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

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 >

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.

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.

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.

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 >

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.

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.

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 >

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)

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

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.

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.

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

Result Electromagnetic and Thermal FE Field at Steady State Initial Temperature : 25 ℃ Ambient Temperaure : 40 ℃ Max. 50.03℃, Min. 44.80℃ (RGB order) < Equivalent Potential Line > < Temperature Distribution >

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 ℃

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 ℃

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%)

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%)

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.