Viktor Berbyuk

Multiobjective optimisation of bogie suspension to boost speed on curves

Abstract To improve safety and maximum admissible speed on different operational scenarios, multiobjective optimisation of bogie suspension components of a one-car railway vehicle model is considered. The vehicle model has 50 degrees of freedom and is developed in multibody dynamics software SIMPACK. Track shift force, running stability, and risk of derailment are selected as safety objective functions. The improved maximum admissible speeds of the vehicle on curves are determined based on the track plane accelerations up to 1.5 m/s2. To attenuate the number of design parameters for optimisation and improve the computational efficiency, a global sensitivity analysis is accomplished using the multiplicative dimensional reduction method (M-DRM). A multistep optimisation routine based on genetic algorithm (GA) and MATLAB/SIMPACK co-simulation is executed at three levels. The bogie conventional secondary and primary suspension components are chosen as the design parameters in the first two steps, respectively. In the last step semi-active suspension is in focus. The input electrical current to magnetorheological yaw dampers is optimised to guarantee an appropriate safety level. Semi-active controllers are also applied and the respective effects on bogie dynamics are explored. The safety Pareto optimised results are compared with those associated with in-service values. The global sensitivity analysis and multistep approach significantly reduced the number of design parameters and improved the computational efficiency of the optimisation. Furthermore, using the optimised values of design parameters give the possibility to run the vehicle up to 13% faster on curves while a satisfactory safety level is guaranteed. The results obtained can be used in Pareto optimisation and active bogie suspension design problems.

Pareto optimisation of railway bogie suspension damping to enhance safety and comfort

This paper presents the optimisation of damping characteristics in bogie suspensions using a multi-objective optimisation methodology. The damping is investigated and optimised in terms of the resulting performances of a railway vehicle with respect to safety, comfort and wear considerations. A complete multi-body system model describing the railway vehicle dynamics is implemented in commercial software Gensys and used in the optimisation. In complementary optimisation analyses, a reduced and linearised model describing the bogie system dynamics is also utilised. Pareto fronts with respect to safety, comfort and wear objectives are obtained, showing the trade-off behaviour between the objectives. Such trade-off curves are of importance, especially in the design of damping functional components. The results demonstrate that the developed methodology can successfully be used for multi-objective investigations of a railway vehicle within models of different levels of complexity. By introducing optimised passive damping elements in the bogie suspensions, both safety and comfort are improved. In particular, it is noted that the use of optimised passive damping elements can allow for higher train speeds. Finally, adaptive strategies for switching damping parameters with respect to different ride conditions are outlined and discussed.

Vibration energy harvesting using Galfenol-based transducer

In this paper the novel design of Galfenol based vibration energy harvester is presented. The device uses Galfenol rod diameter 6.35 mm and length 50mm, polycrystalline, production grade, manufactured by FSZM process by ETREMA Product Inc. For experimental study of the harvester, the test rig was developed. It was found by experiment that for given frequency of external excitation there exist optimal values of bias and pre-stress which maximize generated voltage and harvested power. Under optimized operational conditions and external excitations with frequency 50Hz the designed transducer generates about 10 V and harvests about 0,45 W power. Within the running conditions, the Galfenol rod power density was estimated to 340mW/cm3. The obtained results show high practical potential of Galfenol based sensors for vibration-to-electrical energy conversion, structural health monitoring, etc.

Computational model of conventional engine mounts for commercial vehicles: validation and application

In this paper, a computational model of conventional engine mounts for commercial vehicles comprising elastic, viscous and friction functional components, which expresses the nonlinear behaviour of the dynamic stiffness and damping of mounts as functions of both frequency and amplitude of excitation, is developed. Optimisation approach is implemented to identify model parameters using measurement data. The developed model has been validated against measurement data for harmonic excitations with a frequency range of 5–100 Hz and an amplitude range of 0.025–2 mm employing three different engine mounts used in heavy trucks. The model shows good and admissible agreement with measurement data keeping the tolerance of estimation below 11%. Simulations of engine vibration dynamics are presented with both proposed model and commonly applied Kelvin–Voigt model of the mounts. The developed model can be used in complete vehicle advanced dynamic analyses and also in the design of semi-active and active engine mounting systems for commercial vehicles.

Mathematical modeling of the dynamics of the human gait in the saggital plane

We propose a new formulation of the problem of mathematical modeling of the human gait as an optimal control problem for a nonlinear multidimensional mechanical system with phase constraints given by expeimental data. We give the results of a solution of this optimal control problem obtained using Fourier-spline approximation of independently varying functions and minimizing an objective function over maximally likely directions.

Towards Pareto Optimization of Performance of a Generic Synchronizer of Transmission Systems

Manual transmissions for passenger cars and trucks are equipped with synchronizer mechanisms. A synchronizer mechanism as a key component of a transmission system must be able to prevent transmission gears from shocking, reduce the noise and it has a great impact on driving comfort and transmission efficiency. Gear shifting improvement with respect to smooth, quick and energy efficient synchronizer’s performance is still an important issue for automotive industry. A synchronization process comprises several phases within which presynchronization, main synchronization, pre-engagement and engagement phases can be recognized. Aiming an understanding of internal dynamics and existing possibilities for optimization of synchronization processes in transmission systems during the main synchronization phase an engineering model of a generic synchronizer mechanism is proposed. The synchronizer mechanism is modeled by a contacting triple-body system consisting of the selector sleeve, the blocker ring and the gearwheel. The algorithm has developed to solve the direct dynamics synchronization problem for the generic synchronizer mechanism. By using the developed algorithm the rotational motion of the contacting triple-body system and the synchronizing torques between contacting interfaces are determined for given vehicle resistance torque, the drag torque, and the control torque applied to the selector sleeve that all together satisfy the equations of motion and guarantee synchronization of the rotational speeds of the sleeve, the blocker ring and the gearwheel for the final time. It is shown that the solution to the direct dynamics synchronization problem for the generic synchronizer mechanism is not unique and it allows formulation different optimization problems. Mathematical statement of multi-objective Pareto optimal control problem for synchronizer mechanism is given. Within the proposed model of the generic synchronizer mechanism the time-comfort Pareto optimal control problem is considered. Assuming that the resistance torque on the synchronizer owing to the vehicle inertia, the drag torque, and the synchronizing torques at the contacting interfaces are substantially constant during the main phase of a synchronization process, the solution to the time-comfort Pareto optimal control problem has been obtained. It was shown that there exist the external control torque (or shift force) applied to the selector sleeve such that the synchronization of rotational speeds of the sleeve, the blocker ring and the gearwheel is guaranteed and the synchronization process is optimal both with respect to minimal possible synchronization time as well as lowest possible inertial load acting on the synchronizer mechanism. Analysis of the obtained Pareto solution is presented.

Multibody Systems Modeling and Optimization Problems of Lower Limb Prostheses

To study the effect of prosthesis design on the kinematic, dynamic, energetic and other characteristics of an amputee’s locomotion and to improve and create new efficient lower limb prostheses it is expendient to use mathematical modeling of a human walk process and dynamic optimization techniques. There are a number of mathematical models of the biped walk, having different degrees of adequacy [1–8]. In addition, different experimental methods have been used for solving these problems [9–11].

On the controlled rotation of a system of two rigid bodies with elastic elements

The problem of controlling the plane rotational motions of two rigid bodies connected by an elastic rod is studied. One end of the rod is attached to the support by a hinge with a spring, the latter modelling the elastic compliance of the fastening, and the other end is rigidly joined to the load. The Hamilton principle is used to obtain the integrodifferential equations and boundary conditions describing the motion of the system support — spring — rod — load. The following problem is posed: it is required to rotate the system by a given angle by means of the controlling force moment, with quenching of the relative oscillations of the load elements which appear as a result of the deformability of the rod and of the elastic torsion of the spring. Similar problem arise in the study of the dynamics and control of the motion of devices used in transporting loads through space (robots, manipulators, load lifting machines, etc.). In computing their control modes a significant part is played not only by the deformability of the elements, but also by the elastic compliance of the connecting joints. Asymptotic methods are used to botain a solution of the control problem in question for two limiting cases: 1) the mass of the load carried is much greater than the mass of the rod and support, and 2) the rod has high flexural rigidity.

Wear/comfort Pareto optimisation of bogie suspension

ABSTRACT Pareto optimisation of bogie suspension components is considered for a 50 degrees of freedom railway vehicle model to reduce wheel/rail contact wear and improve passenger ride comfort. Several operational scenarios including tracks with different curve radii ranging from very small radii up to straight tracks are considered for the analysis. In each case, the maximum admissible speed is applied to the vehicle. Design parameters are categorised into two levels and the wear/comfort Pareto optimisation is accordingly accomplished in a multistep manner to improve the computational efficiency. The genetic algorithm (GA) is employed to perform the multi-objective optimisation. Two suspension system configurations are considered, a symmetric and an asymmetric in which the primary or secondary suspension elements on the right- and left-hand sides of the vehicle are not the same. It is shown that the vehicle performance on curves can be significantly improved using the asymmetric suspension configuration. The Pareto-optimised values of the design parameters achieved here guarantee wear reduction and comfort improvement for railway vehicles and can also be utilised in developing the reference vehicle models for design of bogie active suspension systems.

Optimal Design of Magnetostrictive Transducers for Power Harvesting From Vibrations

Methodology is proposed for designing of magnetostrictive electric generator having maximal mean power output for a given amount of active material in a transducer and a prescribed vibration excitation. The methodology is based on dimensional analysis of constitutive linear equations of magnetostriction and numerical solution of constrained optimization problem in transducer’s dimensionless design parameters space by using Sequential Quadratic Programming algorithm. The methodology has been used to design optimal Terfenol-D based transducer for power harvesting from vibrations. It was shown that for steady state operations there exists possibility to choose only 4 new design parameters being the functions of dimensionless parameters of the transducer. Magnetostrictive strain derivative, Young’s modulus and magnetic permeability were determined as functions of magnetic bias and prestress by using experimental data of Terfenol-D. Contour plots and numerical analysis of design parameters show that within the considered concept of magnetostrictive electric generator there exists a set of structural parameters of the transducer that lead to its optimal performance with given amount of active material and prescribed vibration excitation. Examples of solution of optimal design problem demonstrate that for harmonic kinematic excitation with amplitude 0,0002m and frequency 100Hz it is possible to design a magnetostrictive electric generator with 3,2W mean power output having mass of active material 0,01kg.