On the Dynamics of the Rigid Body Lying on the Vibrating Table with the Use of Special Approximations of the Resulting Friction Forces

2016 ◽  
pp. 351-360
Author(s):  
Michał Szewc ◽  
Grzegorz Kudra ◽  
Jan Awrejcewicz
Keyword(s):  
Rigid Body ◽  
Friction Forces ◽  
Vibrating Table

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

On Some Problems With Modeling of Coulomb Friction in Self-Locking Speed Reducers

2014 ◽  
Author(s):  
Marek Wojtyra
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Equations Of Motion ◽  
Velocity Ratio ◽  
Friction Forces ◽  
Friction Law ◽  
Rigid Body Model ◽  
Feasible Sets ◽  
Unstable Solutions ◽  
Coulomb Friction Law

A simple mathematical model of friction in speed reducers is presented and discussed. A rigid body approach, typical for multibody simulations, is adopted. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms. The first version of the model is purely rigid, i.e. no deflections of the mechanism bodies are allowed. Constraints are introduced to maintain the ratio between input and output velocity. It is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, coefficient of friction and inertial parameters) two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints and Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Examples of all indicated paradoxical situations are provided and discussed. The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input-output velocity ratio are introduced). In non-paradoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previously paradoxical situations no multiple solutions of friction force are found, however, the amended model does not solve all problems. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. Numerical examples showing behavior of the model are provided and analyzed.

On the identification of a single body immersed in a Navier-Stokes fluid

2007 ◽  
Vol 18 (1) ◽  
pp. 57-80 ◽  
Author(s):  
A. DOUBOVA ◽  
E. FERNÁNDEZ-CARA ◽  
J. H. ORTEGA
Keyword(s):  
Inverse Problem ◽  
Rigid Body ◽  
Stokes Equations ◽  
Outer Boundary ◽  
Unique Continuation ◽  
Uniqueness Result ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Friction Forces ◽  
Regularity Results

In this work we consider the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Navier-Stokes equations. It is assumed that friction forces are known on a part of the outer boundary. We first prove a uniqueness result. Then, we establish a formula for the observed friction forces, at first order, in terms of the deformation of the rigid body. In some particular situations, this provides a strategy that could be used to compute approximations to the solution of the inverse problem. In the proofs we use unique continuation and regularity results for the Navier-Stokes equations and domain variation techniques.

scholarly journals Sliding-vibrating responses of elastic structures

1988 ◽  
Vol 21 (3) ◽  
pp. 190-197
Author(s):  
Yu-An Fu
Keyword(s):  
Rigid Body ◽  
Harmonic Excitation ◽  
Body Motion ◽  
Shake Table ◽  
Reciprocating Motion ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Analytical Expressions ◽  
Vibrating Response

By using simulated friction forces, analytical expressions were derived from the sliding-vibrating response of a single degree of freedom system under harmonic excitation or the "disadvantageous period reciprocating motion", taking the mass of the sliding base into consideration. Some of the general laws were studied and some new characteristics determined which had previously been ignored by assuming rigid body motion. The analysis methods adopted in this paper have been confirmed in comparison with the results of model tests on a shake table.

Dynamic Modeling and Experimental Testing of a Piano Action Mechanism

2005 ◽  
Vol 1 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Martin Hirschkorn ◽  
John McPhee ◽  
Stephen Birkett
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Experimental Testing ◽  
Individual Action ◽  
Action Mechanism ◽  
Friction Forces ◽  
Multibody Dynamic ◽  
Main Action ◽  
Grand Piano

A model for a grand piano action is proposed in this paper. The multibody dynamic model treats each of the five main action components (key, whippen, jack, repetition lever, and hammer) as a rigid body, and incorporates a contact model to determine the normal and friction forces at 13 locations between each of the contacting bodies. All parameters in the model are directly measured from experiments on individual action components, allowing the model to be used as a prototyping tool for actions that have not yet been designed or built. The behavior of the model was compared to the behavior of an experimental grand piano action and found to be very accurate for high force blows, and reasonably accurate for low force blows.

Kinematic Error Analysis of Parallel Machine Tool Based on Rigid Body Dynamics

2015 ◽  
Vol 743 ◽  
pp. 71-78
Author(s):  
Xiao Gang Chen ◽  
Zhao Tang Xu ◽  
Hai Bing Wu
Keyword(s):  
Rigid Body ◽  
Machine Tool ◽  
Parallel Machine ◽  
Position Error ◽  
Rigid Body Dynamics ◽  
Friction Forces ◽  
Analytical Expression ◽  
Body Dynamics ◽  
Position And Orientation ◽  
Parallel Machine Tool

To estimate influence of velocity on kinematic accuracy for a cross-linked Stewart type Parallel Machine Tool, position and orientation errors of the moving tool platform are researched. Based on rigid body dynamics, inertial and friction forces and moments are considered. Firstly, analytical expression of driving force is derived for each link. Secondly, change of length is derived using Hooke’s Law for each link. Then mapping matrix between change of link length and change of platform position and orientation is derived based on both Euler angle and revolving angle around a spatial axis. Finally, analytical expression of position and orientation errors of the moving platform is derived. Figures of distribution of position and orientation errors in workspace under two velocities are obtained respectively. The results show that, in frequently used workspace, all of the three components of position error are less than 3.5μm. All of them increase with z coordinate of platform center. Position error is influenced slightly by velocity. The difference of position error between two velocities is less than 2%.

On Some Problems With Modeling of Coulomb Friction in Self-Locking Mechanisms

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
Marek Wojtyra
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Coulomb Friction ◽  
Kinetic Regime ◽  
Friction Forces ◽  
Friction Law ◽  
Joint Friction ◽  
Body Model ◽  
Rigid Body Model ◽  
Coulomb Friction Law

Friction significantly influences the mechanical system dynamics, especially when self-locking property is observed. The Coulomb model is frequently adopted to represent friction in multibody analysis and simulation. It can be shown that in some extreme cases of joint friction modeling, problems with solution uniqueness and existence are encountered, even when only bilateral constraints and kinetic regime of friction are considered. These problems are studied in detail in the paper. To approach the investigated subject, a wedge mechanism, viewed as a simplified model of a speed reducer, is studied. Two different mathematical models of joint friction are used, both based on the Coulomb friction law. The first version of the model is purely rigid, i.e., no deflections of the mechanism bodies are allowed. Constraints are imposed to maintain the ratio between input and output velocity. The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input–output velocity ratio). Using the rigid body model, it is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, friction coefficient, and inertial parameters), two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints, and the Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Investigation of the flexible body model reveals that in nonparadoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previous paradoxical situations, no multiple solutions are found; however, problems with stability of solutions emerge. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. The origins of paradoxical behavior are identified and discussed. The key factors determining the model performance are pointed out. Examples of all indicated problematic situations are provided and analyzed. Finally, the investigated problems are commented from more general perspectives of multibody system dynamics.

Dynamic Modelling and Experimental Testing of a Piano Action Mechanism

2005 ◽  
Author(s):  
Martin C. Hirschkorn ◽  
John McPhee ◽  
Stephen Birkett
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Experimental Testing ◽  
Dynamic Modelling ◽  
Individual Action ◽  
Action Mechanism ◽  
Friction Forces ◽  
Multibody Dynamic ◽  
Main Action ◽  
Grand Piano

A new model for a grand piano action is proposed in this paper. The multibody dynamic model treats each of the five main action components (key, whippen, jack, repetition lever, and hammer) as a rigid body, and incorporates a contact model to determine the normal and friction forces at 13 locations between each of the contacting bodies. All parameters in the model are directly measured from experiments on individual action components, allowing the model to be used as a prototyping tool for actions that have not yet been designed or built. The behaviour of the model was compared to the behaviour of an experimental grand piano action and found to be very accurate for high force blows, and reasonably accurate for low force blows.

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