Steady-State Frictional Sliding of Two Elastic Bodies With a Wavy Contact Interface

2000 ◽  
Vol 122 (3) ◽  
pp. 490-495 ◽  
Author(s):  
M. Nosonovsky ◽  
G. G. Adams
Keyword(s):  
Steady State ◽  
Friction Coefficient ◽  
Jacobi Polynomials ◽  
Integral Transform ◽  
Theory Of Elasticity ◽  
Sliding Velocity ◽  
Zone Length ◽  
Frictional Sliding ◽  
Flat Surfaces ◽  
Elastic Bodies

Dry frictional sliding of two elastic bodies, one of which has a periodic wavy surface, is considered. Such a model represents the frictional sliding of two nominally flat surfaces, one of which has periodically spaced asperities. The dependence of the true contact area on loading is analyzed by using the plane strain theory of elasticity. Fourier series and integral transform techniques are applied to reduce the problem to an integral equation which is solved using a series of Jacobi polynomials. For steady-state dynamic frictional sliding with given values of the friction coefficient, materials constants, and sliding velocity, the dependence of the contact zone length on the remotely applied tractions is determined. The results indicate a decrease of the minimum applied traction required to close the gap between the bodies, with an increase of the friction coefficient and/or the sliding velocity. A resonance exists as the sliding velocity approaches the Rayleigh wave speed of the flat body. [S0742-4787(00)01403-X]

Grinding Process Size Effect and Kinematics Numerical Analysis

1999 ◽  
Vol 122 (1) ◽  
pp. 59-69 ◽  
Author(s):  
William L. Cooper ◽  
Adrienne S. Lavine
Keyword(s):  
Steady State ◽  
Removal Rate ◽  
Empirical Relationship ◽  
Three Dimensional ◽  
Depth Of Cut ◽  
Grinding Process ◽  
Zone Length ◽  
Abrasive Grains ◽  
Three Dimensional Modeling ◽  
Stock Removal

The present work developed numerical codes that simulate steady-state grinding process kinematics. The three-dimensional modeling procedure entails the following: specifying the sizes, shapes, and positions of individual abrasive grains on the wheel surface; geometrically calculating the abrasive grains’ depth of cut distributions along the grinding zone as they pass through the grinding zone (neglecting wheel, abrasive grain, and workpiece deflections); using an empirical relationship to relate the abrasive grains’ geometric depths of cut to the grains’ actual depths of cut; and updating the workpiece surface to account for material removal. The resulting data include the abrasive grains’ average depth of cut distribution along the grinding zone, stock removal depth, stock removal rate, grinding zone shape, grinding zone length, percentage of grains impacting the workpiece, grain-workpiece impact frequency, etc. The calculated grinding zone lengths compare favorably with experimental data. This article examines a number of steady-state grinding processes. [S1087-1357(00)00101-5]

Viscous Friction Effect During the Process of Tightening and Loosening of Bolted Joints

2021 ◽  
Author(s):  
Qingyuan Lin ◽  
Yong Zhao ◽  
Qingchao Sun ◽  
Kunyong Chen
Keyword(s):  
Friction Coefficient ◽  
Viscous Friction ◽  
Normal Pressure ◽  
Friction Model ◽  
Bolted Joints ◽  
Critical Parameters ◽  
Bolted Joint ◽  
Sliding Velocity ◽  
Friction Effect ◽  
Bearing Friction

Abstract Bolted connection is one of the most widely used mechanical connections because of its easiness of installation and disassembly. Research of bolted joints mainly focuses on two aspects: high precision tightening and improvement of anti-loosening performance. The under-head bearing friction coefficient and the thread friction coefficient are the two most important parameters that affect the tightening result of the bolted joint. They are also the most critical parameters that affect the anti-loosening performance of the bolted joint. Coulomb friction model is a commonly used model to describe under-head bearing friction and thread friction, which considers the friction coefficient as a constant independent of normal pressure and relative sliding velocity. In this paper, the viscous effect of the under-head bearing friction and thread friction is observed by measuring the friction coefficient of bolted joints. The value of the friction coefficient increases with the increase of the relative sliding velocity and the decrease of the normal pressure. It is found that the Coulomb viscous friction model can better describe the friction coefficient of bolted joints. Taking into account the dense friction effect, the loosening prediction model of bolted joints is modified. The experimental results show that the Coulomb viscous friction model can better describe the under-head bearing friction coefficient and thread friction coefficient. The model considering the dense effect can more accurately predict the loosening characteristics of bolted joints.

Vibration Instability in a Large Motion Bistable Compliant Mechanism Due to Stribeck Friction

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Alborz Niknam ◽  
Kambiz Farhang
Keyword(s):  
Steady State ◽  
Compliant Mechanism ◽  
Equilibrium Points ◽  
Body Representation ◽  
Sliding Velocity ◽  
Normal Contact ◽  
Stribeck Effect ◽  
State Response ◽  
Excited Vibration ◽  
Large Motion

The present paper investigates friction-induced self-excited vibration of a bistable compliant mechanism. A pseudo-rigid-body representation of the mechanism is used containing a hardening nonlinear spring and a viscous damper. The mass is suspended from above with the spring-damper combination leading to the addition of geometric nonlinearity in the equation of motion and position- and velocity-dependent normal contact force. Friction input provided by a moving belt in contact with the mass. An exponentially decaying function of sliding velocity describes the friction coefficient and, thereby, incorporates Stribeck effect of friction. Eigenvalue analysis is employed to investigate the local stability of the steady-state fixed points. It is observed that the oscillator experiences pitchfork and Hopf bifurcations. The effects of the spring nonlinearity and precompression, viscous damping, belt velocity, and the applied normal force on the number, position, and stability of the equilibrium points are investigated. Global system behavior is studied by establishing trajectory maps of the system. Critical belt speed is derived analytically and shown to be only the result of Stribeck effect of friction. It is found that one equilibrium point dominates the steady-state response for very low damping and negligible spring nonlinearity. The presence of damping and/or spring nonlinearity tends to diminish this dominance.

Equivalent Circuits of the Elastic Field

1944 ◽  
Vol 11 (3) ◽  
pp. A149-A161
Author(s):  
Gabriel Kron
Keyword(s):  
Steady State ◽  
Reference Frames ◽  
Three Dimensional ◽  
Elastic Field ◽  
Companion Paper ◽  
Theory Of Elasticity ◽  
Equivalent Circuits ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Nonlinear Stress

Abstract This paper presents equivalent circuits representing the partial differential equations of the theory of elasticity for bodies of arbitrary shapes. Transient, steady-state, or sinusoidally oscillating elastic-field phenomena may now be studied, within any desired degree of accuracy, either by a “network analyzer,” or by numerical- and analytical-circuit methods. Such problems are the propagation of elastic waves, determination of the natural frequencies of vibration of elastic bodies, or of stresses and strains in steady-stressed states. The elastic body may be non-homogeneous, may have arbitrary shape and arbitrary boundary conditions, it may rotate at a uniform angular velocity and may, for representation, be divided into blocks of uneven length in different directions. The circuits are developed to handle both two- and three-dimensional phenomena. They are expressed in all types of orthogonal curvilinear reference frames in order to simplify the boundary relations and to allow the solution of three-dimensional problems with axial and other symmetry by the use of only a two-dimensional network. Detailed circuits are given for the important cases of axial symmetry, cylindrical co-ordinates (two-dimensional) and rectangular co-ordinates (two- and three-dimensional). Nonlinear stress-strain relations in the plastic range may be handled by a step-by-step variation of the circuit constants. Nonisotropic bodies and nonorthogonal reference frames, however, require an extension of the circuits given. The circuits for steady-state stress and small oscillation phenomena require only inductances and capacitors, while the circuits for transients require also standard (not ideal) transformers. A companion paper deals in detail with numerical and experimental methods to solve the equivalent circuits.

Desirability of Tribo-Performance of Natural Based Thermoset and Thermoplastic Composites: A Concise Review

2021 ◽  
Author(s):  
Aravind Dhandapani ◽  
Senthilkumar Krishnasamy ◽  
Thitinun Ungtrakul ◽  
Senthil Muthu Kumar Thiagamani ◽  
Rajini Nagarajan ◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Wear Rate ◽  
Relative Motion ◽  
Operating Temperature ◽  
Natural Fibers ◽  
Specific Wear Rate ◽  
Thermoplastic Composites ◽  
Sliding Velocity ◽  
Concise Review ◽  
Sliding Distance

Tribology, which may be defined as an interdisciplinary subject, deals with relative motion between two or more bodies, i.e., surfaces that are interacting relatively. Thus, tribology is a science covering three vital classes, namely, 1) wear, 2) friction, and 3) lubrication. The focus of this article is to bring out the elements that are influencing the wear-resisting behavior of thermosetting and thermoplastic composites with natural-based constituents. It was also identified from the literature sources that 1) the treatments on the natural fibers acting as reinforcement and 2) the addition of fillers in resin acting as matrix could improve the wear-resisting behavior of the composites. Additionally, other conditions such as 1) sliding speed, 2) sliding velocity, 3) sliding distance, and 4) operating temperature could also influence the friction coefficient and specific wear rate of the natural-based composites.

Axisymmetric Thermal Stresses in a Spherical Shell of Arbitrary Thickness

1957 ◽  
Vol 24 (3) ◽  
pp. 376-380
Author(s):  
E. L. McDowell ◽  
E. Sternberg
Keyword(s):  
Steady State ◽  
Spherical Shell ◽  
Spherical Cavity ◽  
Series Solution ◽  
Thermal Stresses ◽  
Solid Sphere ◽  
Theory Of Elasticity ◽  
Infinite Medium ◽  
Series Solutions ◽  
Arbitrary Thickness

Abstract This paper contains an explicit series solution, exact within the classical theory of elasticity, for the steady-state thermal stresses and displacements induced in a spherical shell by an arbitrary axisymmetric distribution of surface temperatures. The corresponding solutions for a solid sphere and for a spherical cavity in an infinite medium are obtained as limiting cases. The convergence of the series solutions obtained is discussed. Numerical results are presented appropriate to a solid sphere if two hemispherical caps of its boundary are maintained at distinct uniform temperatures.

scholarly journals Variation patterns of landslide basal friction revealed from long-period seismic waveform inversion

2019 ◽  
Vol 100 (1) ◽  
pp. 313-327
Author(s):  
Dan Yu ◽  
Xinghui Huang ◽  
Zhengyuan Li
Keyword(s):  
Steady State ◽  
Friction Coefficient ◽  
Water Waves ◽  
Waveform Inversion ◽  
Time History ◽  
Seismic Signals ◽  
Long Period ◽  
Basal Friction ◽  
Seismic Waveform ◽  
Variation Patterns

Abstract A catastrophic landslide struck the Xiaoba village in Fuquan, Guizhou, southwestern China at about 8:30 p.m. (Beijing Time, UTC + 8) on August 27, 2014. The landslide and induced impulse water waves destroyed two villages and killed 23 persons. By reprocessing seismic signals from a seismic network deployed in the surrounding area of the landslide, we recognized the event from low-frequency seismic signals and subsequently performed a long-period seismic waveform inversion to obtain its force–time history. The inversion results reveal that the maximum force for the landslide is 5 × 109 N, and the duration of the landslide is 38.4 s. The landslide reached its maximum velocity of 12.4 m/s at 13.2 s after its initiation, and the mass center plugged into the quarry at 24.2 s. Based on the inversion results, we estimated basal friction of the landslide. We found the friction coefficient rapidly reduces to a relatively steady-state value of ~ 0.4 at a steady-state distance of 35 m and subsequently reduces in a near-linear manner that satisfies the empirical formula $$ \mu = - 1.4d + 0.44 $$μ=-1.4d+0.44, where $$ d $$d is sliding distance in km. The reduction in friction revealed by the formula is compatible with the finding of previous studies for landslides of similar volume in landslide acceleration stage. However, our result does not make it possible for the friction coefficient to increase again in landslide deceleration stage that a velocity-dependent friction law would allow. The friction variation patterns can be used to constrain input parameters in numerical landslide simulation, which can predicate runout distance and deposit areas for massive landslides to carry out landslide hazard assessment.

Friction Coefficient and Wear Rate of Different Materials Sliding Against Stainless Steel

2013 ◽  
Vol 1 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Dewan Muhammad Nuruzzaman ◽  
Mohammad Asaduzzaman Chowdhury
Keyword(s):  
Stainless Steel ◽  
Friction Coefficient ◽  
Wear Rate ◽  
Normal Load ◽  
304 Stainless Steel ◽  
Sliding Velocity ◽  
Stainless Steel 304 ◽  
Different Types ◽  
Pin On Disc ◽  
Ss 304

This paper examines the relation between friction/wear and different types of steel materials under different normal loads and sliding velocities and to explore the possibility of adding controlled normal load and sliding velocity to a mechanical process. In order to do so, a pin on disc apparatus is designed and fabricated. Experiments are carried out when different types of disc materials such as stainless steel 304 (SS 304), stainless steel 316 (SS 316) and mild steel slide against stainless steel 304 (SS 304) pin. Variations of friction coefficient with the duration of rubbing at different normal loads and sliding velocities are investigated. Results show that friction coefficient varies with duration of rubbing, normal load and sliding velocity. In general, friction coefficient increases for a certain duration of rubbing and after that it remains constant for the rest of the experimental time. The obtained results reveal that friction coefficient decreases with the increase in normal load for all the tested materials. It is also found that friction coefficient increases with the increase in sliding velocity for all the materials investigated. Moreover, wear rate increases with the increase in normal load and sliding velocity. At identical operating condition, the magnitudes of friction coefficient and wear rate are different for different materials depending on sliding velocity and normal load.

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