Comparison of Linear, Nonlinear, Hysteretic, and Probabilistic MR Damper Models

Magnetorheolgical (MR) fluid dampers have the capability of changing their effective damping force depending on the current input to the damper. A number of factors in the construction of the damper, as well as the properties of the fluid and the electromagnet, create a dynamic response of the damper that cannot be fully described with a static model dependent on current and velocity. This study will compare different techniques for modeling the force response of the damper in the current-velocity space. To ensure that all the dynamic response characteristics of the damper are captured in data collection, random input signals were used for velocity and current inputs. By providing a normally distributed random signal for velocity to a shock dynamometer and a uniformly distributed random signal for current to a Lord rheonetic seat damper, the force response could be measured. The data from this test is analyzed as a two dimensional signal, a three dimensional force plot in the current velocity plane, and as a probability density function. Four models are created to fit the data. The first is a linear model dependent solely on current. The second is a nonlinear model dependent on both current and velocity. The third model takes the nonlinear model and includes a filter that affects the force response of the model with time. Each of these three approaches are compared based on the total error in the force response and the models’ ability to match the PDF of the data. Finally, a fourth model is created for the damper that improves the nonlinear model by making one parameter a probability parameter defined by a PDF calculated from the data. However, because it is a probability model, the error cannot be found through comparison to the data.