A study on the application of tripod joints to transmit the driving torque of axial piston hydraulic motor Youna-Boa HAM*, Sung-Dona KIM** *Senior Researcher, Department of Advanced Industrial Technology Korea Institute of Machinery & Materials 171 Jang-Dong, Yusung-Gu, Daejeon, 305-343 Korea (E-mail: hyb665@kimm.re.kr) **Professor, Department of Mechanical Engineering Kumoh National University of Technology 188 Shinpyung-Dong, Kumi, Kyungbuk, 730-701 Korea (E-mail: sdkim@kumoh.ac.kr) ABSTRACT An axial piston hydraulic motor with a tripod joints mechanism is introduced to improve compactness and starting torque in conventional types of motor. If the mechanism is applied in transmission torque to motor shaft, its friction torque loss would be drastically reduced and mechanical efficiency would be improved because the motion of tripod joints mechanism is relatively smaller than that of the conventional plunger motor. In particular, kinematics analysis for the mechanism is done as a preliminary study to investigate the feasibility of the mechanism in the axial piston motor. General formulas are derived from the displacement and velocity analysis of that mechanism, showing relationships between output shaft and shoe holder motion. A series of numerical calculations are carried out for a medium size motor with 160cc/rev using the formulas and their graphical plots are shown as well. KEY WORDS Axial piston hydraulic motor, Tripod joint, Swash plate, Shoe holder, Lateral force NOMENCLATURE Fluid Power. Fifth JFPS International Symposium (c) 2002 JFPS. ISBN4-931070-05-3
direction (j) rslip: Displacement of the slot in the longitudinal direction (i) vslip: Sliding velocity of B, a point of the spherical bearing in the negative i direction Vgap: Sliding velocity of B, a point of the spherical bearing in the negative j direction wp: Angular velocity of the shoe holder ws: Rotating angular velocity of the motor shaft wb: Angular velocity of the spherical bearing X, Y, Z: Orthogonal coordinate system fixed to the space x, r, ľ: Rotating orthogonal coordinate system 1. Introduction An axial piston hydraulic motor is widely used for driving large mechanical apparatuses. Generally, the axial shaft rotating synchronously. The motion of the connecting rod set has been already analyzed in the prior study.[4]-[6] Therefore, in this study, the motion of the tripod joints set has been intensively analyzed. This studying method is to analyze the motion of the tripod joints set theoretically in the first place to derive formulas, and then to conduct a numerical analysis by using the formulas acquired from the theoretical analysis, and further to conduct a quantitative analysis on the basis of the results of the numerical analysis. 2. Construction of Motor and Operation Principle Fig. 1 shows the construction of the swash plate type axial piston hydraulic motor to which the connecting rod set and the tripod joints set are applied. The thrust obtained by applying the hydraulic pressure to the piston is transmitted to the shoe through the connecting rod, and a rotating force takes place by the action of the sliding force between the shoe and the inclined shoe plate. This rotating force is transmitted to the motor shaft through the shoe holder and the tripod joints set. piston motor could be categorized into two types, a swash plate type and a bent axis type. Since the conventional swash plate type axial piston hydraulic motor has a simple construction and fewer components of the reciprocal movement portion in comparison with the bent axis type and its rotating mass is concentrated around the motor shaft, it has a merit to be installable in a place requiring a high-speed rotation and a limited area for installation. However, because the tilting angle of the swash plate is structurally limited, it has also a demerit that it is inferior to the bent axis type in the mechanical efficiency thereof. From a historical viewpoint, as a first model of swash plate type axial piston pump and motor, rod type piston has been attempted to be used much earlier than rodless or plunger type piston mostly used at present. But, owing to the fault of complicated construction, swash plate type piston pump and motor has not developed so much. First of all, after developed the universal joint mechanism by Harvey Williams and Reynolds Janney in 1903, it had been adopted in military applications and manufactured by Vickers in England and Mitsubishi Heavy Industry Co. in Japan.[1]-[3] In this study, the connecting rod piston set, which is adopted for the bent axis type, has been applied to the swash plate type in order to seek for a solution to the problems, such as the limited tilting angle of the swash plate, a strong lateral force of the piston, etc.. And, in order to apply such connecting rod mechanism, the tripod joints set has been applied as a synchronizing device to be required for having the shoe holder and the motor Fig. 1 Structure of axial piston hydraulic motor to which a tripod joints set and a connecting rod set are applied. In the conventional plunger type of the axial piston motor without the connecting rod, the rotating force gets to be transmitted by the action of the force between the plunger edge and the surface of the cylinder bore, and thus, a lateral force acts greatly on the plunger's side. As a result of such action, both the friction force and the wear of the plunger side get to be great. Meanwhile, for the motor shown in Fig. 1, the spherical joint is adopted, and thus, both the lateral force and the friction force of the piston are small, and the abrasion of the piston side takes place to a small extent. While the lubricant condition of the piston side gets to be better,
some additional friction gets to take place in the tripod joints set. However, since the lubricant condition of the tripod joints set is much better than that of the plunger side of the conventional motor, the consequent friction performance is superior. More particularly to say, as the lateral force of the piston of the motor on which this study is conducted is close to 0, the solid friction gets to be removed, and further, as the surface area of the piston side is very small, the viscous friction gets to be decreased. Also, it can be thought that since the tripod joints set is near the center of the motor shaft, the moment radius of the rotational inertia is small, and further that since the relative motion of this set is smalier than the sliding motion of the plunger in the conventional plunger type axial piston motor, the friction torque is small. around the motor shaft. While the piston shoe is in elliptic motion on the center of the motor shaft, it is in circular motion on the central axis of the shoe holder. 3. Analysis of Displacement of One Joint 3.1 Coordinate System Any motion of one point (B) in the outer ring of the square bearing can be expressed by 2 methods, that is to say, the one method for expressing it by using the rotational motion of the motor driving shaft and the other method for expressing it by using the rotational motion of the shoe holder. A coordinate system with which it is convenient to express each motion is applied to each motion, and then the two expressions of the motion are converted into one coordinate system for analysis thereof. The conversion formula between the two coordinate systems expressed in Fig. 3 is described as follows; (a) Front view of tripod joints set (b) Side view of tripod joints set (c) Three-dimensional view of tripod joint mechanism Fig. 2 Construction of tripod joints set As shown in the Fig.2, the front view of tripod joints is shown in Fig.2 (a) and also tripod joints assembled with the inclined shoe holder and three-dimensional modeling gure about combination of them are individually fi shown in Fig.2 (b) and (c). When 3 joints are in symmetry to the motor shaft as shown in the left figure of Fig. 2, the shoe holder gets to be in rotational motion on the axis inclined by 8 to the motor shaft with the central axis of the shoe holder intersecting over the motor shaft. In case the central axis of the shoe holder does not intersect over the motor shaft, the shoe holder gets to be in rotational motion, revolving Fig. 3 Coordinate system for rotational motion of driving shaft and of shoe holder 3.2 Analysis of Displacement Displacement of one point (B) in the square bearing could be expressed through the rotational motion of the
motor driving shaft as follows; (4) In Table 1, we show parameters and input value for analysis. Table 1 Parameters and input value for analysis The position of Point B could be expressed through the rotational motion of the shoe holder by setting Point OP of Fig. 3 as a base, as follows; (5) Wherein, Eq. (4) and (5) should be the same each other by components le, je and ke. (6) (7) In case the square bearing is installed respectively in 3 points of the motor shaft at intervals of 120 as shown in Fig. 2, the gap gets to be changed in a cycle of 120 as shown in Fig. 4. Fig. 5 shows the variation of rsjlp with the angular displacement of the motor shaft, Os. Fig. 6 shows a phase difference between 8S and 8P to 8c, the angular displacement of the motor shaft. (8) From Eq. (6) (9) Form Eq. (7) (10) From Eq. (8) (11) Fig. 4 Variation of the Gap between Point B and P In Eq. (9) and (10), in case the degree of inclination of the axis is so small to the extent of 8= 20, the difference between 8S and 8p, which are angular displacement, is so small that it may be ignored, and thus, it can be assumed that 8S should be equal to Op. On this assumption, Point P and B are the farthest at the point of 8S=8p=0, and as the motor shaft and the shoe holder move in rotation, they get to be nearer and nearer, and then the nearest at the point of Os=Op=90. Thereafter, they get to be farther and farther again. They are in this cyclic motion repetitively. When Eq. (11) is applied together with Eq. (10), the size and the degree of change of rgap, the gap between Point B and P can be known, which is shown in Fig. 4. Fig. 5 Variation of the sliding displacement of spherical bearing with the angular displacement of motor shaft (5=20 )
If we assume the angular velocity of motor shaft ws may be uniform, the relation between ws and the rotation velocity of the shoe holder wp can be displayed as shown in Fig. 7. Fig. 8 shows the variation of the angular velocity of shoe holder with the tilting angle of the shoe holder (ĉ). Fig. 9 shows the variation of the sliding velocity of Fig. 6 Variation of the phase difference (ľs-ľp) with the angular displacement of motor shaft Point B (vsllp) of the square bearing in the negative i direction with the angular displacement of the motor shaft (ľs). As shown in Fig. 6, in case the degree of inclination of the axis is so small to the extent of ĉ=20, the difference between ľs,and ľp, which are angular displacement, is so small that it may be ignored, and thus, it can be assumed that ľs, should be equal to ľp. 3.3 Analysis of Velocity Velocity of one point (B) in the square bearing could be expressed through the rotating motion of the motor driving shaft as follows; Eq. (12) shows the velocity of Point B based on Point OP in the Fig. 3 and intermediated the rotating motion of the shoe holder as follows; Fig. 7 Variation of the wp and ws with the angular displacement of motor shaft (ľs) Wherein, Eq. (12) and (13) should be the same each other by components of iľ, jľ and kľ. And if Eq. (16) is substituted by Eq. (10), it is equal to Eq. (17). Fig. 8 Effect of a tilting angle (ĉ) of swash plate on the variation of the wp
3) A sliding relative motion takes place between the spherical bearing and the shoe holder. It can be thought that such sliding motion is relatively much smaller than the piston sliding motion. That is because the tripod joints locate much closer than those pistons from the center of motor shaft. Therefore, it can be thought the friction loss is smaller in the case that the driving torque is transmitted with the tripod joints set than in the case that the driving torque is transmitted by the lateral force of the piston in the conventional plunger type. REFERENCE Fig. 9 Variation of the vslip with ľs Fig. 10 shows the variation of the vgap, the sliding velocity of Point B on the square bearing in the negative motor direction with ľs, the angular displacement i of the shaft. 1. Sadao Ishihara, Design and Basic of Axial Plunger type Hydraulic Pump and Motor, Oil Hydraulics, 1975, Vol.5, No.2 2. Nishimura, Axial Piston Pump, Hydraulics and Pneumatics, 1983, Vol.14, No.5, pp.344-350 3. Kouoh Kita, About Hydraulics (Progress in Variable Pump/Motor), Hydraulics and Pneumatics, 1988, Vol. 20, No.2, pp.101-108 4. Atsushi Yamaguchi, Performance of Spherical Bearings for Piston Pumps and Motors, Hydraulics and Pneumatics, 1970, Vol.1, No.1 5. Park, T. J. and Lee, C. O.," Hydrodynamic Lateral Force on a Tapered Piston Subjected to a Large Pressure Gradient", Proc. Of 3rd Int. Conf. on Fluid Power Transmission & Control, Int. Academic Pub., 1993, pp.44-48 6. Kim, J. K., Jung, J. Y., Oh, S. H.," A Study on the Driving of rods in Hydraulic Bent-axis-type Axial Piston Pump, Part 1 The Theoretical Analysis of Driving Mechanism", Journal of KSTLE, 1998, Vol. 14, NO.4, pp.51-57 Fig. 10 Variation of the vgap with ľs 4. Conclusion In this study, the hydraulic motor to which the connecting rod piston set and the tripod joints set are applied has been analyzed, and the main results of such analysis are summarized as follows; 1) The rotation angular displacement of the shoe holder shows a phase difference of }1.7 or so to the rotation angular displacement of the driving shaft. 2) The angular velocity of shoe holder deviates from that of motor shaft. The extent of the deviation increases as the tilting angle of swashplate increases. In case the tilting angle is 20 and the motor speed is 2000 rpm, the maximum deviation is about 6.25 % against the motor speed. The deviation } appears as a cyclic pattern, and shows 2 times cyclic motion for one revolution of the motor shaft.