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100T液壓機泵站設計,100T液壓機泵站設計,液壓機,泵站,設計 527 Reduction of friction torque in vane pump by smoothing cam ring surface Y Inaguma 1 and A Hibi 2 1 Engineering Department, JTEKT Corporation, Okazaki, Japan 2 Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi, Japan The manuscript was received on 1 November 2005 and was accepted after revision for publication on 4 December 2006. DOI: 10.1243/0954406JMES225 Abstract: This work deals with the influence of surface roughness of cam contours on friction torque in a hydraulic balanced vane pump and it is verified that smoothing the surface of the cam contour can reduce friction torque. In the vane pump, the friction torque arising from the friction between a cam contour and vane tips is significant. In this article, first, the values of the coefficient of friction between the vane tip and its sliding surfaces were measured by using cylindrical test rings with various kinds of surface roughness. Then the torque characteristics of vane pumps having cam ring contours with various values of surface roughness were measured and their results compared with the results of an analysis of the coefficient of friction investigated using test rings. As a result, the friction torque caused by the friction between the cam contour and the vane tip was reduced by lessening the surface roughness of the cam contour, resulting in an improvement of the mechanical efficiency. The coefficient of friction measured by using the test rings could be applied to the actual vane pumps. Keywords: hydraulic power system, balanced vane pump, mechanical efficiency, friction torque, coefficient of friction, surface roughness 1 INTRODUCTION A balanced vane pump is now widely used in many hydraulic power systems because it is compact, lightweight, and inexpensive, and especially suitable for a hydraulic power source in a power steering sys- tem of a vehicle, in which low pressure pulsation and low noise are required. When designing a hydraulic pump including the vane pump, the mechanical effi- ciency as well as the volumetric efficiency constitutes a key factor in evaluating pump performance. Friction torque characteristics of various pumps and motors have been already studied and mathematical models proposed 15. In those studies, however, the compo- nents of the friction torques in the vane pump have Corresponding author: Engineering Department, JTEKT Corporation, Oil Pump Engineering Office, 1-18 Miyama, Shinpukuji-cho, Okazaki-shi, Aichi 444-2106, Japan. email: yoshiharu_inagumajtekt.co.jp not been classified and the proportion of each friction torque has not been quantitatively clarified. In the balanced vane pump, the friction torque caused by the friction between the cam contour and vane tip occupies a large part of the pump fric- tion torque because the vanes are pushed to the cam contour by the delivery pressure. Although a step-vane pump 6 and an intra-vane pump, both of which have special mechanisms to decrease the vane pushing force, have been developed, these are not suitable for the power steering pump of vehicles because of the increase in cost due to complexity in vane-manufacturing. The authors revealed theoretically and experimen- tally that the mechanical efficiency of the vane pump at high pressure conditions is greatly affected by the friction torque between the cam contour and vane tip, and thus depends not only on the parameter defined as the ratio of the cam lift to the vane thickness but also on the coefficient of friction between the cam contour and vane tip 7. In this study, for the vane pump with ordi- nary vanes, reduction in the coefficient of friction JMES225 IMechE 2007 Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science 528 Y Inaguma and A Hibi and improvement in mechanical efficiency were attempted by smoothing the cam ring surface, i.e. by lessening the surface roughness of the cam contour, the sliding surface of the vanes. The former part of this work describes the fundamental test results of the relationships between the coefficient of friction and the surface roughness, which were obtained by using test rings with constant inner radius. The latter part of this work describes the friction torque characteristics and the mechanical efficiencies of actual vane pumps, which were measured by using cam rings with various kinds of surface roughness. The influence of the sur- face roughness of the cam contour on the mechanical efficiency would be examined. 2 MEASUREMENT OF COEFFICIENT OF FRICTION ONVANETIP BY USINGTEST RINGS 2.1 Experimental apparatus The coefficient of friction between the cam contour and vane tip was measured by using test rings with- out cam lift. Figure 1 shows a schematic diagram of the experimental apparatus and hydraulic circuit for measuring the coefficient of friction. The test appa- ratus is originally an actual pump and the test ring is equipped instead of the cam ring and the special side plates without ports connected with pump deliv- ery are also equipped. To investigate the influence of the surface roughness, test rings with various kinds of surface roughness were used in this work. The hydraulic circuit for testing is also shown in Fig. 1. Oil delivered from a feed pump was regulated by a relief valve and fed to the vane back pressure groove of the side plate in the test apparatus. The vanes in the test apparatus were lifted to touch their tips to the inner surface of the test ring by the reg- ulated pressure p 1 . The experiment was performed under the condition that the tip side of the vane was filled with oil of pressure p 2 , which was almost equal to the atmospheric pressure. The shaft of the rotor in the test apparatus was driven by an electric motor via a torque meter. Because the test ring has no cam lift, the apparatus does not work as a pump to deliver Fig.1 Experimental apparatus and hydraulic circuit Fig.2 Dimensions of test ring and vane oil. Namely, the ideal torque T th (=V th Delta1p/2) is zero because the pump displacementV th is zero.Therefore, the measured torque of this apparatus is equal to the total friction torque of the shaft, rotor, and vanes. Figure 2 shows the specifications of the test parts. The rotor and the vanes used in this test were the ones used in mass production of vane pumps. The vanes were made of high-speed tool steel and finished by barrel polishing. The roughness of the vane tip was about 0.3 m Rz. The inner radius of the test ring R C was the same as the small radius of cam ring R 1 . Figure 3 shows five examples of the measured data on the roughness of the inner surface of the test ring. The measuring direction of the surface roughness made a right angle with the sliding direction of vanes. As shown in Fig. 3, the inner surface was finished by nor- mal grinding for No. 1 test ring, by fine grinding for Nos. 2 and 3, by ultra-fine grinding for No. 4, and by lapping after grinding for No. 5, and the surface roughness becomes finer following figures in numeric order. The material of test rings from Nos. 14 was car- burized and quenched ferro-sintered alloy, the same material as that of the actual cam ring, and that of No. 5 was quenched tool steel. The inner surfaces of the test rings were finished by grinding or lapping to roughness of 0.11.5 m Rz individually. For measur- ing the coefficient of friction, other test rings were also used besides the test rings shown in Fig. 3. The hydraulic fluid used was commercial mineral oil and its density and viscosity at 40 Care 855 kg/m 3 and 0.0293 Pa s, respectively. 2.2 Experimental results of coefficient of friction Figure 4 shows friction torque Delta1T against the pres- sure difference between the bottom and tip of the vane Delta1p(=p 1 p 2 ) for No. 1 test ring. In Fig. 4, Delta1T increases linearly with an increase in Delta1p and the slope of Delta1p Delta1T line is smaller with an increase in the rota- tional speed of the rotor N. In this case, (a) the friction torque due to the viscous friction between the rotor and side plates, (b) the friction torque caused by the Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science JMES225 IMechE 2007 Reduction of friction torque in vane pump 529 Fig.3 Surface roughness of test rings friction between the pump shaft and oil seal, (c) the friction torque at the bush bearing, and (d) the friction torque of vane, namely, the friction torque caused by the friction between the cam contour and vane tip are included in Delta1T. In the above friction torque components, only the friction torque of the vane increases with an increase in Delta1p, because the pushing force of the vane is pro- portional to Delta1p.Therefore, the values of Delta1T at Delta1p = 0, namely, Y -intercept T 0 in Fig. 4 can be considered to be the sum of the friction torques except the friction torque of the vane. The friction torque of the vane T n can be calculated by subtracting T 0 from Delta1T as shown in Fig. 4. Then, the coefficient of friction at the vane tip is calculated from T n by the following equation = T n (zbwR C Delta1p) (1) Fig.4 Relationships between Delta1p and Delta1T Fig.5 Relationships between Delta1p and T n where z is the vane number, b is the rotor width, w is the vane thickness, and R C is the inner radius of the test ring. Figure 5 shows the relationships between Delta1p and T n for five test rings from No. 1 to 5. As seen from Fig. 5, T n decreases with a decrease in the value of the inner surface roughness of test ring. The change of T n against Delta1p is not linear clearly for the test ring Nos. 2 and 3, which have a surface roughness of 0.3 0.6 m Rz, and the increasing rate of T n against Delta1p becomes higher at high Delta1p regions. For Nos. 4 and 5 test rings, this tendency is slight. This fact means that the coefficient of friction is not constant to Delta1p for these test rings. Figure 6 shows the values of measured at Delta1p = 5.88 MPa. This figure shows that depends greatly on the surface roughness and tends to decrease slightly with an increase in N. Although is 0.100.12 in the case of No. 1 test ring, ground by normal grinding with the surface roughness of 1.4 m Rz, decreases clearly with a decrease in the surface roughness. When the surface roughness is 0.7 m Rz. The constant values of are different for N and the value is lower with an increase in N. When the surface roughness becomes 0.3 m Rz, the reduction of becomes slight. The reason for the phenomena shown in Fig. 7 is explained in Fig. 8, which illustrates the conditions for the lubrication between a ring surface and a vane tip. Although the radius of roundness at the vane tip is much smaller than the inner radius of the test ring, it is well known from the elastohydrodynamic lubrication theory that a thin oil film can be formed between the cam contour and the vane tip. The vane is lifted up from the ring surface due to the forma- tion of the oil film by the sliding of the vane. The lifting height of the vane tip from the ring surface, h f , depends strongly on the sliding speed of the vane as well as the force loaded on the vane and the viscosity of oil. With lifting of the vane by h f due to the oil film, the vane is perfectly floated without metal-to-metal con- tact between the vane tip and the ring surface when the surface roughness of the ring is extremely fine, as shown in Fig. 8(a). In the experiments of this work, it seems that most of the vane force is supported by the oil film in the case of ring surface roughness of 0.3 m Rz. In this situation, the coefficient of friction becomes extremely low. When some of the surface peaks become larger than h f , the lifting height of the vane due to the oil film, a part of the vane tip is in contact with the inner sur- face of the test ring, as shown in Fig. 8(b). Then, the coefficient of friction becomes larger because of par- tial metal-to-metal contact. The coefficient of friction increases due to the increase in the metal-to-metal contact area with an increase in the value of the ring surface roughness. When the roughness of most surface peaks become much larger than h f , as shown in Fig. 8(c), the oil film could not support the vane. In this condition, the coef- ficient of friction becomes high and it remains con- stant in boundary lubrication despite further increase in the surface roughness. Fig.8 Conditions of lubrication between ring surface and vane tip Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science JMES225 IMechE 2007 Reduction of friction torque in vane pump 531 Fig.9 Cross-sectional view of the vane pump 3 EXPERIMENT IN ACTUALVANE PUMPS 3.1 Construction of vane pump tested Figure 9 shows a cross-sectional view of a balanced vane pump, composed of a cam ring with an elliptic inner bore, a rotor with a series of radially disposed vanes, and two side plates located on both sides of the rotor. The rotor is driven by a shaft through a very loose-fitting spline, and the rotor and the vanes rotate between two side plates with running clearance. The balanced vane pump has a double displace- ment process, with two cycles of suction/discharge per revolution. The pump is so designed that both suction and delivery ports in the pump are diamet- rically opposed, providing a complete balance of all internal radial forces. In this pump, the side plates have vane back pressure grooves at the sides facing the rotor to introduce delivery pressure at the bottom of the rotor vane slot. During the pump operation, the vanes are always pushed from the bottom by delivery pressure and rotate on the cam contour with the loads imposed by the vane tip. The dimensions of the test pump are given in Table 1. The details of the test cam rings are as follows: they were made of ferro-sintered alloy and the inner sur- faces of the cam ring were ground with various values of surface roughness. In this study, 19 cam rings with difference in the surface roughness of the cam con- tour were prepared and tested. Figure 10 shows two examples of the surface roughness on the cam con- tour of the test cam rings. The upper one in Fig. 10 was Table 1 Dimensions of test pump Cam ring small radius R 1 (mm) 20.0 Cam ring large radius R 2 (mm) 23.0 Cam lift R 2 R 1 (mm) 3.0 Rotor radius R r (mm) 19.5 Rotor width b (mm) 15.0 Vane thickness w (mm) 1.4 Vane tip radius R v (mm) 2.0 Pump displacement V th (cm 3 /r) 10.8 Fig.10 Surface roughness of test cam rings finished by normal grinding and its surface rough- ness was 1.23 m Rz. In contrast, the lower one in Fig. 10 was finished by fine grinding and its surface roughness was 0.40 m Rz. Although the delivery pressure p d acts constantly on the entire vane bottom, the area acting p d on the vane tip changes according to the rotational position of the vane. It is defined that the rota- tional angle of the vane is zero at the middle point of the small radius part of the cam contour, 1 is the starting angle of the suction, 2 is the fin- ishing angle of the suction, 3 is the starting angle of the delivery, and 4 is the finishing angle of the delivery. Figure 11 illustrates the pressure acting on the bot- tom and tip of the vane and the vane force F v caused by the pressure difference in the small radius part (0 1 ), suction part ( 1 2 ), large radius part ( 2 3 ), and delivery part ( 3 1.0 m Rz and m increases gradually as the surface roughness of the cam contour becomes smaller to the extent of 0.8 m Rz, it decreased with a decrease in the surface roughness. With the surface roughness of 0.3 m Rz, the coefficient of friction could reduce nearly to 0.02. It could be considered that this effect was derived from the increase of the vane force support by the oil film with a lessening the surface roughness. In the actual vane pump also, the friction torque of the vane decreased with a decrease in the sur- face roughness of the cam contour to the extent of 0.8 m Rz.This study verified that the friction torque of the vane reduced to about half and the mechani- cal efficiency of the vane pump becomes nearly 90 per cent with an improvement of 5 per cent when the surface roughness of the cam contour decreased to 0.4 m Rz. It was revealed that the values of the coefficient of friction at vane tip measured with the test rings could be applied to the actual vane pump. REFERENCES 1 Wilson, W. E. Rotarypump theory. Trans. ASME, 1946, 68(4), 371384. 2 Wilson, W. E. Performance criteria for positive- displacement pumps and fluid motors. Trans. ASME, 1949, 71(2), 115120. 3 Schlsser, W. M. J. Ein mathematisches Modell fr Verdrngerpumpen undmotoren. Oelhydraul. Pneum., 1961, 5(4), 122129. 4 Hibi, A. and Ichikawa, T. Mathematical model of the torque characteristics for hydraulic motors. Bull. JSME, 1977, 20(143), 616621. 5 Inaguma, Y., Watanabe, K., Kato, H., and Hibi, A. Energy-saving and reduction of oil temperature rising in hydraulic power steering system. SAE paper 199901 0392, 1999. 6 Mortenson, P. C. Vane pumps for the mobole and industrial market. In Proceedings of 18th National Con- ference on Industrial hydraulics, 1962, pp. 148153. 7 Inaguma, Y. and Hibi, A. Vane pump theory for mechanical efficiency. Proc.IMechE,PartC:J.Mechanical Engineering Science, 2005, 219, 12691278. APPENDIX Notation b width of cam ring, rotor and vane (mm) F v pushing force of the vane (N) N pump speed (r/min) p d delivery pressure (MPa) p s suction pressure (MPa) R C inner radius of test ring (mm) R 1 small radius of cam ring (mm) R 2 large radius of cam ring (mm) T driving torque of the pump (Nm) T 0 friction torque independent of Delta1p (Nm) T n friction torque of vanes (Nm) T th ideal torque of the pump (=Delta1pV th /(2) (Nm) V th pump displacement (cm 3 /r) w vane thickness (mm) z number of vanes Delta1p pressure difference (=p d p s ) (MPa) Delta1T total friction torque (=T T th ) (Nm) m mechanical efficiency (=T th /T) coefficient of friction rotational angle of the vane (rad) Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science JMES225 IMechE 2007