Sliding of a solid body supported by a circular area on a horizontal plane with orthotropic friction. Part 3. Pressure distribution following the Hertzian law

Dmitriev, N. N.

doi:10.3103/s1068366610040021

Cited by 3 publications

(7 citation statements)

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“…The same results are achieved using method described in [], which reduces the problem into the solution of this system:

\begin{matrix} true \\ right T_{n} (β^{*}, ϑ^{*}) & left = 0, \\ right β^{*} - \frac{I T_{τ} (β^{*}, ϑ^{*})}{M_{O z} (β^{*}, ϑ^{*})} & left = 0 . \end{matrix}

For both

μ_{+} = 0.12

and

μ_{+} = 0.24

value of parameter

β (t)

at the end of the motion is higher in case of friction asymmetry. The variation in final values is more than 30%. However, the main difference is seen in the behavior of

ϑ (t)

.…”

Section: Resultsmentioning

confidence: 94%

“…There is some value of

μ_{+}

when the solution of the system will give us

ϑ^{*}

in the third quadrant, but

β^{*} \to \infty

. In [] for symmetric orthotropic friction the interrelations between inertia moment and coefficients of friction leading to

β^{*} \to \infty

and

β^{*} = 0

were achieved analytically.…”

Section: Resultsmentioning

confidence: 99%

“…Using Equations and elementary friction force is obtained in the following form:

bold-italicτ = - p [f_{x} false(ϑ, γ false) cos false(ϑ + γ false) i + f_{y} false(ϑ, γ false) sin false(ϑ + γ false) j],

comparing to [] friction coefficients here are functions of

ϑ, γ

.…”

Section: Asymmetric Friction Force and Momentmentioning

confidence: 99%

“…One is able to integrate Equations – over r . Integrating the derived equations over γ, if G is located outside the contact area leads to the following:

0true T_{x} = - p_{0} R^{2} \sum_{ν} f_{x ν} {[prefixcos ϑ G_{1}^{e x t} (β, γ) - prefixsin ϑ G_{2}^{e x t} (β, γ)]}_{γ_{i ν}}^{γ_{j ν}},

0true T_{y} = - p_{0} R^{2} \sum_{ν} f_{y ν} {[prefixsin ϑ G_{1}^{e x t} (β, γ) + prefixcos ϑ G_{2}^{e x t} (β, γ)]}_{γ_{i ν}}^{γ_{j ν}},

\begin{matrix} true \\ right M_{G z} & = & left - \frac{p_{0} R^{3} π}{32} \sum_{ν} [{sin}^{3} 2 γ prefixcos 2 ϑ \frac{5 μ_{ν} β^{4}}{12} + γ (() \frac{1}{2} (f_{x ν} + \frac{μ_{ν}}{2}) false(8 - β^{4} + 8 β^{2} false) - \frac{μ_{ν}}{2} cos 2 ϑ β^{2} false(6 - β^{2} false)) \\ left + prefixsin 2 γ ((), -) \end{matrix}

…”

Section: Asymmetric Friction Force and Momentmentioning

confidence: 99%

“…The friction force is asymmetric orthotropic and is defined in the frame of Amontons‐Coulomb law. Motion of a solid body with circular contact area on a plane surface assuming symmetric orthotropic friction was studied with Hertz pressure distribution in [] and with Boussinesq pressure law in []. Impact of inertia moment and friction coefficients relations was demonstrated.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A study of sliding motion of a solid body on a surface with asymmetric friction*

Silantyeva

Dmitriev

2018

Z Angew Math Mech

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Recent studies show growing interest in materials with asymmetric friction forces. We investigate terminal motion of a solid body with a circular contact area. Assuming that friction forces are asymmetric orthotropic, we consider Hertz and Boussinesq laws for pressure distribution. Equations for friction force and moment are formulated and solved for both cases. Numerical examples demonstrate significant impact of the asymmetry of friction on the motion. Our results can be used for more accurate prediction of contact behavior for bodies made of new materials with asymmetric surface textures.

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“…The same results are achieved using method described in [], which reduces the problem into the solution of this system:

\begin{matrix} true \\ right T_{n} (β^{*}, ϑ^{*}) & left = 0, \\ right β^{*} - \frac{I T_{τ} (β^{*}, ϑ^{*})}{M_{O z} (β^{*}, ϑ^{*})} & left = 0 . \end{matrix}

For both

μ_{+} = 0.12

and

μ_{+} = 0.24

value of parameter

β (t)

at the end of the motion is higher in case of friction asymmetry. The variation in final values is more than 30%. However, the main difference is seen in the behavior of

ϑ (t)

.…”

Section: Resultsmentioning

confidence: 94%

“…There is some value of

μ_{+}

when the solution of the system will give us

ϑ^{*}

in the third quadrant, but

β^{*} \to \infty

. In [] for symmetric orthotropic friction the interrelations between inertia moment and coefficients of friction leading to

β^{*} \to \infty

and

β^{*} = 0

were achieved analytically.…”

Section: Resultsmentioning

confidence: 99%

“…Using Equations and elementary friction force is obtained in the following form:

bold-italicτ = - p [f_{x} false(ϑ, γ false) cos false(ϑ + γ false) i + f_{y} false(ϑ, γ false) sin false(ϑ + γ false) j],

comparing to [] friction coefficients here are functions of

ϑ, γ

.…”

Section: Asymmetric Friction Force and Momentmentioning

confidence: 99%

“…One is able to integrate Equations – over r . Integrating the derived equations over γ, if G is located outside the contact area leads to the following:

0true T_{x} = - p_{0} R^{2} \sum_{ν} f_{x ν} {[prefixcos ϑ G_{1}^{e x t} (β, γ) - prefixsin ϑ G_{2}^{e x t} (β, γ)]}_{γ_{i ν}}^{γ_{j ν}},

0true T_{y} = - p_{0} R^{2} \sum_{ν} f_{y ν} {[prefixsin ϑ G_{1}^{e x t} (β, γ) + prefixcos ϑ G_{2}^{e x t} (β, γ)]}_{γ_{i ν}}^{γ_{j ν}},

\begin{matrix} true \\ right M_{G z} & = & left - \frac{p_{0} R^{3} π}{32} \sum_{ν} [{sin}^{3} 2 γ prefixcos 2 ϑ \frac{5 μ_{ν} β^{4}}{12} + γ (() \frac{1}{2} (f_{x ν} + \frac{μ_{ν}}{2}) false(8 - β^{4} + 8 β^{2} false) - \frac{μ_{ν}}{2} cos 2 ϑ β^{2} false(6 - β^{2} false)) \\ left + prefixsin 2 γ ((), -) \end{matrix}

…”

Section: Asymmetric Friction Force and Momentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A study of sliding motion of a solid body on a surface with asymmetric friction*

Silantyeva

Dmitriev

2018

Z Angew Math Mech

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show abstract

Harmonic expansion and nonsmooth dynamics in a circular contact region with combined slip-spin motion

Antali

2024

Nonlinear Dyn

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We analyse a rigid body in planar motion while touching a rough plane at a finite-sized, circular contact area. Assuming Coulomb friction between the tangential and normal pressure distributions, the resultant forces and torques can be expressed formally with a nonsmooth dependence on the kinematic variables. In the literature, the exact form of the tangential forces is available for special pressure distributions expressed by transcendent functions; recently, an approximate linear model was introduced. Now, we present a nonlinear extension of the approximation, which can be used effectively to characterise slipping-sticking transitions between the bodies.

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On the Motion of an Axisymmetric Rigid Body Supported at a Horizontal Plane under Conditions of Orthotropic, Dynamically Consistent Friction

Dmitriev

2022

Mech. Solids

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Sliding of a solid body supported by a circular area on a horizontal plane with orthotropic friction. Part 3. Pressure distribution following the Hertzian law

Cited by 3 publications

References 0 publications

A study of sliding motion of a solid body on a surface with asymmetric friction*

A study of sliding motion of a solid body on a surface with asymmetric friction*

Harmonic expansion and nonsmooth dynamics in a circular contact region with combined slip-spin motion

On the Motion of an Axisymmetric Rigid Body Supported at a Horizontal Plane under Conditions of Orthotropic, Dynamically Consistent Friction

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