Abstract
Dynamic sliding friction was studied based on the angular velocity of a golf ball during an oblique impact. This study used the analytical model proposed for the dynamic sliding friction on lubricated and non-lubricated inclines. The contact area A and sliding velocity u of the ball during impact were used to describe the dynamic friction force Fd = λAu, where λ is a parameter related to the wear of the contact area. A comparison with experimental results revealed that the model agreed well with the observed changes in the angular velocity during impact, and λAu is qualitatively equivalent to the empirical relationship, μN + μη′dA/dt, given by the product between the frictional coefficient μ and the contact force N, and the additional term related to factor η′ for the surface condition and the time derivative of A.
Highlights
Golf, one of the most popular sports worldwide, has a long history and the physics of golf has been studied for centuries[1,2]
A study of the angular velocity ω demonstrated the following[6]: (i) the experimental value of ω increased in the initial phases of contact and decreased; (ii) there was a significant discrepancy between the experimental results and analytical velocity ω derived from μN; and (iii) the experimental results agreed with the analytical velocity ω given by μN +μη′dA/dt
To study influential factors, sliding tests conducted under different surface conditions demonstrated the following: (i) the sliding velocity of polyurethane (PU) rubber on oiled inclines[30] was significantly dependent on the contact area; (ii) the contact area of polytetrafluoroethylene (PTFE) spheres on dry inclines[31] increased with wear, while the sliding velocity decreased; and (iii) the analytical model indicated that the contact area and sliding velocity are key factors on oiled surfaces[30], while the wear of the contact surface can be an influential factor on dry surfaces[31], implying that the dynamic friction force can be expressed as Fd =λAu
Summary
Dynamic sliding friction was studied based on the angular velocity of a golf ball during an oblique impact. A comparison with experimental results revealed that the model agreed well with the observed changes in the angular velocity during impact, and λAu is qualitatively equivalent to the empirical relationship, μN + μη′dA/dt, given by the product between the frictional coefficient μ and the contact force N, and the additional term related to factor η′ for the surface condition and the time derivative of A. To clarify the correlation with the present model, a cursory examination was made of equation (3) using the following approximations: (i) u ~ uo (1 − b + b cos φt) in equation (7); (ii) differentiating equation (1) with respect to t, we obtain cos φt = (φ/Ao)dA/dt; and (iii) the relation Fd ~ λuo (1 − b)A + λuo bφ (A/Ao)dA/dt was obtained This approximate expression for equation (3) is qualitatively equivalent to the previous relationship, since A depends on N. This implies that equation (3) more closely describes the dynamic friction force during an oblique impact
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