Chapter 5 Design of a scaled-down MB motor for portable disk drives
5.3 Design and analysis
For identifying the proposed system, the magnetic forces were calculated by applying the Maxwell stress method, according to the govern equation of magnetic field that is Maxwell’s equation. To perform these calculations, the FEA software Magnet 6.18 was used. The 3D half model of the design motor shown inFig. 5- 3was provided with the number of tetrahedral 252987.
To design a stable micro magnetic bearing system, there were three main subjects that must be considered. These subjects were as follows. (1) Static stable state. (2) Dynamic stable state. (3) Well-controlled axial force. First, to achieve the static stable state, the system must induce the enough restoring torque when it suffered an additional tilt torque. Suppose that the shaft was tilted at an angle theta, relative to the pivot point, in the clockwise direction along the positive y-axis refer to the coordinate system inFig. 5-3. Since it was a critical condition when the theta was 2 degree, the principle parameters
that were sensitive to the stable state of the proposed system were estimated when the theta was chosen to this value. To analyze the distribution profile of the restoring torque Ty, the fluctuation of the Ty due to the axial gap Zgap and the rotation angle was calculated as shown inFig. 5- 4. The Zgapwas positive when outer one higher than inner
one magnetic ring of the MMB in positive axial direction. The initial rotation angle between the rotor and stator is shown inFig. 5- 5. TheFig. 5- 4revealed that the stable region of the micro magnetic bearing system appeared when the Zgap ranged from 0.1 to 0.3 mm.
Second, to obtain the dynamic stable state, the develop bearing must generate the enough radial restoring force which was two times the radial loading at the rated speed and this was referred to our laboratory data base. For the radial run-out (RRO) of this prototype was assigned to 10μm(peak), the restoring force must greater than 7.506×10-4 N. This corresponding RRO-constrain the tilt angle was 0.0785 degree and the desired RRO could be maintained according to the FEA estimation of magnetic radial forces that were -0.02956 and -0.02215 N when the Zgapwere 0.1 and 0.3 mm respectively. To verify the dynamic stable state could be maintained under the magnetic coupling effect, the restoring radial force changed due to the rotation angle and Zgap was calculated as shown in Fig. 5- 6. It is manifest that the restoring force is high enough to resist the radial loading force when the Zgap are operated between 0.1 and 0.3 mm. This guarantees that the target RRO could be satisfied and the system could be stable in the dynamic state.
Third, for achieving the well-controlled axial force, four constrains should be specified as follows. P < 106kg/m2, V < 7 m/sec, PV < 105kg/(msec) and the target
friction loss < 2.92610-4Nm. The first three and the last items were constrained due to
the specification of the thrust plate and the desired friction loss must be lower than the MBB type motor respectively. According to these considerations, the corresponding final axial force criterion that must be smaller than 5.081 N was decided. The calculation shows that the axial force varies with the rotation angle steadily for each chosen Zgap (0.1, 0.2 and 0.3 mm) and each maximum value of these axial forces is smaller than 5.081 N when the Zgap ranges from 0.1 to 0.3 mm and the maximum goes from 1.339 to 3.599 N.
Refer to earlier mention that it is manifest that the restoring torque and radial force are not highly related to the variation of the rotation angle, but the friction loss is.
According to FEM estimation the friction loss due to the magnetic axial force is shown in theFig. 5- 7. Fig. 5- 8shows the original cogging torque represented by crosses, after the magnetic bearing system was assembled into the motor, the cogging torque was increased and deformed to the dragging-torque curves when Zagp = 0~0.3 mm, i.e., the
dragging-torque is equivalent to the friction loss plus the cogging torque. However, the absolute peak values of these profiles were well controlled smaller than 1.9310-4Nm.
It was assumed that the thrust plate contacted with the shaft in 1/4 times the shaft diameter. The kinetic friction coefficient of the thrust plate was 0.06. The total friction loss caused by the MMB was equivalent to the friction loss contributed by the magnetic
axial force added by the dragging torque, then the total friction torque loss (peak) generated by the MMB were -1.1610-4, -1.4910-4, -1.7310-4 and -1.9310-4 Nm
when the Zgap were 0, 0.1, 0.2, and 0.3 mm respectively. This leads to that design motor has the lower friction loss than the MBB type perfectly.
5.4 Experiment
Based on the analytical simulation that the stable state of the MMB motor appears when the Zgap = 0.1, 0.2 and 0.3 mm. During this region, the experimental data of the MMB motor shows that motor speed 1850 rpm and the running current 0.18 A and this is consisted with the prediction. As the Zgap= 0.2 mm, the total friction loss and radial vibration of the MMB motor were measured and represented in the following.
To measure the friction loss of a micro motor, the motor was operated at various constant speeds, then the friction loss was equivalent to the running current times the torque constant of the motor. The torque loss varies with the speed are shown inFig. 5-9. It is apparently that the MMB motor had a lower friction loss than ball bearing type.
For observing the radial vibration of the micro motor, the motor was fixed to a free table, an accelerometer was attached to the motor in the radial direction and a spectrum analyzer was employed to detect the output signal of the accelerometer. The time response signals were probed as shown inFig. 5- 10, when the rotor was rotated at the
(peak-peak) of MBB and MMB motor were 5.954 mG and 4.668 mG, respectively.
Thrust plate Shaft
Yoke
MQ
Base
M agnetic bearing
Stator Thrust plate
Shaft
Yoke
MQ
Base
M agnetic bearing
Stator
Fig. 5- 1. The micro magnetic bearing motor.
-6000 -4000 -2000 0 0 1000 2000 3000 4000 5000 6000 7000
H (Oe)
B (Ga u ss )
NdFeB MQ
Fig. 5- 2. B-H curve of MQ.
Fig. 5- 3. The 3D mesh model of the MMB motor.
0 5 10 15 20
-5 -4 -3 -2 -1
0 x 10
-3Rotation angle (degree)
T y (N m )
Zgap= 0 mm Zgap= 0.1 mm Zgap= 0.2 mm Zgap= 0.3 mm
Tilt angle @ 2 degree
Fig. 5- 4. Restoring torque varies with the rotation angle and Zgap.
Fig. 5- 5. Schema of the initial rotation angle between the rotor and stator.
Tilt angle @ 2 degree
0 5 10 15 20 Tilt angle @ 2 degree
Fig. 5- 6. Restoring radial force varies with the rotation angle.
0 5 10 15 20 -1
0 1
x 10
-4Rotation angle (degree)
T z (N m )
Zgap= 0 mm Zgap= 0.1 mm Zgap= 0.2 mm Zgap= 0.3 mm
Tilt angle @ 2 degree
Fig. 5- 7 Friction loss due to magnetic axial force
0 5 10 15 20
-1 0 1
x 10
-4Rotation angle (degree)
T z (N m )
Zgap= 0 mm Zgap= 0.1 mm Zgap= 0.2 mm Zgap= 0.3 mm Cogging torque
Tilt angle @ 2 degree
Fig. 5- 8. Total friction loss as a function of the rotation angle.
0 1000 2000 3000 4000 5000 0
1 2 3 4
x 10
-4Speed (rpm)
T o rq ue (N m )
MBB motor MMB motor
Fig. 5- 9. The comparison of friction loss of the MBB and MMB motor.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -4
-2 0 2 4
Radialvibration(mG) (a)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
-4 -2 0 2 4
Time (sec)
Radialvibration(mG) (b)
Fig. 5- 10. Radial vibration history of the (a) MBB and (b) MMB motor.
Chapter 6
Axial vibration study of a mobile fan motor
6.1 Introduction
A mobile fan motor for use in portable devices such as cell phones, ultra-mobile PCs, and mobile internet devices must be designed with low power consumption, low noise, and low vibration. Since the small fan is used for cooling the main digital signal processor chips or other integrated circuits, large vibration of the fan may become confused with an intentional vibration indicating a paging signal. So, ideally, the vibration should be reduced as much as possible. Therefore, the issue of suppressing the vibration of a mobile fan motor is very important.
From the view of bearing design, in this case a sleeve bearing, the axial load functions as an attractive force to prevent the rotor from jumping out of the micro motor when it encounters an external shock in the static or dynamic status. In general, for a flat-type motor, the axial preload is introduced using the magnetic attraction force between a permanent magnet (PM) and a magnetic sheet. Unfortunately, along with the axial thrust force, an Unbalanced Magnetic Force (UMF) is simultaneously created; i.e., they can not be decoupled for this type of motor. As is known, UMF and cogging torque
are main factors contributing to magnetically induced vibration. Jang et al. [63]
performed an experimental study to show that rotor and stator eccentricities mainly generate a radial vibration at the first harmonic frequency and at the harmonics of the pole number. Hartman et. al. [64] reported that the sources of UMF fall into the following categories: an eccentric rotor, an eccentric stator, and uneven magnetization.
Yao et. al. [65]-[66] showed that the mechanism of the reduction of cogging is illustrated by the minimum net integral of the product of normal and tangential magnetic flux with respect to the contour between the stator and rotor; and they proposed a method achieving a high efficiency and low cogging torque motor by altering the magnetization profiles of the permanent magnet and the design of the teeth of the stator in a motor. A few researchers [67]-[68] have focused on the characteristics of UMF related to a motor, adopting numerical and analytical approaches.
However, the axial load effect, which accompanies UMF and results in the vibration of a miniature motor, is not addressed. The main goal of this paper is to understand the axial load effect related to the axial vibration in the development of a mobile fan motor.
The axial vibration of the micro motor is due to three essential factors: the radial vibration, the UMF, and the axial load. These are studied and analyzed. First, this paper deals with a simple physical model of the sleeve bearing motor to determine the relation between radial and axial vibrations, and it is presumed that the magnitude in the 1X
(where X designates the fundamental frequency) axial vibration harmonic should be a fraction of the radial one because the axial one is only a sine of a tilt angle times the magnitude of the 1X radial vibration harmonic due to the mass unbalance of the rotor.
This assumption is experimentally validated. In addition, the frequency contents of the axial load coupled with the UMF for micro motors are numerically analyzed using FEM and compared with the experimental results. Furthermore, both the axial load effect with and without excited UMF are reported.
6.2 Design and force calculation
Fig. 6- 1 (a)shows the sketch of the developed motor. It consists of a spindle motor, a sleeve bearing system, a PCB, and a Base. The motor has 6 slots and 8 poles. The axial air gap between the coil and PM is 3 x 10-4 m; the PM is made of high energy product NdFeB with an inner radius of 2 x 10-3 m, an axial length of 5 x 10-3 m, and an outer radius of 4 x 10-3m. Outside the PM, an iron yoke with a radial thickness of 6 x 10-4m is mounted. The rotational speed of the micro motor is 6360 rpm, and the rated current is below 25 mA. The sleeve bearing has an inner radius of 4 x 10-4m, an outer radius of 8 x 10-4 m, and an axial length of 2.5 x 10-3m, and the clearance is 4 micro meters. To identify the model mentioned above, identical motors, M1 to M3, are the type with a symmetric magnetic sheet to preload the rotor; also, motor M1 is utilized to study the
axial load effect without UMF (motor M1P). To investigate the axial load effect under UMF, the second type micro motor, M4, with an asymmetric magnetic sheet, has been fabricated; the ratio of pole number to slot number is 6:2, and the other mechanical constraints are the same as those of the first type. In general, the shape of the magnetic sheet in motor M4 should be asymmetric in order to avoid the dead point[69]. M1P and M4P designate motors M1 and M4 without the sheet, respectively.
Fig. 6- 1 (b) displays the simplified model of a rotating rotor of the small motor.
Referring to Newton’ssecond law,theunbalanceforceoftherotorcan berepresented
as
)
2sin( e
m
F (46)
where m, e,and denote the mass unbalance of the rotor, the rotor eccentricity, and rotor rotational speed, respectively. Since the bearing clearance is only 4 μm, it is believed that the tilt angle theta rotates about the Y-axis, as shown inFig. 6- 1 (b), and can be small enough to lead to the result that the undesired axial vibration force is only a fraction of the radial one for a well designed sleeve bearing motor. Therefore, once the axial vibration of a motor is greater than the radial one, then both the preload and UMF may be regarded as the principal contributors to the vibration. Definitely, based on this assumption, the mass unbalance of each motor has to be maintained close to a level which avoids propagating radial vibration which, in turn, leads to the rise of the axial
vibration.
Fig. 6- 2 presents the FEM model of the proposed motor with 892,892 tetrahedral elements. The sampling mechanical angle interval of one degree is utilized in estimating the preload force distribution of the motor. The preload profiles versus mechanical rotation angles and the corresponding frequency spectra after the FEM calculation are shown inFig. 6- 3.
The mean values of the axial forces for motors M1, M4, and M4P are 32.11, 27.95, and 3.07 mN, respectively. While the axial force curve for motor M1 contains only a DC term, those of motors M4 and M4P contain 6X and 12X axial force harmonics, and the first two peak values in magnitude for motors M4 and M4P both occur at 6X (M4:
1.66 mN; M4P: 1.10 mN) and 12X (M4: 0.12 mN; M4P: 0.10mN) harmonics.
Nonetheless, the 1X component is not generated; i.e., although the UMFs are induced in the motors M4 and M4P, they do not contribute to the 1X harmonic. For motors M4 and M4P, mass unbalance of these two motors are almost the same, and the simulated result indicates that the UMFs of these two motors do not contain the 1X axial force harmonic (which dominates the axial vibration of time domain). These results suggest that the axial load will effectively affect the axial vibration of the motors.
6.3 Experimental measurements
For measurement of the axial load, the rotor was tightly fixed to an accurate balance (seeFig. 6- 4), and the magnetic sheet was arranged above and locked at a manual xyz stage. After a centering device was applied to center the rotor and the magnetic sheet, the axial attraction force versus different axial air gaps was obtained. As the working distance was reached, the axial forces for M1 and M4 were 32.48 mN and 26.83 mN, respectively, which is consistent with the numerical results. To verify the vibration properties of the mobile fan motor, the measurement plant was constructed as shown in Fig. 6- 5. A precise accelerometer was utilized to detect the vibration. While the testing
was performed, the motor was rotating at the rated speed of 6360 rpm. The accelerometer was attached to the motor to sense the traveling vibration signals; then the vibration was calculated and recorded by a spectrum analyzer. Finally, the vibration harmonics can be determined by using the fast Fourier transform method.
Three motors, M1 to M3, were prepared for identifying the simple model mentioned above. The corresponding frequency spectra of radial and axial vibrations are shown in Fig. 6- 6. It is clear that the magnitudes of the 1X components are the dominant reasons
for the vibrations of the motors in both the radial and axial directions.
Table 6-1 summarizes the magnitudes of the 1X harmonics of the radial and axial vibrations for these motors; the ratio of the axial vibration to the radial one is between
65 and 75 percent, which supports the model that the axial vibration of the small motor is only a fraction of the radial one. In addition, the result reveals that mass unbalance of the rotor is a key factor affecting the vibration of the motors.
6.4 Results and discussion
Fig. 6- 7shows frequency spectra of radial and axial vibrations for the motors M1P (motor M1 without the magnetic sheet), M1, M4P (motor M4 without the magnetic sheet), and M4. It indicates that the 1X harmonic of the axial vibration is slightly increased to a value of 0.99 mG (see Table I, where 1G = 9.8 m/s2) after the symmetric magnetic sheet is installed; i.e., the preload has slightly increased the axial vibration and its 1X harmonic. Fig. 6- 8(a) and Fig. 6- 8(b) show the axial vibration of the motors M1P and M1, respectively, and the amplitudes in peak-to-peak (pk-pk) are 11 mG and 15 mG for the former and latter, respectively.
Comparing the two graphs inFig. 6- 7 (d), the motor M4P (top graph) demonstrates the 6X and 12X axial vibration harmonics due to the UMF, while the motor M4 merely includes the latter harmonic (see Table 6- 2). However, these two harmonics (6X and 12X) in magnitude were predicted by FEM analysis. The unexpected disappearance of the 6X harmonic for the motor M4 is believed to be associated with its asymmetrical coil (this means some defects in the coil were developed during the fabrication process),
and the induced UMF harmonics due to the defects are related to the pole number of magnets[64].
As mentioned earlier, the axial vibration results from three primary contributors: the UMF, the radial vibration, and the axial load. According to the numerical results, the UMFs of these two motors do not contribute to the 1X axial vibration harmonic. In addition, the measured magnitudes of the 1X radial vibration harmonic for these two motors are maintained nearly the same (M4P:5.986 mG; and 6.266 mG). However, the measured magnitude of the 1X axial vibration harmonic is enormously raised, and the ratio of this harmonic of motor M4 to motor M4P is approximately 41 percent. The reason might be that the lack of axial load leads to the growth of the magnitude of the 1X axial vibration harmonic; i.e., a weak axial load may result in an increase in the magnitude of the 1X axial vibration harmonic if the shaft is loose. Therefore, the axial preload plays an essential function in the reduction of the 1X axial vibration harmonic of the micro motor. Furthermore, comparing the axial vibrations of motors M4 and M4P reveals that the axial vibration is significantly reduced for motor M4. The amplitudes (pk-pk) of the axial vibrations for the motors M4P and M4 are 38 mG and 21 mG, respectively (seeFig. 6- 8 (c)andFig. 6- 8 (d)).
Table 6- 1 The magnitudes of 1X radial and axial vibration harmonics for motors M1P and M1 to M3.
Table 6- 2 The magnitudes of radial and axial vibration harmonics for motors M4P and M4
Frequency 1X 6X 12X
Motor No. Radial Axial Radial Axial Radial Axial M4P 5.986 9.083 0.163 3.382 0.168 0.879 M4 6.266 3.680 0.403 0.074 0.236 2.352 Unit (mG)
Motor No. Radial (mG) Axial (mG)
M1P 6.279 3.051
M1 6.255 4.041
M2 5.850 4.124
M3 5.624 4.134
Fig. 6- 1. The sketch of (a) the micro motor and (b) the tilted rotor.
Fig. 6- 2. The FEM model of the mobile fan motor.
Fig. 6- 3.The simulated axial loads of spatial domain for motors: (a) M4P; and (b) M1 and M4; the frequency spectra for motors: (c) M4P; and (d) M4.
Fig. 6- 4. The structure of the test setup for the axial load measurement.
Fig. 6- 5. Configuration of the test setup for vibration measurement.
Fig. 6- 6. Frequency spectra of (a) radial and (b) axial vibrations for motors M1 to M3.
Fig. 6- 7. The frequency spectra of the radial and axial vibrations for motors. Radial vibration: (a) M1P and M1; and (b) M4P and M4; axial vibration: (c) M1P and M1; and (d) M4P and M4.
Fig. 6- 8. The axial vibrations for motors: (a) M1P; (b) M1; (c) M4P; and (d) M4.
Chapter 7 Conclusion
Referring to the above results and discussion, the conclusions of this dissertation are summarized below.
A credible mathematical model has been developed to predict the dynamic behaviour of the MB motor, and the numerically simulated RRO of the MB motor has good agreement with the experimental one. The system utilizing repulsive magnetic force is the one in which the rotor can be stably levitated in the radial direction, i.e., the highly compact MB configuration applying only a single pivot point can successfully getaround Earnshaw’s theorem and make achievable contact less of the
rotor along radial direction. In addition, it is experimentally validated that in comparing this MB motor with the conventional ball type motor for small motor applications, it shows that the MB motor posses the lower torque loss. Furthermore, the gyroscopic effect actively suppresses the radial vibration of the rotor due to the mass unbalance response while the spindle was operated within a speed range between 3000 and 6000 rpm. Accordingly, it is believed that a scaled-down version of the MB motor could be
rotor along radial direction. In addition, it is experimentally validated that in comparing this MB motor with the conventional ball type motor for small motor applications, it shows that the MB motor posses the lower torque loss. Furthermore, the gyroscopic effect actively suppresses the radial vibration of the rotor due to the mass unbalance response while the spindle was operated within a speed range between 3000 and 6000 rpm. Accordingly, it is believed that a scaled-down version of the MB motor could be