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Velocity dependence during the stick-slip process in the surface friction of fibrous polymers
LITERATURE
240 ness so found, the cone angle, and the yield stress is given. The results agree well with the indentation theory of Lockett based on classical slip line analysis. This shows that for a work-hardened material the hardness increases with increasing cone angle for cone angles above 105”. Lockett’s theory is degenerate below 105" and the experiments here also show a change in deformation mode in this region. Although this agreement with theory appears satisfactory, the deformation process appears to be substantially different from that implied in Lockett’s analysis. For large angle cones the deformation resembles a “radial” compression similar to that described by Samuels and Mulhearn: for small cone angles the deformation resembles more clearly the classical slip-line form given by Lockett, though this is precisely the region where the theory becomes degenerate. The effective strain produced by each cone during the indentation process itself is determined for each cone and it is shown that it is possible to construct the stress-strain curve of a given material from a series of cone indentations. On “Indenting with Pyramids”. (Letter to the editor.) A. G. Atkins and D Tabor, I&em. J. Mech. Sci., 7 (1965) 647-650; z figs., I table, 7 refs. The Deformation of Metals by Highvelocity Impact. J. H. Brunton, J. E. Field, G. P. Thomas and M. P. W. Wilson, 5th Plansee Proc. 1964, pp. 137-148; rr figs., 8 refs. The Friction and Hardness of Refractory Compounds. C. A. Brookes and A. G. Atkins, 5th Plansee Proc. 1964, pp. 712-721; 8 figs., 12 refs. 2. FRICTION Change in the Shape of the Surface of Contact between a Rigid Sphere and an Elastic Plane during Sliding Friction. P. Ya. Sukiennik, Soviet Phys.-Doklady, 9 (8) (1965) 700-702. (Transl. Doklady Akad. 1Vauk
SSSR, 157 (4) (1964) 84g-851 by American Institute of Physics, New York, N.Y.) For abstract see Appl. Mech. Rev., 18 (9) (1965) 779; see also Wear, 8 (1965) 30. 408. Torsional Instability tions. J. D. Kemper, J.
from
Franklin
(1965) 254-267. For
abstract
Frictional
see Appl.
Inst.,
Oscilla-
,279 (4)
Mech. Rev., 18 (IO)
(1965) 864. Friction-induced C. A. Brockley,
Vibration. R. Cameron
and A. F. Potter, Trans. ASME, Paper No. 65-Lub-5, 7 pp.; 8 figs., 2 tables, 12 refs. Wear, 9 (1966) 239-247
AND
CURRENT
EVENTS
Friction-induced vibration has been studied in a system consisting of an elastically suspended, damped slider which is loaded against a surface moving at a constant velocity. Exact analysis reveals a critical velocity which limits the incidence of vibration. The critical velocity depends on damping, load, stiffness, and friction characteristics which vary with time and velocity. Approximations in the theory yield an amplitudevelocity equation and another critical velocity relationship. Reasonable agreement is found to exist between the exact and approximate theories for critical velocity. Experimental results for several systems illustrate amplitude- velocity relationships and the existence of critical velocities. The correlation between the experimental results and the approximate theory indicates that the analytical method could be used to predict the vibration behavior of actual systems. On Testing Glass for Surface Friction. L. N. Kopytov, Ind. Lab., 30 (2) (1964) 2g2293. (Transl. Zavod. Lab., 30 (2) (1964) 231~ 232 by Instruments Society of America. Pittsburgh, Pa.) For abstract see Appl. Mech. Rev., r8 (IO) (1965) 818. Velocity Dependence during the Stick-slip Process in the Surface Friction of Fibrous Polymers.
W. J. Lyons and S. C. Scheier, J. Appl. Phys., 36 (6) (1965) 2020~2023; 5 figs., IO refs. Examination of chart tracings representing frictional force during the slip phase of the stick-slip process, in fibers of two polymer types, revealed that these tracings do not have the sinusoidal character associated with a constant coefficient of kinetic friction. Considerations of the dynamics of the system of fiber surface and measuring instrument led to the suggestion that a velocity-dependent term be introduced into the equation of motion of the slider. The new force represented by this term was assumed to be directly proportional to the velocity of the slider. Curves for the displacement of the slider as a function of time, based on solutions of the modified equation of motion, for both the underdamped and overdamped cases, were found to be in excellent agreement with typical examples of the experimentally-observed curves for the two fiber types. An expression is obtained for the coefficient of friction, which predicts the well-known experimental fact that, for most materials, the kinetic coefficient is less than the static. Reduction of Polymeric Friction by Minor Concentrations of Partially Fluorinated Compounds. R. C. Bowers, N. L. Jarvis and W. A. &man,
240 ness so found, the cone angle, and the yield stress is given. The results agree well with the indentation theory of Lockett based on classical slip line analysis. This shows that for a work-hardened material the hardness increases with increasing cone angle for cone angles above 105”. Lockett’s theory is degenerate below 105" and the experiments here also show a change in deformation mode in this region. Although this agreement with theory appears satisfactory, the deformation process appears to be substantially different from that implied in Lockett’s analysis. For large angle cones the deformation resembles a “radial” compression similar to that described by Samuels and Mulhearn: for small cone angles the deformation resembles more clearly the classical slip-line form given by Lockett, though this is precisely the region where the theory becomes degenerate. The effective strain produced by each cone during the indentation process itself is determined for each cone and it is shown that it is possible to construct the stress-strain curve of a given material from a series of cone indentations. On “Indenting with Pyramids”. (Letter to the editor.) A. G. Atkins and D Tabor, I&em. J. Mech. Sci., 7 (1965) 647-650; z figs., I table, 7 refs. The Deformation of Metals by Highvelocity Impact. J. H. Brunton, J. E. Field, G. P. Thomas and M. P. W. Wilson, 5th Plansee Proc. 1964, pp. 137-148; rr figs., 8 refs. The Friction and Hardness of Refractory Compounds. C. A. Brookes and A. G. Atkins, 5th Plansee Proc. 1964, pp. 712-721; 8 figs., 12 refs. 2. FRICTION Change in the Shape of the Surface of Contact between a Rigid Sphere and an Elastic Plane during Sliding Friction. P. Ya. Sukiennik, Soviet Phys.-Doklady, 9 (8) (1965) 700-702. (Transl. Doklady Akad. 1Vauk
SSSR, 157 (4) (1964) 84g-851 by American Institute of Physics, New York, N.Y.) For abstract see Appl. Mech. Rev., 18 (9) (1965) 779; see also Wear, 8 (1965) 30. 408. Torsional Instability tions. J. D. Kemper, J.
from
Franklin
(1965) 254-267. For
abstract
Frictional
see Appl.
Inst.,
Oscilla-
,279 (4)
Mech. Rev., 18 (IO)
(1965) 864. Friction-induced C. A. Brockley,
Vibration. R. Cameron
and A. F. Potter, Trans. ASME, Paper No. 65-Lub-5, 7 pp.; 8 figs., 2 tables, 12 refs. Wear, 9 (1966) 239-247
AND
CURRENT
EVENTS
Friction-induced vibration has been studied in a system consisting of an elastically suspended, damped slider which is loaded against a surface moving at a constant velocity. Exact analysis reveals a critical velocity which limits the incidence of vibration. The critical velocity depends on damping, load, stiffness, and friction characteristics which vary with time and velocity. Approximations in the theory yield an amplitudevelocity equation and another critical velocity relationship. Reasonable agreement is found to exist between the exact and approximate theories for critical velocity. Experimental results for several systems illustrate amplitude- velocity relationships and the existence of critical velocities. The correlation between the experimental results and the approximate theory indicates that the analytical method could be used to predict the vibration behavior of actual systems. On Testing Glass for Surface Friction. L. N. Kopytov, Ind. Lab., 30 (2) (1964) 2g2293. (Transl. Zavod. Lab., 30 (2) (1964) 231~ 232 by Instruments Society of America. Pittsburgh, Pa.) For abstract see Appl. Mech. Rev., r8 (IO) (1965) 818. Velocity Dependence during the Stick-slip Process in the Surface Friction of Fibrous Polymers.
W. J. Lyons and S. C. Scheier, J. Appl. Phys., 36 (6) (1965) 2020~2023; 5 figs., IO refs. Examination of chart tracings representing frictional force during the slip phase of the stick-slip process, in fibers of two polymer types, revealed that these tracings do not have the sinusoidal character associated with a constant coefficient of kinetic friction. Considerations of the dynamics of the system of fiber surface and measuring instrument led to the suggestion that a velocity-dependent term be introduced into the equation of motion of the slider. The new force represented by this term was assumed to be directly proportional to the velocity of the slider. Curves for the displacement of the slider as a function of time, based on solutions of the modified equation of motion, for both the underdamped and overdamped cases, were found to be in excellent agreement with typical examples of the experimentally-observed curves for the two fiber types. An expression is obtained for the coefficient of friction, which predicts the well-known experimental fact that, for most materials, the kinetic coefficient is less than the static. Reduction of Polymeric Friction by Minor Concentrations of Partially Fluorinated Compounds. R. C. Bowers, N. L. Jarvis and W. A. &man,