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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