- Email: [email protected]
Pressure distribution in scraper ring contacts
Wear, 115
(1987)
PRESSURE
31
31
- 40
DISTRIBUTION
HAKAN
LINDGREN
Division
of Machine
Elements,
IN SCRAPER
Chalmers
University
RING CONTACTS*
of Technology,
GBteborg
(Sweden)
Summary This report deals with methods for the determination of the pressure distribution in the contact between a hydraulic cylinder and a scraper ring. A study of some of the parameters, which are important for the formation of the contact pressure distribution, has also been made. The distributions have been calculated using the finite element method. Two different material models have been used, one is the usual Hooke description and the other is a hyperelastic description. Experiments have been performed on a commercially available scraper ring to obtain the stress-strain relation for the used type of elastomer and to verify the calculated pressure distributions. The results show a fairly good agreement between calculation and experiment. A comparison between Hooke’s and the hyperelastic theory shows that both theories can be used in this case. The diameter of the scraper ring seems to have little influence on the pressure distribution. This implies that the stresses caused by bending the seal lip are more significant than those caused by stretching the seal ring. Another significant factor in the formation of the pressure distribution is the geometry in the contact zone.
1. Introduction A hydraulic cylinder should have a minimum loss of energy, i.e. minimum leakage and friction, and a maximum service life. These factors mainly depend on the seals in the cylinder and they are especially influenced by the piston rod seals. The sealing of a piston rod in a hydraulic cylinder is always achieved by means of two seal elements. There is an inner piston rod seal, which is the main seal element, and an outer scraper ring or rod scraper. The inner piston rod seal prevents hydraulic fluid from leaking out of the cylinder and the scraper ring removes contaminants from the piston rod before it enters the piston rod seal and the interior of the hydraulic cylinder. Thus the scraper ring can be regarded as an element that protects the piston *Paper Technology,
presented at the Nordic Symposium Lule%, Sweden, June 15 - 18, 1986.
0043-1648/87/$3.50
@ Elsevier
on Tribology,
Sequoia/Printed
Lule% University
in The Netherlands
of
32
rod seal and the cylinder from damaging contaminants. If the two seal elements are considered separately one can say that they both should be as tight as possible in order to prevent leakage and contaminant transportation. E-Iowever, if the sea2 e2ements are too tight the lubricating fluid films will be too thin and the friction too high. Thus for optimum function the seal element combination should allow such a fluid film thickness that the friction, the net leakage after a double piston stroke and the transport of contaminants during an in-stroke taken together become reasonable. Co-operation between piston rod seals and scraper rings has been treated by Johannesson in ref. 1. In this work the inverse hydrodyn~i~ theory was applied. This method requires knowfedge of the pressure dist~bution in the seal contact. If the pressure d~tribution is known it is inserted in Reynolds’ equation and then the oil film thickness, the leakage flow and the frictional force can be calculated. Reports that deal with pressure distribution calculations are presented by Johannesson and Kassfeldt in refs. 2 and 3. These reports deal with pressure calculations in hydraulic seals of compact type. Yang and Hughes have in ref. 4 used the finite element method (FEM) to calculate the pressure distributions in seal contacts. In this study linear elasticity theory was used to obtain the pressure distribution. The seals treated were mainly of the rectangular compact type. They were preloaded and then exposed to an internal pressure. The hypere2astic expression for treating large deformations is based on the power of strain invariants and it therefore provides a fair2y good way of modelling complicated material behaviour (see ref. 1). A basic restriction is that the theory is isotropic. Since it was proposed a number of authors have discussed it. In ref. 5 Morman gives a survey of the field. Methods to determine the elastic constants have for instance been treated by Hubbard in ref. 6. Scraper rings have been treated by Parker in ref. 7. In this paper an experimental investigation for determining scraper ring efficiency was presented. The ability of the rings to remove contaminant particles from the piston rod was studied. In this comparative study a metal scraper was used as a baseline and the scraper efficiency was measured as the amount of cont~ination bypassing the scraper. It was also noted if there was any damage on the chromium piston rod. The investigation shows that scraper rings for use in highly contaminated areas should incorporate a non-absorbent scraper material. This material should be able to seal the static side of the scraper gland as well as to scrape effectively contaminants from the dynamic rod surface. Lip-type rubber spring-actuated scrapers effectively accomplish these requirements. 2, Theory The majority of today’s scraper rings are made of elastomers and have a basic geometry as shown in Fig. 1. They usually have a “lip” which is used
33
Fig. 1. Basic
geometry
of a scraper
ring.
for “scraping”. The lip is attached to the “base”. The base is usually vulcanized onto a metal shell which is mounted tightly in the hydraulic cylinder. The two most common materials used for scraper rings are polyurethane and nitrile rubber. Stresses, including the contact pressure, are built up with elastic deformations in the lip. 2.2. Assumptions The basic assumption is that the deformation of the piston rod is negligible compared with the deformation of the scraper ring. The material in the scraper ring is isotropic, purely elastic and incompressible. This means that many material properties are neglected, for example stress-relaxation viscoelasticity, temperature dependence, aging, anisotropy and (creep), compressibility. Furthermore, the analysis does not consider misalignment, i.e. a purely axi-symmetric model is used. There is no friction at the contacts and there is no hydrostatic pressure difference over the scraper ring. 2.3. The finite element method The FEM calculations are made using the program ABAQUS. The basic idea of this program is to solve the equations by using the full NewtonRaphson method. Two material models are used. One is Hooke’s material description and the other is a hyperelastic description. The formulation of a Hooke material model with large rotation and small strains is based on the Chauchy (true) stress and logarithmic strain. The basic restrictions are that it is inconsistent for the volume description and that it just has one constant to describe the deviation stresses. The hyperelastic material description is basically isotropic. It is consistent in volume even for large strains and it is a polynomial series in the strain invariants. In ABAQUS the virtual work W is expressed as W=
2
Cij(ll-3)'(1*-3)'+
i+j=l
_~~,~+~~~,;p--_~_~~~~
4
I
2i
i
l+“,
--l
(1)
34
Here Cij are the elastic constants, Di are the compressibility constants and R is the volume change due to temperature. Furthermore, Ii and I, are strain invariants and J is the volume change defined as I, = trace(E)
(2)
-1, = + (Ii - trace(BB))
(3)
J = det(F)
(4)
Here F is the deformation gradient and E = % T. The type of element used is an eight node isoparametric element. Here two types are used, axi-symmetric and plane strain elements. To handle the incompressible behaviour, a hybrid formulation is used, separating the hydrostatic pressure from the deviation stresses. Then the incompressibility is “in hand” with a penalty formulation. Furthermore, contact elements are used in order to model the contact between the rigid surface and the elastic structure. A plane or a line is defined and some chosen nodes are connected to this plane or line. If there is contact the plane will be changed to a boundary, otherwise the node is free to move. 2.4. Elastic constants One interesting thing is to find a relation between Young’s modulus and the Rivlin constants. If eqn. (1) is shortened to N = 1 and if the material is incompressible the Mooney form will be obtained. Furthermore, if the comparison of the energy E is made with uniaxial stressing, and strains of a higher order than E are neglected, the relation will be
E = 6(C,o + Cod This relation can be treated in different ways. One way is to put C,i = 0 the constants in the and obtain E = 6C10. The usual way of determining hyperelastic expression is a matter of adjusting the curves to the empirical data. The problem is obtaining good test results, because it is very difficult to carry out tests that will give a good description of the elastic properties of the elastomer. This is a problem especially for large strains. In the application treated in this paper the strains are relatively small. This implies that the stress-strain relationship should be fairly linear. The chosen experimental method is to examine the uniaxial tension of a cylindrical bar with a diameter of 30 mm and a length of 150 mm. It is loaded and unloaded a couple of times and then, while measuring the force, slowly loaded. The results are shown in Fig. 2. The major problem is that compression and tension can differ a lot in stress-strain relationships but for small strains the difference is not a major problem. Instead the problem is that the elastic properties will depend on the previous load cycles. This means that the calculated elastic constants give more or less an indication of the elastic behaviour. The theory for obtaining the constants for a uniaxial case can be taken from ref. 8. It states
35
Fig. 2. Cross-sectional
basic geometry
of a scraper
ring.
(6) Here X equals the deformed force f becomes
f=oA=
length divided
by the original length.
+
Then the
(71
A
where CJ is the normal stress, A is the deformed loaded area and A0 is the undeformed loaded area. It should be noted that the different signs of the constants will give solutions where the stresses become zero and even negative. For uniaxial stressing this will occur when ClOX = --Cei. Since the experiments are made by examining the tension and the main part of the deformations in the application is in compression, it is meaningless to try to obtain a close fit between the entire measured curve and the theory. Here the stiffness at very small strains is used and only one constant is fitted to this curve. The constants for polyurethane determined from Fig. 3 are Cl0 = 8 MPa and Co, = 0. area
(MPa)
d
Fig. 3. Results Fig. 4. Basic
from geometry
a uniaxial
tension
test for a cylindrical
used in the calculations
bar.
(all dimensions
in millimetres).
36
3. FEM calculations The geometry used in the calculations is shown in Fig. 4. The diameter of the rod d = 44.2 mm and the radial displacement A = 0.4 mm. The calculated strains can be seen in Fig. 5. Figure 6 shows a comparison between different material models. We notice that the difference is very small. This will make it possible to calculate the pressure distribution with both material models. A comparison between the pressure distributions obtained with different diameters is shown in Fig. 7. If d is changed from 44.2 to 62.2 mm and infinity but the rest of the structure remains as in Fig. 4, the results shown in Fig. 7 will be obtained. The elements used when the diameter is infinite are plane strain elements. These results show that the shape of the pressure distribution is relatively insensitive to diameter changes. This implies that the stress caused by the bending of the seal lip is more significant than that caused by the stretching of the seal ring. Calculations of pressure distributions for the different deflections A are shown in Fig. 8. At a first glance these results are surprising. The maximum pressure is higher for small deflections than for large deflections, i.e. the scraper will scrape more efficiently when the deflections are small. The results show that the pressure distribution is very sensitive to the geometry of the lip, i.e. the
I (a) Fig.
5. Strains
(b)
in orthogonal directions. ID values (a) strain in direction 1: *, -8 X 1oe2; l, -4, x 10m2; n , -4 X lo-*; A, -2 X lo-*; V, 0; +, 2 X 10V2. (b) Strain in direction 2: *, -2 x lo-*; l, -2 x lo-+; n , 1.6 x lo-*; A, 3.4 x lo-*; r, 5.2 X lo-*;b, 7 X lo-‘.
37
3.0
2.0
1.0
0.0 10.00
10.05
lO.iO
10.15
10.20
10.25
10 .30
(mm)
Fig. 6.Pressure distributions for different material models 8 MPa and C,l= 0, curve I_[ (Hooke) with E = 50 MPa).
( MPa)4.0
,
I
I
3.0
I
I
I
I
(curve M (Mooney)
with Cl0 =
1
I
/
/‘i”
2.0.
d\\l
I
\\ I
i.0
I
O.OL
10.00
I I 10.05
I 10.10
I 10.15
Fig. 7. Pressure distributions 62.2 mm; 3, d = 44.2.
I
I
10.20
10.25
for various
J 10
3o(mm)
diameters
of the scraper
ring:
1, d = 00; 2, d =
(MPd6.0
5.0
4.0
3.0
2.0
1.0
I
o.oi 10.00
Fig. 8. Pressure
10.05
10.10
distributions
I 10.15
I 10.20
I 10.25
I 10.30(mm)
for various values of
major parameter that infkences angle of the scraper ring lip.
A.
the shape of the pressure distribution
is the
4. Experiment Measurements of the pressure distribution in the scraper ring contact zone have been performed using the device shown in Fig. 9. The basic idea
38
I PREssmE
QAUQE
VALVE
1
i_HoL, --=-
[
PI
TONRW
T-l SCFIAPER
i
I
Fig. 9. Experimental zone.
RINQ
set-up for measurements of the pressure distribution in the contact
of the measurement procedure is to pressurize a small hole in a piston from the inside. The hole is placed in the seal contact zone and pressurized. The pressure is then allowed to fall and when it stops it should equal the actual pressure at this point, see ref. 2. The physical data for the experimental set-up are as follows: piston diameter, 63 mm; hole diameter, 0.04 mm; oil viscosity, 10 cSt. Experiments are made on a scraper ring made of polyurethane, If there is a very rapid change in pressure, the pressure values that are measured will equalize the pressure on the low pressure side of the hole as shown in Fig. 10. The relatively large hole, compared with the actual width, will make it impossible to obtain the maximum pressure more exactly than the hole diameter (see Fig. 10). The measured points are taken after 2 min (Fig. 11). With the previous observations in mind it is obvious that the measured points should be corrected. The correction should be a separation between
HOLE DIARETER
Fig. 10. Comparison between measuring the hole diameter and the contact measured pressure is located at the low pressure side edge of the hole.
length, The
39
0
Fig. 11. Measured
100
pressure
zoo
300
(urn)
distribution.
the left-hand and right-hand pressure derivatives with a maximum distance equal to the hole diameter. If this is done new corrected measured curves will be obtained as shown in Fig. 12. A correction of magnitude can also be discussed with respect to the time when the points were taken. Another possible correction of magnitude depends on the pressure derivatives, i.e. how fast the leaking part of the hole gets smaller. Different corrections in different parts should be made. The reverse effect will result from the possible history dependence in the material, i.e. viscoelastic effects. In such a case there can be a channel in the material where the oil has run which will cause a lower measured pressure than the real pressure. None of these factors seem to be significant. As can be seen in Fig. 12 a fairly good correlation between measurement and calculation is obtained, especially considering the problems involved in the measurements. The major problem with the measurements is that the contact zone is small (0.2 mm) and owing to this the pressure derivatives vary very rapidly. These two factors will make the measurements very sensitive to the correct location of the hole. This is a problem because when the piston is moved the contact zone can follow owing to the elasticity in the scraper ring and friction in the contact zone. Another problem occurs if there are particles in the oil. These will influence the measurements even if the particles are very small owing to the fact that it is only that part of the hole that is on the low pressure side that will leak oil. There could also be problems if the scraper ring surface is not smooth. Because of this influence
Fig. 12. Corrected distribution.
measured
pressure
distribution
compared
with the calculated
pressure
40
local pressure differences can occur and, depending on where in the hole this variation is observed, some measurement errors can occur. 5. Conclusions In Section 2 it was stated that there was no difference between the results obtained with the different material models. Thus it is possible to calculate pressure distributions for both material models. However, when using the Hooke model one must be very careful. Another conclusion in that section was that the ring stresses are small compared with the bending stresses. Because of this it should be possible to simplify the calculations. The shape of the pressure distribution is primarily based on two parameters and these are the angles of the lip sides in the deformed case. In Section 4 the measurement method used in ref. 2 has been developed. Primarily by taking the hole diameter influence into account. If this is done a relatively good agreement between the measurements and the theory can be obtained. Acknowledgments The work described in this paper was supported by the Swedish Work Environment Fund. The author wishes to thank this organization for their support and also the staff of the Division of Machine Elements, Chalmers University of Technology, especially Dr. Hans Johannesson for his valuable help during the work. References 1 H. L. Johannesson, Computer simulations of the co-operation of piston rod seals and scraper rings in hydraulic cylinders, Internal Rep., 1986 (Division of Machine Elements, Chalmers University of Technology, Giiteborg, Sweden). 2 H. L. Johannesson, Calculations of the pressure distribution in an O-ring seal contact, Proc. 5th Leeds-Lyon Symp. on Tribology, Leeds, September 1978, Institution of Mechanical Engineers, London, Paper 1 l( 2). 3 H. L. Johannesson and E. Kassfeldt, Calculations of the pressure distribution in an arbitrary elastomeric seal contact, Research Rep. 1985 02,1984 (Division of Machine Elements, Lule% Universivy of Technology, Lule%, Sweden). 4 Y. Yang and W. F. Hughes, An elastohydrodynamic analysis of preloaded sliding seals, ASLE Trans., 27 (3) (1983) 197 - 202. 5 K. N. Morman, Jr., Rubber Viscoelaeticity a Review of Current Understanding, Ford Motor Company, Dearborn, MI, 1984. 6 G. D. Hubbard, Rubber properties for stress-strain analyses (Design and Performance Engineering Technology Division, Dunlop Ltd., Kingsbury Road, Birmingham B24 9&U, U.K.). 7 B. G. Parker, Rod Scraper Eualuation in Severe Contamination Enuironments, Green, Tweed and Co., 1984. 8 Hibbit, Karlsson and Sorensen Inc., ABAQUS manual, Version 4.5, 1984. 9 A. G. Green and W. Zerna, Theoretical Elasticity, Oxford University Press, London, 1954.
(1987)
PRESSURE
31
31
- 40
DISTRIBUTION
HAKAN
LINDGREN
Division
of Machine
Elements,
IN SCRAPER
Chalmers
University
RING CONTACTS*
of Technology,
GBteborg
(Sweden)
Summary This report deals with methods for the determination of the pressure distribution in the contact between a hydraulic cylinder and a scraper ring. A study of some of the parameters, which are important for the formation of the contact pressure distribution, has also been made. The distributions have been calculated using the finite element method. Two different material models have been used, one is the usual Hooke description and the other is a hyperelastic description. Experiments have been performed on a commercially available scraper ring to obtain the stress-strain relation for the used type of elastomer and to verify the calculated pressure distributions. The results show a fairly good agreement between calculation and experiment. A comparison between Hooke’s and the hyperelastic theory shows that both theories can be used in this case. The diameter of the scraper ring seems to have little influence on the pressure distribution. This implies that the stresses caused by bending the seal lip are more significant than those caused by stretching the seal ring. Another significant factor in the formation of the pressure distribution is the geometry in the contact zone.
1. Introduction A hydraulic cylinder should have a minimum loss of energy, i.e. minimum leakage and friction, and a maximum service life. These factors mainly depend on the seals in the cylinder and they are especially influenced by the piston rod seals. The sealing of a piston rod in a hydraulic cylinder is always achieved by means of two seal elements. There is an inner piston rod seal, which is the main seal element, and an outer scraper ring or rod scraper. The inner piston rod seal prevents hydraulic fluid from leaking out of the cylinder and the scraper ring removes contaminants from the piston rod before it enters the piston rod seal and the interior of the hydraulic cylinder. Thus the scraper ring can be regarded as an element that protects the piston *Paper Technology,
presented at the Nordic Symposium Lule%, Sweden, June 15 - 18, 1986.
0043-1648/87/$3.50
@ Elsevier
on Tribology,
Sequoia/Printed
Lule% University
in The Netherlands
of
32
rod seal and the cylinder from damaging contaminants. If the two seal elements are considered separately one can say that they both should be as tight as possible in order to prevent leakage and contaminant transportation. E-Iowever, if the sea2 e2ements are too tight the lubricating fluid films will be too thin and the friction too high. Thus for optimum function the seal element combination should allow such a fluid film thickness that the friction, the net leakage after a double piston stroke and the transport of contaminants during an in-stroke taken together become reasonable. Co-operation between piston rod seals and scraper rings has been treated by Johannesson in ref. 1. In this work the inverse hydrodyn~i~ theory was applied. This method requires knowfedge of the pressure dist~bution in the seal contact. If the pressure d~tribution is known it is inserted in Reynolds’ equation and then the oil film thickness, the leakage flow and the frictional force can be calculated. Reports that deal with pressure distribution calculations are presented by Johannesson and Kassfeldt in refs. 2 and 3. These reports deal with pressure calculations in hydraulic seals of compact type. Yang and Hughes have in ref. 4 used the finite element method (FEM) to calculate the pressure distributions in seal contacts. In this study linear elasticity theory was used to obtain the pressure distribution. The seals treated were mainly of the rectangular compact type. They were preloaded and then exposed to an internal pressure. The hypere2astic expression for treating large deformations is based on the power of strain invariants and it therefore provides a fair2y good way of modelling complicated material behaviour (see ref. 1). A basic restriction is that the theory is isotropic. Since it was proposed a number of authors have discussed it. In ref. 5 Morman gives a survey of the field. Methods to determine the elastic constants have for instance been treated by Hubbard in ref. 6. Scraper rings have been treated by Parker in ref. 7. In this paper an experimental investigation for determining scraper ring efficiency was presented. The ability of the rings to remove contaminant particles from the piston rod was studied. In this comparative study a metal scraper was used as a baseline and the scraper efficiency was measured as the amount of cont~ination bypassing the scraper. It was also noted if there was any damage on the chromium piston rod. The investigation shows that scraper rings for use in highly contaminated areas should incorporate a non-absorbent scraper material. This material should be able to seal the static side of the scraper gland as well as to scrape effectively contaminants from the dynamic rod surface. Lip-type rubber spring-actuated scrapers effectively accomplish these requirements. 2, Theory The majority of today’s scraper rings are made of elastomers and have a basic geometry as shown in Fig. 1. They usually have a “lip” which is used
33
Fig. 1. Basic
geometry
of a scraper
ring.
for “scraping”. The lip is attached to the “base”. The base is usually vulcanized onto a metal shell which is mounted tightly in the hydraulic cylinder. The two most common materials used for scraper rings are polyurethane and nitrile rubber. Stresses, including the contact pressure, are built up with elastic deformations in the lip. 2.2. Assumptions The basic assumption is that the deformation of the piston rod is negligible compared with the deformation of the scraper ring. The material in the scraper ring is isotropic, purely elastic and incompressible. This means that many material properties are neglected, for example stress-relaxation viscoelasticity, temperature dependence, aging, anisotropy and (creep), compressibility. Furthermore, the analysis does not consider misalignment, i.e. a purely axi-symmetric model is used. There is no friction at the contacts and there is no hydrostatic pressure difference over the scraper ring. 2.3. The finite element method The FEM calculations are made using the program ABAQUS. The basic idea of this program is to solve the equations by using the full NewtonRaphson method. Two material models are used. One is Hooke’s material description and the other is a hyperelastic description. The formulation of a Hooke material model with large rotation and small strains is based on the Chauchy (true) stress and logarithmic strain. The basic restrictions are that it is inconsistent for the volume description and that it just has one constant to describe the deviation stresses. The hyperelastic material description is basically isotropic. It is consistent in volume even for large strains and it is a polynomial series in the strain invariants. In ABAQUS the virtual work W is expressed as W=
2
Cij(ll-3)'(1*-3)'+
i+j=l
_~~,~+~~~,;p--_~_~~~~
4
I
2i
i
l+“,
--l
(1)
34
Here Cij are the elastic constants, Di are the compressibility constants and R is the volume change due to temperature. Furthermore, Ii and I, are strain invariants and J is the volume change defined as I, = trace(E)
(2)
-1, = + (Ii - trace(BB))
(3)
J = det(F)
(4)
Here F is the deformation gradient and E = % T. The type of element used is an eight node isoparametric element. Here two types are used, axi-symmetric and plane strain elements. To handle the incompressible behaviour, a hybrid formulation is used, separating the hydrostatic pressure from the deviation stresses. Then the incompressibility is “in hand” with a penalty formulation. Furthermore, contact elements are used in order to model the contact between the rigid surface and the elastic structure. A plane or a line is defined and some chosen nodes are connected to this plane or line. If there is contact the plane will be changed to a boundary, otherwise the node is free to move. 2.4. Elastic constants One interesting thing is to find a relation between Young’s modulus and the Rivlin constants. If eqn. (1) is shortened to N = 1 and if the material is incompressible the Mooney form will be obtained. Furthermore, if the comparison of the energy E is made with uniaxial stressing, and strains of a higher order than E are neglected, the relation will be
E = 6(C,o + Cod This relation can be treated in different ways. One way is to put C,i = 0 the constants in the and obtain E = 6C10. The usual way of determining hyperelastic expression is a matter of adjusting the curves to the empirical data. The problem is obtaining good test results, because it is very difficult to carry out tests that will give a good description of the elastic properties of the elastomer. This is a problem especially for large strains. In the application treated in this paper the strains are relatively small. This implies that the stress-strain relationship should be fairly linear. The chosen experimental method is to examine the uniaxial tension of a cylindrical bar with a diameter of 30 mm and a length of 150 mm. It is loaded and unloaded a couple of times and then, while measuring the force, slowly loaded. The results are shown in Fig. 2. The major problem is that compression and tension can differ a lot in stress-strain relationships but for small strains the difference is not a major problem. Instead the problem is that the elastic properties will depend on the previous load cycles. This means that the calculated elastic constants give more or less an indication of the elastic behaviour. The theory for obtaining the constants for a uniaxial case can be taken from ref. 8. It states
35
Fig. 2. Cross-sectional
basic geometry
of a scraper
ring.
(6) Here X equals the deformed force f becomes
f=oA=
length divided
by the original length.
+
Then the
(71
A
where CJ is the normal stress, A is the deformed loaded area and A0 is the undeformed loaded area. It should be noted that the different signs of the constants will give solutions where the stresses become zero and even negative. For uniaxial stressing this will occur when ClOX = --Cei. Since the experiments are made by examining the tension and the main part of the deformations in the application is in compression, it is meaningless to try to obtain a close fit between the entire measured curve and the theory. Here the stiffness at very small strains is used and only one constant is fitted to this curve. The constants for polyurethane determined from Fig. 3 are Cl0 = 8 MPa and Co, = 0. area
(MPa)
d
Fig. 3. Results Fig. 4. Basic
from geometry
a uniaxial
tension
test for a cylindrical
used in the calculations
bar.
(all dimensions
in millimetres).
36
3. FEM calculations The geometry used in the calculations is shown in Fig. 4. The diameter of the rod d = 44.2 mm and the radial displacement A = 0.4 mm. The calculated strains can be seen in Fig. 5. Figure 6 shows a comparison between different material models. We notice that the difference is very small. This will make it possible to calculate the pressure distribution with both material models. A comparison between the pressure distributions obtained with different diameters is shown in Fig. 7. If d is changed from 44.2 to 62.2 mm and infinity but the rest of the structure remains as in Fig. 4, the results shown in Fig. 7 will be obtained. The elements used when the diameter is infinite are plane strain elements. These results show that the shape of the pressure distribution is relatively insensitive to diameter changes. This implies that the stress caused by the bending of the seal lip is more significant than that caused by the stretching of the seal ring. Calculations of pressure distributions for the different deflections A are shown in Fig. 8. At a first glance these results are surprising. The maximum pressure is higher for small deflections than for large deflections, i.e. the scraper will scrape more efficiently when the deflections are small. The results show that the pressure distribution is very sensitive to the geometry of the lip, i.e. the
I (a) Fig.
5. Strains
(b)
in orthogonal directions. ID values (a) strain in direction 1: *, -8 X 1oe2; l, -4, x 10m2; n , -4 X lo-*; A, -2 X lo-*; V, 0; +, 2 X 10V2. (b) Strain in direction 2: *, -2 x lo-*; l, -2 x lo-+; n , 1.6 x lo-*; A, 3.4 x lo-*; r, 5.2 X lo-*;b, 7 X lo-‘.
37
3.0
2.0
1.0
0.0 10.00
10.05
lO.iO
10.15
10.20
10.25
10 .30
(mm)
Fig. 6.Pressure distributions for different material models 8 MPa and C,l= 0, curve I_[ (Hooke) with E = 50 MPa).
( MPa)4.0
,
I
I
3.0
I
I
I
I
(curve M (Mooney)
with Cl0 =
1
I
/
/‘i”
2.0.
d\\l
I
\\ I
i.0
I
O.OL
10.00
I I 10.05
I 10.10
I 10.15
Fig. 7. Pressure distributions 62.2 mm; 3, d = 44.2.
I
I
10.20
10.25
for various
J 10
3o(mm)
diameters
of the scraper
ring:
1, d = 00; 2, d =
(MPd6.0
5.0
4.0
3.0
2.0
1.0
I
o.oi 10.00
Fig. 8. Pressure
10.05
10.10
distributions
I 10.15
I 10.20
I 10.25
I 10.30(mm)
for various values of
major parameter that infkences angle of the scraper ring lip.
A.
the shape of the pressure distribution
is the
4. Experiment Measurements of the pressure distribution in the scraper ring contact zone have been performed using the device shown in Fig. 9. The basic idea
38
I PREssmE
QAUQE
VALVE
1
i_HoL, --=-
[
PI
TONRW
T-l SCFIAPER
i
I
Fig. 9. Experimental zone.
RINQ
set-up for measurements of the pressure distribution in the contact
of the measurement procedure is to pressurize a small hole in a piston from the inside. The hole is placed in the seal contact zone and pressurized. The pressure is then allowed to fall and when it stops it should equal the actual pressure at this point, see ref. 2. The physical data for the experimental set-up are as follows: piston diameter, 63 mm; hole diameter, 0.04 mm; oil viscosity, 10 cSt. Experiments are made on a scraper ring made of polyurethane, If there is a very rapid change in pressure, the pressure values that are measured will equalize the pressure on the low pressure side of the hole as shown in Fig. 10. The relatively large hole, compared with the actual width, will make it impossible to obtain the maximum pressure more exactly than the hole diameter (see Fig. 10). The measured points are taken after 2 min (Fig. 11). With the previous observations in mind it is obvious that the measured points should be corrected. The correction should be a separation between
HOLE DIARETER
Fig. 10. Comparison between measuring the hole diameter and the contact measured pressure is located at the low pressure side edge of the hole.
length, The
39
0
Fig. 11. Measured
100
pressure
zoo
300
(urn)
distribution.
the left-hand and right-hand pressure derivatives with a maximum distance equal to the hole diameter. If this is done new corrected measured curves will be obtained as shown in Fig. 12. A correction of magnitude can also be discussed with respect to the time when the points were taken. Another possible correction of magnitude depends on the pressure derivatives, i.e. how fast the leaking part of the hole gets smaller. Different corrections in different parts should be made. The reverse effect will result from the possible history dependence in the material, i.e. viscoelastic effects. In such a case there can be a channel in the material where the oil has run which will cause a lower measured pressure than the real pressure. None of these factors seem to be significant. As can be seen in Fig. 12 a fairly good correlation between measurement and calculation is obtained, especially considering the problems involved in the measurements. The major problem with the measurements is that the contact zone is small (0.2 mm) and owing to this the pressure derivatives vary very rapidly. These two factors will make the measurements very sensitive to the correct location of the hole. This is a problem because when the piston is moved the contact zone can follow owing to the elasticity in the scraper ring and friction in the contact zone. Another problem occurs if there are particles in the oil. These will influence the measurements even if the particles are very small owing to the fact that it is only that part of the hole that is on the low pressure side that will leak oil. There could also be problems if the scraper ring surface is not smooth. Because of this influence
Fig. 12. Corrected distribution.
measured
pressure
distribution
compared
with the calculated
pressure
40
local pressure differences can occur and, depending on where in the hole this variation is observed, some measurement errors can occur. 5. Conclusions In Section 2 it was stated that there was no difference between the results obtained with the different material models. Thus it is possible to calculate pressure distributions for both material models. However, when using the Hooke model one must be very careful. Another conclusion in that section was that the ring stresses are small compared with the bending stresses. Because of this it should be possible to simplify the calculations. The shape of the pressure distribution is primarily based on two parameters and these are the angles of the lip sides in the deformed case. In Section 4 the measurement method used in ref. 2 has been developed. Primarily by taking the hole diameter influence into account. If this is done a relatively good agreement between the measurements and the theory can be obtained. Acknowledgments The work described in this paper was supported by the Swedish Work Environment Fund. The author wishes to thank this organization for their support and also the staff of the Division of Machine Elements, Chalmers University of Technology, especially Dr. Hans Johannesson for his valuable help during the work. References 1 H. L. Johannesson, Computer simulations of the co-operation of piston rod seals and scraper rings in hydraulic cylinders, Internal Rep., 1986 (Division of Machine Elements, Chalmers University of Technology, Giiteborg, Sweden). 2 H. L. Johannesson, Calculations of the pressure distribution in an O-ring seal contact, Proc. 5th Leeds-Lyon Symp. on Tribology, Leeds, September 1978, Institution of Mechanical Engineers, London, Paper 1 l( 2). 3 H. L. Johannesson and E. Kassfeldt, Calculations of the pressure distribution in an arbitrary elastomeric seal contact, Research Rep. 1985 02,1984 (Division of Machine Elements, Lule% Universivy of Technology, Lule%, Sweden). 4 Y. Yang and W. F. Hughes, An elastohydrodynamic analysis of preloaded sliding seals, ASLE Trans., 27 (3) (1983) 197 - 202. 5 K. N. Morman, Jr., Rubber Viscoelaeticity a Review of Current Understanding, Ford Motor Company, Dearborn, MI, 1984. 6 G. D. Hubbard, Rubber properties for stress-strain analyses (Design and Performance Engineering Technology Division, Dunlop Ltd., Kingsbury Road, Birmingham B24 9&U, U.K.). 7 B. G. Parker, Rod Scraper Eualuation in Severe Contamination Enuironments, Green, Tweed and Co., 1984. 8 Hibbit, Karlsson and Sorensen Inc., ABAQUS manual, Version 4.5, 1984. 9 A. G. Green and W. Zerna, Theoretical Elasticity, Oxford University Press, London, 1954.