1. 2004/01/17 Sangjin Park PREM, Hanyang University
Finite Element Analysis of Electro-thermal Field in a Brushless DC Motor
Good afternoon! I am Sangjin Park and from Hanyang University in Korea.
The topic of presentation is Finite Element Analysis of Electromechanical Field of a HDB Spindle Motor at Elevated Temperature.
2004/01/17
Sangjin Park
PREM, Hanyang University

2. Motivation Thermal Problem in a Brushless DC Motor
Increase of Power Consumption
High Speed Drive
Hydrodynamic Bearing
High Heat Generation in a Computer Hard Disk Drive
Performance Variation due to Elevated Temperature
Hub
Shaft
York PM
Stator
Coil
Thrust pad
Thrust Bearing
Journal Bearing
Sleeve
The recent trend in a spindle motor of a computer hard disk drive is an use of hydrodynamic bearing instead of ball bearing.
This figure shows the structure of hydrodynamic bearing spindle motor. The brushless dc motor is outer rotor type and consists of stator, coil, permanent magnet and back york, like this. The hydrodynamic bearing consists of journal and thrust bearings.
Operating temperature of a hydrodynamic bearing spindle motor has been one of the important design considerations because it affects not only the magnetic characteristics such as the demagnetization of permanent magnet, but also the mechanical characteristics such as the vibration characteristics.
< Structure of HDB Spindle Motor >

3. Prior Research
Liu Z.J., Howe D., Mellor P.H. and Jenkins M.K., "Coupled thermal and electromagnetic analysis of a permanent magnet brushless DC servo motor," Sixth International Conference on Electrical Machines and Drives, 1993.
Sebastian T., "Temperature effects on torque production and efficiency of PM motors using NdFeB magnets," IEEE Transactions on Industry Applications, 1995.

4. Method of Analysis Electro-thermal Field Analysis
Electromagnetic Field
Time-stepping Finite Element Method
Thermal Field
Finite Element Method of Heat Conduction Equation
Temperature Dependent Parameters
Electrical Parameters: Coil Resistance, PM Characteristics
Mechanical Parameters: Viscosity of Fluid Lubricant
This research presents the electromechanical analysis of a hydrodynamic bearing spindle motor.
Time-stepping finite element method is applied to analyze the electromagnetic field.
The analysis of hydrodynamic bearing is performed by finite element method of Reynolds equation and the spindle motion is calculated by Newton’s equation of motion.
The temperature dependent parameters are the coil resistance and PM characteristics in the electromagnetic field and the viscosity of fluid lubricant of HDB in the mechanical field.

5. Electromagnetic Field Analysis
Maxwell Equation (2D)
FE Formulation by Galerkin Method
2 dimensional Electromagnetic field is from the Maxwell equation as follows and this shows the FE formulation by Galerkin method.

6. Voltage Equation of Inverter Circuit
Consider PWM switching action of inverter circuit
Consider freewheeling current through diode
< Commutation >
This shows the driving circuit of a brushless DC motor.
Maxwell equation is coupled with the driving circuit equation, which includes the switching action of PWM inverter and the current flow through freewheeling diodes in the non-energized phase.
< Duty On >
< Duty Off >

7. Time Dependency (Backward Difference Method)
Torque Calculation
Maxwell Stress Tensor
Equation of Motion of a Rotor
Moving Mesh Algorithm
Backward difference method is applied to solve the time differential terms and force and torque are calculated by Maxwell stress tensor.
New coordinates of the moving meshes are determined by locating moving meshes in the radial direction, and by rotating them along the sliding line in the air gap.

8. Thermal Field Analysis
Transient Heat Conduction Equation (Axisymmetric Case)
Governing Equation
Boundary Condition
FE Formulation by Galerkin Method
Similar Procedure as Electromagnetic Field
Time Differential Term : Backward Difference Method
This shows the model of the hydrodynamic bearing and the Reynolds equations of the journal and thrust bearing in terms of cylindrical coordinates, respectively.
The bearing force and friction torque can be determined by integrating the pressure and the velocity gradient in the bearing area.

9. Heat Source Model Copper Loss Iron Loss Disk Windage Loss
Experimental Data
Disk Windage Loss
HDB Friction Loss
Consider Viscosity Variation
< Power Consumption Test of Analysis Model >

10. Boundary Model Natural Convection Boundary Condition
Heat Transfer Coefficient (Simplified Form)
Upper Surface of HDD (S1)
Lower Surface of HDD (S2)
Side Surface of HDD (S3)

11. Coupled Variable Temperature Dependent Variables Phase Resistance
Residual Flux Density of Permanent Magnet
Viscosity of Fluid Lubricant

12. Electro-thermal Analysis
Analysis Procedure
Difference of Time Constant
Modified Time-Step in the Thermal Field
Magnetic Field Analysis considering Driving Circuit
PI Controller
Maxwell
Equation +
Voltage
Mechanical Field Analysis
TON
TOFF
Carrier Wave -
Ωref
Inverter Ω
Heat Conduction Analysis
(Temperature Determination)
Equation of Motion
Torque e u
Speed
Heat Source Calculation
Current
Temperature Dependent Variables
Coil Resistance
Br of PM
Viscosity Factor
Moving Mesh Algorithm
by Angular Displacement
This shows the analysis procedure of the electromechanical field.
Once the PI controller sets the control input u, which is compared with the triangular carrier wave, the variable time-step is determined by the on and off period of the inverter. In this process, the voltage equation is modified by considering the current in the freewheeling diode, and is coupled with the Maxwell equation to obtain the time-stepping finite element equation for the analysis of magnetic field. After the HDB field and rotor motion are solved, the new angular and radial positions of a rotor are obtained. Then the moving mesh technique rearranges the magnetic finite element model to recalculate the magnetic field at the next time-step. The control input u is determined again by the speed error signal and PI controller. This procedure is repeated until the rotor reaches the reference speed from standstill.

13. Analysis Model Specification of Analysis Model
Hydrodynamic Bearing Brushless DC Motor
Quantity
Value
Input Voltage
12 V
PWM frequency
40,000 Hz
Rated speed
7,200 rpm
Air gap length
0.25 mm
Phase resistance
1.933 Ω
Residual flux density of permanent magnet
0.7 T
This table shows the major specification of the analysis model.

14. Magnetic FE Model Thermal FE Model < 8,464 Triangular Elements >
Disk
Base Plate
Cover
< 8,464 Triangular Elements >
< 7,004 Triangular Elements >

15. Result Electromagnetic and Thermal FE Field at Steady State
Initial Temperature : 25 ℃
Ambient Temperaure : 40 ℃
Max ℃, Min ℃ (RGB order)
< Equivalent Potential Line >
< Temperature Distribution >

16. Result Thermal Parameters
Temperature Profile
Coil and Permanent Magnet
Temperature at the steady state
Phase Resistance : 9.53% increase
Br of PM : 2.35% decrease
Temperature
Coil
48.8 ℃ PM
48.5 ℃

17. Temperature Profile Bearing Area Temperature at the steady state
Friction Torque : 47.7% decrease
Temperature
Upper Journal
49.4 ℃
Lower Journal
49.2 ℃
Upper Thrust
48.8 ℃
Lower Thrust
48.3 ℃

18. Result Electrical Parameters
Phase Current Profile
< Electromagnetic Analysis 25 ℃ >
< Electro-thermal Analysis >
Electromagnetic Analysis
Electro-thermal Analysis
PWM Duty Ratio
82.8 %
80.3 % (+ 2.5%)
Phase Current
385 mA
320 mA (- 17%)
Copper Loss
573 mW
434 mW (- 24%)

19. Torque Profile < Electromagnetic Analysis 25 ℃ >
< Electro-thermal Analysis >
Electromagnetic Analysis
Electro-thermal Analysis
Average Load Torque
4.25 mN-m
3.30 mN-m (- 22.4%)

20. Conclusion
This research proposes a transient finite element method to analyze the electro-thermal field of a HDB brushless DC motor.
The electro-thermal analysis may predict the motor performance of a HDD, effectively.
Problem
Non-axisymmetric model
Numerical heat source calculation
Consideration of air flow
Experimental Validation
This research proposes a finite element method to analyze the electromechanical field of a hydrodynamic bearing spindle motor.
The electromechanical characteristics are investigated at the normal and elevated operating temperature.
It shows that the decreased viscosity of fluid lubricant plays the major role in the reduction of torque, phase current and the increase of a rotor orbit.
Thank you for your attention.