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�MATHEMATICAL MODELING AND OPTIMIZATION OF MAGNETIC GEAR INVOLVED MECHANICAL SYSTEMS WITH DIFFERENTIAL EVOLUTION METHOD AND RESPONSE SURFACE METHOD�

Submitted by:

Sooryadas sudhakaran

B180494PE

S6-PE

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CONTENTS

  • Introduction
  • Literature Review
  • Objective
  • Methodology
  • Results
  • Conclusions
  • References

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INTRODUCTION

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  • Mechanical gears are used to transfer motion and torque between machine components by physical contact between the gear pairs

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  • As there is contact between the gear pairs the friction, wear and tear are inevitable during power transmission

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  • Thereby mechanical efficiency in power transmission is less

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Figure 1: Mechanical gear

Courtesy: Unsplash.com

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  • Magnetic gears are becoming promising devices.

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  • Due to the fact that there is no contact required, no gear lubrication, no mechanical fatigue, inherent overload protection and reduced maintenance etc.

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  • Motor-gear pair is selected based on dimension, mass and efficiency .

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  • Develop high Torque within small volume.

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INTRODUCTION(Contd…)

Figure 2:Topology of the investigated magnetic gear. (Zanis, R. et al.,2016).

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LITERATURE REVIEW

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Sl.no

Author

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Title

Contents

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Zanis, R., Jansen, J.W., Lomonova, E.A

Modeling and design optimization of a Shaft-coupled motor and magnetic gear.(2016).

  • Response surface methodology (RSM) can be used to reduce the number of design variables.

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  • This is achieved by representing the optimized torques of the electrical motor and magnetic gear as polynomial functions of their respective dimensions

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Wang, Y., Filippini, M., Bianchi, N., and Alotto, P

Parametric design and optimization of magnetic gears with differential evolution method.(2018).

  • Global optimization of design based on cost and performance can be carried out using differential evolution algorithm.

Table 1: Literature Review

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LITERATURE REVIEW (Contd…)

  • In the paper by Wang, the gear considered for study is coaxial magnetic gear.

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  • In the paper by Zanis the motor-gear arrangement taken for study is shaft coupled motor.

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Figure 3:Integration possibilities of electrical motor and magnetic gear: (a) shaft-coupled motor and

gear; (b) “pseudo” direct-drive motor. (Zanis, R et al.,2016).

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OBJECTIVES

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  • To model an actuator consisting of electric motor and magnetic gear.

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  • To simultaneously optimize an electrical motor and a magnetic gear for the intended application.

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  • Thereby, to minimize overall actuator dimension.

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  • Optimize magnetic gear based on cost and performance.

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METHODOLOGY

  • High-accuracy analytical electromagnetic models of an electrical motor and a magnetic gear are developed based on the harmonic modeling method.

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  • The models are used to derive the objective and constraint functions from optimization problem.

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  • The optimization of the motor and magnetic gear are treated simultaneously.

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  • Thereby, high number of design variables are involved which results in a slow and computationally-intensive numerical optimization task.

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METHODOLOGY (contd…)

  • Design variables can be reduced by representing the optimized torques of the motor and magnetic gear as polynomial functions of their respective dimensions.

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  • The polynomial functions are approximated by the application of response surface methodology (RSM) on the optimization routines that are defined for the motor and magnetic gear.

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  • Using differential evaluation methodology (DEM) cost and performance of magnetic gear is optimized.

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ELECTROMAGNTIC MODELLING

Harmonic modelling

Assumptions

  • The electromagnetic problem can be described in a 2D polar coordinate system (r, j).

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  • For a given region, the material has linear and homogenous magnetic properties in the r-direction.

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  • The ferromagnetic material is infinitely permeable. Consequently, no analytical expression of the magnetic flux density can be obtained within the ferromagnetic material.

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ABBREVIATIONS

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ELECTROMAGNTIC MODELLING(contd…)

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ELECTROMAGNTIC MODELLING(contd…)

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HARMONIC MODELLING OF ELECTRICAL MOTOR

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Figure 5: Slot winding region simplification. (Zanis, R. et al.,2016).

Figure 4:Fractional-slot concentrated-windings PM motor. (Zanis, R. et al.,2016).

 

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HARMONIC MODELLING OF ELECTRICAL MOTOR

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…………(10)

Figure 6: Representation of the electrical motor structure for modeling purpose. (Zanis, R. et al.,2016).

…………(11)

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HARMONIC MODELLING OF MAGNETIC GEAR

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Figure 7: Geometric parameters of the pole-pieces. (Zanis, R. et al.,2016).

Figure 8: Representation of the magnetic gear structure for modeling purpose. (Zanis, R. et al.,2016).

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OPTIMIZATION

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OPTIMIZATION

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  • Optimizes a problem iteratively by improving a candidate solution with regard to a given measure of quality.
  • Makes few or no assumptions.

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OPTIMIZATION USING DEM

Figure 9: Optimization results with DE algorithm.

(Wang, Y. et al., 2018)

Figure 10: MG topology achieving maximum TPE.

(Wang, Y. et al., 2018)

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RESULT

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Figure 11: Pareto front constructed from the multi-objective optimization results. (Zanis, R. et al.,2016).

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RESULT

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Parameter

Shaft-Coupled Motor and Magnetic Gear

Electrical Motor Only

Diameter

24 mm

30 mm

Axial length (incl. housing)

48 mm

45 mm

Volume

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Table 2: Comparison between outer dimensions and volume of the shaft-coupled motor and magnetic

gear, and an electrical motor.

 

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CONCLUSIONS

  • High-accuracy analytical electromagnetic models of the electrical motor and magnetic gear are developed.
  • Based on these models, design optimization objective and constraint functions are formulated.
  • Higher the magnetic transmission ratio, lower will be the size of motor.
  • The simultaneous optimization of the electrical motor and magnetic gear is achieved by response surface methodology (RSM).
  • RSM helps to reduce the number of design variables originating from the two electromagnetic devices.

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  • Representing their optimized torques as polynomial functions of their respective outer dimensions and transmission ratio.

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  • From the constructed Pareto front, actuator size can be reduced by increasing the magnetic gear transmission ratio up to a certain level.

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  • After the certain level, magnetic gear torque density limitation becomes more apparent and no further actuator size reduction can be achieved.

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  • Using differential evaluation methodology optimum conditions for magnetic gear with cost and performance objectives were achieved.

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CONCLUSION (contd…)

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REFERNCES

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  • Jian, L., and Chau, K., 2009. Analytical calculation of magnetic field distribution in coaxial magnetic gears. Progress in Electromagnetics Research. 92, 1-16.

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  • Wang, Y., Filippini, M., Bianchi, N., and Alotto, P., 2018.Parametric design and optimization of magnetic gears with differential evolution method of Thirteenth International Conference on Electrical Machines (ICEM), Alexandroupoli, 919-925.

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  • Zanis, R., Jansen, J.W., Lomonova, E.A., 2016. Modeling and design optimization of a Shaft-coupled motor and magnetic gear. Actuators. 5(1), 1-10

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THANK YOU !!