DESIGN OF A NOVEL COMPLIANT TRANSMISSION FOR ...

Proceedings of DETC ‘02 2002 ASME Design Engineering Technical Conference September 29–October 2, 2002, Montreal, Canada

DETC2002/MECH-34208 DESIGN OF A NOVEL COMPLIANT TRANSMISSION FOR SECONDARY MICROACTUATORS IN DISK DRIVES Sridhar Kota Professor Department of Mechanical Engineering University of Michigan

Charles Kim Graduate Student Research Assistant Department of Mechanical Engineering University of Michigan

ABSTRACT One of the bottlenecks limiting the data density in conventional disk drives is the resonant frequency of the suspension arm connecting the actuator and the read-write elements. In this paper we present a compliant transmission to be integrated with a secondary microactuator to deal with this limitation. The compliant transmission was designed to reduce overall footprint. This paper presents an optimization scheme which maximizes energy efficiency while constraining natural frequency, maximum stress, and axial loading. The final design meets both kinematic and dynamic criteria. INTRODUCTION In the semiconductor industry, the 10-10 rule measures growth of the industry, stating that every ten-year period brings a tenfold increase in the level of technology. One subset of the semiconductor industry that has consistently out-performed this measure is the area of data storage. The last decade has seen a growing need for increased data capacity in smaller spaces. Increased storage of personal digital data and the shrinking size of computing technology both contribute to the need for high density data storage. Figure 1 shows the actuation scheme of a typical disk drive. Data is stored on a rotating disk. The slider contains the read-write head, which houses the elements used to read and write data onto the disk. The slider is suspended above the disk via a suspension connected to a voice-coil motor (VCM). As the VCM rotates, the suspension arm and slider move radially across the disk. There is a direct relationship between the precision of the actuation scheme and the areal density of a hard disk. To achieve high areal density, it is necessary to pack data close together. Actuation precision dictates how closely data can be packed. A servo controlled VCM must operate at relatively high

frequencies to achieve precise actuation. The bandwidth of servos using the current actuation scheme, however, is limited by the resonant frequency of the suspension arm. Because the precision of the current actuation scheme is limited by a feature critical to its operation (i.e. the suspension arm), it is necessary to develop a new design that facilitates higher data density. Nearly a decade ago, researchers in the magnetic storage community contemplated the use of a secondary microactuator placed in between the slider and the suspension arm to alleviate effects introduced by the dynamics of conventional designs (Fig. 2). A piggy-back microactuator operates (in translation or rotation) at high frequencies to augment the operating frequency currently limited by resonance of the suspension arm. Several researchers have designed such devices [1, 3, 4].

Voice Coil Motor Suspension Disk

Slider

Figure 1: Conventional actuation scheme

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Copyright © 2002 by ASME

There exist some unresolved issues encountered by those conducting research on piggy-back actuators. Electrostatic actuators have typically been used in this application. Due to the relatively large slider mass, the force required from the actuator is large by MEMS standards. This imposes an expensive cost on the voltage necessary to drive the actuator. Voltages available to hard disks (typically less than 10 V) are much lower than voltages required to drive high force electrostatic micro-actuators (typically less than 100 V). In addition to this problem, the actuators tend to be very large. The lateral dimensions of a typical slider are 1 mm by 1.2 mm. In one work, the lateral dimensions of the designed microactuator were 2.7 mm by 1.7 mm [3]. The footprint of the device reflects directly onto its cost. The actuators must be batch fabricated to justify introduction into the commercial market so a larger footprint is undesirable. Thus it is necessary to reduce the overall size of the actuator. The current work focuses on reducing the footprint of the actuator by introducing a compliant transmission between an electrostatic actuator and the slider. Although this work does not focus directly on resolving the issue of reducing the required voltage, it is possible that the result may facilitate a lower voltage requirement.

in the vertical direction, it is necessary to transmit the vertical input from the actuators to a horizontal output at the slider. If the actuators operate 180 degrees out of phase, the problem becomes anti-symmetric across the horizontal axis and results in a net torque. The objective of this work is to reduce the overall footprint of the micro-actuator. With the configuration of Fig. 3, the entire device fits beneath the slider, thereby meeting footprint requirements. This development involves introducing a transmission to transmit motion from the actuators to the slider. Assuming that sufficient force and displacement can be obtained from the actuators (assumption confirmed in subsequent section), the design problem is narrowed to designing the transmission. The transmission must satisfy the following kinematic requirements: Positive y input at points A and B, negative y input at points C and D, negative x output at point E, and positive x output at point F. 480 µm

480 µm y x

C

E

150 µm A

Suspension Actuator

Actuator

900 µm

Microactuator Design Space

Read-write element

Figure 2: Piggy-back actuation scheme (adapted from [3]) PROBLEM STATEMENT From a mechanical perspective, the piggy-back actuation scheme requires one task – moving the slider mass with adequate stroke and frequency. The read-write elements must scan over a limited area at a high frequency in order to cancel out undesirable dynamic effects introduced by resonance of the suspension arm. Due to inertial properties, rotating the slider requires less input than translating it. It is necessary, then, to apply a torque to the slider. To apply torque to the slider, two points near the edge of slider may be linearly actuated in opposite directions (points E and F of Fig. 3). Two linear electrostatic actuators are placed side by side to drive the motion. With desired actuator operation

D

F

B 150 µm

1000 µm

Figure 3: Configuration of actuators and design space

Motion in directions other than those prescribed above are highly undesirable since (i) electrostatic actuators are extremely sensitive to lateral motion and (ii) perpendicular motion in the output introduces wasted motion. One can state the objective of the problem as: Reduce the overall footprint of a piggy-back actuator by implementing a transmission satisfying the kinematic requirements stated above, fitting in the dark shaded area indicated on Fig. 3.

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Specifications To accomplish the objective described above, it is necessary to establish physical goals to assess the quality of the design. Below a number of design specifications are listed. Some of these specifications arise from general properties of good transmissions (good dynamic properties, protection against failure, etc). Other specifications arise from typical slider properties and process capabilities [7, 8, 9]. Design specifications: 1. Good dynamic properties. In order to effectively counter-act the resonance from the slider, the actuatortransmission-slider assembly must satisfy one the following: a. No resonance below 15kHz b. One resonant frequency near 1 kHz, but no more until 15 kHz These specifications arise from assuming that the actuator-transmission-slider will be servo controlled. It is necessary for the entire assembly to be well behaved in order to be easily controlled. In this paper we ignore the stiffness of the actuator suspension as prescribed by Ummethala [8]. 2. Protection against failure (yield or fracture). 3. High energy efficiency. The formulation of energy of efficiency is from [2]. 4. Volume constraint. The transmission must have a minimal amount of material. 5. Sufficient output. It is necessary to drive the slider at 4 kHz with a 2 µm stroke. For a typical slider, this requires a 0.648 mN force at each point of application (points E and F from Fig. 3). The available footprint for each actuator is approximately 480 µm X 900 µm. With these specifications, it is possible to attain a net force of approximately 0.5 mN from each actuator [7]. 6. Avoiding buckling. These parameters are derived assuming a slider mass of 1.8 mg with dimensions 1.2 mm × 1.0 mm × 0.05 mm. The material to be used for the transmission and actuators is polysilicon (E = 150 GPa).

Topology Generation The kinematic requirements state that a positive vertical input at point A of Fig. 3 must transmit to a negative horizontal output at point E. Figure 4 shows a double slider rigid link mechanism that satisfies the kinematic requirements. (In Fig. 4 through Fig. 7, solid arrows indicate the described motion while dashed arrows indicate the negative displacement.) As slider A translates in the negative x-direction, slider B translates in the positive y-direction. Both instant centers (as indicated by dotted lines) are located at an infinite distance along a line perpendicular to the line of action of each slider. For sufficiently small displacements, this mechanism can be approximated by the mechanism shown in Fig. 5. As point A translates in the negative x-direction, point B translates in the positive y-direction. By mirroring this mechanism over the vertical link, the mechanism in Fig. 6 is obtained. If all of the pin joints are held fixed while the links are free to deform, the mechanism becomes exactly the compliant mechanism found in Fig. 7. Linear beam theory predicts that this constrained mechanism will yield the same desired motion if displacements are small. Since the scale of the mechanism is on the order of hundreds of microns while the displacements are on the order of microns, these assumptions are valid. By this theory, the input and output beams will respond such that motion will occur in their respective tangential directions. y A x

∞

∞ B

Figure 4: Double Slider Mechanism A

DESIGN APPROACH A number of researchers have performed compliant mechanism synthesis [6, 5]. Two tasks common to most research done in this area are (i) topology generation and (ii) size and shape optimization. Although much research has been performed in the area of topology optimization, this work approaches topology generation by deriving a compliant topology from a rigid link mechanism. The subsequent paragraphs describe this approach, as well as the method used for size and shape optimization.

B

Figure 5: Four-Bar Mechanism

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Output

Input

Input

Figure 6: Six-bar mechanism

Output

Input

Input

Size and Shape Optimization It is necessary to optimize the dimensions and shape of the topology to obtain an energy efficient mechanism satisfying the specifications stated above. Size optimization involves adjusting the dimensions of the elements obtained from the topology. Figure 9 shows a discretized version of half of the topology obtained in Fig. 7 with element numbers as indicated. Note that only half of the mechanism is discretized since the design is symmetric about the vertical elements. Shape optimization in this work is restricted to relocating the position of the nodes (changing the geometry). In this particular problem, node a is permitted to wander in the horizontal direction. The method of optimization is described in the next section. OPTIMIZATION The size and shape optimization problem can be stated as: maximize η subject to Frequency constraint: ξn ∈ [0.9 kHz, 1.1 kHz] or ξn ≥ 15 kHz Stress constraint Volume constraint Buckling constraint hi ∈ [hmin, hmax], i = [ 1, 15 ] xa ∈ [xa_min, xa_max]

Figure 7: Compliant mechanism

The device pictured in Fig. 8 is obtained by mirroring the topology of Fig. 7 over the horizontal axis. Each output port is fixed to the slider, while each mechanism is driven in the directions shown by electrostatic actuators. Given this configuration and the resulting output forces and motions, the slider will rotate with respect to its principle axis.

Actuator

Actuator

Slider

Figure 8: Transmission with actuators and slider

where η is mechanical energy efficiency as described by Hetrick [2], ξn is the natural frequency of the actuatortransmission-slider assembly, hi is in-plane element height, and xa is the location of the wandering node a. Mechanical energy efficiency, η, relates the reciprocal work done at the input to the sum of the reciprocal work at the output and the compliance (strain energy) stored in a mechanism [2]. The original problem statement puts a constraint on the resonant frequency of the actuator-transmission-slider assembly. The natural frequency corresponds to the frequency at which resonance occurs when a sinusoidal driving force is applied to the device. In the size and shape optimization, the natural frequency is constrained. Also, the optimization problem statement restricts the neighborhood of 1 kHz to 1 kHz ± 0.1 kHz for the first constraint on natural frequency. Note: The following convention will be used to refer to the constraints on natural frequency: Constraint I: 0.9 kHz ≤ ξn ≤ 1.1 kHz Constraint II: ξn ≥ 15 kHz

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The constraint on in-plane element height is based on the limits of fabrication. Sandia’s SUMMiT V process was used as a reference [7]. In this particular problem, hmin = 2µm and hmax = 15 µm (Constraint I) or 25 µm (Constraint II). 6 5

7 8

4

9 3 2 1

10 a 15

14

13

12

11

Optimization results Figure 11 shows the resulting mechanism from optimization while imposing Constraint I. The mechanical energy efficiency of this mechanism is 92.96%. The natural frequency of the actuator-transmission-slider assembly is 979.77 Hz, which satisfies the constraint on the natural frequency. Figure 12 shows the deformation of the actuated mechanism (slider and actuator not pictured for clarity). The prescribed vertical input displacement of 4 µm yields a 2.26 µm horizontal displacement at the output. The required force at each input port is 0.243 mN.

Figure 9: Discretized topology

Optimization in ANSYS The ANSYS software package was used to perform optimization. This package was selected due to the existence of both finite element and optimization modules. Figure 10 is a flow chart of the optimization scheme used in this work. First, several random designs are generated by ANSYS to provide a variety of starting points. After selecting the most efficient designs, two consecutive optimizations using the subproblem method are implemented. The subproblem method uses an approximation of the finite element model for evaluations of the objective function and constraints on state variables (i.e. quantities derived from the design variables). The problem is converted to an unconstrained one by placing penalty terms inside the objective function for each constraint. The unconstrained problem is then optimized using a sequential unconstrained minimization technique.

Figure 11: Optimized mechanism with Constraint I imposed

Random Design Generation Select most efficient designs

Select most efficient designs

Finite Element Analysis Subproblem Optimization Finite Element Analysis Subproblem Optimization Solution

Figure 12: Deformed shape

Figure 13 shows the resulting mechanism from the optimization while imposing Constraint II. The mechanical energy efficiency of this mechanism is 8.43%. The natural frequency of the actuator-transmission-slider assembly is 15.01 kHz, which satisfies the constraint on the natural frequency. Figure 14 shows the deformation of the actuated mechanism (slider and actuator not pictured for clarity). The prescribed vertical input displacement of 4 µm yields a 2.3 µm horizontal displacement at the output. The required force at each input port is 6.2 mN.

Figure 10: Flow chart of optimization scheme

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load is minimal, leading to lower efficiency. even so, this design meets all kinematic requirements.

Figure 13: Optimized mechanism with Constraint II imposed

Figure 14: Deformed shape DISCUSSION Both designs obtained from the optimization satisfy the kinematic requirements posed earlier. Due to higher efficiency and lower required input force, the mechanism shown in Fig. 11 is a better candidate for this particular application. This design contains a number of relatively thin elements. All of the thin elements are located at positions corresponding to the pin joints of the six-bar mechanism shown in Fig. 6. The design appears to fall into the class of lumped compliance mechanisms. The thin elements seem to function as flexure pivots. This is not an unexpected result since the range of motion of the mechanism is relatively small. The displacements are on the order of microns, while the size of the mechanism is on the order of hundreds of microns. The design obtained from imposing Constraint II has a relatively low energy efficiency. This result can be explained by considering how the transmission matches the application. The force to move the input 4 µm at each input is 6.2 mN. This is significantly larger than the applied external load of 0.648 mN. If there is no load applied to the output, the force at each input port is 5.98 mN with an output displacement of 3.2 µm. A good part of the above-mentioned 6.2 mN force is used to deform the mechanism and is not transmitted to the external load. Also, the external load does not deform the mechanism significantly. If the external load is increased to 10 mN, the energy efficiency increases to 50.4%. Higher efficiency would result if the stiffness of the mechanism more closely matched the desired stiffness of the input and output. In this application the external

CONCLUSION Secondary microactuators used in disk drives can be greatly enhanced by integrating them with compliant transmissions. The transmission described in this paper decreases the overall footprint of the actuator while meeting performance goals. The ANSYS software package enables optimization with respect to energy efficiency while considering natural frequency, maximum stress, volume, and buckling. ACKNOWLEDGMENTS The authors acknowledge the collaboration of Steven M. Rodgers and MEMX in consultation regarding MEMS process capabilities. Additionally, the authors acknowledge Upendra Ummethala and Long-Sheng Fan for their correspondences regarding the use of secondary microactuators in disk drives. REFERENCES 1. Fujita, H., Suzuki, K., Ataka, M., and Nakamura, S., 1999, “A microactuator for head positioning system of hard disk drives,” IEEE Transactions on Magnetics, 35, pp. 10061010. 2.

Hetrick, J.A., 1999, “An Energy Efficiency Approach for Unified Topological and Dimensional Synthesis of Compliant Mechanisms,” Ph.D. thesis, University of Michigan, Ann Arbor, Michigan, pp. 48-51.

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Horsley, D. A., Cohn, M. B., Singh, A., Horowitz, R., and Pisano, A. P., 1998, “Design and Fabrication of an Angular Microactuator for Magnetic Disk Drives,” Journal of Microelectromechanical Systems, 7, pp. 141-148.

5.

Howell, L.L., Midha, A., 1996, “A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms,” Journal of Mechanical Design, 118, pp. 121-125.

6.

Kota, S., Joo, J., Li, Z., Rodgers, S.M., and Sniegowski, J., 2001, “Design of Compliant Mechanisms: Applications to MEMS,” Proceedings, Analog Integrated Circuits and Signal Processing Conference.

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Rodgers S.M., Kota S., Hetrick J., Li Z., Jensen B.D., Krygowski T.W., Miller S.L., Barnes S.M., and Burg M.S., 2000, “A New Class of High Force, Low-Voltage Compliant Actuation Systems,” Solid-State Sensor and

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Actuators (Biennial) Conference, Hilton Head Island, South Carolina. 8.

Personal correspondence with Quantum Corporation, 2000.

Upendra

Ummethala,

9.

Personal correspondence with Long-Sheng Fan, IBM Corporation, 2000.

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