scholarly journals Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
W. J. Stronge
Keyword(s):  
Energy Dissipation ◽  
Equations Of Motion ◽  
Oblique Impact ◽  
Rigid Bodies ◽  
Contact Period ◽  
Analytical Mechanics ◽  
Normal Contact ◽  
System Of Rigid Bodies ◽  
Energy Gains ◽  
The Impact

Analytical mechanics is used to derive original 3D equations of motion that represent impact at a point in a system of rigid bodies. For oblique impact between rough bodies in an eccentric (unbalanced) configuration, these equations are used to compare the calculations of energy dissipation obtained using either the kinematic, the kinetic, or the energetic coefficient of restitution (COR); eN,eP, or e*. Examples demonstrate that for equal energy dissipation by nonfrictional sources, either eN≤e*≤eP or eP≤e*≤eN depending on whether the unbalance of the impact configuration is positive or negative relative to the initial direction of slip. Consequently, when friction brings initial slip to rest during the contact period, calculations that show energy gains from impact can result from either the kinematic or the kinetic COR. On the other hand, the energetic COR always correctly accounts for energy dissipation due to both hysteresis of the normal contact force and friction, i.e., it is energetically consistent.

High-Fidelity Modeling of a Backhoe Digging Operation Using an Explicit Multibody Dynamics Code With Integrated Discrete Particle Modeling Capability

2013 ◽  
Author(s):  
Shahriar G. Ahmadi ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Multibody Dynamics ◽  
Search Algorithm ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Friction ◽  
Contact Detection ◽  
High Fidelity ◽  
Normal Contact ◽  
Contact Search

A high-fidelity multibody dynamics model for simulating a backhoe digging operation is presented. The backhoe components including: frame, manipulator, track, wheels and sprockets are modeled as rigid bodies. The soil is modeled using cubic shaped particles for simulating sand with appropriate inter-particle normal and frictional forces. A penalty technique is used to impose both joint and normal contact constraints (including track-wheels, track-terrain, bucket-particles and particles-particles contact). An asperity-based friction model is used to model joint and contact friction. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm is used to allow fast contact detection between polygonal contact surfaces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model can help improve the performance of construction equipment by predicting the actuator and joint forces and the vehicle stability during digging for various vehicle design alternatives.

Rigid body collisions with friction

1990 ◽  
Vol 431 (1881) ◽  
pp. 169-181 ◽  
Keyword(s):  
Energy Dissipation ◽  
Rigid Body ◽  
Rigid Bodies ◽  
Consistent Theory ◽  
Contact Points ◽  
Collision Processes ◽  
Inconsistent Theory ◽  
The Impact ◽  
Impact Hypothesis ◽  
Alternative Theories

An energetically consistent theory is presented for dynamics of partly elastic collisions between somewhat rough rigid bodies with friction that opposes slip. This theory is based on separately accounting for frictional and non-frictional sources of dissipation. Alternative theories derived from Newton’s impact law or Poisson’s impact hypothesis are shown to be valid only for central (collinear) or non-frictional collisions; generally the latter theories yield erroneous energy dissipation if small initial slip stops during collision between eccentric bodies. Collision processes are complex when small slip is stopped by friction; then either the direction of slip reverses or contact points roll without slip. An inconsistent theory based on Newton’s impact law can yield erroneous energy increases when slip stops during collision; the consistent theory always dissipates energy. The impact law that specifies a simple proportionality between normal components of contact velocity for incidence and rebound is not applicable in any range of incident velocities with small slip if the collision is non-collinear with friction. In Percussion the force or Impetus whereby one body is moved may cause another body against which it strikes to be put in motion, and withal lose some of its strength or swiftness. (J. Wallis, 1668)

A geometrical interpretation of Kane’s Equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 69-87 ◽  
Keyword(s):  
Tangent Space ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Analytical Mechanics ◽  
Kane’S Method ◽  
Kane's Method ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Spanning Set ◽  
Geometric Picture

The method for the development of the equations of motion for systems of constrained particles and rigid bodies, developed by T. R. Kane and called Kane’s Equations, is discussed from a geometric viewpoint. It is shown that what Kane calls partial velocities and partial angular velocities may be interpreted as components of tangent vectors to the system’s configuration manifold. The geometric picture, when attached to Kane’s formalism shows that Kane’s Equations are projections of the Newton-Euler equations of motion onto a spanning set of the configuration manifold’s tangent space. One advantage of Kane’s method, is that both non-holonomic and non-conservative systems are easily included in the same formalism. This easily follows from the geometry. It is also shown that by transformation to an orthogonal spanning set, the equations can be diagonalized in terms of what Kane calls the generalized speeds. A further advantage of the geometric picture lies in the treatment of constraint forces which can be expanded in terms of a spanning set for the orthogonal complement of the configuration tangent space. In all these developments, explicit use is made of a concrete realization of the multidimensional vectors which are called K -vectors for a K -component system. It is argued that the current presentation also provides a clear tutorial route to Kane’s method for those schooled in classical analytical mechanics.

Dynamic modeling and simulation of impact in hydraulic cylinders

2020 ◽  
pp. 095440622098047
Author(s):  
Osama Gad
Keyword(s):  
Contact Force ◽  
Dynamic Models ◽  
Maxwell Model ◽  
Hydraulic Cylinder ◽  
Rigid Bodies ◽  
Solid Model ◽  
Contact Period ◽  
Suitable Model ◽  
Hydraulic Cylinders ◽  
The Impact

In this paper, modeling impact dynamics of a piston and its cylinder body in a hydraulic cylinder is investigated. The studied system consists of two identical hydraulic cylinders controlled by a pressure sequence valve. The impact is assumed as a linear one dimensional and purely translational viscoelastic impact of rigid bodies. Four impact models, the Kelvin-Voigt, the Maxwell, the standard-solid, and the Hunt-Crossley, are considered. Measurements of the transient variations of the cylinders operating pressures and both pistons strokes, at different loading conditions, are conducted. A comprehensive dynamic model of the studied system, considering the four models, is deduced. The Kelvin-Voigt model produced tensile forces by the end of the contact period and it resulted in discontinuities in the contact force during its steady state period. Both results are physically impossible in rigid bodies impacting. In the Maxwell model, large amount of discontinuities appeared in the contact force, which causes the piston to make an infinite number of rebounds during the contact period. In the standard-solid model, the discontinuities in the contact force were found to be much less than those of the Maxwell model. As a result, when the impact occurs, the cylinder pressure gets an overshoot accompanied with large oscillations when the Maxwell model is applied, however, these oscillations do not approximately appear when the standard-solid model is applied. The simulation results showed also that the Hunt-Crossley nonlinear model presented very high penetration depth, which is certainly unrealistic in rigid bodies impacting. The validation of the proposed dynamic models showed that the standard-solid is the most suitable model that may represent the impact in the studied cylinders.

Impact With Friction

1986 ◽  
Vol 53 (1) ◽  
pp. 1-4 ◽  
Author(s):  
J. B. Keller
Keyword(s):  
Frictional Force ◽  
Equations Of Motion ◽  
Coefficient Of Restitution ◽  
Rigid Bodies ◽  
The Impact ◽  
Impact With Friction

A theory of the impact or collision of two rigid bodies, taking account of friction, is presented. It determines how the direction of sliding varies during the impact, which must be known to calculate the direction of the frictional force and thence the frictional impulse. This is accomplished by analyzing the equations of motion of the bodies during the collision. The normal impulse is determined by using a coefficient of restitution. When the direction of sliding is constant throughout the collision, the theory agrees with that given by Whittaker, which is correct only in this case.

Impact of a drop onto a wetted wall: description of crown formation and propagation

2002 ◽  
Vol 472 ◽  
pp. 373-397 ◽  
Author(s):  
I. V. ROISMAN ◽  
C. TROPEA
Keyword(s):  
Surface Tension ◽  
Liquid Film ◽  
Equations Of Motion ◽  
Liquid Films ◽  
Oblique Impact ◽  
High Impact ◽  
Momentum Balance ◽  
Single Drop ◽  
Crown Shape ◽  
The Impact

The impact of a drop onto a liquid film with a relatively high impact velocity, leading to the formation of a crown-like ejection, is studied theoretically. The motion of a kinematic discontinuity in the liquid film on the wall due to the drop impact, the formation of the upward jet at this kinematic discontinuity and its elevation are analysed. Four main regions of the drop and film are considered: the perturbed liquid film on the wall inside the crown, the unperturbed liquid film on the wall outside the crown, the upward jet forming a crown, and the free rim bounding this jet. The theory of Yarin & Weiss (1995) for the propagation of the kinematic discontinuity is generalized here for the case of arbitrary velocity vectors in the inner and outer liquid films on the wall. Next, the mass, momentum balance and Bernoulli equations at the base of the crown are considered in order to obtain the velocity and the thickness of the jet on the wall. Furthermore, the dynamic equations of motion of the crown are developed in the Lagrangian form. An analytical solution for the crown shape is obtained in the asymptotic case of such high impact velocities that the surface tension and the viscosity effects can be neglected in comparison to inertial effects. The edge of the crown is described by the motion of a rim, formed due to the surface tension.Three different cases of impact are considered: normal axisymmetric impact of a single drop, oblique impact of a single drop, and impact and interaction of two drops. The theoretical predictions of the height of the crown in the axisymmetric case are compared with experiments. The agreement is quite good in spite of the fact that no adjustable parameters are used.

Dynamic Analysis of Mechanisms Using Constrained Lagrangian Bond Graphs

1992 ◽  
Author(s):  
Y. A. Khulief
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Bond Graph ◽  
Rigid Bodies ◽  
Interconnected System ◽  
Lagrangian Equations ◽  
System Of Rigid Bodies ◽  
Reaction Forces ◽  
Bond Graph Modeling ◽  
Generalized Constraint

Abstract A method for dynamic analysis of mechanisms using the Lagrangian equations of motion for an interconnected system of rigid bodies is presented. The method stems from a recent extension to the bond graph modeling technique. Intrinsically, this approach allows the formulation of the final form of equations for holonomic systems without recourse to the Lagrangian function. Consequently, the burdens of deriving the expressions for kinetic and potential energies, and performing the necessary differentiations have been eliminated. This method calls only for constructing the Jacobian matrix of constraints, and then employing a bond graph that accounts for the generalized constraint reaction forces.

Hertz Contact Force Model With Permanent Indentation in Impact Analysis of Solids

1992 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Parviz E. Nikravesh
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Equations Of Motion ◽  
Solid Particles ◽  
Hertzian Contact ◽  
Contact Period ◽  
Force Model ◽  
Unknown Parameters ◽  
Contact Force Model ◽  
Energy And Momentum

Abstract A continuous analysis method for the direct-central impact of two solid particles is presented. Based on the assumption that local plasticity effects are the sole factor accounting for the dissipation of energy in impact, a Hertzian contact force model with permanent indentation is constructed. Utilizing energy and momentum considerations, the unknown parameters in the model are analytically evaluated in terms of a given coefficient of restitution and velocities before impact. The equations of motion of the two solids may then be integrated forward in time knowing the variation of the contact force during the contact period. For Illustration, an impact of two soft metallic particles is studied.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

SIMULATION OF DYNAMIC EVENT OF IMPACT USING EXPLICIT 3D FEM MODEL AND VALIDATION BY EXPERIMENT AND CONTACT MODELS

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Akshay Mallikarjuna ◽  
Dan Marghitu ◽  
P.K. Raju
Keyword(s):  
Material Properties ◽  
Permanent Deformation ◽  
Oblique Impact ◽  
Coefficient Of Restitution ◽  
Impact Behavior ◽  
3D Fem ◽  
Dynamic Event ◽  
Contact Models ◽  
Explicit Dynamic ◽  
The Impact

— In this study, an optimized method to simulate the dynamic 3D event of the impact of a rod with a flat surface has been presented. Unlike the 2D FEM based contact models, in this study both the bodies undergoing the impact are considered elastic(deformable) and simulation is the dynamic event of the impact, instead of predefined 2D symmetric contact analysis. Prominent contact models and plasticity models to define material properties in ANSYS are reviewed. Experimentation results of normal and oblique impact of the rod for different rods provided the coefficient of restitution. Experimental results of permanent deformation on the base for different impact velocity is derived out of a prominent impact study. The simulation results are in co-relation with experiment and both indentation and flattening models on the coefficient of restitution (COR) and permanent deformation of the base and rod after the impact. Thus, the presented 3D Explicit Dynamic simulation of impact is validated to analyze the impact behavior of the 2 bodies without any predefined assumptions with respect to boundary conditions or material properties.

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