Screw Pump for Electro-Hydrostatic Actuator that Enhances Backdrivability

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1 20 th IEEE-RAS International Conference on Humanoid Robots Bled, Slovenia, October 26-28, 20 Screw Pump for Electro-Hydrostatic Actuator that Enhances Backdrivability Hiroshi Kaminaga, Hirokazu Tanaka, Kazuki Yasuda, and Yoshihiko Nakamura Abstract Force sensitivity and backdrivability are vital functionality of actuators to be used in robots that physically interact with humans. Electro-Hydrostatic Actuator (EHA is a type of a hydraulic actuator with backdrivability. To improve backdrivability of an EHA, reduction of friction, especially static friction is important. This, however, is difficult because most of the hydraulic pumps require sliding contacts between mechanical components. A viscous screw pump is a variation of a viscous pump that transfers mechanical kinetic energy to fluidic kinetic energy with viscous friction of the fluid. Since this class of pumps does not require mechanical contacts between the rotor and the stator, they are pumps with least static friction. In this paper, design and development of a screw pump targeted for use in an electro-hydrostatic actuator to improve the backdrivability of the actuator system is presented. Pressure-Flow discharge performance of the developed pump and backdrivability performance when combined with a vane motor were evaluated. I. INTRODUCTION Backdrivability is one of the vital features of actuator system in realizing force sensitivity and enhancing controllability. This, however, is not easy due to transmission friction and reflected inertia. It is widely known that from the link side, motor side friction becomes N -times lager (here N is the reduction ratio, and reflected inertia of the motor rotor becomes N 2 -times lager when seen from the link side. This relation is fixed in gear drives, which are most commonly used in robot actuators; making it worse, they often have large N. Series elastic actuation[] is one of the classical method that decouples motor side and link side dynamics with a spring connected in series to the gear drive output. By decoupling motor side and link side dynamics, SEA (Series Elastic Actuator overcame the curse of motor side friction and reflected inertia. SEA and its variations are widely used in robot systems that physically interact with human[2], [3], [4]. However, SEAs suffer from complicated vibration modes induced by the spring that becomes more relevant when soft springs were used to enhance backdrivability and force sensitivity. Kaminaga et al.[5] developed low friction hydrostatic transmission and constructed highly backdrivable EHA This work was supported by Research Grant from Fluid Power Technology Promotion Foundation, Grant-in-Aid for Scientific Research (S (No of the Japan Society for the Promotion of Science, and Grant-in-Aid for Young Scientists (B (No of the Japan Society for the Promotion of Science. H. Kaminaga, H. Tanaka, K. Yasuda, and Y. Nakamura are with Graduate School of Information Science and Technology, The University of Tokyo, 7-3- Hongo, Bunkyo-Ku, Tokyo, Japan kaminaga@ynl.t.u-tokyo.ac.jp //$ IEEE Fig.. Basic Structure of Single Axis Screw Pumps (Electro-Hydrostatic Actuator. EHA decouples motor side and link side dynamics with internal leakage of the hydraulic components. From its nature of being series dissipative actuator[6], EHA is less likely to oscillate. In the EHA developed in [5], authors tried to reduce mechanical contacts as much as possible. The EHA used in the knee power assist [7] has minimum mechanical contacts in the hydraulic systems; contacts are at axis packing and trochoid pump, both of them being inevitable from its principle. In this paper, we present the design methodology of constructing pump that minimizes the mechanical friction by eliminating the gear mesh in the pump. Viscous type screw pump was examined from its principle of not having mechanical contact within the pump. Basic characteristics and the design methodology of screw type viscous pump was explained. Prototype was developed and its characteristics on basic pump functionality and backdrivability when used in EHA were evaluated. II. VISCOUS SCREW PUMP Screw pumps are viscous type pump that does not have any gear meshing in the pump. As in other types of viscous pumps as [8], [9], they transfer the mechanical energy from the pump to the fluid by shear stress between the rotor and the fluid. Screw pump has following benefits: the fluid path along the rotor is spiral and long that enable screw pumps to produce high pressure, and the fluid path follows the path on the rotor with maximum speed that enable screw pumps to generate high flow rate. The basic structure of the pump is illustrated in Fig.. The rotating screw transfers kinetic energy to the fluid at the surface. They are often used in injection extruders, axis seals, concrete pumps, and grease pumps that operate in one direction and with high viscosity fluid. 434

2 The principle of the pump is simple that carries the fluid along its groove of the thread by the shear stress between the screw and the fluid, but not many theoretical studies have been done[0], [], [2], [3]. We follow the method of Asanuma[], [4] due to its simple linear result. The application of the screw pump was limited to very high viscosity fluid as mentioned above. One of the reasons was that the amount of the gap was large due to the machining precision that increased the leakage loss of the pump significantly; the leakage resistance is inverse proportional to cubic of the gap amount. Today, with the contribution of the improvement in the machining precision, gap amount can be reduced to tens of microns. This fact enables us to consider high pressure usage of such screw pumps with normal hydraulic oil. Screw pumps have following advantages over gear pumps: Small friction. Since there is no gear meshing in this pump, mechanical contact can be minimized, that contributes in reduction of static friction. 2 No pulsation. Since the pumping is fully continuous, there is no pulsation in pressure and flow rate. This feature contributes to more stable and accurate pressure control. 3 High speed operation. Since majority of modern high power motors are high speed, higher pump operation requires less reduction ratio before the pump. Feature and 3 are expected to enhance backdrivability when the pump is used in EHA via reduction of friction. Feature 2 is expected to realize smooth torque output. From the discussion above, screw pumps might serve as a suitable device in EHA to realize smooth force control. III. GOVERNING EQUATIONS OF SCREW PUMPS A. Basic Fluidic Property of Screw Pumps In screw pump shown in Fig. 2, screw rotates in the cylinder (hereafter denoted as a sleeve. Fluid receives shear stress from the rotating screw that accelerates the fluid along the screw groove. The grooves are separated to each other by ridges. We assume x axis with the direction of the groove and tangential to the sleeve surface, having its origin on the sleeve surface. z axis is taken in the direction of the groove depth and having its origin coinciding x axis. y axis is chosen so the x y z axes form a right hand system. We assume x y z coordinate system is fixed to the screw. When the diameter of the screw is sufficiently larger than the depth of the groove, thus d t >>, flow in the groove can be approximated with the laminar flow between two parallel planes. Nomenclature of the parameters are listed in Table I. The groove length l c then becomes l c = l t / cos θ c, with the width of w c and depth of. We assume the fluid to be Newtonian with viscosity μ and non-compressive. Analysis on the fluid is done assuming the screw is fixed and cylinder is moving in opposite direction. Letting p(x This assumption is reasonable since hydraulic oil is sufficiently incompressive in the pressure range we use in EHA, that is below 6MPa. TABLE I NOMENCLATURE Description Parameter Screw length l t Bore diameter of the sleeve d t Groove width w c Groove depth Ridge width w b Number of helices in the thread n t Lead angle of the screw θ c = asin( wc+w b πd t ɛ nt Rotation speed of the screw ω Rotatioal torque of the screw τ Discharge pressure p Viscosity μ Density of the fluid ρ Dynamic viscosity ν = μ/ρ Fig. 2. Parameters in Screw Pumps denote the pressure at point x, and the pressure difference along the groove is constant, Navier-Stokes equations of the model become as follows. p y = p z 2 v x y v x z 2 = μ = 0 ( p x = μ p sin θ c l t = c 0 (2 Here, c 0 is a constant. Literature [] gives solution to (2 under boundary conditions listed in (3, in Fourier series form, as in (5. All the parameters in the equation were modified from [] to meet SI unit because the gravitational metric system was used in original literature. v x = where V x z =0 0 z = 0 (y =0, 2 w cand h g z (h g zv x z(h g z c0 2 (y =0, 2 w cand 0 z h g (3 V x = 2 d tω cos θ c (4 435

3 v x =( z V x z( z c 0 [ sin( nπz cosh{( nπ ( wc 2 y} cosh( nπwc 2 { ( V x h g + c 0h g 2 ( nπ 2 sin( nπh g B. Flow Characteristics [] +c 0 ( nπ 3 (cos( nπh g ( n }] Discharge flow rate of the pump can be calculated with the forward flow rate induced by the friction of the fluid with the screw and the leak flow at the ridge that is induced by the pressure difference. Discharge flow rate q is the difference between the forward flow and the leakage flow as in (7. Forward flow can be calculated by integrating v x for the section of the groove, thus y z plane. q = n t hc h g wc 0 v x dydz πd th 3 gp 2μl t ( ɛ (5 (6 = 2 K (α, βn t w c V x ( (7 K 2 (α, βn t w c h 3 c sin θ c + πd th 3 g 2μl t ɛ p where K and K 2 are dimensionless function that takes dimensionless input α = wc and β = hg that are determined from form factor of the pump. K (α, β =( β 2 8 π 4 αβ n 4 sin(nπβ {cos(nπβ ( n } tanh( nπα 2 (8 K 2 (α, β =( β 2 ( + 2β 24β π 4 α n 4 sin(nπβ {cos(nπβ ( n } tanh( nπα 2 48 π 5 α n 5 {cos(nπβ ( n } 2 tanh( nπα 2 (9 Parameter ɛ gives the ratio of the groove and the ridge width. ɛ = w c w c = (0 w c + w g πd t sin θ c Flow rate - speed - discharge pressure can be concluded by (. q = 2 K d t 2 2 w c ω 2 K 2 = K n t cos θ c K 22 = K 2 n t sin θ c + β 3 sin θ c ɛ( ɛ w c h 3 c μl t K 22 p ( TABLE II DESIGN SPECIFICATION OF SCREW PUMP Description Value Unit Maximum Discharge Pressure.2 MPa Maximum Flow Rate m 3 /sec C. Torque Characteristics [] With similar discussion to previous section, torque characteristics can be derived from (5. Torque acting between the sleeve and the screw are divided to the ridge and the groove. The torque acting on groove can be calculated by integrating shear stress across the groove on sleeve surface. The total torque τ necessary to generate pressure of p at the speed of ω is given as follows. τ = n t μd t l t 2tanθ c = wc 0 ( vx z dy z=0 + μd3 t l t π( ɛω 4h g sin θ c { d 2 t 4 μw c (cos θ c 2 } l t T n t + μd3 t l t π( ɛ sin θ c 4h g sin θ c + d t 4 w c T 2 cos θ c n t p (2 T and T 2 are dimensionless function of α and β. T (α, β =+ 4 π 2 αβ T 2 (α, β = 4 β π 2 α 8 π 3 α ω n 2 sin(nπβtanh(nπα 2 (3 n 2 sin(nπβtanh(nπα 2 n 3 {cos(nπβ ( n } tanh( nπα 2 (4 IV. MECHANICAL IMPLEMENTATION To study the feasibility of the pump in EHA, we decided to design a screw pump that can actuate hydraulic motor. Table II shows the design specification of the pump. The design process is not simple since the system is highly nonlinear regarding the parameters as w c,, and w b.also there are constraints on the fabrication feasibility. ( and (2 were recursively used to decide the parameter values. To reduce the inertia of the pump, we chose engineering plastic as the screw material. The largest constraint on the fabrication was on the gap precision between the screw and the sleeve. We chose this value first as 5 μm. For the pump to have decent volumetric efficiency, it is advantageous to use multi-helix screw. Considering the balance of flow rate and the discharge pressure, triple helix screw was chosen. Other parameters of the pump is shown in Table III. 00W brushless DC motor was chosen to drive pump. As an unmodelled friction, we took in account of 0.Nm additionally. Pulley reduction was applied in between the pump and the motor. 436

TABLE III DESIGN PARAMETER OF SCREW PUMP Description Value Unit Dynamic viscosity (ν 00 cst Fluid density (ρ 882 kg/m 3 Axial screw length (l t 62 mm Bore diameter (d t 28 mm Groove width (w c 9 mm

6. Pressure-Flow Rate Characteristics Test Setup Fig. 3 shows the simulated pressure - flow rate characteristics of the pump.

4 TABLE III DESIGN PARAMETER OF SCREW PUMP Description Value Unit Dynamic viscosity (ν 00 cst Fluid density (ρ 882 kg/m 3 Axial screw length (l t 62 mm Bore diameter (d t 28 mm Groove width (w c 9 mm Groove depth ( 0.5 mm Ridge width (w b.0 mm Screw - sleeve gap (h g 5 μm Number of helices (n t 3 - Reduction before pump 2 - Fig. 5. Outlook of Developed Screw Pump Fig. 3. Pressure-Flow Rate Characteristics of Designed Screw Pump Fig. 6. Pressure-Flow Rate Characteristics Test Setup Fig. 3 shows the simulated pressure - flow rate characteristics of the pump. This simulation includes torque - speed characteristics to make the simulation realistic. From this figure, it can be seen that the specified pressure and flow rate are botovered by the operation region. Fig. 4 shows the designed screw pump. The screw is supported with a pair of ball bearings to realize high precision rotation of the screw to maintain the precision of the gap between the screw and the sleeve that affects the performance significantly. The housing have 3 ports on each side to connect tubes and pressure sensors. Fig. 5 shows the outlook of the developed screw pump. Major components that support pressure are made of 5000 series aluminium alloy. The screw is made of ABS polymer. V. EXPERIMENTS A. Evaluation on Pressure - Flow Rate Characteristics To evaluate the performance of developed screw pump, pressure to flow rate characteristics was examined. Fig. 6 shows the hydraulic circuitry used in the evaluation. The motor of the pump was driven witonstant current (thus torque while load was changed using a choke valve. Flow rate was measured using flow meter. Pump discharge pressure was monitored using a pair of pressure sensors located at the ports of the pump. Test was done by changing the choke continuously. The rate of the change was kept sufficiently lower than the system dynamics because the pressure to flow rate characteristics is a static characteristics..0mpa of pressurization was applied to the system to avoid cavitation. Fig. 7 and Table IV shows the result of the evaluation. From the figure, linearity of the characteristics can be observed. It can also be observed that the relation of the flow rate and pressure changes linearly with the applied torque. This can easily be derived from ( and (2 by canceling out ω from these equations. LS Fit in Fig. 7 denotes the line was drawn using the least square to a linear function. From the simulated parameter in previous section, the characteristics of the pump was estimated as follows. Fig. 4. Cross Section of Screw Pump Design q = p τ (5 In Table IV, Slope denote the coefficient of the first term, thus dq dp. Y Intercept / Pump Torque denotes the coefficient 437

5 TABLE IV RESULT OF PRESSURE-FLOW RATE CHARACTERISTICS. Pump Torque Slope Y Intercept/Pump Torque mnm 0 2 m 3 /s/pa 0 6 m 3 /s/nm TABLE V BACKDRIVABILITY COMPARISON RESULT OF TROCHOID PUMP AND SCREW PUMP (UNITS IN Nm Description Trochoid Pump [7] Screw Pump Output Backdriving Torque < 0.2 < 0.2 Total Backdriving Torque Fig. 8. Backdrivability Evaluation Test Apparatus of the second term on the right hand side of (5, thus q τ p=0. The result shows stable behavior despite of change in applied torque. The parameter discrepancy is expected to come from the error of the gap and unmodeled friction around the bearings and axis seal. B. Evaluation on Backdrivability Realizing high backdrivability is one of the important objective of this study. To evaluate the backdrivability, a vane type hydraulic motor used in [7] was connected to the designed pump. Evaluation was performed by applying torque to the hydraulic motor through a wire as in Fig. 8 while measuring movement of hydraulic motor with link side encoder and pump with pump side encoder. Applied torque was measured with force gauge attached to the wire..0mpa of pressurization was applied to the system to avoid cavitation. Fig. 9 and Fig. 0 shows the movement history of hydraulic motor and pump respectively. Both data were acquired synchronously. In Fig. 9, the point that the marker leaves the x axis shows the torque that the output backdriving started. From this figure it can be said that the output backdriving happens with very small torque. Fig. 0 shows the movement of the pump induced by the pressure generated by the movement of hydraulic motor. Similar to Fig. 9, the point that the markers leave x axis shows the point where total backdriving started. This value is always lager than the output backdriving torque since output backdriving is necessary in generating the pressure to backdrive the pump. Table V shows the result of the evaluation and their comparison with the case of trochoid pump being connected instead of the screw pump that were presented in [7]. From the comparison, in either case, output backdriving torque was too small to be measured, but the total backdriving toque was /3 of the case with trochoid pump. Hence, the efficacy of the screw pump in enhancing the backdrivability was experimentally shown. Fig. 9. Output Backdrivability Evaluation to realize smoother force control and significant improvement in backdrivability that is expected to play an improtant roll in robotics, especially humanoid. Design concept of utilizing viscous pump to realize actuator system with minimum mechanical contacts to maximize backdrivability was presented. 2 Introduced the fluidic property of the screw pump, first proposed by Asanuma []. The form of the equation was modified to be used for the mechanical design. 3 Presented mechanical design of the screw pump prototype that realize maximum discharge pressure of VI. CONCLUSOINS This paper proposed a design concept and methodology to use single axis screw pump in Electro-Hydrostatic Actuators Fig. 0. Total Backdrivability Evaluation 438

6 Fig. 7. Result of Pressure-Flow Rate Characteristics Evaluation. LS Fit shows the lines fit with least-square method..2mpa and maximum flow rate of m 3 /sec. The design was based on the relationship derived in section III. 4 Pressure-flow rate characteristics were evaluated on the developed prototype. The result showed linear behavior and the estimated parameter from the experimental data showed only limited error to the value estimated in the simulation. The discrepancies between the experimental results are expected to come from the mechanical precision, especially the gap amount. 5 Backdrivability was evaluated on the prototype with the hydraulic motor used in knee power assist [7]. From the result, output backdriving torque was smaller than the measurement range as in the case of [7]. Total backdriving torque was reduced more than /3 of the case with trochoid pump that was presented in [7]. REFERENCES [] G. A. Pratt and M. M. Williamson, Series Elastic Actuators, in Proc. of IEEE/RSJ Int l Conf. on Intelligent Robots and Systems, vol., 995, pp [2] J. E. Pratt, B. T. Krupp, C. J. Morse, and S. H. Collins, The RoboKnee: An Exoskeleton for Enhancing Strength and Endurance During Walking, in Proc. of IEEE Int l Conf. on Robotics and Automation, 2004, pp [3] J. S. Sulzer, R. A. Roiz, M. A. Peshkin, and J. L. Patton, A Highly Backdrivable, Lightweight Knee Actuator for Investigating Gait in Stroke, IEEE Trans. on Robotics, vol. 25, no. 3, pp , [4] M. Grebenstein, A. Albu-Schäffer, T. Bahls, M. Chalon, O. Eiberger, W. Friedl, R. Gruber, S. Haddadin, U. Hagn, R. Haslinger, H. Höppner, S. Jörg, M. Nickl, A. Nothhelfer, F. Petit, J. Reill, N. Seitz, T. Wimböck, S. Wolf, T. Wüsthoff, and G. Hirzinger, The DLR Hand Arm System, in Proc. of IEEE Int l Conf. on Robotics and Automation, 20, pp [5] H. Kaminaga, T. Yamamoto, J. Ono, and Y. Nakamura, Anthropomorphic Robot Hand With Hydrostatic Actuators, in Proc. of 7th IEEE-RAS Int l Conf. on Humanoid Robots, 2007, pp [6] H. Kaminaga, T. Amari, Y. Katayama, J. Ono, Y. Shimoyama,, and Y. Nakamura, Backdrivability Analysis of Electro-Hydrostatic Actuator and Series Dissipative Actuation Model, in Proc. of IEEE Int l Conf. on Robotics and Automations, 200, pp [7] H. Kaminaga, T. Amari, Y. Niwa, and Y. Nakamura, Development of Knee Power Assist using Backdrivable Electro-Hydrostatic Actuator, in Proc. of IEEE/RSJ Int l Conf. on Intelligent Robots and Systems, 200, pp [8] N. Tesla, Turbine, United States Patent No.06206, 93. [9] I. Etsion and R. Yaier, Performance Analysis of a New Concept Viscous Pump, Trans. ASME J. of Tribology, vol. 0, pp , 988. [0] H. S. Rowell and D. Finlayson, Screw Viscosity Pumps, Engineering, vol. 4, pp , 922. [] T. Asanuma, Study on the Sealing Action by Viscous Fluid (The st Report, On the Pump-performances of a Screw-type Viscous Pump, Journal of JSME, vol. 7, no. 60, 95, in Japanese. [2] M. L. Booy, Influence of Channel Curvature on Flow, Pressure Distribution, and Power Requirements of Screw Pumps and Melt Extruders, Trans. ASME J. of Engineering for Industry, vol. 86, pp , 964. [3] H. G. Elrod, Some Refinements of the Theory of the Viscous Screw Pump, Trans. ASME J. of Lubrication Technology, vol. 94, pp , 973. [4] T. Asanuma, Study on the Sealing Action by Viscous Fluid (The 2nd Report, On the Sealing-performances of a Screw-type Viscous Pump, Journal of JSME, vol. 7, no. 60, pp , 95, in Japanese. 439

Electro-Hydrostatic Actuators with Series Dissipative Property and their Application to Power Assist Devices

Proceedings of the 2010 3rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, The University of Tokyo, Tokyo, Japan, September 26-29, 2010 Electro-Hydrostatic Actuators