# Investigation of Hysteresis Effect in Torque Performance for a Magnetorheological Brake in Adaptive Knee Orthosis

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## Abstract

**:**

## 1. Introduction

_{c}) and reluctance (S) in the electrical and magnetic circuit. The MR fluid filled inside this MR brake is MRF 140-CG which was manufactured by Lord company [25]. The response time of the fluid is very less compared to the RL electrical circuit inside the MR brake.

## 2. Hysteresis Effect on MR Brake

## 3. Simulation Model

#### 3.1. Electromagnetic Model of MR Brake with Hysteresis

_{c}) which has the value of 2.5 Ω, and the number of turns (N) in the coil is 150. The PWM signal is given to the H-bridge which drives the coil at 5 V and a maximum current of 2 A.

_{c}). It is the time taken for the current in the coil to reach the steady state, and it also defines the response time of the MR brake. It is given by Equation (1).

_{c}is the inductance and R

_{c}is the resistance of the coil. In MR brake’s the inductance of the coil is not constant. The coil inductance depends on the sum of all the reluctance in the magnetic circuit and is given by the ratio of the square of the number of turns to the reluctance in the magnetic circuit Equation (2).

_{Σ}is the sum of the reluctance in the magnetic circuit.

_{r}is the relative permeability of the material and µ

_{o}is the permeability constant.

_{r}and S. The physical geometry and the B-H curve parameters of the core and MR fluid are incorporated in the block. The materials inside the MR brake which acts as reluctance are divided into segments with regular geometry. Each segment is represented with the block nonlinear reluctance with hysteresis and connected in series to provide a closed magnetic flux path. It estimates the drop in the flux density across the segments during OFF pulses of the PWM signal. A flux sensor is placed after the MR fluid reluctance to find the flux in the fluid. From Equation (3) the ratio of the flux flowing through the fluid to the area of the fluid gives the flux density (B). It is passed to the MR fluid model to calculate the yield stress of the MR fluid.

#### 3.2. Mechanical Model of MR Brake

_{MR}).

#### 3.2.1. MR Fluid Model

#### 3.2.2. MR Brake Model

_{2}), and inner radius (r

_{1}) of the rotor disc, angular velocity (ω), and the amount of current passing through the coil (I). The number of layers increases the viscosity of the MR fluid. The net torque of a single-pole multilayer MR brake is calculated by Equation (11). (${T}_{fric}$) is the frictional torque of the MR brake.

#### 3.3. MR Brake ANSYS Simulation

## 4. Simulation and Experimental Results

#### 4.1. DC Actuation Signal

#### 4.2. PWM Actuation Signal

_{1}) of the MR brake. The ripple in the current (∆I) must be minimized to obtain a stable magnetic field and torque. This is achieved in two steps. First, the frequency of the PWM signal is increased up to 5 kHz which reduced ∆I and ∆T

_{1}to considerably low 3.3% and 0.2% respectively. Before we tune the second step, we need to know ∆T

_{2}is the difference between torque obtained from the DC signal and PWM signal.

_{1}is high at low frequencies (1–100 Hz) and low at high frequencies (500 Hz–5 kHz). This phenomenon is because of the self-inductance and hysteresis effect in the MR brake. They oppose the rate of change in the current and magnetic field. At low frequencies, the current has enough time to rise to the maximum level and decay to the minimum level. This causes a high ripple in the current leading to the ripple in the magnetic field and the torque. In such cases, the back emf generated by the inductor is also high to oppose the change in the current. At high frequencies, the current does not have enough time to rise and decay to peak levels. Therefore, the rising and decaying levels of the current reduces which gives less ripple and low back emf. It leads to a stable magnetic field and torque.

_{2}varies with the duty cycle at optimal frequency. During pulse switching voltage rises and drops instantly but the current does not. This is because of back emf, the coil does not allow the current to change instantly. It instead takes one time constant to change the current through it. If the ON time is greater than the time constant of the circuit, current reaches the steady state maintains it until the OFF pulse. To save more power ON time is reduced to less than the time constant such that current immediately falls when it reaches steady state. Figure 9 shows that ∆T

_{2}at 60% duty cycle is nearly zero. It means the PWM signal consumed only 60% of the input power to obtain the equivalent torque of DC signal with 0.2% ripple. Variable torque can be obtained by changing the duty cycle between 0–60%. It is clear from the simulation results that at 5 kHz frequency and 60% duty cycle are the optimal values for the selected MR brake with PWM actuation signal. At these optimal values, MR brake can obtain 99.8% steady torque by consuming 6 W of power. As explained earlier hysteresis in the core, the current and magnetic field in the coil does not collapse instantly. This maintains steady torque of the MR brake during the off pulse of the input signal due to the hysteresis effect which was explained previously. This effect is turned into an advantage by choosing PWM as an actuation signal which saves 40% power consumption of MR brake. Therefore, choosing a PWM signal is advantageous over a DC signal.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 10.**Torque performance of MR brake (

**a**) Simulation and Experimental torque of MRB with PWM signal at 60% duty cycle (

**b**) torque comparison of MR brake with PWM and DC signal.

Verification Type | Parameters | Actuation Signal | ||
---|---|---|---|---|

B (T) | T (N-m) | I_{max} (A) | ||

EM model | 0.38 | 14.2 | 2 | DC |

ANSYS | 0.36 | 13.08 | ||

Experiment | Not measured | 12.2 |

Verification Type | Parameters | Actuation Signal | ||
---|---|---|---|---|

B (T) | T (N-m) | I (A) | ||

EM model | 0.37 | 14 | 1.2 | PWM |

Experiment | 12 |

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**MDPI and ACS Style**

Shiao, Y.; Gadde, P. Investigation of Hysteresis Effect in Torque Performance for a Magnetorheological Brake in Adaptive Knee Orthosis. *Actuators* **2021**, *10*, 271.
https://doi.org/10.3390/act10100271

**AMA Style**

Shiao Y, Gadde P. Investigation of Hysteresis Effect in Torque Performance for a Magnetorheological Brake in Adaptive Knee Orthosis. *Actuators*. 2021; 10(10):271.
https://doi.org/10.3390/act10100271

**Chicago/Turabian Style**

Shiao, Yaojung, and Premkumar Gadde. 2021. "Investigation of Hysteresis Effect in Torque Performance for a Magnetorheological Brake in Adaptive Knee Orthosis" *Actuators* 10, no. 10: 271.
https://doi.org/10.3390/act10100271