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Precursors of Global Slip in a Longitudinal Line Contact Under Non-Uniform Normal Loading

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Abstract

This article describes the mechanism of precursor events; the mechanism was determined through an experiment and simulation by considering non-uniform normal loading. In the experiment, real-time observations of a contact zone were performed using a longitudinal line contact of PMMA specimens (i.e., a slider on a stationary base block) under a total normal load of 400 N. Partial propagations of the detachment front were considered as precursor events, and it was found that non-uniform normal loading influences the occurrence frequency of the precursor events and the increasing rate of the propagation length. In the simulation, the time evolution of a multi-degree-of-freedom system with Coulomb friction was studied. The model considered in the simulation comprised multiple masses serially connected by linear springs on a stationary rigid plane. By regarding the precursor in the experiment to correspond to a partial slip (i.e., simultaneous slip of some of the masses) in the simulation, the influence of non-uniform normal loading on the precursor events can be explained to a certain extent. Additionally, it was found that the apparent static friction coefficient (i.e., the ratio of the maximum tangential load to the total normal load) could be lesser than the real static friction coefficient due to the residual strain in the slider.

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Fig. 10
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Abbreviations

E :

Young’s modulus of PMMA (Pa)

f i :

Friction (N) (Eq. 4)

\( f_{\text{k}}^{(i)} \) :

Kinetic friction (N) (Eq. 6)

\( f_{\text{s}}^{(i)} \) :

Static friction (N)

\( f_{\text{smax}}^{(i)} \) :

Maximum static friction (N) (Eq. 5)

F X :

Tangential load (N) (Eq. 3)

F Xmax :

Maximum tangential load (N)

F Z :

Total normal load (N) (Eq. 8)

F ZA :

Partial normal load (N) (Fig. 1a)

Fig. 1
figure 1

Schematic diagram of the experimental apparatus with a transmissive optical system: a front view and b side view

Full size image
F ZB :

Partial normal load (N) (Fig. 1a)

k :

Stiffness of the material section (N/m) (Eq. 10)

K :

Stiffness of the loading section (N/m)

L :

Length of the slider (m)

L p :

Propagation length of precursors (m)

m :

Mass (kg) (Eq. 9)

M :

Mass of the slider (kg)

N :

Number of blocks

S :

Cross-section area of the slider (m2)

t :

Time (s)

V :

Driving speed (m/s)

w i :

Normal load (N) (Eq. 7)

x i :

Position (m)

y i :

Spring compression (m) (Eq. 11)

\( y_{i}^{\max } \) :

Maximum spring compression (m)

θ:

Degree of non-uniformity of normal loading

μk :

Kinetic friction coefficient

μs :

Static friction coefficient

μsapp :

Apparent static friction coefficient (Eq. 1)

(•):

Derivative with respect to time t

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Authors and Affiliations

  1. Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama, 240-8501, Japan

    Satoru Maegawa & Ken Nakano

  2. Power Train Material Engineering Division, Toyota Motor Corporation, Toyota, 471-8572, Japan

    Atsushi Suzuki

Authors
  1. Satoru Maegawa
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  2. Atsushi Suzuki
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  3. Ken Nakano
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Correspondence to Ken Nakano.

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Maegawa, S., Suzuki, A. & Nakano, K. Precursors of Global Slip in a Longitudinal Line Contact Under Non-Uniform Normal Loading. Tribol Lett 38, 313–323 (2010). https://doi.org/10.1007/s11249-010-9611-7

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