Simulation of processes in machines using orthogonal meshes

The paper presents an experience of using orthogonal hexahedral meshes for simulation of different processes in machine-building products. Stress state of the details of suspension of a cargo vehicle during the movement on random road profile was simulated. Orthogonal hexahedral meshes for lower suspension levers and housing and piston rod of shock adsorber were used. Thermal state of the elements of drive axle and its housing during the movement of a cargo vehicle with constant speed was calculated using hexahedral orthogonal meshes for details and inner volume of housing of the drive axle. Lubrication fluid circulation in the reducer of a cargo vehicle was modelled. Orthogonal mesh for inner volume of the reducer was used to calculate the parameters of lubrication fluid circulation.


Introduction
Computer simulation is widely used in the development of machine-building products. [1] Computers are used in design process (CAD systems), modeling (CAE and MBS systems), product lifetime management, document management. Modern conception called Industry 4.0, which was first introduced by Klaus Schwab, implies the ongoing automation of traditional manufacturing and industrial practices and includes further development of instruments for modeling and processes simulation. [2] Numerical simulation allows to decrease the expenses on the development of machine-building products. [3] The use of mathematical model and numerical experiment leads to lower quantity of built experimental prototypes and shortens the time of product improvement. This paper presents an experience of using hexahedral orthogonal meshes in stress analysis of the details of suspension of vehicles, analysis of temperature fields in these details and circulation of lubricating fluid in different assemblies and details of machines.

Materials and methods
Orthogonal hexahedral meshes of higher dimensions for CAD assemblies are used in this work. Method for generation of such meshes was developed. In this method unitary normals for border elements of mesh are used. It allows to increase the quality of mesh on border. In the most common case mesh generation consists of the following steps: -setting boundary conditions on the source CAD geometry of an assembly; -surface triangulation of details of an assembly; -generation of 3D hexahedral orthogonal mesh; -setting boundary conditions from source geometry to border elements of mesh.

Heating process in the elements of a reducer and its housing
Thermal stress calculation of the details of drive axle and its housing during the movement of a cargo vehicle with constant speed was performed using orthogonal meshes.

Lubrication fluid circulation in the reducer
Simulation of lubrication fluid circulation is very important as it lets significantly decrease the costs on the experimental elaboration of parts of machines. Current methods are based on resource-intensive numeric integration of Navier-Stokes equations. [6] It is very difficult to use them for complex assemblies with lots of details. A new method, which uses particle-in-cell method and Monte Carlo method, is used to calculate statistic parameters of the flows of lubrication fluid in the reducer of a cargo vehicle. In this method a volume of lubricant is presented as a set of particles, which move in the field of gravity without any interaction between each other inside the volume and slide along inner surfaces of a model with particle velocity, damping coefficient and normal to this surface taken into account. The method is described in [7].  On the Figure 9 areas with lack of lubricant are shown and these areas correspond to broken parts of real reducer.

Conclusion
Orthogonal hexahedral meshes can be used for simulation of different processes in machines and mechanisms. The examples of these processes are stress state, thermal state, lubrication oil circulation. For some cases it is necessary to use orthogonal meshes for CAD geometry in the form of assembly, for othersmesh models for inner volumes.
Though it is often very difficult to generate hexahedral mesh models for assemblies in view their complexity, they are very convenient to make calculations and to be visualized.