Wolfgang Steiner

The ongoing transition towards electromobility and the consequent absence of combustion engine noise have drawn attention to gear noise reduction. To analyze and optimize the NVH (noise, vibration and harshness)—characteristics of a gearbox numerically, high-quality excitation data is essential. The primary source of excitation is the force generated by the contact of meshing teeth, which are transmitted to the housing. As real gears usually have manufacturing deviations and surface modifications that result in a non-ideal tooth geometry, which can notably influence the transmission error and contact forces, these effects should be considered when predicting the excitation. The simulation model of a real-world single-flank test bench allows us to study the behavior of a gear pairing and to calculate the necessary excitation data for a NVH calculation. The simulation is validated by comparing the simulation results with test bench measurements. Finally, a comparison is made between a simulation with ideal gears and gears with measured tooth geometries. The results show that the measured, non-ideal geometry results in a higher transmission error and higher forces in the bearings. In this study a multibody simulation model, that can handle complex real-world tooth geometry deviations, is presented. For this purpose, the multibody simulation software FreeDyn is used in combination with the Polygonal Contact Model. This study is not positioned as an industry-specific, fully validated tool for gear design. It is not intended to derive any new insights in the field of NVH or the gear engineering field in general, but rather to show the capabilities of such a simulation model.

The solution of two-point boundary value problems (TPBVPs) in multibody system dynamics is a tough challenge. In this article, a double shooting method (DSM) tailored for TPBVPs is presented. The method builds upon the classical single shooting method while incorporating optimization strategies to overcome numerical instability and sensitivity to initial guesses. Conventional shooting methods are associated with some numerical problems: The numerical gradient computation for updating initial values causes problems in many cases, since the disturbance parameter for determining the numerical derivative must be selected appropriately in order to achieve sufficient accuracy. Moreover, integrating the initial value problem can be numerically challenging, especially when the interval is large and the differential equations have unstable modes. The DSM is designed to address these challenges. Therefore, the method incorporates a discrete costate variable approach to cope with the numerical gradient computation, which is often the Achilles’ heel of classical shooting methods. Finally, the method is formulated using a discrete implicit integration scheme to determine, as a first example, a double pendulum upswing maneuver, as a second example, the energy-optimal control of a robot multibody model and, as a third example, trajectories of the restricted three-body problem.

This article presents a novel adjoint approach for solving optimal control problems in multibody dynamics. The equations of motion are governed by a set of differential-algebraic equations leading to a classical two-point boundary value problem. One solution strategy for the underlying boundary value problem is offered by gradient-based methods. However, the numerical evaluation of a gradient with respect to a high number of time steps is a time-consuming task. The approach presented in this article employs the adjoint method to compute the gradient of a cost functional, which decouples the boundary conditions by integrating sequentially the equations of motion and the adjoint equations, by a forward and a backward time integration. In order to satisfy a set of final conditions the system of equations is extended by the influence equations to associate the change of the controls and the change of the final conditions. By solving all three systems of equations, the gradient of the cost functional can be computed efficiently. This proposed method impacts the free final time while approaching the prescribed final conditions. Moreover, the paper presents an iterative optimization approach finding the optimal solution and is evaluated in the application of a three-arm multibody robot.

Extremal values of a system output pose major issues in various disciplines, e.g., the maximum velocity in human-robot collaboration results in high contact forces in the event of a collision, or force and stress peaks cause faster crack growth or fatigue of components. Reducing these extremal values implies a reduction in the risks to humans and an increase in the durability of the components. Therefore, the present paper focuses on minimizing an extremal value of a system output of dynamical system, whereby a gradient-based solution strategy based on the adjoint method is proposed. Since several local extremal values can occur in the time evolution of the system output, it is necessary to apply multi-objective optimization, whereby in particular the largest value is to be minimized. One promising approach in this regard is found in the goal attainment method, which is implemented in the MATLAB function , or alternatively, the so-called minimax problem can be investigated in a smoothed objective open for any nonlinear programming software package. In the scope of these minimax problems, the maximum reaction force of a one-mass oscillator and the maximum velocity of the tool center point of a two-axis robot during a rest-to-rest maneuver are minimized efficiently using the proposed adjoint gradient.

Extremal values of a system output pose major issues in various disciplines, e.g., the maximum velocity in human-robot collaboration results in high contact forces in the event of a collision, or force and stress peaks cause faster crack growth or fatigue of components. Reducing these extremal values implies a reduction in the risks to humans and an increase in the durability of the components. Therefore, the present paper focuses on minimizing an extremal value of a system output of dynamical system, whereby a gradient-based solution strategy based on the adjoint method is proposed. Since several local extremal values can occur in the time evolution of the system output, it is necessary to apply multi-objective optimization, whereby in particular the largest value is to be minimized. One promising approach in this regard is found in the goal attainment method, which is implemented in the MATLAB function fminimax, or alternatively, the so-called minimax problem can be investigated in a smoothed objective open for any nonlinear programming software package. In the scope of these minimax problems, the maximum reaction force of a one-mass oscillator and the maximum velocity of the tool center point of a two-axis robot during a rest-to-rest maneuver are minimized efficiently using the proposed adjoint gradient.

Various special effects occur during the operation of vibratory conveyors, e.g., multiple feeding velocities at the same excitation amplitude or so-called microthrows. In this work, a model for the simulation and prediction of the behavior of such a conveying system is presented. The simulation model is based on the bouncing ball model which is known from literature. The introduced impact law is coupled in horizontal direction by a frictional force which enables modeling a feeding process. The mentioned effect of multiple feeding velocities is studied with the developed simulation model. For the estimation of the critical excitation amplitude where a second feeding velocity appears, an analytical approach is developed. The corresponding feeding velocity can also be calculated with this approach. Moreover, the sensitivity of the initial conditions is investigated and criteria for the estimation are found. These can be applied to optimally adjust the conveyor in practice. Furthermore, the effects of microthrows are studied and analytical formulas for the estimation of characteristic values of the microthrows are derived. The dragging process following a sequence of microthrows is also investigated. All the developed formulas are validated by the simulation model.

In this work, a simulation model of a vibratory conveying system is presented. The simulation model is based on a continuous contact formulation in vertical direction which is extended by a friction force in horizontal direction to simulate a conveying process. In contrast with complex 3D simulation tools, it enables the understanding of previously unexplained phenomena such as multiple feeding velocities at the same excitation amplitude, which are observed in practical measurements. The parameters that have an influence on this effect are investigated, and a method for predicting and adjusting the occurrence of multiple solutions is developed. It is shown that the calibration of the system is very difficult in practice, as it depends significantly on the initial conditions which are difficult to reproduce and predict. It is also shown that the system can exhibit chaotic behavior in some configurations. These chaotic states are shown with the simulation model by means of parameter studies, and the point at which the system becomes chaotic is predicted with the method of Lyapunov exponents and fractal dimensions. Knowledge of the chaotic states can be used to calibrate the conveyor, as they depend only on the excitation and not on the initial conditions. The interdependencies of the initial conditions are also discussed in more detail. Therefore, this work provides a deeper understanding of complex conveying processes using a simple simulation model.

Nachdem Verfahren zur Beschlussfassung im Umlaufweg und unter Nutzung technischer Hilfsmittel, insb Videokonferenzen, bei Kollegialorganen iwS bis 2020 nur punktuell geregelt waren und eher vereinzelt zur Anwendung kamen, erfreuen sich diese Formen nunmehr (pandemiebedingt) zunehmender Beliebtheit. Neben praktisch/technischen Fragen ergeben sich dabei eine Reihe von Rechtsfragen, die sich auch bei und in Verfahren vor den VwG stellen. Im vorliegenden Beitrag werden die Rahmenbedingungen und Herausforderungen dargestellt, Ansätze zu deren Lösung und Bewältigung erörtert sowie Thesen zur Weiterentwicklung der Rechtsgrundlagen aufgestellt.

In mechanics, the term jerk, which is usually defined as the time derivative of acceleration, is often used incorrectly to interpret shock loads. Unfortunately, it is often very difficult to convince technicians with less insight into the basic laws of mechanics that their views are invalid, since jerky motions undoubtedly have certain effects on the dynamics of mechatronic systems. The fact is, however, that according to Newton the magnitude of the force acting on a body is determined exclusively by the acceleration itself and not by its derivative. From Newton's law follows only the trivial statement that the change of force is proportional to the change of acceleration. The effects of the jerk only become apparent in structural‐dynamic applications, such as in robotics or in biomechanics. In this presentation, such effects are discussed for a simple mechanical model to make fundamental phenomena such as component vibrations, which are related to the jerk, understandable. Quantitative relations between the jerk and the amplitude of such vibrations are derived analytically.

In the last few years, the demand for efficient and reliable algorithms for solving optimal control problems in dynamics has increased. Among all optimal control problems, time-optimal problems are probably the most challenging ones. Within the framework of this contribution, we pursue a novel approach for the determination of time-optimal controls for dynamic systems under