Application of SimulationX -based Optimization Technique ...1st V-type, 2nd U-type, and 2nd V-type notches and showed that the 2nd V-type one is more effective in reducing pressure

Application of SimulationX®-based Optimization Technique to Valve-Plate Notch Design of Variable Swash-

Plate Type Axial Piston Pump

San Seong Lee1, Won Jee Chung1, Jun Rak Hong1, Soo Tae Kim1, Jeong Sil Lee2

1School of Mechatronics, Changwon National University, Changwon-si, Gyeongsangnam-do, South Korea 2Segae Hydraulic, Changwon-si, Gyeongsangnam-do, South Korea

Abstract - The technique of considering the shape of valve plate in design is very important one in reducing the pulsation phenomenon, which is negative factor in pump performance. The purpose of this study is to propose an optimized method for valve plate V-type notch of piston pump by modeling & simulation using SimulationX , a commercial hydraulic analysis program, and to provide data to be used in designing notch. The opening areas are determined by performing kinematic analysis of notch part where the opening area changes rapidly. And the main effect on maximum pressure pulsation and maximum backflow according to notch design factors are analyzed by using full factorial method of experiments design after applying the result analysis. The optimization solutions are derived for notch design variables, based on the analyzed data.

Keywords: Modeling, Notch, Valve-plate, Application of SimulationX®, Optimization

1 Introduction

The axial hydraulic piston pump is widely used in industry because of advantages such as easiness in variable displacement, excellent responsiveness, and high energy efficiency. This pump is classified into swash plate type and bent-axis type ones according to the association between the driving axle and the cylinder block into which seven or nine pistons are inserted. [1] The source flow pulsation of hydraulic pump causes pressure pulsation and is a major source of vibration and noise in hydraulic system. The rapid backflow from source port to cylinder chamber at near the bottom dead center (BDC) due to the compressibility of working oil is a characteristic of the axial piston pump. These abnormal leakage flows are known to have higher amplitude of pulsation, compared to those of flow pulsation based on the finite number of piston of pumping instrument. [2] The flow pulsation in hydraulic pump is also influenced highly by the design values of notches installed in valve plate and the pre-pressurization and expansion section, operation conditions (such as RPM (Revolutions Per Minute), source pressure, and swivel angle etc.), and bulk modulus of elasticity of working oil. This means that, from the perspective of pump design, the

technique of considering the shape of valve plate according to the performance and specification in designing pump is very important one in reducing the pulsation phenomenon, which is negative factor in pump performance.

Sa et al. [3] analyzed the effect of the b factor, considered in designing valve plate, on the pulsation of pump and found that the presence of three openings rather than one or two ones in each suction and discharge parts is benefit for pump performance. The paper[3] also analyzed and compared 1st V-type, 2nd U-type, and 2nd V-type notches and showed that the 2nd V-type one is more effective in reducing pressure pulsation than other two ones. [3] The study, however, analyzed just according to the shape of notch and did not address the pulsations caused by design factors determining the shape of notch. It is necessary, in designing notch of valve plate, to calculate the area of openings according to the design values of notch and, by applying the results to analysis model, to identify abnormal pressure and flow resulting from combination of the design values of notch.

The purpose of this paper is, therefore, to analyze the opening area varying by design value of notch to be used in designing valve plate of the variable swash plate type axial piston pump, as shown in Fig. 1, Then we propose an optimized method for V-type notch by drawing and analyzing data on unnecessary pressure or flow with the modeling by using SimulationX , a commercial hydraulic analysis program.

Fig. 1 Swash-plate type axial piston pump [3]

160 Int'l Conf. Scientific Computing | CSC'18 |

ISBN: 1-60132-473-1, CSREA Press ©

2 Analysis of Vale-plate and Geometry 2.1 Analysis of Valve-plate

The discharged amount should be kept constant when the hydraulic working oil, in the swash plate type piston pump, is circulated by repeated suctions and discharges. The pressure and flow pulsations, however, are inevitable because of rapid change in openings area due to the shape of valve plate. The consideration of these rapidly changed openings area, therefore, is necessary and contributes to the durability and credibility of pump. [3] The valve plate consists of, as shown in Fig. 2, suction port, discharge port, and internal & external seal land, though there may be slight differences according to the type of pump. The cylinder port, a red part in Fig. 2, is used in the processes of suction and discharge. The notch groove, as indicated by the red arrow in Fig. 3, is designed on valve plate in order to prevent instable fluctuation of pressure and flow in suction and discharge ports after initiating suction and discharge.

Fig. 2 Basic valve plate with notch

When the pressure difference , as shown in Eq. (1), is generated, the compressed volume is derived, therefore, it is necessary theoretically to distribute this over the rotation time taken to rotate the length of notch of valve plate in order to minimize the instable pressure and flow in suction and discharge. [4]

(1) [4]

where

Fig. 3 Valve-plate notch model

2.2 Geometrical Analysis The calculation of precise area of opening of notch

according to design values of notch, applying the result in analysis model, and identifying the pressure and flow pulsations over broad operational zone are essential in designing the optimized notch. The increase and decrease in opening area in the suction and discharge ports section except for notch part are calculated linearly, however the notch section called a transition region (to be explained later), is of interest, therefore, we will perform geometrical analysis for this notch section before analyzing the characteristics of pulsation and flow. The V-type notch, a most common one, as shown in Fig. 3 is selected as an analysis model.

The theoretical opening area is a cross-sectional area perpendicular to the flow line. However, the precise identification of opening shape is very hard because it is impossible to estimate the flow of fluid and shape of flow line. It is assumed, therefore, that the opening area is a minimum one at that moment. [5] When the opening area is considered through valve plate of one cylinder port, as shown in Fig. 4, the sections are determined according to the angle of cylinder port and designated as follows. [4]

Fig. 4 Section of opening areas in valve plate

: Transition Region (A1)

: Suction Region (A2)

: Pressure difference between inside cylinder and openings of valve-plate

: Bulk modulus of elasticity : Change in volume due to pressure difference

: Volume of inside cylinder.

Int'l Conf. Scientific Computing | CSC'18 | 161


: Trapping Region (A3)

: Transition Region (A4)

: Discharge Region (A5)

: Trapping Region (A6)

The change in opening area through each section is as follows: as the cylinder port rotate clockwise, the opening area is effected only by the notch in A1. And, when cylinder port is going through , the effects of A1 and A2 are mixed. The opening area is kept constant, regardless of change in angle of cylinder port, after the cylinder port deviates completely from A1. The opening area, when the cylinder port goes through and enters into A3, reduces and finally converges to 0. Once opening area enters A4, the change pattern is repeated as with A1-A3 regions.

Figures 5 and 6 show the geometrical analysis of opening area at A1 at which notch exists. The opening area according to dislocation of cylinder port is, as mentioned above, a minimum one at that moment. Therefore, when the top view area (AT) and side view area (AS), as shown in Fig. 7, are compared, the smaller opening area at that section is used in analysis. The calculation formulas for Figs. 5 and 6 are as follows:

(2)

(3)(4)

where , and are depicted in Figs. 5

and 6. Equation (5) is to determine AT for Fig. 7 calculated using formulas (2)-(4).

(5)

and Eq. (6) is to determine AS.

(6)

The AT and AS according to determined by

displacement of cylinder port are calculated using Eqs. (5) and (6), respectively and the smaller one of two areas are used in analysis. The results in Fig. 8 showed that AS is smaller than AT at all points, therefore AS was used as the opening area at one point. The total opening area increases as the cylinder port enter into A2 through A1, however, as the opening area decreases at notch part, AS is smaller than AT at all points, therefore the decreased areas are calculated using Eq. (6).

Fig. 5 Geometric analysis in top view of A1

Fig. 6 Geometric analysis in side view of A1

Fig. 7 Top view (left) and side view (right) of the notch

Fig. 8 Opening areas by



Next, the increased area generated by the movement of cylinder port to suction area is one resulting from linking of cylinder port and suction port, and as mentioned above, is calculated linearly. The changed area due to movement to discharge area is the same to those due to the movement to suction region because of symmetry of valve plate.

3 Modeling and Experiments Design 3.1 Modeling of Valve-Plate Notch by using

SimulationX® The analysis of design factor of valve plate notch

requires kinematic analysis of the swash plate type piston pump. Jang et al. [6] already reported the results, as shown in Eq. (7), by using the fixed angle frame as shown in Fig. 9 .

(7)

Where

Figure 10 shows the model of single piston pump based on kinematic analysis by using the SimulationX . Table 1 shows the specifications for operation conditions and specification of analysis model. The properties of hydraulic fluid applied to analysis model are shown in Table 2.

Fig. 9 Variables at the axial piston pump [6]

Fig. 10 Single piston pump model using SimulationX

Table 1 Parameters of the model

No. Variable Value

1 Piston mass 212 [g]

2 Rotational speed 2000 [RPM]

3 Piston diameter 21 [mm]

4 Radius piston-shaft(R) 20 [mm]

5 Maximum piston stroke 2R [mm]

6 Relief valve set pressure 300 [bar]

7 Swash plate angle( ) 14°

8 Notch type V-type

Table 2 Technical properties of the hydraulic fluid

Properties Factors

SAE GRADE 30

Density at 15°C 0.895 [ ]

Viscosity at 40°C 105 [ ]

Viscosity at 100°C 11.5 [ ] SAE: Society of Automotive Engineers

3.2 Experiments Design using Full Factorial Method

The maximum value of and values of and in Figs. 5 and 6 were selected as response factors in experiment plan, in order to determine the pressure and flow characteristics according to design factors of V-type notch. The simulations were carried out following the full factorial method and the level of response factors, as shown in Table 3, was two-level, each increase and decrease by 10% of design values of V-type notch such as = 16 , = 14 , and =

9 . Eight (three factors and two-level; 23) kinds of experiments were designed and the design values in Table 3 were applied in Fig. 11, resulting in eight models.

: Pitch circle diameter

: Swash-plate angle : Rotation angle of cylinder block



The data on maximum pressure pulsation and maximum backflow in cylinder were obtained by simulation. Then optimized design values were selected based on the full factorial method.

Table 3 Level of Notch design value

Variables Factors Concentration

-1 Level 1 Level

A Max 14.4° 17.6°

B 12.6° 15.4°

C 8.1° 9.9°

Fig. 11 8 cases of Single piston pump model

4 Simulation Results and Analysis 4.1 Simulation Results

Figure 12 shows the opening areas of notch in eight experiments and Figs. 13 to 16 show the maximum pressure pulsation and maximum backflow as analysis results of applying opening areas. The results overlapped on each graph and thus unseen are skipped. Table 4 shows the data on the maximum pressure pulsation and maximum backflow results from eight experiments carried out following steps using full factorial method.

Fig. 12 Open-areas of 8 cases

Fig. 13 8 case result of Pressure pulses

Fig. 14 Main results of Pressure pulses

Fig. 15 8 case result of back flow

Fig. 16 Main result of back flow



Table 4 Result data

Case Max pressure(bar)

Max back flow(l/min)

1 14.4° 12.6° 8.1° 307.089 3.491

2 17.6° 12.6° 8.1° 310.391 4.696

3 14.4° 15.4° 8.1° 307.674 4.732

4 17.6° 15.4° 8.1° 307.860 6.112

5 14.4° 12.6° 9.9° 307.090 3.503

6 17.6° 12.6° 9.9° 310.392 4.671

7 14.4° 15.4° 9.9° 307.674 4.747

8 17.6° 15.4° 9.9° 307.860 6.126

4.2 Data Analysis

The data drawn from experiments and shown in Table 4 were analyzed using SimulationX , a commercial hydraulic analysis program. The main effect plots of the maximum pressure pulsation and maximum backflow were developed in order to estimate the independent effect among each factor. The higher angle of the horizontal line and graph in the main effect plot represents the bigger effect. [7] Figure 17 shows the main effect plot for maximum pressure pulsation. The graph of maximum is directing right and top, meaning the higher value is related to the stronger maximum pressure pulsation, while the pattern of is opposite to those in , meaning that the higher value is related to the weaker maximum pressure pulsation. The graph is steeper in compared to , indicating that the has stronger effect on the maximum pressure pulsation compared to . The slope of graph for is close to zero, meaning that this value has not significantly effect on the maximum pressure pulsation compared to and . Figure 18 shows the main effect plot for maximum backflow.

The graphs of and are directing right and top, meaning the higher values are related to the stronger maximum backflow. The slopes of these two graphs are similar, indicating that they have similar effect on maximum backflow. The is shown, like the case of maximum pressure pulsation, to have no major effect on the maximum backflow.

The related theories show that the pressure gradient generated inside cylinder according to pre-pressurization sections of valve plate has significant effect on maximum pressure pulsation and maximum backflow. [4] The analysis results show that the higher maximum decreases pre-pressurization section, and therefore internal pressure increases, leading to increase in the maximum pressure pulsation and maximum backflow. In addition, the various combination of maximum and values of and , as shown Fig. 19, lead to various pressure gradient inside

cylinder, effecting the pressure pulsation and backflow inside cylinder. It is suggested, therefore, that the proper combination of maximum and values of and may be used in minimizing the abnormal pressure pulsation and backflow.

Fig. 17 Main effect plot for max pressure pulse

Fig. 18 Main effect plot for max back flow

Fig. 19 Pressure gradient inside the cylinder

The optimal conditions to minimize the maximum pressure pulsation and maximum backflow were identified, finally, by using response optimization function of Minitab . Figure 20 and Table 5 shows the process and results of calculating optimization solution satisfying the negotiated conditions. The most optimized values were = 16.01 , =14.06 an = 8.98 respectively.



Fig. 20 Response Optimization

Table 5 Optimized value Max

pressure(bar)

Max

back flow(l/min)

16.01° 14.06° 8.98° 308.23 4.79

5 Conclusion

This paper has dealt with the optimization of design value of valve plate V-type notch according to performance and specification of pump, in order to reduce the abnormal pressure pulsation and backflow phenomenon which has negative effect on performance of hydraulic axial piston pump. The purpose of this paper is, therefore, to analyze the opening area varying by design value of notch to be used in designing valve plate of the variable swash plate type axial piston pump. Then we have proposes an optimized method for V-type notch by drawing and analyzing data on unnecessary pressure or flow with the modeling by using SimulationX , a commercial hydraulic analysis program.

First, the opening areas of notch parts, on which the areas are changed rapidly, were analyzed geometrically and calculated precisely. The opening areas in V-type notch in transition region were determined as AS, not AT, by the definition. Second, total of eight experiments (three factors and two sets; 23) were carried out using full factorial method of experiments design and set , , and as response factors and the optimization of each model was carried out using SimulationX . The analysis results were used in acquiring data on maximum pressure pulsation and maximum backflow, and the each main effect plots for , , and

were analyzed to determine the effects of these three angles on pressure gradient inside cylinder. The results showed that the higher decreases pre-pressurization section, and therefore internal pressure increases, leading to increase in the maximum pressure pulsation and maximum backflow. In addition, the various combination of maximum and values of and , are expected to lead to various pressure gradient inside cylinder, effecting the pressure pulsation and backflow inside cylinder.

Finally, the optimal conditions to minimize the maximum pressure pulsation and maximum backflow were

identified, finally, by using response optimization function of Minitab . It was found, in this study, that the optimization of notch design factor of valve plate may be useful in reducing the unnecessary pressure change and flow pulsation which are negative for performance of axial piston pump. The studies on optimization method according to various operation conditions of hydraulic pump will be planned for later investigation.

6 Acknowledgment

This research was supported by the Ministry of Trade, Industry & Energy (MOTIE), Korea Institute for Advancement of Technology (KIAT) through the Encouragement Program for The Industries of Economic Cooperation Region. (R0005818)

7 Reference [1] J. H Park, “The Study on Development of Fixed Displacement Piston Pump for Special Access Vehicle,” J. of KSMPE, 2010. [2] K. Edge and J. Daling, “A Theoretical Model of Axial Piston Pump Flow Ripple,” 1th Bath Int. Fluid Power Workshop, 1988 [3] J. W. Sa, W. J. Chung, “Simulation/Modeling of Pressure and Torque Pulsation for a Swash-plate Type Piston Motor by using SimulationX®” Proceedings of the International Conference on Scientific Computing, 2013. [4] J. G. Kim, “Performance Characteristics with Valve Plate Shapes in Swash Plate Type Oil Piston Pumps,” A Thesis for a Doctorate, Chonbuk National University, Republic of Korea. 2003. [5] B. S. Kim, “A Study on Open-area Planning of Main Control Valve for Excavators” A Master’s Thesis, Ulsan National University, Republic of Korea. 2007. [6] J. H. Jang, W. J. Chung, “Application of Simulation X® Based Simulation Technique to Notch Shape Optimization for a Variable Swash Plate Type Piston Pump” Proceedings of the International Conference on Scientific Computing, 2013. [7] Y. B. Lim, “Design-expert 7 & minitab®” Free Academy Publication, 2008. [8] SimulationX® user manual and library manual, ITI GmbH, 2011 [9] J. Pan, “Minitab® Tutorials for Design and Analysis of Experiments” Industrial and Mabufacturing Engineering California Polytechnic State University, 2004 [10] R. A. Johnson, G. K. Bhattacharyya, “ Statistics: Principles and Methods” Wiley, six edition



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Application of SimulationX -based Optimization Technique ...1st V-type, 2nd U-type, and 2nd V-type notches and showed that the 2nd V-type one is more effective in reducing pressure