Hysteresis model parameters identification for the SAS rotational MR damper

Comfort, reliability, functionality performance which provide a longer life cycle requires thourogh understanding and analysis of the vibrations, this is a general rule for most of the static and dynamic when studying the functionality performance of any application. Vibrations is an extremely important issue to consider when designing various systems.The hysteresis in the dampers is very important issue when characterizing the damper used to suppress the vibrations, it is a very complex phenomena but very important to understand and consider during the design phase. The hysteresis equations of Bouc-Wen, Lugre, and Dahl have been modeled and simulated in Matlab/Simulink. Afterward, the different parameters in the models was manipulated and their effects on the outcome was analyzed. The hysteresis models of Bouc-Wen, Dahl and LuGre have been analyzed and compared analytically to really show the difference in the models. At last the Bouc-Wen model was implemented together with the SAS(Semi Active Suspension) system. The model parameters were tuned manually to try to fit the response of the system. In this paper a predefined methodology has been applied for determining the hysteresis loop parameters using the data collected for vibration analysis under predefined test specifications. The following data has been used later to regenerate the vibration signal, so on get as closer to the real signal.In the coming work, advanced method will be used to determine the exact parameters for the hysteresis loop as well as using the inverse hysteresis to improve the of the vibration suspension in the Semi Active Suspension system.The behavior of MR dampers can be presented with different mathematical models. The Bouc-Wen model was found to be model to both illustrate the MR damper and recreate the behavior of the SAS system. Key–Words: Bouc-Wen model, Dahl model, Hysteresis, Lugre model, Magnetorheological damper,Parameters identification, Semi-Active Suspension System 1 Vibration analysis The hysteresis identification can be a complex process, understanding the static and the dynamic vibration in the system enable facilitating the process of the hysteresis identification, In this work different vibration responses of the MR damper. When using fluid dampers the exerted force, or torque, will respond differently to vibrations with respect to the system’s natural frequency and the exerted vibration on the damper. We will discuss the static response compared to the dynamic response using the models discussed in 3. 1.1 Static vibration Static vibration on the MR damper is interpreted as when the damper is working without the mechanical dynamics of the system. The damper’s exerted force, or torque, is then a function fully described by the current and velocity. To illustrate the effects of the vibration, the Matlab Simulink models are used to simulate the maximum torque of the damper with respect to frequency when the displacement is forced in a sine motion. The result using the Bouc Wen model is shown in Figure 1 When using a dynamic model, here Bouc Wen, someone can observe high torque even at low frequencies. WSEAS TRANSACTIONS on SYSTEMS and CONTROL Yousef Iskandarani, Hamid Reza Karimi ISSN: 1991-8763 371 Issue 10, Volume 6, October 2011 Figure 1: Vibration response with respect to frequency using the Bouc Wen model. Displacement is forced in a sine motion creating a frequency dependent torque. 1.2 Dynamic vibration Considering the dynamics in a system, it is important to have knowledge of its vibrational response. The system will have a natural frequency and applying a harmonic excitation near the system’s natural frequency can create a highly unstable system. We use the semi-active damper to control and mute these critical vibrations. To analyze, the mechanical system is built up using T = Iθ̈ = − ( ksθ + Tmrθ̇ + Tin ) (1) Figure 2: The physical system with the MR damper The model is shown in Figure 2 with fictitious values. The system has a natural frequency of