The Sliding Velocity Flow of Rough Collisions in Multibody Systems

1996 ◽  
Vol 63 (3) ◽  
pp. 804-809 ◽  
Author(s):  
J. A. Batlle
Keyword(s):  
Multibody Systems ◽  
Single Point ◽  
Nonlinear Flow ◽  
Qualitative Behavior ◽  
Sliding Velocity ◽  
Collision Point ◽  
Coulomb’S Friction ◽  
Tangential Stiffness ◽  
Velocity Flow ◽  
Phase Space Geometry

Single-point rough collisions in multibody systems with perfect constraints, under the assumptions of Coulomb’s friction and infinite tangential stiffness at the collision point, require usually an integration over the normal impulse. The evolution of the sliding velocity, which is needed in the integration, is determined by an autonomous nonlinear flow. The phase-space geometry of this flow depends upon five parameters associated with the system collision configuration and the friction coefficient μ, and gives a global picture of the system behavior in collisions with the configuration considered and arbitrary initial velocities. This geometry is studied using μ, as a control parameter, and a set of threshold values of μ, associated with changes in qualitative behavior are determined.

On Newton’s and Poisson’s Rules of Percussive Dynamics

1993 ◽  
Vol 60 (2) ◽  
pp. 376-381 ◽  
Author(s):  
J. A. Batlle
Keyword(s):  
Multibody Systems ◽  
Single Point ◽  
Equations Of Motion ◽  
Sliding Velocity ◽  
Collision Point ◽  
Linear Solution ◽  
Coulomb’S Friction ◽  
Tangential Stiffness ◽  
Constant Coefficients ◽  
Broad Condition

Newton’s and Poisson ’s rules are widely used in percussive dynamics because they lead to an “all linear” solution. However, they are in general energetically inconsistent in rough collisions. The equivalence between both rules and a broad condition for them to be energetically consistent is presented for single point collisions in multibody systems with perfect constraints. It is fulfilled in collisions described by equations of motion with constant coefficients—sliding in the same direction or no sliding—and in “balanced” collisions—sliding velocity would not change if friction were negligible—Coulomb’s friction and infinite tangential stiffness are assumed at the collision point.

Rough Balanced Collisions

1996 ◽  
Vol 63 (1) ◽  
pp. 168-172 ◽  
Author(s):  
J. A. Batlle
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Sliding Velocity ◽  
Systematic Method ◽  
Linear Solution ◽  
Central Collisions

In multibody systems, balanced collisions—in which the sliding velocity would not change if friction was negligible—are a generalization of central collisions. For them Newton’s and Poisson’s rules are energetically consistent, but even though they are applied an “all linear solution” does not exist if the sliding varies its direction and does not stop. The properties of these collisions are reviewed, the hodographs of the sliding velocity are calculated and used to develop a systematic method to integrate the equations of motion that relies on a single integration from which the remaining unknowns are calculated by means of algebric expressions.

Stability and Bifurcations of Nonlinear Multibody Systems

1993 ◽  
Vol 46 (11S) ◽  
pp. S156-S159
Author(s):  
Edwin J. Kreuzer
Keyword(s):  
Multibody Systems ◽  
Qualitative Behavior ◽  
State Behavior ◽  
Bifurcation Phenomena ◽  
Nonlinear Mathematical Models ◽  
Mechanical Models ◽  
Stability And Bifurcations ◽  
Local And Global Bifurcations ◽  
Dynamics Problems

Many technical systems are adequately described only by means of nonlinear mathematical models. Multibody systems became the most important mechanical models for analyzing engineering dynamics problems. The long-term or steady-state behavior of such systems can have a periodic, quasi-periodic, or chaotic character. Changes of the qualitative behavior are characterized by local and global bifurcations. This paper deals with stability problems in multibody system dynamics and explains different bifurcation phenomena as well as methods for analyzing them. Results from a simple oscillator prove the applicability of the methods.

Analysis and Computation of Two Body Impact in Three Dimensions

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Yan-Bin Jia ◽  
Feifei Wang
Keyword(s):  
Closed Form ◽  
Contact Point ◽  
Positive Definiteness ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Sliding Velocity ◽  
Form Analysis ◽  
Coulomb’S Friction ◽  
The Matrix ◽  
Single Contact Point

A formal impulse-based analysis is presented for the collision of two rigid bodies at single contact point under Coulomb's friction in three dimensions (3D). The tangential impulse at the contact is known to be linear in the sliding velocity whose trajectory, parametrized with the normal impulse and referred to as the hodograph, is governed by a generally nonintegrable ordinary differential equation (ODE). Evolution of the hodograph is bounded by rays in several invariant directions of sliding in the contact plane. Exact lower and upper bounds are derived for the number of such invariant directions, utilizing the established positive definiteness of the matrix defining the governing ODE. If the hodograph reaches the origin, it either terminates (i.e., the contact sticks) or continues in a new direction (i.e., the contact resumes sliding) whose existence and uniqueness, only assumed in the literature, are proven. Closed-form integration of the ODE becomes possible as soon as the sliding velocity turns zero or takes on an invariant direction. Assuming Stronge's energy-based restitution, a complete algorithm is described to combine fast numerical integration (NI) with a case-by-case closed-form analysis. A number of solved collision instances are presented. It remains open whether the modeled impact process will always terminate under Coulomb's friction and Stronge's (or Poisson's) restitution hypothesis.

Partitioning the Parameter Space According to Different Behaviors During Three-Dimensional Impacts

1995 ◽  
Vol 62 (3) ◽  
pp. 740-746 ◽  
Author(s):  
V. Bhatt ◽  
J. Koechling
Keyword(s):  
Parameter Space ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flow Patterns ◽  
The Body ◽  
Qualitative Behavior ◽  
Sliding Velocity ◽  
Physical Behavior ◽  
Rule Out

The equations of motion that define three-dimensional rigid-body impact with finite friction and restitution cannot be solved in a closed form. Previous work has shown that for general shapes and initial conditions, the direction of sliding velocity keeps changing continuously throughout the duration of impact. The flow patterns defined by the trace of the sliding velocity can be classified into a finite number of qualitatively distinct physical behavior. We identify three dimensionless parameters that completely specify the sliding behavior, and determine regions in this parameter space that correspond to each of the different flow patterns. The qualitative behavior during impact can now be determined based on the region which contains the parameters for a given impact configuration. The analysis is also used to study the sensitivity of the sliding behavior to changes in shape or configuration of the body and to rule out the occurrence of certain ambiguities in the post-sticking behavior during impact.

Conditions for Dual Compression in Perfectly Elastic Three-Dimensional Collisions

1999 ◽  
Vol 66 (3) ◽  
pp. 607-611 ◽  
Author(s):  
J. A. Batlle
Keyword(s):  
Friction Coefficient ◽  
Multibody Systems ◽  
Single Point ◽  
Three Dimensional ◽  
Threshold Value ◽  
Restitution Coefficient ◽  
Compression Phase ◽  
Elastic Collisions ◽  
S Model

The jamb (self-locking) process in single-point three-dimensional rough collisions in multibody systems may lead to a dual compression: a second compression phase develops after an initial compression-expansion one. In such a case the usual energetical restitution coefficient ew is ill defined. This article presents a thorough analysis, by means of the incremental Routh ’s model, of the conditions leading to dual compression in the case of perfectly elastic collisions. For a given general collision configuration and for each value of the friction coefficient greater than the threshold value for jamb, there is always a domain of directions of the incident velocity leading to dual compression. An application example is presented.

Dynamic Analysis of Planar Multibody Systems Considering Contact Characteristics of Ball Bearing Joint

2021 ◽  
pp. 2150159
Author(s):  
Yu Chen ◽  
Kailei Liu ◽  
Rui Qiu ◽  
Chengtao Yu ◽  
Xianfei Xia ◽  
...  
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Multibody Systems ◽  
Ball Bearing ◽  
Multibody System ◽  
Design Parameters ◽  
Continuous Contact ◽  
Coulomb’S Friction ◽  
Driving Speed ◽  
Selection Of

A comparative study of dynamic analysis for planar multibody systems with ball bearing joints is conducted in this study. The transmission mechanism is used as the exemplar case for illustrating the effect of ball bearing joints on the dynamic behavior of multibody systems. To reflect the energy loss, the models of continuous contact force and modified Coulomb’s friction are considered in the kinematic equations for the multibody system with ball bearing joint. With this, the dynamic characteristics of the mechanism are studied. Meanwhile, an experimental platform is built to generate the test data for demonstrating the effectiveness and correctness of the proposed method. Moreover, the effects of driving speed and clearance size on the dynamic behavior of the multibody system are investigated. The numerical results indicate that the dynamic behavior of the mechanical system is sensitive to the variation of the design parameters and the selection of parameters can affect greatly the accuracy of the mechanism with clearance joints.

Study on the Natural Vibration Characteristics of Single-Point Diamond Fly Cutting Machine Tool Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Yuanyuan Ding ◽  
Xiaoting Rui ◽  
Gangli Chen ◽  
Xingbao Liu ◽  
Xiaoyun Zeng
Keyword(s):  
Machine Tool ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Natural Vibration ◽  
Single Point ◽  
Vibration Characteristics ◽  
Cutting Machine ◽  
Natural Vibration Characteristics

Natural vibration characteristics play a very important role in the evaluation of the dynamics characteristics and the machined surface of a single-point diamond fly cutting machine tool (SDFCMT). In this paper, the natural vibration characteristics are studied from aspects of theory, computation, and experiment. By adopting the transfer matrix method for multibody systems (MSTMM), the dynamics model and its topology figure are established, and its natural vibration characteristics are computed. The computation results are verified by a modal test.

Study on the Model of a Single-Point Diamond Fly Cutting Machine Tool at Different Rotational Speed Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Yu Chang ◽  
Jianguo Ding ◽  
Hui Zhuang ◽  
Peng Chen ◽  
Wei Wei ◽  
...  
Keyword(s):  
Machine Tool ◽  
Transfer Matrix Method ◽  
Rotational Speed ◽  
Multibody Systems ◽  
Natural Vibration ◽  
Single Point ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Cutting Machine ◽  
Natural Vibration Characteristics

Natural vibration characteristics are important factors affecting the processing quality for an ultra-precision machine tool. The rapid and accurate calculation method for solving natural vibration characteristics has a significance in machine tool dynamics design. By applying the transfer matrix method for multibody systems (MSTMM), the dynamics model of a single-point diamond fly cutting machine tool is established and the rapid computation of natural vibration characteristics at different rotational speed is completed. The results calculated by MSTMM is compared with those by finite element software ABAQUS, the error between the first ten frequencies calculated by MSTMM and ABAQUS is less than 5.68%. However, as the rotational speed increases, the first eight frequencies and mode shapes have no obvious change, while the 9th and 10th modal change significantly. The mode shapes of 9th and 10th orders are vacillation of the spindle. The results show that the rotation of aerostatic spindle has significant effect on the spindle system and little effect on the other parts.

scholarly journals A Study on the Mechanism of Impact between Curved Bridge Segments Using Nonsmooth Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Wenshan Li ◽  
Yong Huang ◽  
Guangming Xie
Keyword(s):  
Contact Point ◽  
Single Point ◽  
Nonsmooth Dynamics ◽  
Curved Bridges ◽  
Curved Bridge ◽  
Coulomb’S Friction ◽  
The Coefficient Of Friction ◽  
Mechanism Of Impact ◽  
The Impact ◽  
Impacts With Friction

It has been observed in many previous earthquakes that impact often occurs between the main girders in curved bridges. An earthquake can result in deck-unseating leading to catastrophic destruction of the structure. In this paper, the nonsmooth multirigid body dynamics method and the set-valued formulation were used to model and analyze the mechanism of impact between the curved bridge segments. The analysis demonstrated that these impacts are the major cause of segment rotation. The main contribution of this paper is to use Newton’s impact law and Coulomb’s friction law to describe the interaction between the curved bridge segments in the form of a set-valued function and to express impacts with friction as a linear complementary problem. For frictionless and frictional contact, the paper considers the single-point and multipoint impacts using the linear complementary formula to detect the unique actual slip-stick conditions of these states. A variety of criteria for distinguishing each case are presented and the results provide the kinetic characteristics of each contact case. The analysis has shown that the impact between the segments of a curved bridge and the tendency of the segments to rotate (and thus detach) are related to the overall geometry, the coefficient of restitution, the coefficient of friction, and the preimpact conditions in the plane of motion. Finally, a theoretical relationship diagram of the impact, rotation slip, and stick condition of the curved bridge segments at the contact point is given. The presented results will be useful for the seismic design of curved bridges.

Sign in / Sign up

Export Citation Format

Share Document