination ................. 70
2.6.1 TheoreticalCondition ............................. 70
2.6.2 ProcessCondition ................................ 72
2.6.3 CorollaryandFlowchart ........................... 72
2.7 ApplicationandAnalysis .................................. 74
2.7.1 VerificationofLocatingPoint’sNumber ............. 75
2.7.2 VerificationoftheLayoutofLocatingPoints ......... 77
References .................................................... 80
3 AnalysisofWorkpieceStability ................................. 83
3.1 ModelingofWorkpieceStability ........................... 83
3.1.1 StaticEquilibriumConditions ...................... 85
3.1.2 FrictionConeConstraints .......................... 90
3.1.3 AnalysisModel ................................... 91
3.2 SolutionTechniques ...................................... 93
3.2.1 LinearProgrammingTechniques .................... 93
3.2.2 SolutiontotheModelofForm-Closure .............. 94
3.2.3 SolutiontotheModelofForce-Closure .............. 100
3.3 NumericalExamples ...................................... 102
3.3.1 AnalysisofForceExistence ........................ 102
3.3.2 AnalysisofForceFeasibilityWithoutFriction ........ 104
3.3.3 AnalysisofForceFeasibilitywithFriction ........... 106
References .................................................... 109
4 AnalysisofClampingReasonability ............................. 111
4.1 LocalDeformation ....................................... 111
4.1.1 ContactDeformation .............................. 113
4.1.2 FixelDeformation ................................ 117
4.1.3 LocalDeformation ................................ 119
4.2 WorkpiecePositionError .................................. 120
4.2.1 StaticEquilibriumEquation ........................ 121
4.2.2 FrictionCone .................................... 122
4.2.3 Relationship Between Local Deformation
andContactForce ................................ 123
4.2.4 RelationshipBetweenWorkpiecePositionError
andLocalDeformation ............................ 123
4.2.5 SolutionMethod .................................. 127
4.3 WorkpieceDeformation ................................... 128
4.4 ModelingofClampingReasonability ........................ 128
4.5 ApplicationandAnalysis .................................. 129
4.5.1 AnalysisoftheClampingErrorDuetotheWeak
StiffnessWorkpiece ............................... 129
4.5.2 Evaluation of the Clamping Error of High
StiffnessWorkpiece ............................... 131
Contents ix
References .................................................... 136
5 AnalysisofWorkpieceAttachment/Detachment .................. 139
5.1 AttachmentandDetachmentModel ......................... 139
5.2 JudgmentMethodoftheAttachmentandDetachment ......... 142
5.3 AnalysisAlgorithmoftheAttachmentandDetachment
Direction ................................................ 145
5.3.1 CalculationAlgorithmoftheGeneratorMatrix
oftheNon-PositiveDualMatrix .................... 146
5.3.2 ClassificationMethodofCoefficientMatrix .......... 148
5.3.3 ApplicationofPivotAlgorithm ..................... 149
5.4 AnalysisandApplicationofAttachmentandDetachment ...... 159
5.4.1 ThreeDimensionalWorkpiece ...................... 159
5.4.2 TwoDimensionalWorkpiece ....................... 166
References .................................................... 173
6 AnalysisofLocatingAccuracy .................................. 175
6.1 AnalysisModel .......................................... 175
6.1.1 LocatingSourceError ............................. 176
6.1.2 WorkpiecePositionError .......................... 177
6.1.3 LocatingError ................................... 182
6.2 PositionErrorModelofContactPoint ....................... 183
6.2.1 DirectionalDimensionPath ........................ 183
6.2.2 DirectionalDimensionChain ....................... 185
6.3 ExamplesandExperiments ................................ 189
6.3.1 OneVeeBloke-OneSupportingPinLocating
Scheme ......................................... 189
6.3.2 TwoCylindricalPinsLocatingScheme .............. 192
6.3.3 OnePlane-TwoHolesLocatingScheme .............. 197
6.3.4 ExperimentalValidation ........................... 205
References .................................................... 208
7 SelectionAlgorithmofLocatingDatum ......................... 209
7.1 HierarchicalStructureModel .............................. 209
7.1.1 SurfaceRoughness ................................ 210
7.1.2 SurfaceFeature ................................... 211
7.1.3 ValidLocatingDomain ............................ 211
7.1.4 DimensionError .................................. 212
7.2 JudgementMatrix ........................................ 212
7.3 LayerWeightVector ...................................... 214
7.4 CombinationWeightVector ................................ 215
7.5 ReconstructionofJudgmentMatrix ......................... 217
7.6 AlgorithmandApplication ................................ 218
7.6.1 AlgorithmandFlow ............................... 218
7.6.2 PracticalExample ................................ 220
References .................................................... 228
x Contents
8 PlanningAlgorithmofLocatingPointLayout .................... 229
8.1 LocatingPointLayoutScheme ............................. 229
8.2 CausesofLocatingNon-determination ...................... 232
8.3 GenerativePlanningAlgorithm ............................. 237
8.4 ApplicationandDesignProcess ............................ 239
References .................................................... 243
9 PlanningAlgorithmofClampingForcesforRigidWorkpieces .... 245
9.1 MechanicalModelofFixturingScheme ..................... 245
9.1.1 WorkpieceStaticEquilibriumConstraints ............ 246
9.1.2 DirectionConstraints .............................. 247
9.2 AnalysisofForceExistence ............................... 247
9.3 AnalysisofForceFeasibility ............................... 248
9.4 PlanningAlgorithmof1-clampingForce .................... 250
9.5 PlanningAlgorithmofn-clampingForce .................... 253
9.6 CalculationofClampingForces ............................ 257
9.6.1 SingleClampingForceof2DWorkpiece ............. 257
9.6.2 SingleClampingForceof3DWorkpiece ............. 261
9.6.3 DoubleClampingForcesof2DWorkpiece ........... 263
References .................................................... 270
10 DeterminationMethodofClampingPointLayoutforRigid
Workpieces ................................................... 271
10.1 WorkpieceStability ....................................... 271
10.1.1 StabilityIndex .................................... 271
10.1.2 StabilityMeasurement ............................. 275
10.2 PlanningAlgorithmofApplicationRegion ................... 276
10.3 PlanningMethodofFixturingLayout ....................... 280
10.4 NumericalTestsofApplicationRegionPlanning .............. 283
10.4.1 PlanningofApplicationRegionforOneClamping
Force ........................................... 283
10.4.2 Calculation of Stable Region in Dynamic
MachiningProcess ................................ 286
10.4.3 Planning of Application Region for Multiple
ClampingForces ................................. 290
10.5 ExamplesofFixturingLayoutOptimization .................. 294
10.5.1 FixturingLayoutOptimizationof2DWorkpiece ...... 294
10.5.2 FixturingLayoutOptimizationof3DWorkpiece ...... 297
References .................................................... 301
11 FixturingLayoutOptimizationofThin-WalledWorkpieces ....... 303
11.1 FiniteElementAnalysisofFixturingDeformation ............ 303
11.1.1 StaticEquilibriumConditions ...................... 303
11.1.2 FrictionConeConstraints .......................... 304
11.1.3 UnilateralContactConstraints ...................... 305
11.2 PredictionMethodforFixturingDeformation ................ 305