Spatial Algorithms for Geometric Contact Detection in Multibody System Dynamics

In the present work, different algorithms for contact detection in multibody systems based on smooth contact modelling approaches are presented. Beginning with the simplest ones, some difficult interactions are subsequently introduced. In addition, a brief overview on the different kinds of contact/impact modelling is provided and an underlining of the advantages and the drawbacks of each of them is determined. Finally, some practical examples of each interaction are presented and analyzed and an outline of the issues arisen during the design process and how they have been solved in order to obtain stable and accurate results is given. The main goal of this paper is to provide a resource for the early-stage researchers in the field that serves as an introduction to the modelling of simple contact/impact events in the context of multibody system dynamics.

Symmetric and Asymmetric Multiple Impulsive Constraints Without Friction and Their Characterization

We present two meaningful and effective non-ideal constitutive characterizations for a multiple impulsive constraints $${\mathcal {S}}$$ S comprising a finite number of non-ideal frictionless constraints of codimension 1, described in the geometric setup given by the space–time bundle $${\mathcal {M}}$$ M of a mechanical system in contact/impact with $${\mathcal {S}}$$ S . Thanks to the geometric structures associated to the elements of $${\mathcal {S}}$$ S , we introduce a symmetric characterization, that does not distinguish the elements forming $${\mathcal {S}}$$ S as regards mechanical behavior, and an asymmetric one that makes this distinction. Both the characterizations provide a generalization of the characterization of ideal multiple constraints presented in Pasquero (Q Appl Math 76(3):547–576, 2018). The iterative nature of these characterizations allows the introduction of two algorithms determining the right velocity of the system in case of single or multiple contact/impact with symmetric or asymmetric constraints $${\mathcal {S}}$$ S , once the elements forming $${\mathcal {S}}$$ S and the left velocity of the system are known. We show the effectiveness of the two possible choices with explicit implementations of these algorithms in two significant examples: a simplified Newton’s cradle system for the symmetric characterization and a disk in multiple contact/impact with two walls of a corner for the asymmetric one.

A methodology for dynamic behavior analysis of the slider-crank mechanism considering clearance joint

The slider-crank mechanism is used widely in modern industrial equipment whereby the contact-impact of a revolute clearance joint affects the dynamic behavior of mechanical systems. Combining multibody dynamic theory and nonlinear contact theory, the computational methodology for dynamic analysis of the slider-crank mechanism with a clearance joint is proposed. The differential equations of motion are obtained considering the revolute clearance joint between the connecting rod and slider. In the mechanical system, the contact force is evaluated using the continuous force model proposed by Lankarani and Nikravesh, which can describe the contact-impact phenomenon accurately. Then, the experimental study is performed whereby the numerical results are compared with the test data to validate the proposed model. Moreover, the dynamic response analysis is conducted with various driving velocities and clearance sizes, which also explains that the sensitive dependence of a mechanical system on the revolute clearance joint.

Meshing Contact Impact Properties of Circular Arc Tooth Trace Cylindrical Gear Based on Rotating Knife Dish Milling Process

Taking the circular arc tooth trace (CATT) cylindrical gear as a research object, in order to obtain the CATT cylindrical gear’s meshing contact impact properties, the meshing contact impact hypothesis of the CATT cylindrical gear was put forward based on the contact dynamics theory and gear transmission physical model, and the gear mesh contact impact model was set up further. The finite element solution algorithm for solving the impact problem was given. Then, the accurate 3D model was set up based on the gear tooth surface equation, and the finite element analysis models of the meshing contact impact with different impact positions were established further. The model was to study the distribution rule of the gear surface meshing contact impact stress and relationship between the impact velocity, impact position, and the impact stress. Moreover, the reason for the maximum impact stresses distribution rule of primary and secondary impact tooth surface was discussed. Research result shows the driven wheel dangerous areas of gear root impact are the gear top of the primary impact tooth surface and the gear root of the secondary impact tooth surface; the driven wheel dangerous areas of gear top impact are the gear root of the primary impact tooth surface and gear top of the secondary impact tooth surface; the driven wheel dangerous areas of pitch circle are the gear root and pitch circle of secondary impact tooth surface; and impact velocity and impact position have a major influence on the impact stress. The study results provide a theoretical basis for the dynamic design and industrial application of CATT cylindrical gears.