Defects coming from processing and assembly inevitably bring geometric and concentricity error to the fitting gap between valve core and frame. To overcome this problem, grooving was proven to be the most simple and effective method to reduce the hydraulic clamping force, and widely used on cylinder valve cores. Theoretically unbalanced forces kept going smaller with the increase of pressure equalizing grooves. When groove width increased, linearly the gap leakage extended. When the width was relatively small leakage was gradually reduced when depth increased. When the width was 1 mm, 1.5 mm or 2 mm, and the depth to width ratio was less than 1, leakage got worse with the increment of depth

Chenbo Yin

Donghui Cao

Wenhua Jia

Ye Yi

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Sensors & Transducers, Vol. 23, Special Issue, July 2013, pp. 44-48 
 44 
  
Sensors & Transducers 
© 2013 by IFSA
http://www.sensorsportal.com  
 
 
 
 
 
The Gap Seal’s Influences on the Leakage  
and Clamping of Multi-way Directional Valves 
 
1 Wenhua Jia, 2 Chenbo Yin, 3 Donghui Cao, 4 Ye Yi 
1 School of Mechanical Engineering, Nanjing Institute of Technology, No. 1 Hongjing Road, 
Jiangning Science Park, Nanjing, Jiangsu Province, 211167, China 
1, 2, 4 School of Mechanical and Power Engineering, Nanjing University of Technology,  
No. 30 Pu Chu Road, Pukou District, Nanjing, Jiangsu Province, 211816, China 
1, 3 SANY Co., Ltd, Shanghai, 215300, China 
1 E-mail: wenhuajia163@163.com 
 
 
Received: 20 May 2013   /Accepted:19 July 2013   /Published: 30 July 2013 
 
 
Abstract: Defects coming from processing and assembly inevitably bring geometric and concentricity error to 
the fitting gap between valve core and frame. To overcome this problem, grooving was proven to be the most 
simple and effective method to reduce the hydraulic clamping force, and widely used on cylinder valve cores. 
Theoretically unbalanced forces kept going smaller with the increase of pressure equalizing grooves. When 
groove width increased, linearly the gap leakage extended. When the width was relatively small leakage was 
gradually reduced when depth increased. When the width was 1 mm, 1.5 mm or 2 mm, and the depth to width 
ratio was less than 1, leakage got worse with the increment of depth. Copyright © 2013 IFSA 
 
Keywords: Directional valves, Leakage grooves, Dynamic stability. 
 
 
 
1. Introduction 
 
Gap seal is the kind of seal implemented when 
there is tiny radial gap with sufficient axial length 
between components. The sealing performance 
varied significantly with different types of gap. As 
given years of experiments, convergence gap sealing 
was proven to have the minimum leakage, followed 
by flat type. Expansion ones may be the worst among 
the three in leakage prevention, but better in dynamic 
stability [1-4]. Considering the gap between the 
frame and valve core of a directional valve was a 
regular cylinder, flat-seal was adopted here. 
Massive research on gap seal had been done in 
last hundred years. However, a more comprehensive 
proportional valve model is necessary to design and 
analyze the similarity system. A variety of 
proportional valve mathematic model, as in [5-7] 
have described the complexity transformation 
relationship of the proportional valve electric, 
proportional valve machine and proportional valve 
liquid, but did not describe the nonlinear flow 
characteristics induced by the geometrical feature of 
valve in the variety flow zone. 
Gap size, pressure difference, sealing length and 
surface quality are major determinants of sealing 
effects. Thus high geometric accuracy and surface 
processing demands are posed on the component if 
chosen for gap sealing. However, defects coming 
from processing and assembly inevitably bring 
geometric and concentricity error to the fitting gap 
between valve core and frame. Several typical 
gapping structures with tapered angle and 
eccentricity were listed in Table 1. 
Article number P_SI_400 
Sensors & Transducers, Vol. 23, Special Issue, July 2013, pp. 44-48 
 45
Table 1. Various of valve geometry model. 
 
Axis parallel 
 
No parallel of axis 
 
     
 
cos12  exl
c
rrh  
cos
coscos
1
2 
 ex
l
cr
rh  
 
(a) 
 
 
(d) 
 
 


cos)(
)(
cos)(
'
'122
'
'121




elx
ll
c
rrh
elx
l
c
rrh
 




cos)(
cos)(cos
cos)(
coscos
'
'
1
22
'
'
1
21






elx
ll
cr
rh
elx
l
cr
rh
 
 
(b) 
 
 
(e) 
  


cos)(
)(
cos
'122
'121




exl
ll
c
rrh
ex
l
c
rrh
 




cos)(
cos)(cos
cos
coscos
'
1
22
'
1
21






exl
ll
cr
rh
ex
l
cr
rh
 
 
(c) 
 
(f) 
 
 
In which was the eccentricity between inner and 
outer ring, was the gap at on arbitrary angle. Due to 
the eccentric phenomenon, was not constant, the 
specific expression was given in Table 1. In 
reference [8], Jia studies the radial pressure 
unbalancing brought by geometry error and coaxial 
error in a slide valve pair through CFD method. As 
given in Table 1 (d), clamping was more likely to 
occur in the case when not only eccentric 
phenomenon existed between the centerline of the 
core and the frame, but also the core was an inverted 
cone. In the following chapters, case (d) in Table 1 
was taken as an important scenario for studying the 
gap flow in the radical gap of a slide valve pair. 
 
2. Compensation Research on Hydraulic 
Clamping Force and Pressure 
Equalizing Groove in a Slide Valve  
 
As shown in Fig. 1 that is caused in Table1 (d), in 
the gap between a valve chamber and a core with 
length L, the gap length at arbitrary circumferential 
angle was given as follows. 
The expression for pressure at arbitrary h is 
 
    phhhhpp  )1//(1/ 21211 ）（ , (1) 
 
where  
Sensors & Transducers, Vol. 23, Special Issue, July 2013, pp. 44-48 
 46 
121 rrh 
 cos/122 ecorccorrrh 
 
(2)
 
 
     
 
Fig. 1. Gap between a valve chamber and a core  
with length L. 
 
 
The force applied on unit width of the 
circumferential is  
 
   
'
0
2
1
1 20
1 2 11 2
2
1
1 2
d
1
// 1
L
L
F p x
hp
p dx
h h h x Lh h
h
p p L
h h
 
                
 
    


 
(3) 
 
To obtain the force on the core, infinitesimal 
lengths were taken on circumferential direction, 
  d2/d , as shown in Fig. 1. Then the infinitesimal 
lateral pressure to the eccentric side is given as 
2/cosd' dF  . 
Note the expression, 
 
,cos
101
ehh   cos
202
ehh  , 
 
where 
10h , 02h  is the gap clearance of inlet and out 
when valve chamber and a valve core were at 
concentricity, e is the eccentricity clearance, α is the 
angle measured from where gap clearance was  
the largest. 
Then, the total compression towards the eccentric 
side on the valve core is expressed in equation, 
 
   
2
1 2
2 2 1 1 2
2 '
0
2 1 0
0
0 0
22
0 0 0 0 0
cos d
2
( cos
cos d
/ 2 cos ) 2
/ (4 ) 1/ 1 4 / 1
d
F F
p h e d
L
h h e p
h h h Ld p e e h h


 

 


 
  
      
        


（ ）
（ ） (4) 
 
From Eq. (1), it can be seen that the lateral force, 
known as the hydraulic clamping force, was related 
to the clearance height ratio between inlet and outlet, 
when gap fitting length, eccentricity clearance, and 
pressure difference were given and fixed. 
As shown in the directional valve’s profile on 
Fig. 3, pressure difference existed between the high-
pressure oil chamber on the right and the low-
pressure oil to the left. 
When the valve core is grooved, the lateral radial 
force decreased when number of pressure grooves 
increased, as shown in Fig. 2. Since the depths of 
pressure equalizing grooves were larger than the gap 
clearance, they gave interconnections to regions with 
different pressures on the cylinder, and evenly 
distributed the pressure. Those grooves, on the other 
hand, divided the cylinder outer rim into sections, 
flattened unbalanced radial forces, and made the 
pressure distribution tends to be uniform along the 
gap axes. Grooving was proven to be the most simple 
and effective method to reduce the hydraulic 
clamping force, and widely used on cylinder  
valve cores.  
 
 
0 2 4 6
0
7
14
(P
-T
) 
(/
M
P
a
)
x/0.001 (mm)
Three
 Two
One
 
 
Fig. 2. Result of radial pressure with grooves. 
 
 
What was important is that the sidewalls of 
grooves must be done vertically to the outer surface 
of the core, to avoid oil dirt wedging. The width of 
grooves must also been maintained constant around 
the entire circumference, to prevent additional 
unbalanced forces generated from fluid pressures. On 
the other hand, theoretically unbalanced forces kept 
going smaller with the increase of pressure 
equalizing grooves, the actual problem is that, they 
brought higher possibility of leakage. 
 
 
3. Study on the Influence to Gap Sealing, 
Brought by Pressure Equalizing 
Grooves 
 
Fig. 3 shows the directional valve’s profile. 
Pressure difference existed between the high-pressure 
oil chamber on the right and the low-pressure oil to 
the left. Inter communication was achieved with the 
directional valve. The valve core was put there to cut 
off the gap within the walls and oils. Grooves on the 
core were cut to reduce the hydraulic clamping force, 
but at the same time increased the risk of leakage. 
Sensors & Transducers, Vol. 23, Special Issue, July 2013, pp. 44-48 
 47
The following section was presented to address the 
gapping problem and the optimized design of gap 
sealing to reduce leakage. Fig. 4 shows a test model 
of directional valve. 
 
 
 
 
Fig. 3. Directional valve’s profile. 
 
 
 
 
Fig. 4. Test model of directional valve. 
 
 
Previous studies, as in [9] indicated a linear 
relationship between the flow rate and pressure 
difference at the inlet. The relationship was in 
consistency with the Bernoulli equation. Thus only 
one set of initial pressure boundary condition was 
needed for the research of gap leakage. All following 
researches were conducted under such a boundary 
condition, inlet boundary pressure: 4 MPa, outlet 
boundary pressure: 0.4 MPa. 
 
 
3.1. Effect of Groove Width on Leakage 
 
With other initial conditions fixed, studies on the 
effect of groove width were conducted with several 
depths of 0.2 mm, 0.5 mm, 1 mm, 1.5 mm and 2 mm. 
Seen from the Fig. 5, when groove width increased, 
linearly the gap leakage extended. 
 
 
3.2. Effect of Groove Depth on Leakage 
 
With the number of grooves fixed, studies on the 
effect of groove depth were conducted with several 
widths of 0.2 mm, 0.5 mm, 1 mm, 1.5 mm and 2 mm. 
The results were given in Fig. 6. 
When the width was relatively small, namely 
0.2 mm and 0.5 mm, leakage dropped gradually with 
increment in depth. It was preferred for a gap seal. 
When the width was 1mm, leakage got worse as the 
depth went from 0.5 mm to 1.5 mm, but reversibly 
started to drop again as the depth went beyond 
1.5 mm towards 2 mm. With 1.5 mm groove width, 
leakage continued to increase along with the depth 
extending from 0.2 mm to 1.5 mm, then turned to 
alleviation. The overall trend was similar when the 
width was 2 mm and depth ranging from 0.2 mm to 
2 mm. 
 
 
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
3.8
4.0
4.2
4.4
4.6
4.8
Depth=2.0mm
L
ea
ka
ge
(m
l/
s)
Groove widths(mm)
Depth=1.5mm
 
Fig. 5 a. Effect of groove width on leakage. 
 
 
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
3.8
4.0
4.2
4.4
4.6
4.8
Depth=1mm
Depth=0.5mm
L
ea
ka
ge
(m
l/
s)
Groove widths(mm)
Depth=0.2mm
 
Fig. 5 b. Effect of groove width on leakage. 
 
 
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
3.8
4.0
4.2
4.4
4.6
4.8
width=2mm
width=1.5mm
width=1mm
width=0.5mm
L
ea
ka
ge
 (
m
l/
s)
Groove depths(mm)
width=0.2mm
 
Fig. 6. Effect of groove depth on leakage. 
Sensors & Transducers, Vol. 23, Special Issue, July 2013, pp. 44-48 
 48 
When the width was relatively small, such as 
0.2 mm, 0.5 mm, leakage was gradually reduced 
when depth increased. It was preferred for gap seal. 
When the width was 1 mm, 1.5 mm or 2 mm, and the 
depth to width ratio was less than 1mm, leakage got 
worse with the increment of depth; but it tended to 
alleviation when that ratio was larger than 1 mm. 
 
 
4. Conclusions 
 
Defects coming from processing and assembly 
inevitably bring geometric and concentricity error to 
the fitting gap between valve core and frame. 
Clamping was more likely to occur in the case when 
not only eccentric phenomenon existed between the 
centerline of the core and the frame, but also when 
the core is an inverted cone. 
When the valve core is grooved, the lateral radial 
force decreased when number of pressure grooves 
increased. But grooving also increased the possibility 
of leakage. That was why the optimization design of 
groove size was demanded. 
When the grooving width was relatively small, 
gap leakage dropped as the depth increased, and was 
preferred for sealing. When the width was larger, and 
was approximately equal to the depth, the leakage 
expended, grew and turned to alleviation after 
reaching the maximum. 
 
 
Acknowledgements 
 
This work was supported in part by Jiangsu 
Province Science and Technology Support Program, 
Nanjing Institute of Technology Fund for Talents and 
Youth, SANY Co., Ltd in Jiangsu. Lecturer, Supports 
Fund No. YKJ201101, QKJA201201, BE2011187. 
 
 
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The Gap Seal's Influences on the Leakage and Clamping of Multi-way Directional Valves

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The Gap Seal's Influences on the Leakage and Clamping of Multi-way Directional Valves

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