Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 177 (2017) 247 – 254
XXI International Polish-Slovak Conference “Machine Modeling and Simulations 2016”
Simulation of the hydrostatic load of the valve plate-cylinder block system in an axial piston pump Tadeusz Zloto* Czestochowa University of Technology, Institute of Mechanical Technologies, Armii Krajowej 21, Czestochowa,Poland
Abstract The paper analyses the load of the cylinder block and the valve plate in an axial piston pump. Torques are established of the hydrostatic forces acting on the cylinder block for positive overlap, negative overlap and the construction with relief grooves. The resultant pressing and relieving hydrostatic forces are obtained as functions of the rotation angle of the cylinder block. The values of the relief coefficient of the cylinder block are specified as function of its rotation angle as well. Trajectories are presented of the resultant hydrostatic forces pressing the cylinder block towards the valve plate and of the resultant hydrostatic forces relieving the cylinder block as functions of the rotation angle for the three constructional variants of the valve plate. © 2017 2017The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of MMS 2016. Peer-review under responsibility of the organizing committee of MMS 2016 Keywords: axial piston pump; cylinder block-valve plate system; hydrostatic load; hydrostatic forces trajectories;
1. Introduction Hydraulic units and especially hydraulic machines with axial pistons have become indispensable elements of drives applied in an increasing number of fields. Under some operating conditions, however, such devices generate significant losses. The history of constructing axial units with mineral oil as a hydraulic liquid goes back to Americans Janney and Williams, who constructed the first axial piston pump with an inclined swash plate, operating with pressures up to 4 MPa in 1990. Soon after that, in 1905, they developed the construction into a hydrostatic drive powering a gun turret on a naval ship [1]. Since then, attempts have been made to improve reliability and efficiency of hydraulic drives in the full range of their operating conditions. Many such attempts have been successful and a number of improved or new designs have been created. Since the mechanisms of losses have not
* Corresponding author. Tel.: +048-34-32-50-509; fax: +048-34-32-50-509. E-mail address:
[email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of MMS 2016
doi:10.1016/j.proeng.2017.02.196
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Tadeusz Zloto / Procedia Engineering 177 (2017) 247 – 254
been well investigated to date, designing new products or modernizing existing ones often involves considerable costs. One of the crucial kinematic nodes which generates significant energy losses in an axial piston pump is the system cylinder block-valve plate. The right shaping of the valve plate is one of the most difficult tasks in the process of designing an axial piston unit. The construction of the valve plate interacting with the cylinder block affects the key parameters of the axial piston pump, such as volumetric efficiency, capacity for producing high pressures, noise emission and durability [2]. Among the valve plates typically used in axial piston pumps are flat and spherical ones, with the flat type being more popular due to its simpler construction, despite certain disadvantages. 2. Hydrostatic load of the cylinder block The shape of the valve plate is so designed that the inlet side is tightly separated from the discharge side and that the hydrostatic forces acting on the cylinder block against the valve place exceed the relieving forces [3]. The difference between the pressing force (Fdoc) and the relieving force (Fodc) should be selected in such a way that the oil film in the gap should preserve its hydrodynamic properties and at the same time the sealing between the cylinder block and the valve plate should be tight. The relief coefficient K is defined as [4]:
K
Fodc 100% Fdoc
(1)
It depends on the pressure of the working liquid, the rotational speed and pump design [5]. When the cylinder block is rotating, the number of active cylinders (under discharge pressure) varies from kt max to kt min as specified below:
kt max
z 0,5 2
and
kt max
z 0,5 2
(2)
Figure 1 presents the system of a cylinder block and a valve plate. The varying position of the cylinder block with respect to the valve plate indicates the number of active cylinders, obtained by means of computer simulation for a positive overlap of the valve plate.
Fig. 1. (a) initial position of the cylinders and the valve plate (M = 0q); (b) panoramic view of positions of the cylinder ports at M = 0q, 10q, 20q and 30q with respect to the valve plate.
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The results of the simulation are presented in Fig. 2a. Assuming that the area of a cylinder bottom is Ad = 0.000104328 m2 and the discharge pressure is pt = 32 MPa, a resultant hydrostatic force relieving the cylinder block was obtained, as presented in Fig. 2b.
Fig. 2. (a) number of active cylinders in the discharge zone of the four- and five-piston zones in the valve system as a function of the angle φ of the cylinder block rotation; (b) resultant hydrostatic force of the cylinder block load of the four- and five-piston zones in the valve system as a function of the angle φ of the cylinder block rotation.
The resultant hydrostatic force pressing the cylinder block towards the valve plate changes its value as a function of the cylinder block rotation angle. The force exerts variable impact when passing from the four- to the five-piston zone. Besides, the load of the cylinder block can be additionally affected by the presence of relief grooves. The study includes three constructional variants of the valve plate: the positive overlap variant, the zero overlap variant with the maximal length of the suction and pressure ports (practically not applied in machines due to technological complications) and the most frequently applied variant with relief grooves [6], as shown in Fig. 3.
a
b
c
Fig. 3. Three constructional variants of the valve plate: (a) positive overlap; (b) zero overlap; (c) with relief grooves
The resultant hydrostatic load force acting on the cylinder block gives rise to torques with respect to the axes X and Y of the valve plate. The torques with respect to the axes X and Y are respectively obtained from: kt
MX
Ad rsd ¦ pti cos Mi
(3)
i 1
kt
MY
Ad rsd ¦ pti sin Mi
(4)
i 1
Figs. 4 and 5 present the torques with respect to the axes X and Y respectively for the three constructional variants of the valve plate.
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The variations in torque with respect to the axis X in the positive overlap and zero overlap variants (Figs. 4a and 4b are discontinuous functions. In the valve plate variant with relief grooves the torque varies within a smaller interval and is a continuous function (Fig. 4c). The values of torque with respect to the) axis Y are large (Fig. 5) and act not only on the valve plate, but also on the inclined swash plate of the pump. The most advantageous variation in torque with respect to the axis Y occurs in the valve plate variant with relief grooves, which is characterized by waveform shape (Fig. 5c). The torques originating from resultant hydrostatic load forces accompanied by torques originating from resultant hydrostatic relief forces cause unbalance of the cylinder block. a
b Y 120
60
M Xw Z [Nm]
Y
100
M Xw D [Nm]
80
40
MXw X
20
X
60
0 -20
40
-40
20 -60
0 -80
0
10
20
30
40
0
10
M>q@
20
30
40
M>q@
c
70
Y
60 50
MXw R X
M Xw R [Nm]
40 30 20 10 0 -10 0
10
20
30
40
M>q@
Fig. 4. Torque MX as a function of the cylinder block rotation angle M for the three constructional variants of the valve plate: (a) positive overlap; (b) zero overlap; (c) relief grooves.
a
b 356
Y 350
M Yw Z [Nm]
M Yw D [Nm]
355
MY
Y
355
MY
354
353
345
X
X
352
340
351 335
350 0
10
20
30
0
40
10
20
30
40
M>q@
M>q@
c Y
M Yw R [Nm]
356
MYw
355 354 353
X
352 351 350 349 348 0
10
20
30
40
M>q@
Fig. 5. Torque MY as a function of the cylinder block rotation angle M for the three constructional variants of the valve plate: (a) positive overlap; (b) zero overlap; (c) relief grooves.
Tadeusz Zloto / Procedia Engineering 177 (2017) 247 – 254
3. Pressure distribution and resultant hydrostatic forces relieving the valve system In the gap between the cylinder block and the valve plate the pressure relieving the cylinder block is distributed in a complex way. Further considerations will be based on a model of pressure distribution on a valve plate with a positive overlap (Fig. 6).
Fig. 6. Model of the pressure distribution on the valve plate
The analysis of pressure distribution concerns the main inlet zone \ (M), the upper transition zone Hg (M) and the lower transition zone Hd (M) for the three constructional variants of the valve plate: a positive overlap, the zero overlap and the variant with relief grooves. In the internal zone between the radii r 1 and r 2 within the variation
range of the angle \(M) corresponding to the operation of the inlet pressure when the cylinder block is rotating, the pressure distribution is logarithmic [4]. When the cylinder block is rotating, the angular ranges vary for the discharge pressure, the inlet pressure and the upper and lower transition zone pressures. Figure 7 presents the pressure distribution and the varying positions of the cylinder block with respect to the valve plate in a cross-section along the pitch diameter of the cylinder block.
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Tadeusz Zloto / Procedia Engineering 177 (2017) 247 – 254
Fig. 7. Simulation of the movement of the cylinder block ports with respect to the valve plate pitch diameter: (a) pressure distribution at the starting position of the cylinder block for M = 0q with respect to the valve plate; (b) simulated positions of the cylinder ports with respect to the valve plate for M = 10q, 20q and 30q; (c) panoramic view of the valve plate represented on a plane.
Figure 7a presents the angular ranges for the particular zones for the starting position of the cylinder block
M = 0q, on the assumption that the pressure changes between the inlet and discharge zones are linear. With the
rotation of the cylinder block by 10, 20 (Fig. 7b) and 30 degrees (Fig. 7c), the angular ranges of the zones change: the discharge zone \(M), the inlet zone \s(M), as well as the transition zones – the upper one Hg(M) and the lower one Hd(M).The operation of the valve plate-cylinder block system is crucially affected by the mutual dependence of the hydrostatic force Fdoc pressing the cylinder block towards the valve plate and the relieving force Fodc acting in the opposite direction. Figs. 8 - 9a present the values of the resultant hydrostatic force pressing the cylinder block towards the valve plate and the resultant force acting in the opposite direction (the relieving force) for various constructional variants of the valve plate depending on the angle φ of the cylinder block rotation. Figure 9b presents a graph representing the percentage load of the cylinder block. The ratios of the resultant hydrostatic relieving force to the resultant pressing force (Fig. 9b) indicate that the constructional variants of the valve plate with the positive overlap and the zero overlap have the relief range from about 85 to 97% when the cylinder block is rotating. For the variant with relief grooves the relief range is smaller and varies from about 88 to 93%. a
b
17000
FodcD
16000 15500 15000 14500
FdocZ, FodcZ [N]
FdocD, FodcD [N]
17000
FdocD
16500
FdocZ
16500
FodcZ
16000 15500 15000 14500
14000
14000
13500 13000
13500
12500
13000 12500
12000 0
10
20
M>q@
30
40
0
10
20
30
40
M>q@
Fig. 8. (a) resultant hydrostatic force FdocD pressing the cylinder block towards the valve plate and the force FodcD acting in the opposite direction as a function of the angle M of the cylinder block rotation for a positive overlap of the valve plate; (b) resultant hydrostatic force FdocD pressing the cylinder block towards the valve plate and the force FodcD acting in the opposite direction as a function of the angle M of the cylinder block rotation for the zero overlap variant of the valve plate.
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a
b 17000
FodcR
15500
KD
98
FdocR
16000
KD, KZ, KR [%]
Fdoc R,Fodc R [N]
16500
15000 14500 14000
KZ
96
KR
94 92 90
13500
88
13000 86
12500
84
12000 0
10
20
30
40
0
10
20
M>q@
30
40
M>q@
Fig. 9. (a) values of the resultant hydrostatic force FdocR pressing the cylinder block and the resultant force FodcR relieving the cylinder block as a function of the angle M of the cylinder block rotation for a valve plate with relief grooves; (b) values of the hydrostatic relief coefficient for the cylinder block as a function of the angle M of the cylinder block rotation for a positive overlap KD, zero overlap KZ and for the construction with relief grooves KR.
The mean values of the relief coefficient of the cylinder block were obtained by integrating the functions presented in Fig. 9b in the interval from 0° to 40°. The results are: 90.80% for the positive overlap, 90.41% for the zero overlap and 90.70% for the construction with relief grooves. According to [4], the value of the hydrostatic relief coefficient varies from 92 to 98%, whereas according to [7] the range is 85 - 98%, depending on the computation model applied. 4. Trajectories of the resultant hydrostatic load and relief forces in the cylinder block-valve plate system When the cylinder block is rotating, the pressure distribution changes in the discharge zone within the range of the angle \ (M), in the upper transition zone within the range of the angle Hg (M) and in the lower transition zone within the range of the angle Hd (M). Figs. 10a, 10b and 11 present the trajectories of the resultant hydrostatic forces pressing the cylinder block towards the valve plate and the trajectories of the resultant hydrostatic forces relieving the cylinder block as functions of the angle of the cylinder block rotation. b 1
R
R
30
0
o
30
5
o
-1
XwD,YwD
-2
XrD,YrD
R
-3
0
20
Y rZ ,Y wZ [mm]
Y rD ,Y wD [mm]
a
21
4 1
XrZ, YrZ
3
XwZ, YwZ 2 1
o
21
o
o
1
-4 0
-5
o
10
0
-6
-1
-7
-2
-8
-3
-9
-4
o
10
20
-10
o
30
o
30
18
19
20
21
22
23
24
25
XrD, XwD [mm]
26
27
28
0
20
o
o
0 18
19
o
o
-5
17
o
o
20
21
22
23
24
25
o
26
27
28
XrZ, XwZ [mm]
Fig. 10. (a) trajectories of the resultant hydrostatic force pressing the cylinder block of the coordinates XwD , YwD and of the resultant hydrostatic force relieving the cylinder block of the coordinates XrD , YrD as functions of the angle M of the cylinder block rotation; positive overlap variant; (b) trajectories of the resultant hydrostatic force pressing the cylinder block of the coordinates XwZ , YwZ and of the resultant hydrostatic force relieving the cylinder block of the coordinates XrZ , YrZ as functions of the angle M of the cylinder block rotation; zero overlap variant.
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Y rR , Y wR [mm]
1 10
0
o
9
o
10
o
9
29
o
o
30
29
o
o
30
o
XrR, YrR XwR, YwR
-1
-2
19
-3
20
o
o
19 20
o
0
o
o
-4 0
o
-5 16
17
18
19
20
21
22
23
24
25
26
27
28
XrR, XwR [mm]
Fig. 11. Trajectories of the resultant hydrostatic force pressing the cylinder block of the coordinates XwR , YwR and of the resultant hydrostatic force relieving the cylinder block of the coordinates XrR , YrR as functions of the angle M of the cylinder block rotation; relief grooves variant.
Based on the analysis of the trajectories of the resultant hydrostatic pressing and relieving forces, it can be stated that in a typical axial piston pump produced by a Polish industrial manufacturer the resultant hydrostatic pressing force is situated beyond the area of the interaction of the cylinder block and the valve plate. This results in axial runout of the cylinder block, which is a constructional flaw of these pumps [8] and may increase intensity of leaks. 5. Conclusion The cylinder block-valve plate system of a hydraulic pump is subject to high loads and difficult operating conditions. The appropriate selection of the hydrostatic load is therefore of primary importance. The present study determined variable hydrostatic pressing and relieving forces acting on the cylinder block. The values of the hydrostatic relief coefficient were obtained as a function of the cylinder block rotation angle and their mean percentage value was established to be about 90%, which is consistent with the data found in theoretical sources [4, 7]. As is indicated by the analysis of the trajectories of the resultant hydrostatic load and relief forces, the torques of these forces are not balanced, which leads to skewing the cylinder block. The computational models of the three variants of the valve plate construction, i.e. the positive overlap, the zero overlap and the relief grooves variant developed in the study are intended to be useful for designers of axial piston pumps. References [1] A. Osiecki, Hydrostatyczny napęd maszyn. WNT, Warszawa 2004 (in Polish). [2] S. Stryczek, Napęd hydrostatyczny. Elementy i układy. WNT, Warszawa 1984 (in Polish). [3] R.M. Pasynkov, Wlijanie pieriekosa cilindrowowo bloka na rabotu tarcowowo razpriedielitiela aksialno-porszniewoj gidromasziny. Viestnik Maszinostrojenia, 10 (1976) 49-50 (in Russian). [4] J. Ivantysyn, M. Ivantysynova, Hydrostatic Pumps and Motors. Academia Books International, New Delhi 2001. [5] T.M. Baszta, S.S. Rubniew, B.B.Niekrasow , O.W. Bajbakow, J.L. Kirilowskij, Gidrawlika, gidromasziny i gidropriwody, Maszinostrojenie, Moskwa 1982 (in Russian). [6] W. Kollek, Problemy czynnego zwalczania hałasu pomp wielotłoczkowych osiowych. Prace Naukowe Inst. Konstr. i Eksploat. Maszyn Pol. Wrocławskiej Nr 32, Monografie nr 7, Wrocław 1976 (in Polish). [7] J. Turza, Stanovenie geometrických rozmerov rotačného rozvodu axiálneho piestového hydrostatického prevodníka. Acta Hydraulica et Pneumatica (Slovak Society for Hydraulics and Pneumatics), 8/2 (2005) 69-75 (in Slovak). [8] M. Guillon, Teoria i obliczanie układów hydraulicznych. WNT, Warszawa 1966 (in Polish).
