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Research Papers

# An Experimental Study of Contact Forces During Oblique Elastic Impact

[+] Author and Article Information
Philip P. Garland1

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canadaphil.garland@unb.ca

Robert J. Rogers

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

Under an assumption of a constant Coulomb friction coefficient, the tangential force is limited to the product of the friction coefficient and the current normal force. For reversed sliding, the tangential force is equal to the negative of this product.

Material No. DS-125 by H.L. Blachford Ltd. (Mississauga, Ontario, Canada).

The impact duration as judged from the normal force waveforms is taken as the time, after initial contact, at which the normal force crosses zero.

The impact duration as judged from the tangential force waveform depends on whether tangential force reversal is expected and clearly present. For near normal incidence angles where tangential force reversal is clearly present, the impact duration is taken as the time at which the tangential force makes its second zero crossing (i.e., the first zero crossing after the reversed force direction phase). For glancing incidence angles, the impact duration as judged by the tangential force waveform is taken as the first zero crossing of tangential force after the initial contact.

The elastic tangential deformation is expected to be on the order of $10−5$ times smaller than the radius of the spherical striker. Therefore, any moment caused by the normal force is negligible compared with that caused by the tangential force. This is different from the findings of the Cross (15) study in which sporting balls that experienced higher tangential deformation were used.

1

Corresponding author.

J. Appl. Mech 76(3), 031015 (Mar 13, 2009) (8 pages) doi:10.1115/1.3063634 History: Received March 11, 2008; Revised September 18, 2008; Published March 13, 2009

## Abstract

Low and high speed impacts frequently occur in many mechanical processes. Although widely studied, rarely are normal and tangential force time-waveforms measured, as generally these are very difficult measurements to do accurately. This paper presents, for the first time, a comprehensive set of experimentally obtained contact force waveforms during oblique elastic impact for a range of initial velocities and incidence angles. The experimental apparatus employed in this study was a simple pendulum consisting of a spherical steel striker suspended from a steel wire. The contact force time-waveforms were collected using a tri-axial piezoelectric force transducer sandwiched between a spherical target cap and a large block. The measured contact forces showed that loading was essentially limited to the normal and tangential directions in the horizontal plane. Analysis of the maximum normal and tangential forces for the near glancing angles of incidence indicated a friction coefficient that varies linearly with initial tangential velocity. The essential features of tangential force reversal during impact predicted by previous continuum models are confirmed by the experimental force results.

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Topics: Force , Friction

## Figures

Figure 1

Schematic of experimental apparatus

Figure 2

Spherical striker and mounting block

Figure 3

Alignment procedure results at 0 deg. (a) Normal force, (b) horizontal force, and (c) vertical force.

Figure 4

Alignment procedure results at +10 deg and −10 deg. (a) Normal force, (b) horizontal force, and (c) vertical force (+10 deg, solid line; −10 deg, dashed line).

Figure 5

Experimental contact force waveforms during impact for initial velocity of 90 mm/s (normal force, left side; tangential force, right side)

Figure 6

Variation of impact force parameters with incidence angle. (a) Maximum normal force, (b) maximum tangential force, (c) minimum tangential force, (d) impact duration, τz, (e) tangential force reversal time, τx,R, and (f) impact duration, τx.

Figure 7

Friction coefficient versus initial tangential velocity

Figure 8

Normalized tangential force waveforms. (a) 30 mm/s data, (b) 60 mm/s data, and (c) 90 mm/s data (friction envelope, dashed line).

Figure 9

Normalized rebound versus normalized incidence angle. (a) 30 mm/s data, (b) 60 mm/s data, and (c) 90 mm/s data.

Figure 10

Impulse ratio versus incidence angle. (a) 30 mm/s data, (b) 60 mm/s data, and (c) 90 mm/s data.

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