Stable Workpiece Fixturing

1994 ◽  
Author(s):  
Joseph P. Donoghue ◽  
W. Stamps Howard ◽  
Vijay Kumar
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Material Removal ◽  
Three Dimensional ◽  
Quality Measure ◽  
Contact Forces ◽  
Force Displacement

Abstract In this paper, we present the spatial and planar force-displacement relationships which characterize individual contacts on a fixtured workpiece. The compliance at each contact is modeled and expressions for the changes in contact forces as a function of the rigid body relative motion between the fixture elements and the workpiece are developed for three-dimensional fixtures. Using these relationships, the stable fixturing of planar workpieces is demonstrated for material-removal operations. By example, we first describe how to choose the clamp geometry so the overall movement of the workpiece is minimized and then determine the “best” two-contact clamping arrangement using a quality measure based on the deviation from the nominal part dimensions.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1996 ◽  
Vol 63 (4) ◽  
pp. 974-984 ◽  
Author(s):  
N. Sankar ◽  
V. Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid-body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

Total Shoulder Arthroplasty Biomechanics: A Study of the Forces and Strains at the Glenoid Component

1998 ◽  
Vol 120 (1) ◽  
pp. 92-99 ◽  
Author(s):  
A. R. Karduna ◽  
G. R. Williams ◽  
J. P. Iannotti ◽  
J. L. Williams
Keyword(s):  
Rigid Body ◽  
Glenohumeral Joint ◽  
Articular Surface ◽  
Total Shoulder Arthroplasty ◽  
Contact Forces ◽  
Glenoid Component ◽  
Rigid Body Model ◽  
Joint Contact ◽  
Component Loading ◽  
Force Displacement

The objective of this study was to examine how changes in glenohumeral joint conformity and loading patterns affected the forces and strains developed at the glenoid. After removal of soft tissue (muscles, ligaments, and labrum), force-displacement data were collected for both natural and prosthetically reconstructed joints. Joints were shown to develop higher forces for a given translation as joint conformity increased. A rigid body model of joint contact forces was used to determined the so-called effective radial mismatch of each joint. For the purposes of this study, the effective radial mismatch is defined as the mismatch required for a rigid body joint to have the same force-displacement relationship as the joint in question. This parameter is an indication of the deformation at the articular surface. The effective radial mismatch dramatically increased with increasing medial loads, indicating that under physiological loads, the effective radial mismatch of a joint is much greater than its measured mismatch at no load. This increase in effective mismatch as medial loads were increased was found to be threefold greater in cartilaginous joints than in reconstructed joints. Rosette strain gages positioned at the midlevel of the glenoid keel in the reconstructed joints revealed that anterior/posterior component loading leads to fully reversible cyclic keel strains. The highest compressive strains occurred with the head centered in the glenoid, and were larger for nonconforming joints (ε = 0.23 percent). These strains became tensile just before rim loading and were greater for conforming joints (ε = 0.15 percent). Although recorded peak strains are below the yield point for polyethylene, the fully reversed cyclic loading of the component in this fashion may ultimately lead to component toggling and implant failure.

Simulation of 1D Abrasive Vibratory Finishing Process

2012 ◽  
Vol 565 ◽  
pp. 290-295 ◽  
Author(s):  
Prakasam Pradeep Kumar ◽  
Subbiah Sathyan
Keyword(s):  
Material Removal ◽  
Aerospace Industry ◽  
Three Dimensional ◽  
Contact Forces ◽  
Vibratory Finishing ◽  
One Dimensional ◽  
Finishing Process ◽  
Body Dynamics ◽  
The Media ◽  
Multi Body

The vibratory finishing process involves three dimensional motion of abrasive media interacting with part surfaces. With the ultimate goal of simulating such media motion in laboratory conditions, we present here a first step that makes use of a tribometer’s recipricating drive to provide one dimensional controlled vibrations. Finishing experiments using this setup are conducted using abrasive media and titanium alloy work material, both of the type typically used in aerospace industry. Material removal rates, surface roughness and contact forces are measured in two different setups. The media motion is also modelled using multi-body dynamics to predict the contact forces between the media and the work surface. Experimental results are seen to follow literature reported and model predicted trends. This work paves the way for a true three dimensional simulator for a vibratory finishing process.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1994 ◽  
Author(s):  
Nilanjan Sarkar ◽  
Vijay Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

Abstract During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

Wedge Damper Modeling and Forced Response Prediction of Frictionally Constrained Blades

2007 ◽  
Author(s):  
Ender Cigeroglu ◽  
Ning An ◽  
Chia-Hsiang Menq
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Harmonic Balance ◽  
Contact Stiffness ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Points ◽  
Contact Surfaces

In this paper, an improved wedge damper model is presented, based on which the effects of wedge dampers on the forced response of frictionally constrained blades are investigated. In the analysis, while the blade is modeled as a constrained structure, the damper is considered as an unconstrained structure. The model of the damper includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the damper is not artificially constrained. When modeling the contact surfaces of the wedge damper, discrete contact points along with contact stiffness are evenly distributed on the two contact surfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the engine rpm, quasi-static contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the centrifugal force. A friction model is employed to determine the three-dimensional nonlinear contact forces and the relationship between the contact forces and the relative motion is utilized by the Harmonic Balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations, in the Harmonic Balance method is in proportion to the number of modes employed, and therefore the number of contact points used is irrelevant. The developed method is applied to tuned bladed disk system and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that, the effect of rotational motion is significant, particularly for the in-phase vibration modes.

Influence of rail flexibility in a wheel/rail wear prediction model

2016 ◽  
Vol 231 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Javier F Aceituno ◽  
Pu Wang ◽  
Liang Wang ◽  
Ahmed A Shabana
Keyword(s):  
Prediction Model ◽  
Rigid Body ◽  
Contact Point ◽  
Three Dimensional ◽  
Contact Forces ◽  
Wear Model ◽  
Material Loss ◽  
Wear Prediction ◽  
Contact Points ◽  
Rail Wear

The aim of this paper is to study the influence of rail flexibility when a wheel/rail wear prediction model that computes the material loss based on an energy approach is used. The wheel/rail wear model used in this investigation is a simplified combined wear hypothesis that is based on the frictional energy loss in the contact patch. In order to account for wear and its distribution in a profiled wheel surface, the contact forces, creepages and location of the wheel/rail contact points are first calculated using a fully nonlinear multibody system (MBS) and three-dimensional contact formulations that account for the rail flexibility. The contact forces, creepages and contact point locations are defined as nonlinear functions of the rail deformations. These nonlinear expressions are used in the wear calculations. The wear distribution is considered to be proportional to the normal force in the contact area. Numerical simulations are first performed in order to compare between the results obtained using the simplified wheel/rail wear model and the results obtained using Archard’s wear model with a focus on sliding when the track is modeled as a rigid body. This simplified wear model is then used in the simulation of the MBS vehicle model in the case of a flexible body track, in which the rails are modeled using the finite element floating frame of reference approach and modal reduction techniques. The effect of the rail deformation on the wear results are examined by comparing these results with those obtained using the rigid-body track model.

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.

A Nonlinear Rail Vehicle Dynamics Computer Program SAMS/Rail: Part 1—Theory and Formulations

2009 ◽  
Author(s):  
Khaled E. Zaazaa ◽  
Brian Whitten ◽  
Brian Marquis ◽  
Erik Curtis ◽  
Magdy El-Sibaie ◽  
...  
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Contact Element ◽  
Contact Forces ◽  
Simulation Code ◽  
Vehicle Performance ◽  
Normal Contact ◽  
Advantages And Disadvantages ◽  
High Speed Trains

Accurate prediction of railroad vehicle performance requires detailed formulations of wheel-rail contact models. In the past, most dynamic simulation tools used an offline wheel-rail contact element based on look-up tables that are used by the main simulation solver. Nowadays, the use of an online nonlinear three-dimensional wheel-rail contact element is necessary in order to accurately predict the dynamic performance of high speed trains. Recently, the Federal Railroad Administration, Office of Research and Development has sponsored a project to develop a general multibody simulation code that uses an online nonlinear three-dimensional wheel-rail contact element to predict the contact forces between wheel and rail. In this paper, several nonlinear wheel-rail contact formulations are presented, each using the online three-dimensional approach. The methods presented are divided into two contact approaches. In the first Constraint Approach, the wheel is assumed to remain in contact with the rail. In this approach, the normal contact forces are determined by using the technique of Lagrange multipliers. In the second Elastic Approach, wheel/rail separation and penetration are allowed, and the normal contact forces are determined by using Hertz’s Theory. The advantages and disadvantages of each method are presented in this paper. In addition, this paper discusses future developments and improvements for the multibody system code. Some of these improvements are currently being implemented by the University of Illinois at Chicago (UIC). In the accompanying “Part 2” and “Part 3” to this paper, numerical examples are presented in order to demonstrate the results obtained from this research.

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