 Open Access
 Total Downloads : 27
 Authors : K. Muthuvignesh, D. Purusothaman, V. Ragupathi, Kalidas
 Paper ID : IJERTCONV7IS06088
 Volume & Issue : ETEDM
 Published (First Online): 24062019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Stress analysis and Design Optimization of Piston Slipper assembly in an Axial Piston Pump

Muthuvignesh, D. purusothaman, V. Ragupathi,
UG scholar
Department Of Mechanical Engineering, Hindusthan Institute Of Technology, Coimbatore.
Abstract – The amount of research carried out on piston assemblies of axial piston pump is a good indication of the problems which have been encountered. Fortunately this is one branch of engineering where research is usually well ahead of production failures. A representative domain for the high development of the axial piston pumps manufacturing is the aeronautics. In this industrial branch, light hydraulic transmissions that operate in very safe conditions are required. The mass reduction must be done according to an optimal design of the machines geometry, taking into account the static and dynamic stress and deflection states of the mechanical components. In this paper, a steady state stress analysis and also an optimization of the piston slipper assembly has been carried out by using ANSYS software. Optimization is done using Subproblem approximation method where the main objective is to minimize the volume of the piston and slipper. Dimensions of the assembly are taken from SPV 22 axial piston pump, made by ZTS Company. This optimization technique minimizes the volume of the piston and also slipper. The paper concludes with the Comparison of the piston and slipper dimensions before and after optimization.
Keywords: Axial piston pump, PistonSlipper assembly, Stress analysis, Optimization

INTRODUCTION
Axial piston pumps are being used extensively in aircraft, industrial and agricultural systems since they can transmit large specific power and the flow rate from them can be varied. The operating concept of this type of pumps is based upon rotating a cylinder block of spring loaded pistons against an angled swash plate in order to provide a pumping action. Controlling the angle of the swash plate controls the output displacement. A basic difference in the design of various models of axial piston pumps is how the pistons contact the swash plate. Many design use a bronze slipper positioned between the piston and the swash plate. With this design, hydraulic fluid is fed through internal passages to the piston/slipper and slipper/swash plate interfaces to supply lubrication at these surfaces. Some axial do not use a slipper, but rather finish each piston with a casehardened spherical dome. The spherical dome contacts the swash plate in such a fashion, much like the contact that occurs in ball bearings. Elimination of the slipper reduces costs and eliminates the disadvantages of the slipper design, but unfortunately, it creates other problems. One of these is wear at the spherical dome/swash plate interface. The piston and slipper of an axial piston pump is undergone through high
Kalidas
Associate professor Department Of Mechanical Engineering,
Hindusthan Institute Of Technology, Coimbatore.
loading condition. Under such high load there can be plastic deformation of the piston and slipper. The material used in piston is stainless steel. Sometime the high compressive strength of such material cannot withstand the high load coming from the hydraulic circuit. Under such condition it is essential to study the stress analysis and proper design of the piston slipper assembly. A good analytical understanding of slipper behavior in piston pumps is crucial to good design. In open literature it is found that few efforts are made to study the present problem. Hui Wang and Fan Long Meng1 studied the simulation and optimal design of cylinder block of axial piston pump Based on
ANSYS. Norhirni M. Z et al2 studied the load and stress analysis for the swash plate of an axial piston pump/motor. The design analysis of the cylinder block of an axial piston pump has been studied by McConnachie J. and Fagan M.J.3. Rosu C et al4 studied the structural analysis of a high pressure hydraulic pump by Finite Elements Method. The computation of dynamic stresses in piston rods caused by unsteady hydraulic loads has been studied by Wang Z W et al5. In 1990, Schoenau et al.6 conducted numerical and experimental studies on a variable displacement pump in which they used regression techniques that generated linear and nonlinear terms for describing the control torque on the swash plate. The coefficients of these terms were generated from the numerical results and the attempt of this research was to simplify the work presented originally by Zeiger and Akers. In 1996, Manring and Johnson7 presented a closed form approximation of the control torque on the swash plate. Unlike previous research, this work simplified the control torque expression without eliminating critical terms.

METHODOLOGY
Dimensions of the assembly are taken from SPV 22 axial piston pump, made by ZTS Company. First the solid model is done in Pro E software. Then it was transformed to ANSYS. Solid 20 node 95 Brick element has chosen for meshing the piston and slipper assembly. This element can tolerate irregular shapes without as much loss of accuracy. Solid 95 elements have compatible displacement shapes and are well suited to model curved boundaries.

BOUNDARY CONDITIONS

The piston and slipper assembly in an axial piston
pump is a moving part. The pressure acting on a piston varies periodically. In this case the piston and slipper are considered to be in a quasistatic equilibrium state. After generating the nodes and elements, different constraints are applied to the models. In case of the piston and slipper assembly, the bottom surface of the slipper is constrained with zero displacement in all direction. Working pressure of the pump will act on the top surface of the piston
Governing Equation
In stress analysis, the governing equations for a continuous rigid body can be obtained by FEThe total potential energy can be expressed as:
where and are the vectors of the stress and strain components at any point, respectively, d is the vector of displacement at any point, b is the vector of body force components per unit volume, and q is the vector of applied surface traction components at any surface point. The volume and surface integrals are defined over the entire region of the structure and that part of its boundary subject to load . The
first term on the right hand side of this equation represents the internal strain energy and the second and third terms are, respectively, the potential energy contributions of the body force loads and distributed surface loads.
Simulation and analysis of the piston and slipper assembly
Stress analysis of the Piston and Slipper assembly The analysis of the piston and slipper assembly is done at 300bar working pressure. From the analysis it has been observed that stresses at some of the nodes are above the safe region. A stress concentration region, represented by red colour has been observed around the neck portion of the piston as shown in figure 1(a). The stepped shape of neck portion of the piston is modified to a smooth one by a fillet. Analysis is performed again for the new modified part at 300 bar working pressure.
The result of this analysis is very
good as the stress concentration is reduced to a great extent, as shown in figure 1(b).The graph, shown in figure 2(a) presents a comparative study of the VonMisses stresses along the Outer path of the piston and ball of the existing the modified model of the piston. Fig:
2(a).
Fig. 1Stress concentrations at the neck portion & Stresse on the new model
Fig. 2Comparison of stresses of the existing and modified model at the outer path & experimental and theoretical VonMisses stresses
Table 1Range of design variables for piston & slipper 

PARAMETER 
MINIMUM VALUE (mm) 
MAXIMUM VALUE (mm) 
A 
10 
15 
B 
0.8 
1.2 
C 
1.5 
2.5 
D 
1.5 
2.5 
E 
1.5 
2.5 
Table 1Range of design variables for piston & slipper 

PARAMETER 
MINIMUM VALUE (mm) 
MAXIMUM VALUE (mm) 
A 
10 
15 
B 
0.8 
1.2 
C 
1.5 
2.5 
D 
1.5 
2.5 
E 
1.5 
2.5 
Experimental Validation
For validation, analysis results are compared with the experimental data8. The components used in the experimental rig were taken from the same SPV 22 axial piston pump. The pressure in the hydraulic motor had been set to the 0, 20, 40, 60, 80 bar. To measure the deflections of the pistonslipper fourtensometric rosettes had been used. The Von Misses stresses as found from ANSYS as well as experiment are shown in fig.2(b)
Optimization of the piston and slipper
Optimization of the piston
(b) 

PARAMETER 
MINIMUM VALUE (mm) 
MAXIMUM VALUE (mm) 
G 
1.5 
3.5 
R 
2.5 
3.5 
S 
1 
3 
T 
0.5 
1.5 
U 
3 
6 
(b) 

PARAMETER 
MINIMUM VALUE (mm) 
MAXIMUM VALUE (mm) 
G 
1.5 
3.5 
R 
2.5 
3.5 
S 
1 
3 
T 
0.5 
1.5 
U 
3 
6 
An optimization is done in ANSYS with actual loading data. The Subproblem approximation method is used for optimization. An axisymmetric parametric model of the piston is created as shown in figure 3. The objective of the optimization is to minimize the volume of the slipper subjected to, the stresses in each node lies below the yield point of the material.
Design and State variables
The maximum von Misses equivalent stress will be limited to 260 N/mm2. The model is parameterized as A, B, C, D and E. The ranges are as follows: Table1(a).
Optimization of the slipper
An axisymmetric parametric model of the slipper is created as shown in figure 3.
Design and State variables
The maximum von Misses equivalent stress will be limited to 250 N/mm2. The model is parameterized as G, S, T, U and R. The ranges are as follows: Table1(b).
Results and discussion
Optimization of the volume of piston is run in ANSYS using Subproblem approximation
.
Fig. 3Axisymmetric parametric model of the piston and Slipper
method. In the process 5 iterations have been performed, which are listed below: Table2(a). From the table2(a), it is easily observed that set number 3 gives the most feasible result, among all the iterations. This optimization technique minimizes the volume of the piston from 306.65 mm3 to 100.65 mm3. Comparison of the piston dimensions before and after optimization is below: Table2(b). Optimization of the slipper is run in ANSYS using Sub problem approximation method. In the process 5 iterations have been performed, which are listed below: Table3(a). It has been observed that set number 2 gives the most feasible set of result, among all the iterations. The optimization technique minimizes the volume of the slipper from 106.31mm3 to71.688mm3. Comparison of the slipper dimensions before and after optimization is stated below: Table3(b).
Table 2 optimization iteration & existing vs final dimensions of piston 

PARAMETER 
SET1 
SET2 
SET3 
SET4 
SET5 
FEASIBLE 
INFEASIBLE 
FEASIBLE 
INFEASIBLE 
INFEASIBLE 

SMAX 
215.46 
384.42 
235.21 
812.9 
313.97 
A 
14.500 
12.473 
12.598 
12.162 
12.138 
B 
1.200 
1.7104 
0.88283 
0.82475 
0.81368 
C 
2.330 
2.6564 
1.9318 
2.0137 
1.8193 
D 
2.200 
2.5090 
1.9155 
1.9152 
1.8429 
E 
2.250 
1.9077 
1.9069 
1.8673 
1.8305 
VOLUME 
156.83 
306.65 
100.75 
240.94 
131.69 
(b) 

PARAMETER 
BEFORE OPTIMIZATION 
AFTER OPTIMIZATION 
SMAX 
384.42 
235.21 
A 
12.473 
12.598 
B 
1.7104 
0.88283 
C 
2.6564 
1.9318 
D 
2.5090 
1.9155 
E 
1.9077 
1.9069 
VOLUME 
306.65 
100.75 
Table 3Optimization iterations & existing dimensions vs. Final dimensions of slipper 

PARAMETER 
SET1 
SET2 
SET3 
SET4 
SET5 
FEASIBLE 
INFEASIBLE 
FEASIBLE 
FEASIBLE 
FEASIBLE 

SMAX 
78.072 
136.06 
67.779 
82.717 
167.89 
G 
1.9069 
2.4273 
1.3441 
1.3434 
3.4951 
R 
3.5000 
3.5902 
3.2892 
3.2900 
3.5447 
S 
2.5000 
1.6774 
2.2840 
2.0076 
2.5056 
T 
2.0000 
1.1267 
1.1641 
1.1295 
1.0881 
U 
1.0000 
1.3862 
0.53204 
0.50912 
0.50575 
VOLUME 
194.8 
71.688 
126.95 
91.491 
106.31 
(b) 

PARAMETER 
BEFORE OPTIMIZATION 
AFTER OPTIMIZATION 
SM AX 
167.89 
136.06 
G 
3.4951 
2.4273 
R 
3.5447 
3.5902 
S 
2.5056 
1.6774 
T 
1.0881 
1.1267 
U 
0.50575 
1.3862 
VO LU ME 
106.31 
71.688 
CONCLUSION
A steady state stress analysis and also an optimization of the piston slipper assembly have been carried out by using ANSYS software. It has been observed that in the neck portion of the existing design, the vonmisses stress goes to plastic state. However this problem is mitigated by incorporating a proposed design that is by using the proposed design the von misses stress lies within the elastic limit. In the later part of this work an optimal design of the piston slipper assembly is simulated by sub problem approximation method under ANSYS environment. For the piston design, the volume of piston of the existing design is 306.65 mm3. After optimization the volume of the piston is minimized and the volume is
100.75 mm3. And also for the slipper design, the volume of slipper of the existing design is 106.31 mm3. After optimization the volume of the slipper is minimized and the volume is 71.688 mm3.
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