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TECHNICAL PAPERS

A Technique for Estimating Linear Parameters Using Nonlinear Restoring Force Extraction in the Absence of an Input Measurement

[+] Author and Article Information
Muhammad Haroon

 Purdue University, School of Mechanical Engineering, Ray W. Herrick Laboratories, 140 S. Intramural Drive, West Lafayette, IN 47907-2031mharoon@purdue.edu

Douglas E. Adams1

 Purdue University, School of Mechanical Engineering, Ray W. Herrick Laboratories, 140 S. Intramural Drive, West Lafayette, IN 47907-2031deadams@purdue.edu

Yiu Wah Luk

Goodyear Tire & Rubber Company, Goodyear Vehicle Systems,  Technical Center D/480C, P.O. Box 3531, Akron, Ohio 44309-3531yw_luk@goodyear.com

1

Corresponding author.

J. Vib. Acoust 127(5), 483-492 (Mar 28, 2005) (10 pages) doi:10.1115/1.2013293 History: Received October 24, 2003; Revised March 28, 2005

Conventional nonlinear system identification procedures estimate the system parameters in two stages. First, the nominally linear system parameters are estimated by exciting the system at an amplitude (usually low) where the behavior is nominally linear. Second, the nominally linear parameters are used to estimate the nonlinear parameters of the system at other arbitrary amplitudes. This approach is not suitable for many mechanical systems, which are not nominally linear over a broad frequency range for any operating amplitude. A method for nonlinear system identification, in the absence of an input measurement, is presented that uses information about the nonlinear elements of the system to estimate the underlying linear parameters. Restoring force, boundary perturbation, and direct parameter estimation techniques are combined to develop this approach. The approach is applied to experimental tire-vehicle suspension system data.

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Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 9

Transmissibility function between the sprung mass and the unsprung mass for a random input of amplitude 0.5 mm (—) and 5.5 mm (⋯)

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Figure 10

Extra mass attached to test vehicle for parameter estimation

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Figure 11

Transmissibility function between the sprung mass and the unsprung mass for a chirp input at an input amplitude of 4 mm. Without additional mass (—), with additional mass (⋯).

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Figure 12

Transmissibility function between the sprung mass and the unsprung mass for a random input at an input amplitude of 5 mm. Without additional mass (—), with additional mass (⋯).

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Figure 1

Idealized forms of simple structural (b) cubic hardening stiffness, (c) bilinear stiffness, (d) saturation force, (e) clearance force, and (f) Coulomb friction damping compared to a linear stiffness restoring force (a).

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Figure 2

Quarter car model

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Figure 3

Velocity restoring force curve for a vehicle suspension system with a nonlinear damping characteristic, for a 4 mm chirp input at a frequency of 2.2 Hz

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Figure 4

Transmissibility function between the sprung mass and the unsprung mass; Without additional mass (—), with additional mass (-----). (Simulink® Mode).

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Figure 5

Shaker testing setup

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Figure 6

(a) Nonlinear shock damping showing saturation at a certain relative clearance velocity and (b) nonlinear hysteretic stiffness showing backlash characteristic in both damping and stiffness; Input amplitude 0.5 mm and input frequency 3.8 Hz

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Figure 7

Curve fit to the nonlinear restoring force in the suspension. Nonlinear damping restoring force (—), curve fit (-----), and error (-·-)

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Figure 8

Transmissibility function between the sprung mass and the unsprung mass for a chirp input of amplitude 1 mm (—) and 4 mm (-----)

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Figure 13

Damping restoring force curve at an input amplitude of 4 mm and a frequency of 3.5 Hz: (xxx) measured, (ooo) estimated

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Figure 14

Damping restoring force curve at an input amplitude of 2.5 mm and a frequency of 2.5 Hz: (xxx) measured, (ooo) estimated

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