AN EXPERIMENTAL INVESTIGATION ON SWASH PLATE CONTROL TORQUE OF A PRESSURE COMPENSATED VARIABLE DISPLACEMENT INLINE PISTON PUMP Rathindranath MAITI and Paritosh NARAYAN Department of Mechanical Engineering Indian Institute of Technology, Kharagpur 70, India (Email : rmaiti@mech.iitkgp.ernet.in) ABSTRACT To avoid or to reduce the costs of experiments, analysis by simulation is preferred to predict the performance in design and development stages. However, accurate modeling and then remodeling after part experiments are usual practice. In in-line piston swash plate type variable displacement pump with pressure compensation swash plate dynamics has a crucial role on pump performance particularly at the vicinity of operation at set pressure. The present investigation is targeted at understanding the reasons of such dynamics. A commercially available pump was chosen for study. The swash plate control torque and relevant data were measured experimentally in a proven test rig. Analysis was made to identify the various forces that give rise to the cradle or swash plate torque about its pivot in a pump. A simplified and concise model was finally developed and simulation was carried out in MATLAB-SIMULINK environment. Analytical results had good agreement with experimental results. KEY WORDS Inline Piston Pump, Pressure Compensated, Swasplate Control Torque INTRODUCTION In line linear piston pumps with swash plate are widely used in both military and civil fluid drive applications. For accurate flow control, particularly in sophisticated applications, the swash plate yawing torque has a great role. Over last fifty years several investigations are carried out globally to understand, assess and optimize the swash plate contol torque. Lewis & Stern [], Green & Crossley [], and Zaki & Baz [] have analyzed the dynamic response of various types of conventional control systems for in-line linear piston pumps (hence forth mentioned only as pump / pumps) following Merritt s [4] approach and using linear transfer function analysis. Most of the models were devoted to the specific control system with simplified linear model representation for the pump. Such models did not incorporate the effect of different geometrical features or the variations in operating conditions. Yamaguchi [5, 6] investigated considering more complex parameters of the hydraulic pump model. The subject of loads on the swash plate was treated from the point of view of power losses. However, he too presented a linear model of a hydraulic pump. He considered the effect of load pressure on the pump dynamics, although based on a pump with simplified configuration. Zeiger & Akers [7] and later with Lin [8] presented a comprehensive mathematical model for the average torque on the pump swash plate. The analysis was limited to steady state conditions only. Zeiger & Akers [9] also analyzed the pump dynamics as an open loop plant to be controlled. The analysis followed a state variable approach in place of a simpler classical approach of transfer function.
Schoenau, Burton & Kavanagh [0, ] investigated in detail the characteristics of such a pump with pressure compensated swash plate control (Vickers PVB5 Model). They developed a comprehensive mathematical model capable of predicting both steady state and dynamic responses. Inertial and viscous damping terms as well as the control-piston and return-spring dynamics were considered in details. Experiments were conducted in support of the theoretical analysis. Manring [] developed a mathematical model to depict the dynamic characteristics of torque exerted on the input shaft of the pump. The approach used was different from understanding this torque with traditional macro inputoutput perspectives. In his analyses he considered all basic forces within the machine to compute the instantaneous torque exerted on the shaft. Manring further analyzed the control and containment forces and moments acting on the swash plate of an axial-piston pump []. Later Zhang, Cho & Nair with Manring [4] presented a new, open-loop, reduced order model for the swash plate dynamics of an axial piston pump. The proposed reduced order model is validated by comparing with a complete nonlinear simulation of the pump dynamics over the entire range of operating conditions. Zeliang [5] in association with Burton [] worked on condition monitoring of an axial piston pump (Vickers model) for his M.Sc. thesis. Results of this investigation are very useful to understand the pump as well as swash plate performances. To understand the swash plate control torque in a better way we considered a Vickers PVB5 model, apparently the same model that was used by Kavanagh et al. [0, ]. Experiments were conducted following civil and military specifications [6]. Later we have also tried to present a concise mathematical model and carried out simulation, following some of the investigations referred above, in support of our experimental results [7]. The experiments have been conducted on a proven test rig which is regularly used to test such hydrostatic units for civil as well as military applications. This paper is a brief report of the investigation. MATHEMATICAL MODEL FOR SWASH PLATE CONTROL TORQUE A schematic view of the pump, considered for study, is illustrated in Figure. The total torque which acts on the swash plate yoke assembly consists of several components, namely torque due to pressure differences and locations of pistons ( T ap ), the yoke damping torque ( T d ), (in the negative direction), the return spring torque ( T sp ) and the torque applied to the yoke by the control piston ( T sp ) (in the negative direction). Therefore, taking a summation of the torques that act on the swash plate yoke assembly yields T T T T T I () y ap d sp c where I is the mass moment of inertia of the swash plate yoke assembly. [7] Pressure Compensatory Part Figure Model Feature of the Pump [] Substituting all expressions derived [7] for different torques and grouping of similar terms yields an equation of the form: P c Acb K pr Pp K pr p p C C C I e () CoefficientC includes all terms that depend only on the angular position of the swash plate. C, the coefficient of angular velocity and C, the coefficient for the square of the angular velocity term [7]. I e represents the total effective mass moment of inertia.
of coefficients have been significantly simplified using linear regression techniques. The approach is justified at this stage because the dynamics of the swash plate have already been considered in their nonlinear form. Only the coefficients are simplified. The coefficients C and C were fit using the equations C S S () and C S (4) (a) Pressure regions as seen by piston centers []. Relief where S, S and S are simplified Pump model Constants whose values have a maximum difference of less than percent with Complete pump model Constants C, C etc. Value of C is found to be a 0.549, thus IC IC( d / dt) I max implying that the term C ( d / dt can be neglected and hence C 0. ) Variation of the coefficient, I e with is small and can be neglected. Thus, the effective inertia can be assumed constant and equal to the average effective inertia Ie I e (5) (b) Detail of valve port plate as in [5]. (It is almost similar to that in the pump under study.) Figure Uni-Pressure Regions on Valve Plate Simplified model. Equation is highly nonlinear if all terms are considered. However, it can be solved using numerical techniques although very unwieldy and cumbersome to.. The comprehensive developed model can be simplified by linearizing the equation set for torque due to piston pressure and the coefficient terms in the remaining describing equations by comparing the various terms in the coefficients and neglecting those terms deemed to have an insignificant effect. The terms in the coefficient equations used in this study have been determined using the physical data of the pump (Vickers PVB5). Certain coefficients in the equation depend on the specific type of pump being used and some of these have to be experimentally measured. Based on the values over a range of swash-plate angles, equations Substituting these results from equations () to (5) into equation () yields, P c Acb K pr Pp S ( S K pr p p ) S Ie (6) Above equation (6) represents the simplified mathematical model of the pump. To verify the dynamic response of the model, Simulation of the Simplified Mathematical Model (equation 6)) has been done using MATLAB SIMULINK and the simulated dynamic responses of the pump have been compared to those obtained experimentally. While estimating the swash plate torque, pressure variations in the valve port and slipper pad were considered in detail [Figure - ]. The developed equations are solved in light of the physical model of a pump to assess and estimate swash plate motions, in the dynamic and the steady state conditions. A SIMULINK block diagram is presented in Figure. The rig tests on pump model were carried out to examine the swash plate behavior. Finally, theoretical and experimental results were compared.
Kpr Pr Torque Constant deltapp Pump Differential Pressure Swashplate Angle vs Time Plot Cust Pc IP 0-0 -K- -K- Unit Conv bar to Pa Ac Control Piston Area b Distance Pressure vs Time Plot /Ie /s /s alphadoubledot alphadot alpha /Ave MOI Integrator Integrator S Pump Model Constant Unit Conv rad to deg alpha To Workspace Pressure To Workspace S Pump Model Constant S Pump Model Constant deltapp Pump Differential Pressure Kpr Pr Torque Constant Figure SIMULINK Model to Estimate the Swash Plate Torque. Table Some specification of the pump (a commercial model). Experimental Results Parameter Delivery Full flow Pressure Zero flow (At set pressure) Flow rate Inlet Pressure Case Drain Pressure Rated Speed Numerical value 0 bar 0 bar 8 LPM - bar 4.5 bar 600 RPM As stated earlier a well established and equipped test rig, which is regularly used to test such hydrostatic units for civil as well as military applications, is used for conducting experiments. Variation in Piston chamber pressure and change in port area (theoretically estimated) are shown in Figure 4 and Table & Figure 5 respectively. It is observed that the swash-plate angle varied from 4 degree inclination to 0 degree inclination in almost 0. seconds where pressure varied from 0 bar to 0 bar respectively. The set pressure was 0 bar in pressure compensator. This means that when system pressure was raised to 0 bar the swash plate inclination was move to 0 degree by the control piston force [Figure ] and the final position was maintained at 0 bar at main system line. With a slight reduction in set pressure the swash plate returned to its original inclined position (4 degree) and the system pressure was increase to new set pressure (close to 0 bar). The nature of change in swash-plate angle with time and pressure is shown in Figure 6. Pressure Variation,Bars ------------------->.5 x 07.5.5 0.5 0-0.5 PRESSURE VARIATION IN PISTON CHAMBER WITH ANGULAR POSITION - 0 4 5 6 7 Angular Position, Radians ----------------> Figure 4 Variation in piston chamber pressure with shaft rotation. 4
The variation of swash plate angle has shown an expected trend. The initial sluggishness is expected for a change of system flow of the order of zero LPM to 8 LPM or viceversa. This behavior may be observed for possible corelation during steady-state loading-unloading of pump assembly. 4 x 0-5 Discharge Area Variation Table Cumulative valve port opening area Angle, Degrees Discharge Area X 0-4 (m ) - 0 to 9 0 0.000 0.4 9 0 to 7 0 0.4-0.49 7 0 to 9 0 0.49-0.94 9 0 to 4 0 0.94 4 0 to 7 0 0.94-0 Discharge Area, Sq meter -------------------->.5.5.5 0.5 0 S w a s h P la te A n g le, D e g re e s --------> 4 0 8 6 4 0 Swash Plate Angle with time -0.5 - -50 0 50 00 50 00 Angle, Degrees -------------------> -0. -0.05 0 0.05 0. 0.5 Time, Seconds ---> Experimental Analytical Figure 5 Port area opening with shaft rotation. The preliminary analysis of response parameters of pump obtained during experimentation has been done. The comparison of response parameters with their limiting values for three pressure cycles is summarized below in Table. It is observed that pressure pulsation (oscillation in steady state pressure value during operation) is moderately low and perhaps well within tolerable limits. The frequency associated with pump rotation and its higher multiples did not affect the steady-state behavior. The response time (response of a system to perturbation) is relatively high. Figure 6 Swash Plate Angle with respect to time. The range of response time for full flow to zero flow is 70 to 00 seconds and for zero flow to full flow, when pressure is regulated, is 98 seconds to 400 seconds. The settling time (time taken to settle down when switched from one to another steady state) within limits for full flow to zero-flow but beyond limits for zero flow to full flow. The overshoot and the undershoot in percentage (maximum and minimum transient pressures during dynamic response) are within limits for full flow to zero flow. However, these are beyond limits for zero flow to full flow operation. 5
Swash Plate Totque,N m -----> 0 8 6 4 0 Experimental and Theoretical curves : Steady State Experimental Theoretical 8 0 0.05 0. 0.5 0. 0.5 0. 0.5 Alpha, Swash plate angle,radians -----> Experimental Analytical (a) Swash Plate angle Increasing Figure 8 Swash Plate Control Torque (Set Pressure 0 bar) Swash Plate Torque, Nm -------------> 0 9 8 7 6 5 4 0 Unloading Loading 9-0.05 0 0.05 0. 0.5 0. 0.5 0. 0.5 0.4 Swash Plate Angle, Radians---------------> Experimental Analytical (b) Swash Plate angle Decreasing Figure 7 Variation of swash-plate angle for pressure regulation Figure 9 Hysteresis observed experimentally. Table- Some Measured Data of the Pump Parameter Response Time (sec) Over and Undershoot Settling Time (sec) Limiting value 00 00-50 Full to Zero Flow 500 45-0 600 00-0 00 50-00 Zero to Full 500 0-45 600 0-00 0.05 max 0.076 0.07 0.0 0.404 0.74 0.98 ± 5% 8% % % 75% 69% 5% max 0.480 0. 0.8.5.946.58 6
Set 0 Zero Flow Delivery Pressure (Bar) Full Flow Time(Seconds) Figure 0 A typical record of experimental results (Delivery pressure, flow rate and time response) Theoretical response During simulation, pressure-time history (0 to 0 bar and 0 to 0 bar) as obtained during experimental work has been used as input. The variation of swash-plate angle for pressure regulation of 0-0 bar has been estimated theoretically and compared with experimental response. The variation of swash plate angle in both the cases has been from 0-4 degrees. The general shape and trend of the theoretical curve agrees with the experimental results, though the experimental values of swash plate angle were derived from flow. Figure 7 shows the respective results. A sample result of the variation in torque when the swash plate start moving at the vicinity of set pressure zone, is shown in Figure 8. The estimated torque has good agreement with the experimental result except at the low flow zone. This is apparently due to the increase in mechanical resistances when swash plate approaches zero angle inclination. Usually such mechanical resistance leads to a hysteresis in forward and backward operation which is also realized during experiments as shown in Figure 9. Some recorded data and specifications of the pump during a test are shown in Table and Figure 0. It is apparent that the theoretical model is well established to estimate the swash plate torque. Such model can be incorporated in on-line control although possibly the model needs further refinements. SUMMARY The investigation was targeted to study and analyze the behavior of swash plate of a variable displacement, pressure compensated, in-line piston pump when subjected to a pressure control signal. The equations have been developed to formulate the equation of motion of swash plate. An important consideration in developing the equations has been the net torque which acts on the swash-plate. In the derivation of the equations care has been taken to include as many parameters as possible viz. reciprocating piston torque, return spring torque, control piston torque and yoke viscous damping torque [7, 8 & ] for carrying out precise steady state and dynamic analysis. Inclusion of inertial terms, viscous damping terms, torque terms for control piston and return spring, has made the mathematical model apt for dynamic analysis. Towards simplification of theoretical simulation, the comprehensive model developed was simplified by linearizing the equation set for torque due to piston pressure and the coefficient terms in the remaining describing equations []. It is observed during the preliminary analysis of the model under steady-state load conditions that the torque induced by the line pressure on the swash plate is quite significant. The pump assembly has been observed to respond in a sluggish manner to load input at extreme swash plate positions, either loading or unloading type. 7
The assembly load-deflection was found to be more or less linear, with intermediate zones of non-linearity. Large hysteresis was observed between loading and unloading. The origin of such losses could not be related to load-deflection characteristics of return spring in isolation. Therefore, the phenomena has its co-relation with friction (stiction, Coulomb and viscous shear) associated with the pump assembly. Based on the correlation between the experimental and theoretical transient responses, it can be concluded that the simulation using simplified model and physical pump parameters does represent the dynamic response behavior of a variable displacement pump. The response of swash plate to dynamic and steady-state pressure inputs or perturbations is linear. Load Deflection characteristics (Spring rate) of return spring play an important role because linearity of the spring has significant influence on the dynamic behavior. The transient period between the steady-states is very much influenced by nonlinearities associated with the pump-assembly as a whole. Acknowledgement Authors gratefully acknowledge HAL and DRDO, Lucknow, India who sponsored the second author for Masters program at IIT, Kharagpur and provided the experimental and research facilities. References. Lewis, E., and Stern, H., Design of Hydraulic Control Systems, McGraw-Hill, New York, N.Y., 96.. Green, W., and Crossley, T., An analysis of control mechanism used in variable delivery hydraulic pumps, Proceedings of the Institution of Mechanical Engineesrs,Vol.85, No.6,97, pp. 6-7.. Zaki, H., and Baz, A., On the dynamics of pressure compensated Axial Piston Pumps, Journal of Fluid Control/fluidics Quarterly, Vol., No., 979, pp. 7-87. 4. Merrit, H., Hydraulic Control Systems, Wiley, New York, N. Y.967. 5. Yamaguchi. A., Study on the Characteristics of Axial Plunger Pumps and motors, Bulletin of JSME, Vol. 9, No. 4, 966, pp. 05-. 6. Yamaguchi. A., and Ishikawa, T., Characteristics of Displacement Control Mechanism in Axial Pistons Pumps, Bulletin of JSME, Vol., No. 65, 979, pp.56-6. 7. Zeiger, G., and Akers, A., Torque on Swash plate of an Axial piston pump, ASME Journal Dynamic Systems, Measurement and Control Vol.07, No, September 985, pp.0-6. 8. Lin, S. J., Akers, A., and Zeiger, G., Oil Entrapment in an Axial piston pump and its effect upon pressures and swash plate torques, Proceeding of the 4 nd national conference on fluid power, Chicago, Mar.987, pp. -4. 9. Zeiger, G., and Akers, A., Dynamic analysis of an axial piston pump swash plate control, Proceedings of Institution of Mechanical Engineers, Vol. 00, No C,986, pp 49-59. 0. Kavanagh, G. P., The Dynamic Modeling of an Axial Piston Hydraulic Pump, M.Sc thesis, Dept. of Mechanical Engineering, Univ. of Saskatchewan, May 987.. Schoenau, G. J., Burton R. T., Kavanagh G. P., Dynamic Analysis of a Variable Displacement Pump, Journal of Dynamic Systems, Measurement, and Control, March 990, Vol., pp -.. Manring, N. D., The Torque on the Input Shaft of an Axial-Piston Swash-Plate Type Hydrostatic Pump, Journal of Dynamic Systems, Measurement and Control, Mar 998, Vol., pp 57-6.. Manring, N. D., The Control and Containment Forces on the Swash Plate of an Axial-Piston Pump, Journal of Dynamic Systems, Measurement, and Control, December 999, Vol., pp 599-605. 4. Zhang, X., Cho, J., Nair, S. S., Manring N. D., New Swash Plate Damping Model for Hydraulic Axial- Piston Pump, Journal of Dynamic Systems, Measurement and Control Sept 00, Vol., pp 46-470. 5. Zeliang, Li., Condition Monitoring of Axial Piston Pump, M.Sc. Thesis, Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Nov. 005. 6. Military Specification MIL-P-969E, General Specification for variable flow hydraulic pumps, 99. 7. Narayan, P., Studies on Swash Plate Behavior of Variable Displacement, Pressure Compensated, In- Line Piston Pump. MTech Dissertation, Mech. Engg. Dept., IIT, Kharagpur, India, May 00. 8