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Computer Simulated Transient Analysis of a Polyimide V-Groove Leg Actuator with Serpentine Heater for a Walking Micro-Robot Ritesh A Khire, Satish G. Kandlikar, Wayne W. Walter Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, N.Y., USA. [email protected], [email protected], [email protected] ABSTRACT A computer-simulated model for transient heat and deflection analysis was developed for the serpentine type heater actuator to be used for a walking micro -robot. Some differences between the simulated and experimental results reported by T. Eberfors at the Royal Institute of Technology, Sweden, were noted in the low frequency domain. A need for an active cooling mechanism was identified. The heater location and the power supplied to each V groove needs to be optimized so that all V-grooves participate equally in the actuation process. The role of thermal conductivity and wall temperature has been investigated. A number of issues have been identified which require future work. INTRODUCTION This shrinkage property of polyimide and its compatibility with standard silicon processes make the fabrication of this actuator achievable. Although the details about the fabrication technique used are beyond the scope of this paper, in short, the fabrication involves standard silicon processes like KOH etching, sputtering, LPCVD, lithography etc. In the work done by Ebefors, two types of heaters were mounted on the actuator. The first was a “serpentine heater”, in which aluminum was used both as a conducting and resistance-heating element. The heaters, located inside the trenches, had a smaller width of aluminum and the conductors (contacts) had a larger width. The second heater type was a “polysilicon heater”, located between two trenches. The contacts in this case are still aluminum [4]. Figure 1 shows the schematic of a serpentine heater type actuator. Heater Insects can be considered as the inspiration behind the development of microrobotics. Using high-speed video photography and computer simulations, traits of insects such as the cockroach have been analyzed [1,2]. One of the important locomotion requirements of a microrobot is large out-of-plane deflection of the actuators forming its legs. Few actuators have been developed for out-of-plane motion [3]. This paper describes the transient computer simulations done on a polyimide V-groove leg actuator for a walking micro -robot, to investigate the optimal transfer of heat. This actuator was fabricated and tested by T. Ebefors et al. [4] at the Royal Institute of Technology, Sweden. The principle of actuation is based on the thermal expansion of polyimide inside a V-groove by an electrical heater. The out-ofplane orientation of the leg is due to the thermal shrinkage of polyimide when cured. Due to the larger absolute contraction length at the top of the V-groove as compared to the bottom, the actuator (cantilever beam) attached to the V-grooves curls out of the plane, forming a freestanding leg [5]. Contacts Pads Polyimide inside V groove After Curing Silicon Wafer Before Curing Figure 1: Schematic of Serpentine heater. It is important to note that Figure 1 is just a schematic representation of the system. For accurate dimensions and details about the device, the reader is encouraged to refer to the PhD thesis of T. Ebefors [4]. This paper deals with the transient analysis of the above actuator done using ANSYS 5.6. The assumptions made in the model will be discussed later in a section on model development. The simulation results were compared with the published experimental data by T. Ebefors [6]. We found that the results of the simulation match with the experimental data in the high frequency domain. This confirms the validity of the assumptions made in the model being used for further simulations at the Rochester Institute of Technology (RIT) to understand the heat transfer process. effect of convection, the entire length of the actuator was modeled. Figure 2 shows the model of the actuator. NOMENCLEATURE ? c k ?x d L Density (kg/m3 ) Specific Heat (kJ/kg ºK) Thermal Conductivity (W/m ºK) Average element length (m) Deflection in vertical direction (m) Length of actuator up to center (m) OBJECTIVE OF THE WORK The objective of the present work is to: (1) develop an FEM model for transient analysis of the actuator, (2) validate the model by comparing the simulation results with the published experimental data, (3) understand the transient phase of the heat transfer for further optimization of the system, and (4) identify the role of conduction and convection in the heat transfer process. The future objective is to understand the micro scale heat transfer and identify any differences with the classical solution. MODEL DEVELOPMENT ANSYS 5.6 was used to develop the model. For generating the mesh “coupled field” “Plane 13” elements were used. This is a two dimensional quadratic element with a maximum of four degrees-of-freedom per node. Displacements UX and UY, in the x and y directions, respectively, and temperature were selected as degrees of freedom per node. The element behavior was set as “plain strain” which refers to no heat transfer in the z direction [7]. The dimensions and material properties were obtained from the Eberfor’s thesis report [4, 6]. The model was simplified using the following assumptions: (1) all the material properties were assumed to remain constant over the operating temperature range, (2) the out-ofplane curling of the actuator was neglected (thus the actuator beam was assumed to remain in the plane of wafer as a straight beam), and (3) the top and bottom edge dimensions of the V-grooves were reduced as per the shrinkage coefficient (~ 45% for curing temperature 350ºC [6]). To identify the Figure 2: Model of the actuator showing polyimide inside the V-grooves Since the modeling was done in two dimensions, the supplied power was converted into an equivalent heat generation rate by dividing the total power by the product of the volume of the aluminum heater times the number of V-grooves. For calculating the volume of the heater, the thickness of the aluminum was assumed to be uniform (1.5 micron) [4,6]. For the contacts, our two dimensional model would assume the width of the contact to be equal to the width of the structure, which would decrease the resistance to the heat flow of the contacts. To correct for this, the thermal conductivity of the aluminum forming the contact was scaled down by multiplying it by the ratio of the actual width of the contact to the entire width of the structure. Further simplification was done by neglecting the oxide layer deposited inside the trenches to act as an electrical insulator, and on top of the wafer to act as a masking layer for etching the V-grooves. Since the power was converted into an equivalent heat generation rate for this simulation, it was reasonable to neglect it. The various regions forming the beam were attached (glued) to each other before meshing. By dividing all the lines forming the model into appropriate portions, uniform meshing (mapping) was obtained. Aluminum Heater Silicon Contact Polyimide Figure 3: Meshed Model (3 V groove model) Transient analysis was done for one heat cycle. The cycle was divided into three steps. Figure 4 shows the graphical representation of these time steps. The first step is applied for a very small time of (~1e-8 sec). This step defines the initial boundary conditions of the system. These initial boundary conditions include: (1) the left wall of the actuator was restrained from having displacements in the x and y directions, (2) a heat sink was created at the same edge by enforcing a constant temperature (20 ºC), and (3) convection was applied on the top and bottom surfaces of the actuator. In the second step, the heat generation rate was applied to the aluminum heaters inside the trench. In order to accommodate various losses, the heat generation rate was truncated by 5%. All other Figure 5: Comparison of different time step values for 90 mW, 10 Hz, and 1 V-groove In the third step, the heat generation rate was equated to zero, which represents the cooling period. RESULTS The three V-groove configuration was first simulated with convection applied at the top and bottom surface of the system (h=20 W/m2 °C), and then with no convection applied (h=0 W/m2 °C). Figure 6 shows the comparison of results obtained from the two simulations. Figure 4: Load steps in one heat cycle boundary conditions applied in the first step were used. The time sub-step was calculated using the Fourier number given in the following equation [7]: ∆t = ρc(∆x) 2 K (1) For micro systems, the average element length is of the order 1e-6 m, which leads to an extremely small time sub-step (~1e-8 sec.). When a simple system of only one V-groove was simulated for this time step, ANSYS stopped the simulation after 1e-4 seconds. The same behavior was observed for a time step equal to 1e-7 and 1e -6 sec. Figure 5 shows the comparison of different time sub-step values. The simulation stopped at point ‘A’ on the graph for time step values from 1e-8 to 1e-6 sec. Also it can be seen from the graph that results nearly match for a time step equal to 1e-4 sec and 1e-5 sec. As a result, for faster simulation, a time sub-step value was taken as 1e-4 sec. Figure 6: Effect of convection on the heat transfer process It is apparent that the output does not change even if convection is neglected. Accordingly, for all further simulations, convection was neglected. Figure 7 shows the comparison of experimental results versus the simulated values for the three V-groove configuration. The bending angle was calculated using the following formula: −1 δ θ = sin L (2) heated the most. Similar behavior was observed in the case of the 3V groove configuration. Figure 7: Comparison of Simulated values with experimental data for 3 V It can be seen from the graph that simulated values agree with the experimental data for the high frequency domain. Differences in the low frequency domain will be addressed in the Parametric Analysis and Discussion sections, which follow. A similar analysis was done for the four V-groove configuration. Figure 8 shows the comparison of results. Figure 9: Temperature evolution at the center of the V- grooves in the 4 Vgroove configuration PARAMETRIC ANALYSIS Effects of various parameters were simulated. The following trends were obtained: Effect of convection: As can be seen from Figure 6, convection plays a very limited role in the heat transfer process, for this actuator. Similar behavior was observed when the heat transfer coefficient was increased to h=100 W/m2 C. This observation leads to the conclusion that an effective cooling mechanism is required for the actuator. Figure 8: Comparison of Simulated values with experimental data for 4 V-grooves When experiments were done on the actuator, it was observed that the outermost Vgroove gets heated more as compared to the innermost V-groove [5]. A similar behavior was also observed in the simulation. Figure 9 shows the simulated temperature evolution at the center point of the top edge of the V-groove. It can be seen that the temperature in the last V-groove is maximum among the four. This is primarily due to the inner V-groove acting as a thermal insulator, which heats up the outer V-grooves. The last V-groove gets Effect of conductivity of silicon: The simulation was run for three different thermal conductivity values of silicon. Figure 10 shows the comparison of simulation results for 3 V grooves. As the conductivity of silicon is reduced, the deflection increases, as a result of increased polyimide heating. It can be seen that the variation in conductivity value causes a small change in deflection at higher frequencies, but at lower frequencies, the magnitude of change is increased. Effect of conductivity of polyimide: The effect of thermal conductivity variation of polyimide is shown in Figure 11. When the conductivity of polyimide is increased, the deflection value increases. This is consistent with the increased heating of polyimide. This increase in deflection is nearly constant over the frequency range. Effect of wall temperature: For the analysis done previously in Figures 7 and 8, the left wall temperature was enforced at a constant value of 20ºC. But from the steady state analysis done on the polysilicon heater by Ebefors, the wall temperature rises to 33.75ºC [4]. Figure 12 shows the effect of linearly increasing wall temperature from 20ºC to 35ºC over the period of 150 ms (settling time obtained experimentally [6]). Figure 12 shows better agreement with experimental results as compared to Figure 7. The trend of the simulation results is more consistent with the experimental data at lower frequencies. A similar trend was observed for the 4 V-groove configuration also. Figure 10: Effect of silicon conductivity. Figure 11: Effect of change in polyimide conductivity. Figure 12: Effect of change in wall temperature. DISCUSSION The curves of deflection vs. frequency are consistent with the experimental data for frequencies of 40 Hz and above. The difference is more in the 3 V-groove configuration as compared to the 4 V-groove configuration for frequencies between 20 and 40 Hz (see Figures 7 and 8). Since the same power is distributed in each case, the power per groove is more in the 3 V-groove configuration. As more power is dissipated per Vgroove here, the temperature rise in each V groove is higher. Since for this analysis, the material properties have been assumed to remain constant with temperature, the difference is more in the case of the 3 V-groove configuration. From Figure 6 it is seen that convection plays a very little role in case of heat dissipation. This leads to the conclusion that an active cooling mechanism will be required for dissipating the entire heat during the cooling cycle. Failure to remove all the heat may result in little deflection over the time period. Further simulation will be required for optimizing the heat transfer. The simulated values differ from the experimental values at lower frequencies. This deviation may be explained due to following reasons: 1) Although the shape of the polyimide is assumed to be a perfect V, in actual practice the shape of the experimental V may not be the same, causing dimensional differences. One of the reasons for this shape difference in the experimental V is due to the presence of the aluminum contact, which expands at the high curing temperature of polyimide (as opposed to shrinkage in polyimide). As a result, the actual shrinkage pattern will be different than assumed. 2) Constant material properties were assumed over the temperature range. As the frequency is reduced, the temperature increases inside the system since the heating time is longer. Therefore, at lower frequencies the assumption of constant material properties rather than temperature dependent properties will induce more error. 3) The inner most V-groove acts as a heat insulator, thereby causing higher temperatures in the outer V- grooves (see Figure 9). This higher temperature increases the resistance of the heating element of the outer V-groove, causing higher power generation inside the outer V- groove. This results in the outermost V-groove contributing more to the total deflection. For this analysis, equal power generation in all V-grooves was assumed. Therefore, at lower frequencies, the simulated heat supplied to the outermost V groove is less than the actual value. The power generation inside each Vgroove needs to be changed over time, to correct this error. 4) Increasing the wall temperature over time gives better results than the constant temperature assumption (see Figure 12). Rather using a linear temperature rise, as was done here, perhaps a exponential rise may prove to be more effective. 5) Due to the thermal expansion coefficient mismatch between polyimide and aluminum, residual stresses get developed in the structure after curing, which have been neglected in the modeling. 6) As reported by T. Ebefors, the data acquisition system used had significant uncertainties [4]. Deviations as high as +/- 0.25º can be involved in the measurement system. CONCLUSIONS A computer-simulated model for transient heat and deflection analysis was validated for the serpentine heater case in the high frequency domain. Some differences between the simulated and experimental results reported by T. Eberfors were noted in the low frequency domain. A need for an active cooling mechanism was identified as convection plays a small role in the heat transfer process. It was also observed that all the V grooves do not contribute equally to the actuation process. Thus, the heater location and the power supplied to each V groove needs to be optimized, so that all Vgrooves participate equally in the actuation process. The role of various parameters (thermal conductivity and wall temperature) has been investigated. A number of issues have been identified which require future work. FUTURE WORK The following issues are scheduled for further investigation: 1) Temperature dependent material properties. 2) Coupled electrical-thermal effects. 3) Wall temperature effects employing an exponential function. 4) Optimal heater location. 5) Residual stress effects. 6) Development of an active cooling mechanism. 7) Fabrication and test of a leg actuator prototype (currently in progress at RIT). REFERENCES [1]. S. Laksanacharoen, A.J. Pollack, G.M. Nelson, R.D. Quinn and R.E. Ritzmann “Biomechanics and Simulations of a Cricket for Microrobot Design,” IEEE International Conference on Robotics and Automation, San Francisco, USA, April 24-28, 2000. [2]. T. Ebefors, J. U. Mattsson, E. Kalvesten, and G. Stemme, “A Walking Silicon Micro-Robot,” The 10th Int. Conference on Solid-State Sensors and Actuators (Transducers ’99), Sendai, Japan, June 1999, pp 1202-1205. [3]. P. Kladitis, V. Bright, K. Harsh, and Y.C. Lee, “Prototype Microrobots for Micro Positioning in a Manufacturing Process and Micro Unmanned Vehicles,” Proc. of IEEE 12th Int. Conference on MicroElectro-Mechanical Systems (MEMS’99), Orlando, USA, 1999,pp. 570-575. [4]. T. Ebefors, “Polyimide V-Groove Joints for Three – Dimensional Silicon Transducers – Exemplified Through a 3-D Turbulent Gas Flow Sensor and Microrobotic Devices,” thesis report, Department of Signals, Sensors, and Systems, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden. [5]. T. Ebefors, E. Kalvesten, and G. Stemme, “New Small Radius Joints Based on Thermal Shrinkage of Polyimide in VGrooves for Robust Self-Assembly 3D Microstructures,” Journal of Micromech .Microeng., vol. 8, pp. 188– 194, 1988. [6]. T. Ebefors, E. Kalvesten, and G. Stemme, “Dynamic Actuation of Polyimide V Groove Joints by Electrical Heating,” Sens. Actuators, vol. A67, pp. 199–204, 1998. [7]. Training Manual “Introduction to ANSYS – part 1” for Release 5.6, Nov 1999. ANSYS® is a registered trademark of SAS IP Inc. [8]. Incropera, Frank P. and DeWitt, David P. Fundamentals of Heat and Mass Transfer, 5th ed, John Wiley & Sons, New York, Aug 2001, ISBN 0-471-38650-2. [9]. Tzou, D. Y., Macro- to Microscale Heat Transfer: The Lagging Behavior (Series in Chemical and Mechanical Engineering), Taylor & Francis, Washington. 1996, ISBN 1-56032-435-X.