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Research Papers: Design and Analysis

Identification of Friction Model Parameters Using the Inverse Harmonic Method

[+] Author and Article Information
Abdallah Hadji

Mem. ASME
BWC/AECL/NSERC Chair
of Fluid-Structure Interaction
Department of Mechanical Engineering,
Polytechnique Montréal,
C.P. 6079, Succursale Centre-ville,
Montreal, QC H3C 3A7, Canada
e-mail: Abdallah.Hadji@polymtl.ca

Njuki Mureithi

Mem. ASME
BWC/AECL/NSERC Chair
of Fluid-Structure Interaction
Department of Mechanical Engineering,
Polytechnique Montréal,
C.P. 6079, Succursale Centre-ville,
Montreal, QC H3C 3A7, Canada
e-mail: njuki.mureithi@polymtl.ca

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received October 16, 2015; final manuscript received August 8, 2016; published online September 29, 2016. Assoc. Editor: Osamu Watanabe.

J. Pressure Vessel Technol 139(2), 021209 (Sep 29, 2016) (13 pages) Paper No: PVT-15-1225; doi: 10.1115/1.4034441 History: Received October 16, 2015; Revised August 08, 2016

A hybrid friction model has been developed by Azizian and Mureithi (2013, “A Hybrid Friction Model for Dynamic Modeling of Stick–Slip Behavior,” ASME Paper No. PVP2013-97249) to simulate the general friction behavior between surfaces in contact. However, identification of the model parameters remains an unresolved problem. To identify the parameters of the friction model, the following quantities are required: contact forces (normal and tangential or friction forces), the slip velocity, and the displacement in the contact region. Simultaneous direct measurement of these quantities is difficult. In the present work, a beam clamped at one end and simply supported with the consideration of friction at the other is used as a mechanical amplifier of the friction effects at the microscopic level. Using this simplified approach, the contact forces, the sliding velocity, and the displacement can be indirectly obtained by measuring the beam vibration response. The inverse harmonic balance method is a new method based on nonlinear modal analysis which is developed in this work to calculate the contact forces. The method is based on the modal superposition principle and Fourier series expansion. Two formulations are possible: a harmonic form formulation and a subharmonic form formulation. The approach based on subharmonic forms coupled with spline fitting gave the best results for signal reconstruction. Signal reconstruction made it possible to accurately identify the parameters of the hybrid friction model with a multiple step approach.

Copyright © 2017 by ASME
Topics: Friction , Excitation
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References

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Hadji, A. , and Mureithi, N. , 2014, “ Nonlinear Normal Modes and the LuGre Friction Model Parameter Identification,” ASME Paper No. IMECE2014-38997.
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Figures

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Fig. 1

Schematic of a nonlinear beam

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Fig. 2

Direction of forces applied at the contact point

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Fig. 3

Schematic of the test rig

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Fig. 4

The effect of slip regime on the shaker (the sensitivity of the shaker slip regime)—zone I: stable sticking (presliding), zone II: beginning slip (stick–slip), and zone III: sliding regime

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Fig. 5

The effect of slip regime on the beam response—zone I: stable sticking (presliding), zone II: unstable slip (stick–slip), and zone III: stable sliding regime (large slip)

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Fig. 6

FFT of the system response at the drive point (at 50 Hz)

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Fig. 7

The frequency response (FRF) of the system (first harmonic)

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Fig. 8

The first nonlinear mode depending on the level of excitement (Fmax = 8 N)

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Fig. 9

The second harmonic and subharmonic form at 8 N excitation level

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Fig. 10

The second harmonic and subharmonic form at 8 N excitation level

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Fig. 11

The evaluation of the first and the second harmonic forms in one period

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Fig. 12

Accelerometer signal reconstruction (Fmax = 8 N)

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Fig. 13

Harmonic number effect in friction force calculation (decoupled harmonic)

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Fig. 14

Harmonic number effect in friction force calculation (coupled harmonic)

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Fig. 15

Friction force (8 N excitation force level)

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Fig. 16

Friction force (IHB method at 8 N excitation force level)

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Fig. 17

Schematic of the hybrid friction model [9]

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Fig. 18

Friction force (Stribeck model simulation)

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Fig. 19

Friction force (Dahl and LuGre models simulation)

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Fig. 20

One DOF friction models simulation

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