Friction-Induced Vibration in Lead Screw Drives

By: Orang Vahid-Araghi, Farid Golnaraghi

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Hardcover | 27 October 2010

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Friction-Induced Vibration in Lead Screw Drives covers the dynamics of lead screw drives with an emphasis on the role of friction. Friction-induced vibration in lead screws can be the cause of unacceptably high levels of audible noise as well as loss of operation accuracy and shortened life. Although lead screw drives have a long history and their mechanical design and manufacturing aspects are very well understood, the role of friction in their dynamical behavior has not been comprehensively treated. The book draws on the vast body of work on the subject of dynamical systems with friction (such as disk brake systems) and offers said treatment, along with:

· Unique coverage of modeling of multi-DOF lead screw systems with friction

· Detailed analysis of negative damping, mode coupling, and kinematic constraint instability mechanisms in lead screws drives

· A practical parameter identification approach for the velocity dependent coefficient of friction in lead screw drives

Friction-Induced Vibration in Lead Screw Drives serves as the definitive text on the friction-induced vibration of lead screws, and includes a practical case study where the developed methods are used to study the excessive noise problem of a lead screw drive system and to put forward design modifications that eliminate the friction-induced vibrations.

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Introduction	p. 1
Friction in Machines and Mechanisms	p. 2
Friction in Lead Screw Drives	p. 3
Outline	p. 5
Lead Screws	p. 7
Screw Threads	p. 7
Lead Screw Engineering	p. 9
Lead Screw and Nut: A Kinematic Pair	p. 12
Effect of Thread Angle	p. 13
Some Background Material	p. 17
Linearized System Equations	p. 17
Equations of Motion with Contact Forces	p. 19
Classification of Linear Systems	p. 21
Stability Analysis	p. 23
Undamped Systems	p. 25
The Averaging Method	p. 27
Friction - Induced Instability	p. 31
Negative Damping Instability	p. 31
Periodic Vibration: Pure-Slip Motion	p. 33
Periodic Vibration: Stick-Slip Motion	p. 36
A Numerical Example	p. 40
Further References on Negative Damping	p. 42
Mode Coupling	p. 42
Example No. 1: Flutter Instability	p. 43
Example No. 2: Mode Coupling	p. 47
Further References on Mode Coupling	p. 50
Kinematic Constraint Instability	p. 51
Painlevé's Paradox	p. 52
Bilateral Contact	p. 54
Self-Locking	p. 55
An Example of Kinematic Constraint Instability	p. 56
Further References on the Kinematic Constraint Instability Mechanism	p. 66
Mathematical Modeling of Lead Screw Drives	p. 67
Velocity-Dependent Coefficient of Friction	p. 68
Dynamics of Lead Screw and Nut	p. 69
Basic 1-DOF Model	p. 71
Inverted Basic Model	p. 72
Basic Model with Fixed Nut	p. 73
Basic Model with Fixed Lead Screw	p. 73
Antibacklash Nut	p. 73
Compliance in Lead Screw and Nut Threads	p. 75
Backlash	p. 77
Axial Compliance in Lead Screw Supports	p. 77
Alternative Formulation	p. 78
Compliance in Threads and Lead Screw Supports	p. 80
Rotational Compliance of the Nut	p. 81
Alternative Formulation	p. 82
Some Remarks Regarding the System Models	p. 83
Negative Damping Instability Mechanism	p. 85
Equation of Motion	p. 85
Local Stability of the Steady-Sliding State	p. 87
Numerical Examples	p. 88
First-Order Averaging	p. 89
Assumptions	p. 90
Equation of Motion in Standard Form	p. 90
First-Order Averaging	p. 94
Steady-Sliding Equilibrium Point	p. 96
Nontrivial Equilibrium Points	p. 97
Numerical Simulation Results: Part 1	p. 101
Numerical Simulation Results: Part 2	p. 104
Conclusions	p. 107
Mode Coupling Instability Mechanism	p. 109
Mathematical Models	p. 109
2-DOF Model with Axially Compliant Lead Screw Supports	p. 110
2-DOF Model with Compliant Threads	p. 111
Linear Stability Analysis	p. 113
Undamped System	p. 113
Examples and Discussion	p. 115
Damped System	p. 118
Examples and Discussion	p. 120
Comparison Between the Stability Conditions of the Two Lead Screw Models	p. 122
Further Observations on the Mode Coupling Instability	p. 124
Frequency and Amplitude of Vibrations	p. 125
Effect of Damping on Mode Coupling Vibrations	p. 128
Mode Coupling in 3-DOF Lead Screw Model	p. 129
Conclusions	p. 133
Kinematic Constraint Instability Mechanism	p. 135
Existence and Uniqueness Problem	p. 135
True Motion in Paradoxical Situations	p. 137
1-DOF Lead Screw Drive Model	p. 140
Linear Stability Analysis	p. 141
Negative Damping	p. 143
Numerical Simulation Results	p. 144
Kinematic Constraint Instability	p. 145
Numerical Simulation Results	p. 147
Region of Attraction of the Stable Equilibrium Point	p. 149
Kinematic Constraint Instability in Multi-DOF System Models	p. 151
2-DOF Model of Sect. 5.6	p. 151
2-DOF Model of Sect. 5.8	p. 154
Conclusions	p. 156
An Experimental Case Study	p. 157
Preliminary Observations	p. 158
Mathematical Modeling	p. 162
Parameter Identification Step 1: Friction and Damping	p. 165
Parameter Identification Test Setup	p. 169
Experimental Results: Step 1	p. 170
DC Motor and Gearbox	p. 172
Identification Results	p. 172
Parameter Identification Step 2: Stiffness and Fine-Tuning	p. 175
Experimental Results: Step 2	p. 179
Parameter Studies	p. 182
Effect of Input Angular Velocity	p. 184
Effect of Damping	p. 185
Effect of Stiffness	p. 185
Conclusions	p. 186
Appendices	p. 189
First Order Averaging Theorem	p. 189
Application of Higher Order Averaging	p. 192
Equation of Motion in Standard Form	p. 192
Higher-Order Averaging Formulation	p. 194
A Numerical Example	p. 198
First-order Averaging Applied to the 2-DOF Lead Screw Model with Axially Compliant Supports	p. 199
References	p. 207
Index	p. 213
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Friction-Induced Vibration in Lead Screw Drives

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