Research Papers

Friction-Induced Vibration in Lead Screw Systems: Mathematical Modeling and Experimental Studies

[+] Author and Article Information
O. Vahid

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadaovahidar@uwaterloo.ca

N. Eslaminasab

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadaneslmin@uwaterloo.ca

M. F. Golnaraghi1

Mechatronic Systems Engineering, Burnaby Mountain Chair, Simon Fraser University, Surrey, BC, V3T 0A3, Canadamfgolnar@sfu.ca


Corresponding author.

J. Vib. Acoust 131(2), 021003 (Feb 13, 2009) (10 pages) doi:10.1115/1.3025837 History: Received August 07, 2007; Revised September 26, 2008; Published February 13, 2009

Lead screw mechanisms are used to convert rotary to linear motion. The velocity-dependent coefficient of friction at the contact between lead screw and nut threads can lead to self-excited vibrations, which may result in excessive noise generated by the system. In this paper, based on a practical example of a powered automotive seat adjuster, the nonlinear dynamics of lead screw systems is studied. A test setup is developed to perform experiments on the horizontal motion drive. The experimental results are used in a novel two-step identification approach to estimate friction, damping, and stiffness parameters of the system. The identified parameters together with other known system parameters are used in the numerical simulations. The accuracy of the mathematical model is validated by comparing numerical simulation results with actual measurements in cases where limit cycles are developed. Using simulation results for a range of lead screw angular velocities and axial forces, regions of stability were found. Also, the effects of damping and stiffness parameters on the steady-state amplitude of vibration were investigated.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 16

Effect of lead screw rotational damping on the threshold of instabilities; the thick black line corresponds to the instability threshold in Fig. 1 for load and velocity-dependent system parameters

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Figure 17

The effects of coupling stiffness and axial loading on the dynamic behavior of the lead screw; gearbox output angular velocity 40 rad/s

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Figure 1

A sample test result showing audible noise generated from the lead screw system

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Figure 2

Schematic view of a lead screw drive

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Figure 3

Schematic view of the 4DOF lead screw system model

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Figure 4

Experiment setup and instrumentation

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Figure 5

Resistive torque from motor and gearbox; (dots) measurements and (dashed line) fitted line to the data points

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Figure 6

Collection of data points showing torque/speed/force

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Figure 7

Sample measurement results. Variation of motor torque with applied axial load at constant speeds. (Dots) measurements and (solid line) fitted line to the data points.

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Figure 8

Curve fitting results; (dotted) measurements and (solid) curve fit

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Figure 9

Identified velocity-dependent coefficient of friction

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Figure 10

Experimentally obtained variation of limit cycle vibration amplitude with input angular velocity (gearbox output) and axial force

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Figure 11

(a) A sample of experimental results showing stick-slip in open-loop tests and (b) zoomed view; (black) lead screw angular velocity and (gray) dc motor angular velocity

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Figure 12

Schematic view of the 2DOF lead screw system

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Figure 13

Measurement versus simulation examples; (a) phase plot and (b) frequency response; (gray) measurements and (black) simulation

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Figure 14

Variation of the system parameters with gearbox output velocity and axial force; (a) coupling stiffness, kC, (b) lead screw damping, cS×103, (c) friction boundary effect, ωBL, and (d) friction scaling, sμ

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Figure 15

Contour plots of the steady-state vibration amplitude versus applied axial force and gearbox output speed




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