Development of a simulation routine for the integration of quantitative thermal calculations into mechanical multibody simulations

Motivation

The presence of multiple heat sources (e.g., friction) or preloads loads in machine tools changes the temperature field and leads to thermal deformation and positional errors at the TCP, which in turn affects the manufacturing quality, tool life and production time. Therefore, the development of a suitable simulation model for the near real-time calculation of thermal stresses and its integration into mechanical multi-body simulations is very important. The structural model based correction of the thermal errors of the mechanical systems is a very helpful energy efficient approach compared to conventional methods such as machine cooling. The results of this project will be helpful to study the thermal effects on complex mechanical systems such as machine tools and their components.

Objective of the project

The aim of the project is to develop a method for integrating thermal models into mechanical multi-body simulations (RecurDyn) for predicting thermal effects on the dynamic behavior of machine tools and their components.

Approach

The approach of the project is to combine the modal reduction of multibody systems with the reduction approach used in thermal simulation by integrating the thermal effects via a displacement force field into the mechanical simulation.

First, the thermal model is developed as part of the structural model. The structural model is represented by partial differential equations. However, using a discretization method (here using Finite Element Analysis or FEA), these are transformed into a system of coupled ordinary differential equations, which allows the simulation (to find deformations) by numerical time integration routines. Since thermal systems are highly damped systems, the static deformation becomes dominant and the heat generation due to deformation becomes insignificant, allowing the thermal and mechanical problem to be solved at different time steps.

To speed up the computation, the equation systems of the FEM model with a very large number of degrees of freedom are projected into significantly smaller reduced systems. For the mechanical system, the modal reduction is applied using eigenvectors. For thermal systems, Model Order Reduction (MOR) based on the Arnoldi algorithm and Krylov subspaces is applied.

Challenges

• The definition of boundary conditions and environmental conditions before starting the simulations: Linking of these conditions to the simulations is the main challenge and must be done through a force field that can only be calculated through the simulation.
• The numerical instability of the model due to asynchronous time steps in the mechanical and thermal models: An algorithm should be developed for the periodic smooth transfer of updated parameters to balance the different time scales and complexity of the simulation approaches.
• The estimation of the eigenmodes of the modal reduction model needed to approximate the interface displacement

Path to solution

The setup of a model, the computation of its temperature fields and the resulting elastic deformations can be summarized in the following solution steps:

• Preparation of the CAD data for the machine components of interest, including geometry defeaturing, functional surface segmentation, and assembly.
• Definition of surfaces with thermal and/or mechanical boundary conditions or coupling conditions to be modeled later.
• Discretization of the geometry into finite elements, parametrization of the time-invariant quantities (e.g., material parameters) and generation of the system matrices in FEA software.
• Export the data from the FEM environment.
• Import data into programming environment with structured data storage and separation of the thermal and mechanical model equations.
• Add time-dependent parameters and boundary conditionsto the parameterization functions, including motion profiles of the machine axes, power loss models, free and forced convection.
• Simulation of the temperature field and computation of the deformation field from the temperature field at discrete points in the time domain. To limit the computation time, the degrees of freedom (DOF) of the system are reduced by applying Model Order Reduction (MOR) techniques.
• Two step approach for combining thermal solver and MBS: Solver coupling and solver integration.

Results

After the implementation of the mathematical approach, the relevant thermal quantities will be simulated for a physical prototype of the system. This results in a complex simulation tool, which for the first time

• will quantitatively map both thermal and dynamically induced displacements.
• Overdeterminations and axis misalignments due to thermal effects (specifically: friction) would be quantitatively identified for the first time already in simulation studies.
• Specifically, about machine tools: would map the displacement of the tool center point due to both dynamic and thermal load effects.

Finally, the results from the proposed method to investigate the thermal effects will be validated using a suitable demonstrator machine. Accessible data (e.g., axes velocities, axes positions, motor currents) will be utilized as input information for the model. Based on this information, the heat sources (e.g., friction), and thermal conduction/convection will be determined for the mechanical systems.

Current status

Currently the workflow for combining thermal solver and MBS via coupling is under development.

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