This document summarizes a post graduate diploma project on an electric vehicle suspension system using magnetorheological (MR) dampers. It describes the components and working of an MR damper, including the MR fluid, solenoid, and controlling solenoid current. It presents a Bouc-Wen mathematical model of the damper and uses a genetic algorithm to determine model parameters. Experimental results at different frequencies and currents are shown and agree with simulations. Tuning the current can make the system behave as underdamped, critically damped or overdamped for vibration control.

1. Post Graduate Diploma in Electric Mobility
College of Engineering Pune
Presented by-
Bhor Saurabh
MIS-242160001

2. Introduction
Suspension System
 Supports weight of the vehicle.
 Provides smoother ride for the driver and
passengers i.e. acts as cushion.
 Protects your vehicle from damage and wear.
 It also keeps the wheels pressed firmly to the
ground for traction.

3. MR Damper
 Solenoid
 MR fluid
 Controlling Solenoid Current
 Rugged and Reliable.
 Simple, Low Power requirement.

4. MR Fluid
 Smart fluids.
 Contains suspended Iron particles.
 External magnetic field converts liquid state to
semi solid state.
 Behaves like Non-Newtonian fluid with
controllable viscosity.
 Reversible.

5. Equivalent Damping Coefficient of MR Damper
 Area of Force-Displacement plots gives the energy dissipated by Damper.
 Area calculated by Numerical Integration using Trapezoidal rule.
𝑾 = 2𝝅2
Ceq𝒇𝑿2
 Here, W is the single cycle energy dissipation, Ceq is the equivalent damping
coeffcient, f is the frequency of excitation, and X is the amplitude of excitation.

6. Mathematical Model
 Bouc-Wen model
𝑭 = 𝒄𝒙 + 𝒌0(𝒙 − 𝒙0) + 𝜶𝒛
𝒛 = −𝜸 𝒙 𝒛 𝒛 𝒏−1
− 𝜷𝒙 𝒛 𝒏
+ 𝑨𝒙
 c is the viscous damping coefficient, k0 is the stiffness coefficient,
×0 is the initial displacement of the spring to compensate for the
effect of accumulator, and z is the evolutionary variable which is
generally expressed in the differential form. The remaining
parameters are the ones that influence the shape of the hysteresis
curve.

7.  Determination of these parameters using different techniques is known
as model fitting.
 Since there are eight parameters to be defined, simple trial and error
method would be impractical.
 Genetic Algorithm
Simulink Block for Bouc-Wen Model
Mathematical Model

8. Results
a Force versus displacement at 0.4 Hz. b Force versus displacement at 1.03 Hz. c Force versus displacement at 2.07 Hz. d Force versus displacement at 3.1 Hz. e Force versus
displacement at 4.14 Hz

9. a Force versus displacement at 0 A current. b Force versus displacement at 0.5 A current. c Force versus displacement at 1 A current

10. Maximum force versus velocity amplitude

11. a Force versus displacement for 2.07 Hz excitation frequency at 0 A current. b Force versus displacement for 2.07 Hz excitation frequency at 0.5 A current. c Force versus
displacement for 2.07 Hz excitation frequency at 1 A current

12. Experimental Results and Discussion
 Energy dissipated and equivalent damping coefficient of MR damper at different values of current supplied at
input excitation frequency of 2.07 Hz and excitation amplitude of 20 mm.
Current supplied I (A) Energy dissipated W (J) Equivalent damping
coefficient
Ceq (Ns/m)
0 21.8029 1.334
0.5 56.9029 3.4816
1 94.4915 5.7814

13. Results
 The plots show that there is a reasonable agreement between the experimental and simulated
results.
 The identified parameters for 2.07 Hz sinusoidal input and 20 mm amplitude are shown in Table below.
Sr. No. Parameters Value
1 c0 (Ns/m) 2069.6I − 833.4
2 k0 (N/m) 6782I
2
+ 18045I + 12907
3 x0 (m) 0.012982
4 α (N/m) − 128.59I
2
+ 639.98I − 276.47
5 γ (/sq m) 44.616
6 n 9.927883
7 β (/sq m) 24.768

14.  Mass of human body to be 60 kg and that of the seat to be 20 kg, the total mass m is 80 kg.
 The spring stiffness of the system k is assumed to be 16 kN/m.
 The natural frequency of the undamped system is 2.251 Hz.
 Input of displacement amplitude of 20 mm.
Results

15.  Vehicle chassis vibration is predominantly in the region of 0.5–7 Hz, thus the natural frequency falls
within this range.
 The critical damping coefficient for this system is 2.2627 kNs/m.
 We can see that the response of the system at 0 A current is similar to the response of an
underdamped system.
 At higher values of current, like 0.5 A and 1 A, the response of the system is similar to that of an
overdamped system.
 Tuning the current supplied to the MR damper, the same damper can make the system behave as an
underdamped, critically damped or overdamped system of vibration.
Conclusion

16. Reference
 S. C. R. &. G. A. Rangaraj Madhavrao Desai, "Evaluation of a commercial MR damper for application in
semi-active suspension," SN Applied Sciences, August 2019.

17. Thank You!