Preface	5
	Contents	8
	Introduction	14
	Abstract	15
	1 General Introduction	16
	Abstract	16
	1.1 Introduction of the Cold Rolling Precision Forming Technology	16
	1.2 Present Situation of Shaft Part Manufacturing Technology	18
	1.2.1 Cutting of the Spline Shafts	19
	1.2.1.1 Cutting with Formed Cutter	19
	1.2.1.2 Generating Cutting Method	20
	1.2.2 Plastic Forming of Spline Shafts	21
	1.2.2.1 Cold Extrusion Forming of the Spline Shafts	22
	1.2.2.2 Cold Rolling Forming of Spline Shafts	23
	1.2.2.3 Striking Rolling of the Spline Shafts	24
	1.2.2.4 Cold Rolling Forming of Spline Shafts with Rack Dies	25
	1.2.2.5 Cold Rolling Forming of Spline Shafts	27
	1.2.3 Manufacturing Methods of Thread Components	28
	1.3 Research Progress on the Cold Rolling Precision Forming Technology of Shaft Parts	31
	1.3.1 The State of the Art on the Manufacturing of Spline Shafts	31
	1.3.2 Theoretical Researches on the Cold Rolling Forming of Spline Shafts	34
	1.3.3 Surface Modification of the Cold Rolling Forming Spline Shafts	35
	1.3.4 Development Status on Cold Rolling Forming of Threads	36
	1.4 Development Trends on Cold Rolling Precision Forming Technology of Shaft Parts	38
	References	40
	2 Principle and Mechanical Analysis on the Cold Rolling Precision Forming of Spline	44
	Abstract	44
	2.1 Principle and Process on the Cold Rolling Precision Forming of Spline Shafts	44
	2.2 Mechanical Analysis	46
	2.3 Analysis on the Cold Rolling Forming Process of the Spline Tooth	47
	2.3.1 Indexing and Biting Conditions [6]	47
	2.3.2 Rotating Conditions	47
	2.3.3 Geometrical Indexing Conditions	50
	2.4 Double-Flank Non-backlash Meshing	52
	2.4.1 Contact Area in the Forming Process	52
	2.4.2 Position of the Contact Points	55
	2.4.2.1 Position of the Contact Point on the Bilateral Tooth Surfaces of the Spline	55
	2.4.2.2 The Position Parameters of the Contact Point on the Rollers	58
	2.5 Sliding of the Contact Point	59
	2.5.1 Sliding Motion of the Contact Point on the Active Tooth Flank	59
	2.5.2 Sliding Motion of the Contact Point on the Driven Tooth Flank	61
	2.5.3 Metal Flow on the Tooth Surface of the Workpiece	62
	2.6 Mechanical Analysis on the Cold Rolling Precision Forming of Spline	63
	2.6.1 Basic Assumption of the Stress Analysis	63
	2.6.2 Fundamental Plastic Forming Theory of Stress Analysis	65
	2.6.2.1 Fundamental Equation of the Plane Strain	66
	2.6.2.2 Yield Criteria	67
	2.6.2.3 The Strengthening Model	68
	2.6.2.4 The Slip-Line Stress Field Theory	68
	2.6.3 Slip-Line Field and Stress Analysis in the Initial Rolling Stage	70
	2.6.4 Slip-Line Field and Stress Analysis in the Stable Rolling Stage	72
	2.7 Average Pressure on the Contact Surface During the Forming Process	75
	References	78
	3 Process Parameters in the Cold Rolling Forming of Spline	80
	Abstract	80
	3.1 Contact Area in the Cold Rolling Forming of Spline Shafts	80
	3.1.1 Calculation Model	81
	3.1.2 Tooth Profile Equation of the Roller and the Workpiece in the Forming Process	82
	3.1.2.1 Tooth Profile of the Roller	82
	3.1.2.2 Tooth Profile of the Workpiece	85
	3.1.3 Contact Boundary Conditions	88
	3.1.4 Calculation of the Contact Area	89
	3.1.5 Main Algorithm of the Subroutine	91
	3.1.5.1 Solution Program for the Judgment of the Intersection Point Between the Involute and the Circle	91
	3.1.5.2 Calculation Program of the Contact Arc Length on the Roller Tooth Addendum Transition Circle	91
	3.1.5.3 Calculation Program of the Arc Length on the Involute	92
	3.1.5.4 Important Parameters Necessary for Calculation	93
	3.1.5.5 Analysis of the Factors Influencing the Unit Length Contact Area	99
	3.2 Rolling Force and Rolling Moment	100
	3.2.1 Theoretical Calculation of the Rolling Force and Rolling Moment	100
	3.2.2 Analysis of the Rolling Force and Rolling Moment in the Forming Process	102
	3.3 Calculation of the Cold Rolling Workpiece Billet Diameter	106
	3.3.1 Theoretical Calculation Formulas	106
	3.3.2 Cross-Sectional Area of a Single Tooth Above the Dedendum Circle	106
	3.3.3 Radius of the Dedendum Transition Arc	109
	4 Numerical Simulation on the Cold Rolling Forming of Spline	112
	Abstract	112
	4.1 Establishment of the Finite Element Model and Boundary Conditions	112
	4.1.1 Finite Element Model	112
	4.1.2 Simulation Parameters and Constrain Conditions	113
	4.2 Numerical Simulation of the Cold Rolling Forming Process	113
	4.2.1 Plastic Deformation Zone	113
	4.2.2 Bulge at the End of the Shafts	114
	4.2.3 Stress and Strain Fields	116
	4.3 Comparison Between the Theoretical Analysis and Numerical Simulation Results	119
	4.3.1 Unit Pressure on the Contact Area	119
	4.3.2 Rolling Force in the Rolling Forming Process	123
	References	124
	5 Metal Flow Rules and Forming Quality of Cold Rolling Forming Spline Shaft	125
	Abstract	125
	5.1 Metal Flow Rules of the Tooth in Cold Rolling Precision Forming of Spline Shafts	125
	5.1.1 Workpiece Billet and the Forming Parameters	125
	5.1.2 Metal Flow Analysis of the Tooth Profile	126
	5.2 Precision of the Spline Cold Rolling Forming Process	128
	5.3 Surface Quality of the Cold Rolling Forming Spline Shaft Parts	130
	5.3.1 Surface Roughness of the Formed Components	130
	5.3.2 Tooth Surface Hardness of the Cold Rolling Forming Components	131
	5.3.3 Microstructure of the Cold Rolling Forming Spline Tooth	133
	5.3.4 Tooth Surface Strengthening Mechanism of the Cold Rolling Precision Forming Spline Shaft	135
	5.4 Forming Error and Defects of the Cold Rolling Forming Spline	136
	5.4.1 Formation and Control of the Accumulated Pitch Error	136
	5.4.1.1 Variation of the Circular Pitch in the Cold Rolling Forming of Spline Shaft	136
	5.4.1.2 Influence of Process Parameters on the Accumulated Pitch Error	138
	5.4.1.3 Control of the Accumulated Pitch Error by Synchronization of the Roller and Workpiece Rotation Speed	140
	5.4.2 Defect Analysis of the Cold Rolling Forming Spline Shaft	141
	5.4.2.1 Disorder of the Tooth and Mistake of the Teeth Number	141
	5.4.2.2 Tooth Profile Defects	142
	5.4.2.3 Rough and Chipped Tooth Surface	143
	5.5 Quality Control Methods of Cold Rolling Forming Spline Shafts	144
	5.5.1 Design of the Cold Rolling Billet	144
	5.5.2 Setting of the Roller and Adjustment of the Tooth Positions	146
	5.5.3 Reasonable Selection of the Process Parameters	147
	References	149
	6 Mechanism and Process Analysis on the Cold Rolling Forming of Threads	151
	Abstract	151
	6.1 Principle of the Thread Cold Rolling Forming Process	151
	6.1.1 Two-Wheel Rolling of Threads	152
	6.1.2 Three-Wheel Rolling of Threads	153
	6.2 Diameter Conditions of Three-Wheel Rolling Threads	154
	6.3 Cold Rolling Forming Process of Threads	155
	6.4 Relative Movement Between the Workpiece and the Rolling Wheel	158
	6.4.1 Axial Motion Relationship	158
	6.4.2 Rotational Motion Relationship Between the Workpiece and the Rolling Wheel	160
	6.4.3 Relative Sliding Between the Rolling Wheel and the Workpiece	162
	Reference	164
	7 Process Parameters in the Cold Rolling Forming of Threads	165
	Abstract	165
	7.1 Thread Billets Before Cold Rolling Forming	165
	7.1.1 Commonly Used Calculation Formulas of the Workpiece Billet Diameter	165
	7.1.2 Solution of the Billet Diameter of the Cold Rolling Forming Thread	167
	7.1.2.1 Flat Addendum and Dedendum of the Thread Tooth	167
	7.1.2.2 Round Addendum and Flat Dedendum of the Rolling Wheel Tooth	169
	7.1.3 Chamfer of the Billet	170
	7.1.4 Material of the Rolling Billet	171
	7.2 Parameters in the Cold Rolling Forming Process of Threads	174
	7.2.1 Rolling Force	174
	7.2.1.1 Mechanical Analysis of the Rolling Process	174
	7.2.1.2 Factors Influencing the Cold Rolling Force of the Thread	176
	7.2.1.3 Calculation of the Rolling Force	181
	7.2.2 Selection of the Rolling Speed	184
	7.2.3 Selection of the Feed Rate in Thread Rolling	185
	7.3 Cold Rolling Forming of Hollow Thin-Walled Thread Components	187
	7.3.1 Cold Rolling Forming of Hollow Threads	187
	7.3.1.1 Elastic Deformation in the Cold Rolling Forming of Hollow Threads	187
	7.3.1.2 Plastic Deformation in the Cold Rolling of Hollow Threads	187
	7.3.1.3 Repairing of the Deformation in the Finishing Stage of the Hollow Thread Rolling	188
	7.3.2 Wall Thickness of the Cold Rolling Hollow Thread Components	188
	7.3.2.1 Wall Thickness Condition in Two-Wheel Rolling of Thin-Walled Thread Components	189
	7.3.2.2 Wall Thickness Condition in Three-Wheel Rolling of Thin-Walled Components	195
	References	199
	8 Numerical Simulation of the Thread Cold Rolling Forming Process	200
	Abstract	200
	8.1 Basic Procedure and Assumptions	200
	8.1.1 Numerical Simulation Procedure of the Thread Cold Rolling Process	200
	8.1.2 Simplification of the Model	201
	8.2 Simulation of the Cold Rolling Forming Process of a M10 × 1.5 Solid Thread	201
	8.2.1 Load and Moment of the Die (Rolling Wheel)	203
	8.2.2 Stress State Analysis of the Workpiece	207
	8.3 Numerical Simulation on the Cold Rolling Forming of Hollow Threads	209
	8.3.1 Analysis of the Rolling Force	210
	8.3.1.1 Radial Load of the Rolling Wheel	210
	8.3.1.2 Tangential Load of the Rolling Wheel	211
	8.3.1.3 Axial Load of the Rolling Wheel	211
	8.3.1.4 Torque	212
	8.3.2 Velocity Field	212
	8.3.3 Stress State of the Workpiece	214
	8.3.3.1 Variation of the Stress Field	214
	8.3.3.2 Stress State of the Characteristic Points in the Threads	214
	8.3.4 Analysis of the Strain State	217
	8.4 Failure Analysis of the Thread Components	217
	8.4.1 Variation of the Effective Stress in the Workpiece	217
	8.4.2 Repairing Action of the Three Rolling Wheels on the Instability of the Hollow Thread	219
	References	221
	9 Metal Flow and Parameter Optimization of Thread Cold Rolling Forming Process	222
	Abstract	222
	9.1 Cold Rolling Forming of Threads with Three-Wheel Rolling Machine	222
	9.1.1 Material of the Billet and the Forming Machine	222
	9.1.2 Factors Influencing the Cold Rolling Forming Process of Threads	223
	9.1.3 Influence of the Hollow Thread Wall Thickness on the Forming of Threads	225
	9.2 Metal Flow Rules in the Cold Rolling Forming Process of Threads	226
	9.3 Hardness Distribution of the Cold Rolling Forming and Cutting Threads	230
	9.4 Optimization of the Rolling Parameters	233
	9.4.1 Determination of the Orthogonal Factors, Levels, and Index of the Thread Cold Rolling Forming Parameters	233
	9.4.2 Hardening Degree Under Different Forming Conditions	235
	9.5 Determination of the Optimized Rolling Parameters	235
	References	238
	10 Cold Rolling Precision Forming Equipments	239
	Abstract	239
	10.1 Summary	239
	10.2 Design of the Cold Rolling Forming Machine and the Rolling Wheel	242
	10.2.1 Structure and Parameters of the Equipment	242
	10.2.2 Design of the Synchronous Spindle Damping Absorption	243
	10.2.3 Modeling and Simulation of the Hydraulic System	245
	10.2.3.1 Structural Principle of the Hydraulic System	245
	10.2.3.2 Setting up of Simulation Model on the Hydraulic System	246
	10.2.3.3 Dynamic Simulation of the Hydraulic System	248
	10.2.4 Design of the Rolling Wheel	253
	10.3 Measuring System of the Mechanical Parameters	255
	10.3.1 Measurement Method of the Spindle Torque	255
	10.3.2 Measuring of the Radial Feeding Force of the Slider	257
	10.3.3 The Data Acquisition System	258
	10.4 Determination of the Process Parameters	259
	10.4.1 Rotation Speed of the Rolling Wheel	259
	10.4.2 Feed Rate of the Rolling Wheel	260
	10.4.3 Control of the Spindle Positions	261
	10.5 Mechanical Parameters in the Cold Rolling Precision Forming Process	262
	10.5.1 Dynamic Load of the Forming Process	262
	10.5.2 Influence of the Process Parameters on the Maximum Forming Force	264
	10.5.2.1 Influence of the Roller Rotation Speed on the Maximum Rolling Force	265
	10.5.2.2 Influence of the Roller Feed Rate on the Maximum Rolling Force	266
	10.5.3 Comparison Between the Theoretical Calculation and Experimental Results	267
	10.6 Brief Introduction of the Cold Rolling Precision Forming Equipments	268
	10.6.1 Cold Rolling Forming Equipments of Kinefac Corporation(Kinefac) in the USA [1]	268
	10.6.1.1 Kine-Roller® Cylindrical Die Rolling Machines	268
	10.6.1.2 PowerBox Two Cylindrical Die Machines	269
	10.6.1.3 Double-Arm Two Cylindrical Die Machines	272
	10.6.1.4 Three Cylindrical Die Rolling Machines	273
	10.6.1.5 Rolling Dies and Typical Components	275
	10.6.2 Cold Rolling Equipments of Profiroll Corporation in Germany [2]	275
	10.6.2.1 Rollex Serial Spline Cold Rolling Machines	276
	10.6.2.2 Thread and Profile Rolling Machines	279
	10.6.2.3 CNC Thread Rolling Machines for Highest Profile Quality	282
	10.6.3 Cold Rolling Forming Equipments of Qingdao Shengjian Machinery Factory [8]	284
	10.6.3.1 Spline Cold Rolling Forming Machine	284
	10.6.3.2 Numerical Control Rolling Machines	285
	References	288