Dynamic Analysis of a Quarter Car Model with Semi-Active Seat Suspension Using a Novel Model for Magneto-Rheological (MR) Damper


Mathematical modeling of magneto-rheological damper has been an intriguing field of research ever since the invention of the device itself. An accurate magneto-rheological damper model results in development of an efficient current controller in a semi-active seat suspension system featuring magneto-rheological damper. Hence, a number of models have been put forward to accurately predict the magneto-rheological damper behavior. This paper presents another mathematical model for magneto-rheological dampers based on their equivalent damping. A commercially available magneto-rheological damper has been used for characterization in this study. The magneto-rheological damper behavior is characterized using two models, Bingham model and equivalent damping model. These models are then used to simulate the magneto-rheological damper in a quarter car model with four degree of freedom featuring semi-active seat suspension that is subjected to bump road input and random road input. The magneto-rheological damper model is supplied with current using two control logics, on–off Skyhook logic and Proportional Integral and Differential logic. The performance of the two models are compared based on driver mass response in each case of seat suspension model and computation time. The results show that equivalent damping model can represent the magneto-rheological damper behavior with sufficient accuracy while reducing computational time by 30% irrespective of type of road input or type of control logic implemented. The reduced computational time is an added advantage when magneto-rheological damper is used in real-time.

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Availability of data and material

Data are available in a public, open access repository.

Code availability

All analyses were completed using R software version 3.5.0 and the core code was simPH package.


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This study was financially supported by Impacting Research Innovation and Technology (IMPRINT) Project No. IMPRINT/2016/7330 titled “Development of Cost Effective Magnetorheological (MR) Fluid Damper in Two wheelers and Four Wheelers Automobile to Improve Ride Comfort and Stability” funded by Ministry of Human Resource Development and Ministry of Road Transport and Highways, Govt. of India.

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Correspondence to Hemantha Kumar.

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Jamadar, MeH., Desai, R.M., Saini, R.S.T. et al. Dynamic Analysis of a Quarter Car Model with Semi-Active Seat Suspension Using a Novel Model for Magneto-Rheological (MR) Damper. J. Vib. Eng. Technol. 9, 161–176 (2021). https://doi.org/10.1007/s42417-020-00218-1

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  • Magneto-rheological damper
  • Equivalent damping
  • Bingham model
  • Quarter car model
  • Seat suspension