The Direct Contact Problem in a Trochoidal-Type Machine

1993 ◽  
Author(s):  
John B. Shung ◽  
Gordon R. Pennock
Keyword(s):  
Direct Contact ◽  
Contact Point ◽  
Element Model ◽  
Contact Forces ◽  
Combined Model ◽  
Normal Contact ◽  
Contact Points ◽  
Satisfactory Method ◽  
Type Machine ◽  
Static Conditions

Abstract Reducing the contact forces in a trochoidal-type machine is important because the machine can not be adjusted for wear. The main difficulty in calculating the contact forces is to determine the forces that are transmitted through each contact point. Since there are many points of contact, at any instant, the problem is quasi-statically indeterminate and no satisfactory method of analysis is available in the current literature. The first part of this paper presents a simplified analytical model of a trochoidal-type machine when friction and deformation at the contact points are neglected. From this model, closed-form equations are derived for the normal contact forces. Then the second part of the paper presents a combined analytical and finite element model of the same machine. The analysis for the combined model includes the effects of friction and deformation at the contact points. The analysis for both models is for quasi-static conditions. The results from the two models are compared and important conclusions are drawn.

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.

Estimation of Graphite Dust Production in a Pebble-Bed Type Nuclear Reflector

2014 ◽  
Author(s):  
Ji-Ho Kang ◽  
Eung Seon Kim ◽  
Seungyon Cho
Keyword(s):  
Adhesive Wear ◽  
Cell Model ◽  
Estimation Method ◽  
Unit Cell ◽  
Contact Forces ◽  
Dust Explosion ◽  
Dust Production ◽  
Pebble Bed ◽  
Normal Contact ◽  
Contact Points

In this study, an estimation method of graphite dust production in the pebble-bed type reflector region of Korean HCSB (Helium-Cooled Solid Breeder) TBM (Test Blanket Module) in the ITER (International Thermonuclear Experimental Reactor) project using FEM (Finite Element Method) was proposed and the amount of dust production was calculated. A unit-cell model of uniformly arranged pebbles was defined with appropriate thermal and mechanical loadings. A commercial FEM program, Abaqus V6.10 was used to model and solve the stress field under multiple contact constraints between pebbles in the unit-cell. Resulting normal contact forces and slip distances on contact points were applied into the Archard adhesive wear equation to calculate the amount of graphite dust. The friction effect on contact points was investigated. The calculation result showed that the amount of graphite dust production was estimated to 2.22∼3.67e−4 g/m3 which was almost linearly proportional to the friction coefficient. The analysis results will be used as the basis data for the consecutive study of dust explosion.

Effect of the Wheel Geometric Design on the Nonlinear Dynamics of Railroad Vehicles

2005 ◽  
Vol 128 (5) ◽  
pp. 1130-1140 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Mahmoud Tobaa ◽  
Khaled E. Zaazaa
Keyword(s):  
Nonlinear Dynamics ◽  
Simple Model ◽  
Single Point ◽  
Contact Forces ◽  
Geometric Properties ◽  
Normal Contact ◽  
Railroad Vehicles ◽  
Contact Points ◽  
Contact Constraint ◽  
Wheel Profile

The effect of the geometry of a wheel profile that allows only a single point of contact with the rail is investigated in this study. The local geometric properties of this profile are compared with the local geometric properties of a profile that allows for two-point contacts in order to understand the basic differences between the two profiles. A simple model is first used to examine the effect of the profile geometry on the stability and nonlinear dynamics of a suspended wheel set. The results obtained using this simple model show that the geometry of the wheel profile can significantly alter the critical speed. A computational approach is then used to investigate and quantify the effect of the wheel geometry wheel on the dynamics and stability of railroad vehicles. Two methods, the contact constraint and elastic formulations, are used. The contact constraint method employs nonlinear algebraic kinematic constraint equations to describe the contact between the wheel and the rail. The contact kinematic constraints, which eliminate one degree of freedom and do not allow for wheel/rail separation, are imposed at the position, velocity and acceleration levels. The system equations of motion are expressed in terms of the generalized coordinates and the nongeneralized surface parameters. In the formulations based on the elastic approach, the wheel has six degrees of freedom with respect to the rail, and the normal contact forces are defined as a function of the penetration using Hertz’s contact theory or using assumed stiffness and damping coefficients. In the elastic approach that allows for wheel/rail separation, the locations of the contact points are determined by solving a set of algebraic equations. The distribution of the contact forces resulting from the use of the two profiles that have different geometric properties is investigated using the two methods. Numerical results are presented for a full railroad vehicle model and the effect of the wheel profile on the vehicle stability is investigated.

Design of Four Contact-Point Slewing Bearing With a New Load Distribution Procedure to Account for Structural Stiffness

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Mireia Olave ◽  
Xabier Sagartzazu ◽  
Jorge Damian ◽  
Alberto Serna
Keyword(s):  
Load Distribution ◽  
Contact Point ◽  
Element Model ◽  
Contact Forces ◽  
Elastic Model ◽  
Slewing Bearing ◽  
Extreme Loads ◽  
Highly Nonlinear ◽  
Rolling Elements ◽  
Bearing Rings

This paper proposes a procedure for obtaining the load distribution in a four contact-point slewing bearing considering the effect of the structure’s elasticity. The uneven stiffness of the rings and the supporting structures creates a variation with respect to the results obtained with a rigid model. It is necessary to evaluate the effect of the elasticity on the increase in the contact forces in order to be able to design the slewing bearing and the structures involved in the connection. Depending on the shape of the structures, the contact force value obtained on the most loaded rolling element is different. The evaluation of this maximum force at extreme loads is essential to design the structures joined to the bearing rings. The new elastic model presented in this paper is highly nonlinear so iterative loops are needed in order to obtain a satisfactory solution. At the same time a finite element model (FEM) has been created for the global model, having also represented the rolling elements and their contact with the raceways. The results obtained using the FEM have been correlated with the results of the new procedure.

On the Influence of Contact Geometry on Grasp Stability

2008 ◽  
Author(s):  
Gert A. Kragten ◽  
Just L. Herder ◽  
A. L. Schwab
Keyword(s):  
Contact Stiffness ◽  
Contact Geometry ◽  
Contact Forces ◽  
Minor Effect ◽  
Dynamic Simulations ◽  
Normal Contact ◽  
Contact Points ◽  
Grasp Stability ◽  
The Stability ◽  
A Minor

This paper demonstrates that the predicted grasp stability is highly sensitive to only small changes in the character of the contact forces. The contribution of the geometry and stiffness at the contact points to the grasp stability is investigated by a planar grasp with three contact points. Limit cases of zero and infinite contact curvatures, and finite to infinite contact stiffnesses are considered. The stability is predicted based on the approach of Howard and Kumar [1], and verified with multibody dynamic simulations. For rigid objects and fingers with only normal contact stiffness, the grasp stability is dominated by the contact geometry, whereas the local contact stiffness and preload have a minor effect. Furthermore, grasps with pointed finger tips are more likely to be stable than grasps with flat finger tips.

scholarly journals A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Filipe Marques ◽  
Fernando Isaac ◽  
Nuno Dourado ◽  
António Pedro Souto ◽  
Paulo Flores ◽  
...  
Keyword(s):  
Friction Force ◽  
Contact Process ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Clearance Joints ◽  
Dissipative Term ◽  
Contact Points ◽  
Spatial Mechanisms

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket, which compose a spherical joint, are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian-based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudopenetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb's law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems' dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four-bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

Pre-Optimization of Asymmetrical Underplatform Dampers

2016 ◽  
Author(s):  
Chiara Gastaldi ◽  
Muzio M. Gola
Keyword(s):  
Contact Surface ◽  
Contact Stiffness ◽  
Contact Point ◽  
A Priori ◽  
Element Model ◽  
Contact Forces ◽  
Friction Coefficients ◽  
Lift Off ◽  
Lower Limits ◽  
Underplatform Damper

The numerical coupled optimization of an underplatform damper is the exploration of its dynamics through a finite element model which includes both the damper and the blades. This is an effective approach if the initial damper mass and geometry have been previously selected in such a way that those parameter combinations leading to undesirable damper behavior (i.e. contact point lift-off, jamming, excessive contact forces) are ruled out a priori. This can be obtained through a pre-optimization where, after choosing the damper type the following main steps are followed: 1. ensure that damper jamming is avoided through an appropriate choice of platform angles, in function of the friction coefficients; 2. ensure that damper lift-off is avoided through an appropriate choice of the shape and position of the damper-platform flat contact surface and the position of the damper mass center; 3. set upper and lower limits to the value of damper-platform contact forces (as a multiple of the damper centrifugal force), the first being related to friction and wear problems, the second to the very existence of bilateral contacts; 4. check the model, and in particular the values of friction coefficients and contact stiffness, against experimental results. Once the above knowledge concerning the most desirable damper shape has been gathered an effective coupled-optimization can safely be performed. This is done by finding the most effective match between the damper size/mass and the bladed disk through a non-linear dynamic calculation (not examined in this paper). The outcome of both the pre-optimization and the coupled optimization are strongly dependent on the assumed values of friction coefficients, which depend on the contact surface type (then, different for the left and right side of the damper) and the contact pressure. The paper capitalizes on already developed tools, presented in previous ASME papers, such as the test rig developed by the AERMEC lab to draw the appropriate values of contact parameters, the numerical model representing the stand-alone dynamics of the damper between the platforms and the automatic random sampling tuning procedure. The purpose of the paper is to illustrate the procedure through the analysis of a family of rigid bar dampers with a curved-flat cross section.

A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

2016 ◽  
Author(s):  
Filipe Marques ◽  
Fernando Isaac ◽  
Nuno Dourado ◽  
António Pedro Souto ◽  
Paulo Flores ◽  
...  
Keyword(s):  
Friction Force ◽  
Contact Process ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Clearance Joints ◽  
Dissipative Term ◽  
Contact Points ◽  
Spatial Mechanisms

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket which compose a spherical joint are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudo-penetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb’s law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems’ dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Ender Cigeroglu ◽  
Ning An ◽  
Chia-Hsiang Menq
Keyword(s):  
Harmonic Balance ◽  
Normal Load ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Response Prediction ◽  
Forced Response ◽  
Contact Forces ◽  
Balance Method ◽  
Frictional Contacts ◽  
Contact Points

In this paper, a forced response prediction method for the analysis of constrained and unconstrained structures coupled through frictional contacts is presented. This type of frictional contact problem arises in vibration damping of turbine blades, in which dampers and blades constitute the unconstrained and constrained structures, respectively. The model of the unconstrained/free structure 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 free structure is not artificially constrained. When modeling the contact surfaces between the constrained and free structure, discrete contact points along with contact stiffnesses are distributed on the friction interfaces. 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 normal force acting on the contact interfaces, quasistatic 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 normal load. 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, are in proportion to the number of modes employed. Therefore the number of contact points used is irrelevant. The developed method is applied to a bladed-disk system with wedge dampers where the dampers constitute the unconstrained structure, 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. Moreover, the effect of partial slip in the forced response analysis and the effect of the number of harmonics employed by the harmonic balance method are examined. Finally, the prediction for a test case is compared with the test data to verify the developed method.

Quasi-Static Analysis on a Large-Sized Four Contact-Point Slewing Bearing with Negative Axial Play

2013 ◽  
Vol 307 ◽  
pp. 219-222
Author(s):  
Yan Shuang Wang ◽  
Yan Wu ◽  
Hai Feng Zhu
Keyword(s):  
Static Analysis ◽  
Applied Load ◽  
Contact Point ◽  
Friction Torque ◽  
Normal Contact ◽  
Absolute Value ◽  
Slewing Bearing ◽  
Contact Points ◽  
Contact Loads ◽  
The Absolute

A quasi-static analysis of a large-sized four contact-point slewing bearing with negative axial play is performed. The values of normal contact loads of a slewing ring bearing between balls and inner/outer ring were computed at different negative axial plays without applied load. The results show that the normal loads of the four contact points increase as the absolute value of negative axial play increases. Slightly changing negative axial play makes big change on normal contact load. Startup friction torque can be improved largely by increasing slightly the absolute value of negative axial play.

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