Transient dynamical-thermal-optical system modeling and simulation

In modern high resolution optical systems like astronomical telescopes or lithographic objectives, performance degradations can be caused by various disturbances. Holistic optical system simulation is required to predict the performance or the high precision systems. In this paper a method for transient dynamical-thermal-optical system modeling and simulation is introduced. Thereby, elastic deformation, rigid body motion, and mechanical stresses due to dynamical excitation are calculated using elastic multibody system simulation and temperature changes are determined using thermal finite element analysis. The deformation, the motion, and the mechanically and thermally induced stress index changes are then considered in a gradient-index ray tracing. Finally, the presented method is applied in a dynamical-thermal single lens system.

Transient Dynamical-Thermal-Optical System Modeling and Simulation

In modern high resolution optical systems like astronomical telescopes or lithographic objectives, performance degradations can be caused by various disturbances. Holistic optical system simulation is required to predict the performance or the high precision systems. In this paper a method for transient dynamical-thermal-optical system modeling and simulation is introduced. Thereby, elastic deformation, rigid body motion, and mechanical stresses due to dynamical excitation are calculated using elastic multibody system simulation and temperature changes are determined using thermal finite element analysis. The deformation, the motion, and the mechanically and thermally induced stress index changes are then considered in a gradient-index ray tracing. Finally, the presented method is applied in a dynamical-thermal single lens system.

New Analytical Model Used in Finite Element Analysis of Solids Mechanics

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

Adaptive LQR-Control Design and Friction Compensation for Flexible High-Speed Rack Feeders

Rack feeders for the automated operation of high bay rackings are of high practical importance. They are characterized by a horizontally movable carriage supporting a tall and flexible vertical beam structure, on which a cage containing the payload can be positioned in vertical direction. To shorten the transport times by using trajectories with increased maximum acceleration and jerk values, accompanying control measures can be introduced counteracting or avoiding undesired vibrations of the flexible structure. In this contribution, both the control-oriented modeling for an experimental setup of such a flexible rack feeder and the model-based design of a gain-scheduled feedforward and feedback control structure are presented. Whereas, a kinematical model is sufficient for the vertical axis, the horizontal motion of the rack feeder is modeled as a planar elastic multibody system with the cage position as scheduling parameter. For the mathematical description of the bending deflections, a one-dimensional Ritz ansatz is introduced. The tracking control design is performed separately for both the horizontal and the vertical axes using decentralized state-space representations. Remaining model uncertainties are estimated by a disturbance observer. The resulting tracking accuracy of the proposed control concept is shown by measurement results from the experimental setup. Furthermore, these results are compared to those obtained with an alternative control concept from previous work.

Simulation of Elastic Gears with Non-Standard Flank Profiles

There exist cases where precise simulations of contact forces do not allow modeling the gears as rigid bodies but a fully elastic description is needed. In this paper, a modally reduced elastic multibody system including gear contact based on a floating frame of reference formulation is proposed that allows very precise simulations of fully elastic gears with appropriately meshed gears in reasonable time even for many rotations. One advantage of this approach is that there is no assumption about the geometry of the gears and, therefore, it allows precise investigations of contacts between gears with almost arbitrary non-standard tooth geometries including flank profile corrections. This study presents simulation results that show how this modal approach can be used to efficiently investigate the interaction between elastic deformations and flank profile corrections as well as their influence on the contact forces. It is shown that the elastic approach is able to describe important phenomena like early addendum contact for insufficiently corrected profiles in dependence of the transmitted load. Furthermore, it is shown how this approach can be used for precise and efficient simulations of beveloid gears.

Spatial Contact Mechanics of CVT Chain Drives

A method for the simulation of spatial dynamics of CVT chain drives is proposed in this paper. Dealing with an elastic multibody system, special care has been taken to describe the contact mechanics of interconnected rigid and/or elastic bodies. Simulation results show the influence of the geometry and the kinematics on the vibrational behavior of the transmission. Furthermore effects on the efficiency and working forces are discussed.

Modelling of a Passenger Coach As Elastic Multibody System

In this paper the multibody model of a railroad passenger coach consisting of two rigid bogies and an elastic car body is presented. The elastic body is introduced by a floating reference frame and superimposed elastic deformations linearized with respect to the reference frame. The governing equations of motion are presented in symbolical form, where the time-invariant matrices describing the elastodynamical behavior are computed numerically in a preprocessor. To increase the computational efficiency, condensation techniques are applied and ten modes are chosen to describe the elastic behavior. Simulations of high speed travelling have been carried out with excitation from measured data of a real track. As a measure of ride comfort the acceleration at characteristic points on the coach are computed. Comparison with results obtained using a less sophisticated rigid body model show significant higher accelerations, depending on the position on the coach, too.

Formulating Dynamic Equations of Elastic Multibody System via the Method of Typical Substructures

In this paper, a method of using multibodies as substructures to establish the dynamic equations of elastic multibody systems involving closed loops is put forward. Plane elastic linkage is divided into four typical substructures, and equations of free two-link dyad — the most general one among the four substructures — are derived. Also some examples of substuctures’ partitioning of mechanisms are given to show the present method’s advantages. By means of the present method, the number of system’s constraint equations can be greatly reduced, and it will facilitate solving dynamic equations on a microcomputer.