Oil film thickness between piston ring and cylinder bore
HANS-OLOF GRUNDBERG
Oil film thickness between piston ring and cylinder bore
Hans-Olof Grundberg
Master of Science Thesis MMK 2006:08 MME 774 KTH Industrial Engineering and Management
Examensarbete MMK 2006:08 MME 774
Oljefilmens tjocklek mellan kolvring och cylinderlopp
Hans-Olof Grundberg
Godkänt
2006-02-17
Examinator
Sören Andersson
Handledare
Ulf Olofsson
Uppdragsgivare
Hägglunds Drives AB
Kontaktperson
Ulf Skytte af Sätra
Sammanfattning
Hägglunds Drives i Mellansel tillverkar hydraulmotorer av radialkolvs typ, främst för
industriella applikationer. I dessa motorer finns flertalet glidande kontakter varav en av dessa är kolvring mot cylinderlopp. Hydraulmotorns stora fördelar är att producera högt vridmoment vid mycket låga rotationshastigheter, vilket medför att den maximala glidhastigheten under ett arbetsslag är mycket låg. Den låga glidhastigheten får som följd att kontakten mellan kolvringen och cylinderloppet, under hela arbetsslaget, befinner sig i gränsskiktssmörjning. Detta medför att kolvringen blir utsatt för nötning, nötning som i sin tur påverkar livslängden på hydraulmotor i mycket hög grad.
För att minimera nötning av kolvringen är det väsentligt att bestämma oljefilmens tjocklek mellan kolvringen och cylinderloppet. Detta för att man sedan skall kunna vidta åtgärder hos de glidande ytornas topografi, vilka i sin tur kan påverka oljefilmens uppbyggnad vid lägre
glidhastigheter.
I detta examensarbete har en metod för att mäta filmtjocklekar utförts i en testrigg som simulerar en hydraulmotor från Hägglunds Drives. Metoden baseras på att använda kapacitiva givare som placeras i cylinderfodret och mäter avståndet från givarens placering till kolvringen. Givarens har placerats med en offset från cylinderloppet varpå oljefilmens tjocklek baseras på avståndet mellan givaren och kolvringen minus avståndet från givaren till cylinderloppet.
En förändring av oljefilmens tjocklek i förhållande till kolvhastigheten har observerats, dock inom området för standard avvikelsen i testet. En tydlig trend kan dock anas för trycket 30 MPa, där oljefilmen ökar med ökad kolvhastighet.
Master of Science Thesis MMK 2006:08 MME 774
Oil film thickness between piston ring and cylinder bore
Hans-Olof Grundberg
Approved
2006-02-17
Examiner
Sören Andersson
Supervisor
Ulf Olofsson
Commissioner
Hägglunds Drives AB
Contact person
Ulf Skytte af Sätra
Abstract
Hägglunds Drives in Mellansel, Sweden, manufacture radial piston hydraulic motors foremost within applications in the industry. These motors have several sliding contacts, one of these, is the contact between piston ring and cylinder bore. The radial piston hydraulic motors advantage is to produce high torque in very low rotation velocity, this result in that the maximum sliding velocity between piston ring and cylinder bore, during the whole stroke, is very low. The consequence of this low sliding velocity is that the contact between piston ring and cylinder bore, during the whole stroke, is bound to the boundary lubrication regime. This result in, that the piston ring is exposed to wear, thus affect the service life of the complete hydraulic motor.
To minimize wear of piston ring, it is essential to determine the oil film thickness between the piston ring and cylinder bore. When the build up of oil film thickness is evaluated, more could be understood about different surfaces ability to build up oil film thickness in low sliding velocities.
The purpose of this master thesis, is to evaluate a method for measuring oil film thickness between piston ring and cylinder bore, in a test rig, simulating the radial piston hydraulic motor from Hägglundes Drives. The method investigated is based on the use of capacitive transducers that are placed in the cylinder bore and measure the distance from the placement of transducer to the piston ring. The transducer is placed with an offset from the cylinder bore whereas the oil film thickness is based on the distance between transducer and piston ring minus the distance from transducer to cylinder bore.
Change in the oil film thickness as a function of piston speed has been observed, though within the area of standard deviation for the tests, despite this, there is a clear trend towards an increase of oil film thickness for the working pressure of 30 MPa.
Preface
This is my Master thesis, and thus the last assignment in which I’m obligated to do before receiving my Master of Science degree at the Royal Institute of Technology, Stockholm, Sweden. Therefore, I would like to take this moment and thank some people I met during the time in which this thesis was written.
Sören Andersson for actually being the one who introduced me to Ulf Skytte af Sätra and this assignment. Ulf Skytte af Sätra for being a positive spirit, a good travel partner in England and for giving me the pleasure to experience the procedure of getting a Ph.D.
degree and having a great party afterwards, congratulations. Ulf Olofsson, my supervisor at the office, for extensive guidance in how a thesis should be written, Krister Sundvall for the intensive discussions that brighten the days in the test cells.
Anders Söderberg, Björn Möller, Jon Sundh, Petter Johansson, Ellen Bergseth and all the other “young guns” at the office, thanks for talking about things that I actually could refer to, things that happened after the oil crisis.
To all the people at the department of Machine Design, during all my years at this school, I’ve never found a more relaxed atmosphere than I did with you people, thanks.
I would also like to thank Ian Sherrington for the hospitality at our visit to the University of Lancashire in Preston, England, showing us around the countryside, especially the pub next to the church in the small village, that, I will not forget. While the Englishmen were drinking tea, Sven Söchting provided us with coffee, a big thanks to that, and for the extensive help in calibrating the transducers.
Finally, I would like to thank my family and friends who makes life worth living, my girlfriend Lin Yue-Wen, for pushing me, without you I would be stuck on this school for eternity.
1 Introduction... 2
2 Background ... 3
2.1 Radial piston hydraulic motor... 3
2.2 Piston ring operation ... 4
2.3 Aim ... 5
2.4 Procedure and Limitations ... 5
3 Theory ... 6
3.1 Introduction... 6
3.1.1 Friction... 6
3.1.2 Wear... 6
3.1.3 Lubrication... 6
3.1.4 Boundary Lubrication ... 7
3.1.5 Surface roughness ... 8
3.1.6 Surface texture ... 9
3.2 Modeling of oil film thickness... 10
3.2.1 Pan and Hamrock... 10
3.2.2 Thermal correction... 11
4 Film thickness measurement... 13
4.1 Methods... 13
4.2 Capacitive technique... 13
4.2.1 Introduction... 13
4.2.2 Working principle ... 13
4.2.3 Transducer... 16
4.2.4 Interference ... 16
4.3 Experimental equipment ... 18
4.3.1 The Sliding Movement Test Rig... 18
4.3.2 Cylinder and Piston assembly... 19
4.3.3 Transducer placement in cylinder bore... 20
4.4 Calibration... 23
4.5 Procedure of measurement... 25
4.5.1 Visualization ... 25
5 Results... 28
5.1 Series A... 28
5.2 Series B ... 30
5.3 Standard deviation ... 31
6 Discussion ... 33
7 Conclusions... 34
References... 35
Appendix A... 38
Appendix B ... 40
1 Introduction
Within the industry, it’s very common to convert any kind of energy into mechanical work. This can be done in a number of different ways and methods. Hägglunds Drives AB in Mellansel, manufacture radial piston hydraulic motors in which torque and rotation are produced from hydrostatic pressurized oil. In the radial piston hydraulic motor, there are several sliding contacts where energy can be lost, the most significant of those, is the piston-ring cylinder bore contact. Any change in profile on piston-ring caused by wear, will reduce the efficiency of the hydraulic motor, and severely affects its service life [1].
To minimize wear on the piston ring, it is of great interest to determine the oil film thickness, a measurement on the surfaces separation, the separation of the piston ring and cylinder bore. Measurement of the oil film thickness is of importance to understand different surfaces influence on the oil film thickness. There are different methods of measure film thickness, and in this thesis a capacitance technique for oil film thickness measurement between piston ring and cylinder bore is investigated.
All the work was performed at the Department of Machine Design, School of Industrial Engineering and Management, The Royal Institute of Technology (KTH), Stockholm, Sweden, 2005 if not stated otherwise.
2 Background
2.1 Radial piston hydraulic motor
Back in 1957 Hägglunds bought a patent for an internal combustion radial piston engine for diesel fuel. Hägglunds did further development on this patent, and the operating principle based on chemical energy, was converted to that of hydrostatic pressurized oil.
Later in 1959, a prototype is presented, and in the beginning of 1960’s the first hydraulic motors were introduced in ship cranes [1].
The solution of turning energy into torque is the essential part of the radial piston hydraulic motor, the thing that distinguishes it from the rest of the energy converters on the market. The radial piston hydraulic motor has an even number of pistons that operate alternately in a reciprocating motion. Torque and rotation are produced when pistons with working pressure pushes against the cam ring and produce a tangential force throughout the cam ring. This tangential force either moves the cam ring casing or the cylinder block, it depends on which to prefer. The shape of the cam ring is such that it produces constant displacement and therefore the hydraulic motor works continuous and gives a stable torque (see Figure 1).
Figure 1: The cam ring profile of the radial piston hydraulic motor.
2.2 Piston ring operation
During the early stage of the radial piston hydraulic motor, the piston itself isolated the oil between the piston and cylinder bore. Piston rings were not introduced until late 1991 after several years of development. When using a piston ring the piston could be shorter, thus size reduction was possible [13]. Research on piston rings became essential, hence the demands on a smaller motor on the market were high, thus in 1994 the model
Compact (see Figure 2.) was introduced [1]. Introduction of the piston ring was not done without problems though, extensive research have now been made over the past years to fully understand the characteristics of the piston ring. The radial piston hydraulic motors now have one piston ring on each piston, mounted near the top [13].
Figure 2: The Hägglunds Compact model hydraulic motor in operation.
Increasing price of oil as a result of the oil crisis in 1973, raised the awareness of the need to conserve energy [12]. It became important to locate the power loss in internal
combustion engines to find the source of frictional losses. Research later found the piston ring cylinder bore contact to be a considerable main source of frictional losses. It is now generally accepted that piston rings are the largest single source of frictional power loss in internal combustion engines [7].
In the hydraulic motor some things are different compared to the internal combustion engine, but all the same very similar. In the internal combustion engine the purpose for the piston ring is to prevent the escape of combustion chamber gases (restrict blow-by) from one side and at the same time prevent oil leakage from the other. In the hydraulic motor however, the oil itself with a working pressure of 30 MPa, work as the energy source, at the same time as it works as a lubricant between the piston ring and the cylinder bore. The purpose of the piston ring in the radial piston hydraulic motor is, to isolate the oil from escaping from the high pressure chamber, and only from that side, generally speaking.
2.3 Aim
Perform test in a sliding movement test rig to establish whether measurement of oil film thickness is possible. Method to be used is a capacitance technique, an evaluation of this method is to be made and whether it’s realistic and gives reasonable values. The method is well known and used in ordinary internal combustion engines.
2.4 Procedure and Limitations
Theoretical study concerning different surfaces ability to build up of oil film thickness has been made to give the thesis a theoretical foundation, though little was to be found, hence that the subject of different surfaces impact on film thickness is still an elusive science. The evaluation of an oil film thickness measurement with capacitive transducers has been made both based on a theoretical study and a bench test in the sliding movement test rig.
Limitations concerning the test have been in form of optimal placement for the transducer in the cylinder bore. The transducers were mounted in the cylinder while honed and thus were honed simultaneously as the cylinder bore. But some transducers were damaged and had to be dismounted. When remounted again, they had to be placed with an offset from the cylinder bore to make sure no contact with the piston ring and transducer could take place. Only one cylinder was tested and thus, no conclusions according to the influence of surface roughness could be made.
3 Theory
3.1 Introduction
The definition of tribology is summarized as the modern science of friction, wear and lubrication. These topics have a common denominator which is the knowledge about different surfaces in relative motion against each other [10]. The case of the piston ring cylinder bore contact would be this kind of contact, and the science to rely on, would be, tribology.
3.1.1 Friction
The friction represents the loss of energy in a contact between two surfaces in relative motion to each other, generates traction and heat, and is commonly used to convert kinetic energy into heat energy. The frictional coefficient is the tangential force of a surface against another divided by the normal force against each other. The lower coefficient of friction the less energy is lost, or in other words, the more slippery it is.
Average value for the coefficient between piston ring and cylinder bore contact are assumed to be 0.01 – 0.1 in between.
3.1.2 Wear
The definition of wear could be summarized as the loss of material from a surface to another surface, note that the loss of material not necessary have to disappear from the system itself, but from its original position on the surface [10]. The wear is decided by the surface characteristics which varies great from the base material. Heating and plastic deformation, changes the tribological characteristics of the surface, in such a large aspect, that friction, changes with it. With friction increasing and the heat with it, the changes of condition may increase the wear even more.
There are different types of wear for sliding contacts. Adhesive wear occurs when the lost material attach on the surfaces, abrasive when the harder surface removes material from the softer one and oxidation when the thickness of wear is in within the thickness of the oxide layer.
3.1.3 Lubrication
Lubrication is the commonly known method to lower the friction, it can be stated that all lubrication methods is to place a friction reducing material between the surfaces in a tribological contact [10]. This material could be solid, fluid or gas. The focus from now on will be on fluid lubrication in the form of oil, which is the case in the hydraulic motor.
Lubrication can lower the friction with two distinct different ways of mechanisms. These two principles of lubrication and a transition between them constitute together the three regimes of lubrication [10], boundary, mixed and full film lubrication.
These different regimes have a significant impact on wear and friction. In boundary lubrication the load is mostly carried by the asperities and the lubricant in between could not separate the two surfaces. When the bigger part of the load is carried by the oil film, but some contact between asperities is present, the regime is called mixed lubrication.
The last regime, full film, is as it refers to, a fully developed lubricant film in between the surfaces. Hence the oil carries the entire load by itself. In the full film regime there are virtually no wear, but as figure 3 shows, the friction coefficient is higher then in the middle of the mixed lubrication regime. This is related to the fact that the shear strength of the oil that separates the surfaces start to take effect. Hence that in full film lubrication, the shear strength of the oil, produces a frictional force.
Figure 3. The Stribeck curve, here with the ranges of the three regimes.
The generalized Stribeck curve (see figure 3) show us the coefficient of friction, as a function of the dimensionless film parameterΛ . Note that the values on x-axis are
generalized. The operational regime for the radial piston hydraulic motor from Hägglunds is bound to the boundary lubrication during the whole stroke, at all speeds [10].
3.1.4 Boundary Lubrication
There are a number of parameters affecting lubrication in general, and the most important of those are as follows: viscosity, contact pressure due to impact, shear strength of the oil, texture of the metal surfaces and normal sliding velocity [14]. Within the boundary lubrication regime though, the bulk properties of the fluid, such as its viscosity, are of less importance, while its chemical composition, as well as that of the underlying surfaces, become increasingly more significant [4]. It can therefore be stated that for the
radial piston hydraulic motor, the importance of surface roughness as well as the composition of the lubricant is very high.
The research on different surface behaviour on film thickness in boundary lubrication is still far from giving quantitative results, and the only reliable information is, that regardless of sliding speed, the specific film thickness at initial boundary lubrication decreases when the surface roughness increases [15]. This however is not the case in full film regime, where surface roughness increases the pressure in the oil film, thus increases the film thickness. These two regimes should not be mix up with each other. The surfaces in the boundary lubricated regime should have flat asperities where the additives in the oil can collect themselves on to protect the surface, between these flat surfaces there should be reservoirs for the lubricant, and from there it could supply the flat asperities with additives.
3.1.5 Surface roughness
The profile of surface topography represents the combined effects of waviness and roughness, superimposed on the geometric shape of the surface. Studies of surface topography have shown that no single numerical parameter could adequately describe the surface geometry. The first two and most widely used are the Ra value of centre-line average and Rq value of root mean square (RMS). They are defined as follows [4], where z being, the deviation from the profiles mean value.
∫
=
L
a zdx
R L
0
1 (1)
∫
= L
q z dx
R L
0
1 2
(2)
The Ra value, which is the most used international roughness parameter, is however, not sufficient to describe the influence of surface roughness on lubrication. Parameters that according to J. Lundberg [14] seem to affect lubrication in a more significant way are, Rmax, that describes the largest peak-to-valley height in five adjoining sampling lengths, and Rt which is the peak to valley height that describes the separation of highest peak and lowest valley. All of these parameters are a measurement of different heights of the asperities.
The Rq value of the Hägglunds radial piston hydraulic motor can be found in the nomenclature in Appendix A, and an oil film thickness at that same magnitude is to be expected.
3.1.6 Surface texture
The behavior of friction and wear in boundary lubricated sliding surfaces is influenced by the surface texture. By introducing controlled depression and undulations in an otherwise flat surface, the tribological properties can be improved. Lubricant can then be supplied even inside the contact by small reservoirs, resulting in a reduced friction. However under other conditions, the texture may impair the contact situation in a negative way [8].
It is hard to control a textured surface, when it starts to change due to wear, and when other properties of the surface reach a certain level, the wear and friction properties could be much worse than in an un-textured surface.
3.2 Modeling of oil film thickness
In order to get some idea of what to expect from the measurements, a model of the oil film thickness was made. The main equation for oil film thickness was based upon the Pan and Hamrock equation for a line contact [2]. This is a commonly used equation, and should be sufficient in this case. Note that the Pan and Hamrock equation describes the minimum film thickness at the outlet constriction for perfectly smooth surfaces [2]. This is not the case in the real hydraulic motor, thus less oil film thickness is expected in the bench test. Several correction parameters could later be added to get a more accurate model, but in this thesis we will only use one, the thermal correction factor. No effects of the surface roughness were taken into account, since very few, or none of the equations found were generally applicable. There are a number of correction factors that tries to describe the influence of surface roughness on film thickness. However, more research on the subject is needed to give a fair estimation of the influence of surface roughness.
This model can, despite its rough approximation tell us what to expect, and in what kind of regime the hydraulic motor operate in. All data and parameters for calculating the film thickness can be found in the nomenclature in Appendix A.
3.2.1 Pan and Hamrock
The contact geometry in this case, is the line contact geometry, which occurs when the radius of curvature in one direction approaches infinity for both surfaces, which is the case for piston ring, cylinder bore contact.
128 . 0 1 568 . 0 694 . 0
min =1.714RU G W−
h x (3)
Here hminbeing the minimum oil film thickness. Rx =Rx1 = Radius of curvature in direction of motion (see figure 4). Rx2 =∞, hence the radius for the cylinder in this direction can be considered infinite.
Figure 4. Piston ring profile showing Rx1.
3.2.2 Thermal correction
The viscous heating of the lubricant will cause lower viscosity at the inlet of the contact and the film thickness will decrease [3]. The equation of oil film thickness will thus look like this:
min
min, C h
h T = T (4)
The thermal correction factor beingCT is calculated from the following formula [3].
(
0.83)
0.6442 . 0
23 . 2 1 213 . 0 1
2 ' . 13 1
L A E L p C
h
T + +
= − (5)
Equation (3) and (5) into (4) gives the oil film thickness in figure 5.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Piston speed [m/s]
Oil film thickness [µm]
Model of oil film thickness
Figure 5. Calculated oil film thickness, based on the Pan and Hamrock equation and thermal correction factor included. Calculated with data presented in Appendix A.
The normal way to determine the lubrication regime is to calculate the magnitude of the film parameter [10].
Sq
hmin
=
Λ (6)
S = the composite surface roughness: q
2 2 2
1 q
q
q R R
S = + (7)
The operational regime for the Hägglunds hydraulic motor based on the previously calculated oil film thickness model is mainly in the boundary lubrication regime but covers a little in mixed lubrication as well, see figure 6. But, being calculated with no consideration taken to the surface roughness, the radial piston hydraulic motor is probably more bound to the boundary lubrication than this model tends show. Note that this result is for piston speeds up to 0.6 m/s.
Figure 7. The Hägglunds hydraulic motor operational range, shown in the Stribeck curve for piston speeds up to 0.6m/s, based on the previously calculated oil film thickness
presented in figure 5.
4 Film thickness measurement
4.1 Methods
There are different methods to measure the oil film thickness between piston ring and cylinder bore. The methods can be divided into electrically, optically and acoustic based methods. Among the electrically based methods there is the, measuring of resistance, inductance or capacitance. Optical based methods include visualization, and laser induced fluorescence (LIF) [7]. Ultrasonic measurement being the only acoustic based method was actually evaluated by U. Skytte af Sätra [11] on the same application as tested in this thesis, the piston-ring cylinder bore contact in a radial hydraulic motor from Hägglunds.
The result of that measurement was, in the terms of oil film thickness, a variation between 0.7 and 1.3 µm at piston speeds from 0.0006 – 0.0012 m/s. The measured oil film thickness did however, not show any dependence on neither speed nor pressure.
In this thesis we will be using an electrically based method with capacitive transducers, a more thorough description on that particular method below.
4.2 Capacitive technique
4.2.1 IntroductionCapacitance measurement was investigated in a diesel engine by Moore and Hamilton (1978) [5], furthermore by N. Grice et.al. (1992) [6] and was found to have good spatial resolution and demanded minimal engine modification. Investigation by Sherrington and Söchting [7] later indicated that a frequency modulated calibration has to be developed to overcome the problem with high piston speeds; hence the system is to slow to be able to measure the piston ring profile. The problem with high speed piston is not the case in the radial hydraulic motor however, where maximum speed of the piston is 6 m/s (in the test rig it is 0.6 m/s) compared to a normal Otto engine with piston speeds up to 25 m/s. The frequency modulated system will not be utilized here where we will rely on the so called amplitude modulated system. The amplitude modulated system is accurate for speeds up to 12 m/s at a ring width of 2mm and we will be far below those criteria. Furthermore, the method was found to be valid over the range of 0.5 µm to 20 µm according to N. Grice et.al. [6].
4.2.2 Working principle
To understand how the measurement with a capacitance transducer is done, the fundamentals of the capacitor are necessary. A capacitor consists of two electrodes or plates, each of which stores an opposite charge. These two plates are conductive and are separated by an insulator or dielectric. The charge is stored at the surface of the plates, at the boundary with the dielectric. Because each plate stores an equal but opposite charge,
the total charge in the capacitor is always zero. The capacitor’s capacitance is a measure of the amount of charge stored on each plate for a given potential difference in voltage, which appears between the plates. If an AC voltage signal is applied to the capacitor a charge is created on the plates, which could be expressed in capacitance. There are three basic factors that affect the capacitance of the capacitor, the plate area, spacing and dielectric material between the plates, also referred to as the relative permittivity. In figure 7, the effect of these three different parameters are illustrated.
Figure 7. The capacitors dependence on different parameters.
A = Plate area: All other factors being equal, greater plate area gives greater capacitance, larger plate area results in more field flux (charge collected on the plates)
B = Plate spacing: All other factors being equal, less distance between the plates gives more capacitance, closer spacing results in greater field force (voltage across the plates), which results in greater field flux (charge collected on the plates)
C = Dielectric material: All other factors being equal, greater permittivity of the dielectric material gives more capacitance. εr = 1 in air, εr = 2.25 in oil
The capacitance of a parallel-plate capacitor is given by:
d CT =εoεrA
(8)
CT = transducer capacitance (between piston ring and transducer, varies) [F]
εo= absolute permittivity (constant) [-]
εr= relative permittivity, dielectric constant (1 in air and 2.25 in oil) [-]
A = cross section area of plate [m2]
d = distance between plates (in this case the oil film thickness) [m]
Amplifier output signal is defined in equation (10) [6].
T osc osc
out C
C
V =−V (9)
Vout=output voltage [V]
Vosc=oscillator input rms volts [V]
Cosc=oscillator capacitance [F]
Equation (8) and (9) together gives:
A d C V V
r o
osc osc
out =− ε ε (10)
Vosc, Cosc, εo,εr and A are all constants, thus:
K
d =Vout (11)
If K is defined as:
A C K V
r o
osc osc
ε
− ε
= (12)
4.2.3 Transducer
The transducers consist of, an insulated inner electrode shielded by an outer screen of hypodermic tubing which, in turn, is insulated from the cylinder [6]. In other words, the transducer is very similar to a coaxial cable with the inner electrode being the probe. The choice of transducer electrode diameter is influenced by two factors. With a small
diameter it will produce a more accurate measurement of the piston-ring and reduce the risk of asperity contact. A small diameter on the other hand, gives lower capacitance as previously mentioned, which in turn, result in a low resolution for the signal. N. Grice et.al. [6] found a diameter of 0.4 mm to be appropriate for this kind of study. In the following bench test measurement, transducers with this particular diameter, constructed and manufactured at the University of Lancashire in Preston, UK, was used. The
transducer is based on a modified M4 bolt as seen in figure 8.
Figure 8. Transducer, the different layers can be observed, the probe being the small electrode in the center.
It should be mentioned that, D. O. Ducu, R.J. Donahue and J.B. Ghandhi [16] found that an optimal probe should be rectangular with a high aspect ratio, having the smaller length in the direction where high spatial resolution is required. Fully shielded circular probes are easier to construct than fully shielded rectangular, but the result with a rectangular probe, is higher spatial resolution in the direction of the ring profile.
4.2.4 Interference
The method of measuring distance with capacitive transducers is not free from problems.
There are a number of things that can interfere with the signal. First of all the interference related to electronics, and then the fact that the test is dynamic and not static makes it even worse. Furthermore there is an environmental surrounding affecting the first two parameters. One of the electrical problems is according to N. Grice et.al. [6] the effects of
stray capacitance. When the distance between the transducer and the piston ring becomes too large, the system output becomes less linear. The stray capacitance effects upon output can be seen in figure 9 where CS indicates stray capacitance and CT indicate transducer capacitance. This stray will indicate a thicker oil film thickness than actually measured, if measurement is affected by it that is.
Figure 9. Effect of stray capacitance (CS) upon output.
Another who mentions stray capacitance is J.P Holman [9] who mention errors like stray capacitance among humidity variations and noise being a probable factor of errors in measurement.
It’s a fact that start and stop produce particles in sliding contacts; these can affect the dielectric constant or work as a conductor on the transducer. The humidity in the test cell is also a factor that affects the dielectric constant, increasing the amount of water
enclosed in the oil. In the oil film between the piston ring and cylinder bore, cavitations can appear on the output side of piston ring oil flow through this can affect the
measurement in many different ways by the creation of air bubbles.
The value on the dielectric constant is approximate and is probably not entirely correct.
For oil with the same characteristics as the oil used in this test, the relative permittivity (dielectric constant) is approximately 2.25. And as mentioned above, it has the
characteristic to change in different environment.
4.3 Experimental equipment
4.3.1 The Sliding Movement Test Rig
The sliding movement test-rig (see figure 10) was intentionally developed to simulate wear in the contact between the piston ring and cylinder bore [1]. Its original two cylinder set was rearranged to that of just one during the test in this thesis. The reciprocating motion is produced by an external electrical motor throughout a transmission, into a crankshaft and finally via a connection rod to the piston.
Figure 10. The sliding movement test rig.
The motion generated by the test rig differs slightly from that of the original hydraulic motor, but in this test we are only looking at the maximum speed that occurs in the mid of the stroke. The speed as maximum in the mid stroke is the same in the test-rig as in the actual motor [1].
4.3.2 Cylinder and Piston assembly
The actual cylinder bore section was machined from an original cylinder block. The piston was machined from a piston blank but is slightly different to that of the original motor. The piston has a piston ring on each side of the center which represents the top of an original piston. Same result would be achieved if two pistons were mounted on top of each other with the piston top facing each other, here, the piston top could be said to be extended to give room for the stroke (see figure 11).
Figure 11. Cylinder and Piston assembly.
A full cycle of the original hydraulic motor contains of two strokes: one stroke at
hydrostatic high pressure, and the other at hydrostatic charge pressure. The big difference between the hydraulic motor and the sliding movement test rig is that the pressure will not change during the strokes but be the same (see figure 12).
The center (in real motor the piston top) will have a constant pressure equal to the high pressure at all time during the test until another pressure is to be measured.
Figure 12. Difference in pressure during one cycle, between the hydraulic motor and the sliding movement test rig.
During a designed service life, the piston-ring will slide a certain total distance; half of this total sliding distance will be under high pressure and half under charge pressure.
4.3.3 Transducer placement in cylinder bore
In the cylinder bore, three transducers are placed radial around at 0, 90 and 180 degrees as seen in Figure 13.
Figure 13. Placement of transducers in cylinder.
The only way of mounting the transducers into the cylinder bore, were to give them an offset to the bore. If they were too close to the cylinder bore, a possibility for breakdown due to piston ring contact with transducer would be high. This is prevented by mounting them with an offset do (see figure 14). The idea is to get do as small as possible.
Figure 14. Transducers offset from cylinder bore
The radial placements of the transducers were measured with a Rank Taylor Hobson Form Talysurf Mk1 (Taylor Hobson Ltd., Leicester, England). In figures 15 and 16 below, the distance to actual probe is shown. During the first tests runs Transducer no.1 became useless due to breakdown and was aborted from the test, therefore, only T2 and T3 in figures below.
2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
−0.025
−0.02
−0.015
−0.01
−0.005 0
Offset for transducer T2
Axial direction [mm]
Radial direction [mm]
Figure 15. Offset from cylinder bore for T2 15 µm
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
−0.08
−0.07
−0.06
−0.05
−0.04
−0.03
−0.02
−0.01 0
Axial direction [mm]
Radial direction [mm]
Offset for transducer T3
Figure 16. Offset from cylinder bore for T3
Transducer T2 having an offset of do2 = 15 µm and T3 an offset of do3 = 60 µm. When having an offset of 15 µm to begin with, it’s on the edge of previously stated validation for this method of measuring oil film thickness, where stated that the method is valid over the range of 0.5µm to 20 µm [6]. With T3 mounted with an offset of 60 µm, measured values from this transducer have to be thorough examined in the tests to come.
60 µm
4.4 Calibration
The calibration of all instruments is important, for it affords the opportunity to check the instrument against a known standard and subsequently to reduce errors in accuracy. The calibration procedures involve comparison of the particular instrument with either a primary standard, a secondary standard (with a higher accuracy than the instrument to be calibrated) or a known input source [9]. In this case the transducers and the multi channel amplifier were to be calibrated against a known input source that gives accurate values of distance. The known source is a piezo electric actuator mounted on a calibration
apparatus (see figure 17) constructed by S. Söchting at the University of Lancashire in Preston, UK. The calibration apparatus has an x-y adjustable table where to mount transducer, this table has the possibility to rotate around the x-axis and y-axis to get transducer surface leveling right and aligned to the surface of the actuator. The distance to the actuator could be adjusted roughly with a knob. To come as close as possible the transducer must be leveling right to the opposing actuator. A way of achieving this is to read the voltage output from the amplifier and try to get it as low as possible without getting a short circuit. To success we go towards the actuator surface and when feeling the opposite surface through higher torque in knob we register the voltage output on a voltage meter and go back a little. Turn the x-y axis until the voltage decreases. Then back up again and se if a lower voltage is achieved. This procedure is repeated until transducer get close enough, i.e. when voltage get close to zero.
Figure 17. Calibration table and piezo electric actuator
When the transducer is aligned with the actuator, calibration begins by increasing the distance in steps of two micrometer at a time. The change in voltage is recorded for each step thus; a relationship between voltage output and actual distance are established as a straight line. The inclination of this line is the constant K in equation (11) whereas calibration completed.
To apply this calibration to the actual test, the relative permittivity (dielectric constant) has to be changed due toεr=1 in air as we have during the calibration, changes to εr =
following figure 20, the dielectric constant has been taken into account and the evaluated constant K for each transducer can now be used to establish the film thickness by
measuring the voltage output from the transducers.
For the piezo electric actuator the operational range is 45 µm, resolution of 0.9 nm to 0.45 nm and linearity of +0.026 % to -0.059% of range [7]. The uncertainty for the calibration is based on the linearity for the actuator over the range of 45 µm. The error a is calculated for the worst case scenario where each step of 2 µm is stated to have the same error as a step of 45µm. Using equation (13) below gives the uncertainty for the actuator. up+= 0.0068 µm and up-= 0.0153 µm [17].
3
u= a (13)
Uncertainty of the piezo electric actuator is not included in figure 18 below due to the fact that the error is too small to view in the graph.
0 5 10 15 20 25 30 35 40 45
0 5 10 15 20
T2
Distance [µm]
Voltage output [V]
0 10 20 30 40 50
0 5 10 15 20 25
Distance [µm]
Voltage output [V]
T3
Figure 18. Calibration of transducer T3 and T3.
The constants are as follows: K2 = 0.41 and K = 0.44 3
The transducers were calibrated simultaneously as the multi channel amplifier at the University of Lancashire in Preston, UK, under the supervision of S. Söchting and I.
Sherrington. Each transducer was calibrated to its own channel on the multi channel amplifier to minimize any possible divergence between the different channels, since the amplifier was found to be having great variations between the channels.
The calibration is probably the most important measurement made and cannot be overemphasized because it is, the calibration, which firmly establish the accuracy of the instrument [9].
4.5 Procedure of measurement
The procedure for the measurement was decided upon the pressure, for each pressure a complete measurement for 18 speeds were made. The speed was altered through a potentiometer connected to the electrical motor running the test rig. For each speed the oscilloscope were trigged three times for each direction of piston, that is, three
measurements describing the working stroke of the piston, and three measurements describing charge stroke. For each measured value, the visualized signal in the
oscilloscope could tell if the signal was influenced by interference, thus only good signals were chosen based on their appearance in the oscilloscope.
Two important test series was measured. Series A, to establish whether the test was repeatable, it contains of three tests with the same pressure, a normal high pressure of 30 MPa. Series B, to establish the influence of pressure on oil film thickness, containing six tests with different pressure, pressure decreasing from 30 MPa to 5 MPa in steps of 5 MPa.
In Appendix B measurements from series A and B are collected for the charge strokes, charge stroke should actually have the charge pressure, but here it is measured with the high pressure as previously mentioned about the SMTR.
4.5.1 Visualization
The voltage output from the multi channel amplifier was sampled by a Tektronix TDS2014 digital oscilloscope with the resolution of 0.02 V for transducer T2 and 0.1 V for transducer T3. The sampling rate in time steps was changed throughout the test due to increasing speed of piston. This was not taken into account of uncertainty.
The uncertainty for each transducer in distance is based on the voltage resolution for the oscilloscope, and by using equation (11). The resolution being 0.02 V for transducer T2 gives the uncertainty in distance uo2 = 0.028 µm and for T3 with the resolution 0.1 V to be uo3=0.13 µm, this based on equation (13), where the error a being calculated from equation (11) and represent d.
The interpretation of the signal that could be visualized in the oscilloscope, is of great interest, here it is possible to see what the transducer is measuring. When comparing the visualized signal, with the real piston assembly, the signal becomes more understandable and assumptions can be made concerning interference and instability.
Figure 19 and 20 below should be compared, so figure 21 and 22 can be understood.
Figure 19. Piston, piston ring and cylinder bore.
Figure 20. Oscilloscope visualization with descriptions.
If piston ring enhanced it will look like this (see figure 21) and is an example of a good signal that would be selected for the measurement.
Figure 21. Oscilloscope visualization with only piston ring, showing a typical good signal.
The problems concerning interference and instability were more severe with working pressures of 10 MPa and 20 MPa. Higher leakage which generates a high flow-by over the piston profile was observed during these pressures. In the figures below different kind of interference or instability was observed and these were taken from different tests at 10 MPa and 20 MPa. In figure 22, (A) shows a small interference, (B) show a severe short circuit and (C) show an offset that look like a “knee” on the piston-ring profile. (C) is somewhat of more interest than the others, hence that some times this “knee” might be out of range and will not be noticed, thus the signal would then have been accepted as a good signal, and taken into the measurement. The signals in the first two figures could not escape through without being disregarded.
Figure 22. Interference problems in signals.
5 Results
Instead of using the offset distance do, measured earlier, each test was given the value of no film thickness (hmin=0) at the first speed measured, hence that every test had a
different oil film thickness relative to each other and the cause of this is probably the dynamic changes, which changes the position of the piston ring inside the cylinder. From this point on the build up of oil film thickness could easily be shown as a function of piston speed.
5.1 Series A
Something interesting concerning the oil film thickness build up between transducer T3 compared with transducer T2 was observed in Series A. As seen in figure 23, transducer T3 tends to measure a build-up of oil film thickness at a ten times higher scale. However, if closely observed, test 3, with transducer T3, shows a lower build up, but still twice the scale as for transducer T2.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
−1 0 1 2 3 4 5 6
Piston speed [m/s]
Oil film thickness [µm]
Series A (T2 and T3)
T2 Test 1 T2 Test 2 T2 Test 3 T3 Test 1 T3 Test 2 T3 Test 3
Figure 23. Difference in oil film measured between transducer T2 and T3.
The instability and high measured build-up of oil film thickness with transducer T3 makes the measured values from that transducer somewhat uneasy to read. Therefore only T2 will be shown from now on.
Series A without T3 could be viewed in figure 24
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Piston speed [m/s]
Oil film thickness [µm]
Series A (T2)
Test 1 Test 2 Test 3
Figure 24. Series A with transducer T2 showing the oil film build up as a function of piston speed.
Figure 24 simplified to give a more readable value of the inclination for each test are shown in figure 25.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Piston speed [m/s]
Oil film thickness [µm]
Series A (T2 simplified)
Test 1 Test 2 Test 3
Figure 25. Series A with transducer T2 and each curve simplified as a straight line.
5.2 Series B
In Series B (see figure 26) the curves seems to indicate that the oil film becomes less than zero, that is not the case here though, the inclination of the curve only indicate if the oil film is decreasing or increasing as a function of piston speed. Here hmin=0 for the first velocity was applied for all the pressures.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
−1.5
−1
−0.5 0 0.5 1 1.5 2
Piston speed [m/s]
Oil film thickness [µm]
Series B (T2)
30 MPa 25 MPa 20 MPa 15 MPa 10 MPa 5 MPa
Figure 26. Oil film thickness dependence on pressure and velocity.
If we simplified each curve with a straight line the inclination of each curve is more easy too overview (see figure 27).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
−1.5
−1
−0.5 0 0.5 1 1.5
Series B (T2 simplified)
Piston speed [m/s]
Oil film thickness [µm]
30 MPa 25 MPa 20 MPa 15 MPa 10 MPa 5 MPa
Figure 27. Oil film thickness dependence on pressure and velocity simplified.
5.3 Standard deviation
The complete process of calculating the standard deviation for a series of n measurements can be expressed mathematically as:
( )
(
1)
0
2
−
=
∑
= − nx s x
n
i i
(14)
where xi is the result of the ith measurement and x is the arithmetic mean of the n results considered [17]. The oscillator being trigged three times for each speed measured gives n=3, and the standard deviation is then calculated according to equation (14). In figure 28 and figure 29 below, the standard deviation for Series A and Series B could be viewed.
The uncertainty is not present in the figures due to the fact that it would be uneasy to read, but for both figures the uncertainty is to be included when reading. The uncertainty is for upper limit u = 0.029 µm and for lower limit 2+ u = 0.032 µm. These values is 2− based on the previously calculated uncertainties for calibration and sample resolution for oscilloscope, according to equation 15 and 16
2 2 2
2 2+ = uo +up +
u (15)
2 2 2
2 2− = uo +up −
u (16)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Piston speed [m/s]
Standard deviation [µm]
Standard deviation for Series A (T2)
Test 1 Test 2 Test 3
Figure 28. Standard deviation for Series A with T2, note that uncertainty is not included.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Piston speed [m/s]
Standard deviation [µm]
Standard deviation for Series B (T2)
30 MPa 25 MPa 20 MPa 15 MPa 10 MPa 5 MPa
Figure 29. Standard deviation for Series B with T2, note that uncertainty is not included.
6 Discussion
As seen in figure 23, there is a clear difference between measured values of film thickness with transducer T2 and T3. The cause of this is probably the effects of stray capacitance upon output investigated by N. Grice et.al. [6]. Where stated that the voltage output will not be constant, but decrease from the calibrated line and thus give a higher values of oil film thickness. With transducer T3 mounted as far as 60 µm from the cylinder bore, the case can very well be so.
In figure 25, transducer T2 seems to show an increase of film thickness with increasing piston speed. The film thickness measured is in the same magnitude as the asperities, this is expected in the boundary lubrication regime. The measured values of film thickness also correspond to the mathematical model in figure 6 very well, but as previously mentioned, the mathematical model is not taking the characteristics of boundary lubrication into account. One thing is clear though, the trend of oil film thickness increasing with increasing piston speed at a pressure of 30MPa. The behaviour is the same in the charge stroke seen in figure 2 and 4 in Appendix B where the pressure 30MPa show a increasing film thickness in the same way as in the working stroke.
As in series A the pressure of 30 MPa in Series B registers a build up in film thickness.
For the other pressures in Series B though, they seems to be very unstable, especially 10 MPa and 20 MPa that have a very negative inclination as seen in figure 27 as well as in the charge stroke (see figure 4 in Appendix B). For these two pressures a high leakage in the system was observed, if that is the explanation for the negative inclination or not is not fully investigated. If higher leakage over the piston ring profile, the more unstable the film thickness would behave.
With the pressure 30MPa, the pressure presses the piston ring against the cylinder bore with such a force it’s hard for the oil to pass through between piston ring and cylinder bore, thus stability in oil film thickness might be the result. For the other pressures the problem is more of a compromise. Having low pressure, the oil has no force to push through between the piston ring and cylinder bore, but, the piston ring does not seal of as good as in the higher pressure either, and a result of that might be a more moveable piston ring or uncontrolled leakage, both will lead to unstable oil film thickness.
The standard deviation is very high for all the tests and in the same magnitude as the film thickness itself. The explanation to this phenomenon is probably as mentioned, the dynamic changes of piston ring placement inside the cylinder. If piston ring is moving around the measured values can change more than the oil film thickness itself. The standard deviation does not however, seems to be affected by the piston speed. But the fact that the test is very unstable and sensitive to any changes is clear.
If a measurement on the relationship between the piston ring the piston could be made for each measured value of film thickness, the deviation would probably decrease, hence that the placement of the piston ring on the piston varies.
7 Conclusions
• The capacitance based measurement system register a build up of oil film thickness of 0.5 µm at 30 MPa with transducer T2 mounted 15µm from cylinder bore.
• The measured values in Series A show a clear trend towards increasing film thickness with increasing speed.
• The effects of stray capacitance are observed on transducer T3 mounted 60µm from cylinder bore, this agrees with results by N. Grice et.al [6].
• Instability in oil film build up is observed for different pressures. Pressure 20 MPa and 10 MPa was the most unstable pressures, at the same time as a high leakage was observed for these pressures.
• The instability in the test being generally very high, the standard deviation being at the same magnitude as the film thickness itself, results in measured data with high scatter.
• The similarity between the measured and calculated oil film thickness at 30 MPa is very high.
• A measurement on the relation between the piston ring and cylinder bore has to be made for each measured value of film thickness to make the standard deviation decrease.
References
[1] U. Skytte af Sätra, Wear of piston rings in hydrostatic transmission, Doctoral Thesis in Machine Design, The Royal Institute of Technology, Departement of Machine Design, Stockholm Sweden 2005, Trita-MMK-2005:18
[2] P. Pan, B.J. Hamrock, Simple formulas for performance parameters used in elastohydrodynamically lubricated line contacts, Journal of Tribology, Transaction of the ASME, v111 no. 2 (1989) pp. 246-251
[3] R. Larsson, E. Kassfeldt, A. Byheden, T. Norrby, Base Fluid Parameters for EHL and Friction Calculations and Their Influence on Lubrication Capacity, Journal of Synthetic Lubrication, v18, n 3, October, 2001,p 183-198
[4] J.A. Williams, Engineering Tribology, Oxford Science Publications, 1994, Oxford University Press ISBN 0-19-856343-4.
[5] S.L. Moore and G.M. Hamilton, The starved lubrication of piston-rings in a diesel engine, J. Mech. Eng. Sci. 20(6) (Dec., 1978)
[6] N. Grice, I. Sherrington, E.H. Smith S.G. O’ Donnel, J.F. Stringfellow, A Capcitance based system for High Resolution Measurement of Lubricant Film Thickness, Proc. of “Nordtrib ’90. 4th Nordic Symposium on Tribology, Lubrication, Friction and Wear. Hirtshals, Denmark. 10 – 13 June 1990.
[7] I. Sherrington, S. Söchting, Evaluating the Lubrication of Piston Rings in internal combustion engines, Jost Institute for Tribotechnology, Department of
Technology, University of Central Lancashire, Preston PR1 2HE, UK.
[8] U. Pettersson, S. Jacobson, Influence of surface texture on boundary lubricated sliding contacts, Tribology International 36 (2003) 857-864
[9] J.P Holman, Experimental Methods for Engineers, Seventh Edition, McGraw-Hill International Edition, Mechanical Engineering Science, ISBN 0-07-118165-2 [10] S. Jacobson, S. Hogmark, Tribologi, friktion, smörjning och nötning, Liber
Utbildning AB, Första Utgåvan, Berlings, Arlöv 1996, ISBN 91-634-1532-1 [11] P. Harper, R.S. Dwyer Joyce, U. Sjödin, U. Olofsson, Evaluating of an ultrasonic
method for measurement of oil film thickness in a hydraulic motor piston ring.
Proceedings of the 31st Leeds-Lyon Symposium on Tribology, Leeds, 7-10 September 2004.
[12] I. Sherrington, N. Grice, E.H. Smith, Modeling the operation of piston rings in internal combustion engines, Proc. of “Nordtrib ’90. 4th Nordic Symposium on Tribology, Lubrication, Friction and Wear. Hirtshals, Denmark. 10 – 13 June 1990.
[13] U. Skytte af Sätra, Characteristics of piston ring operation in a radial piston hydrostatic transmission Technical report, Trita-MMK 2005:14, Department of Machine Design, School of Industrial Engineering and Management, KTH, Stockholm, 2005
[14] J. Lundberg, Influence of surface roughness on normal-sliding lubrication, Tribology International Vol. 28. No. 5. pp. 317-322. 1995
[15] J.H. Horng, Studies of tribological behavior and separation between surfaces at initial boundary lubrication, Wear 216 (1998) 8-14
[16] D.O. Ducu, R.J. Donahue, J.B. Ghandhi, Design of Capacitance Probes for Oil
Combustion Engines, Journal of Engineering for Gas Turbines and Power, July 2001, Vol 123, pp 633-643
[17] S. Bell, A Beginner’s Guide to Uncertainty of Measurement, Centre for Basic, Thermal and Length Metrology, National Physical Laboratory, Measurement Good Practice Guide No. 11 (Issue 2) March 2001.
Appendix A
NOMENCLATURE (index 1 refers to piston ring and index 2 to cylinder bore)
u 1 Piston speed (variable), [m/s]
u 2 Cylinder bore speed = 0 [m/s]
1
R q RMS surface roughness for piston ring = 0.39 * 10-6 [m]
2
R q RMS surface roughness for cylinder bore = 0.21 * 10-6 [m]
E 1 Elastic modules for piston ring = 206 * 109 [N/m2] E 2 Elastic modules for cylinder bore = 175 * 109 [N/m2] ν1 Poisson’s ratio for the piston-ring = 0.3
ν2 Poisson’s ratio for the cylinder bore = 0.3
η0 Viscosity at operating temperature = ηρ [Ns/m2] η Kinematic viscosity = 4.3 * 10-5 [m2/s]
α Pressure viscosity coefficient at operating temperature and atmospheric pressure = 2 * 10-8 [m2/N]
'
w Contact load, 1D-geometry = 3145 [N/m]
ρ Density for the oil = 880 [kg/m3]
K Thermal conductivity of lubricant = 0.12 [W/m/oC]
U Dimensionless speed parameter, U = Rx
E u ' η0
G Dimensionless material parameter, G = αE'
W1 Dimensionless load parameter 1d-geometry (line contact), W1 = Rx
E w '
'
Ph Maximum Hertzian pressure (1-d geometry), Ph = Rx
E w
π 2
'
' [N/m2]
'
E Effective elastic modulus, E = '
1
2 2 2 1
2
1 1
2 1
−
⎟⎟⎠
⎜⎜ ⎞
⎝
⎛ − + −
E E
ν
ν [N/m2]
L Thermal parameter, L = K
u2 βη0
A
2 1
1
2 2
u u
u u
+
−
T temperature [oC]
β Temperature-viscosity coefficient = 0.035 [-]
Rx1 Radius of curvature = 37.5 * 10-3 [m]
Appendix B
Both Series A and Series B at charge stroke with transducer T2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
−0.4
−0.2 0 0.2 0.4 0.6 0.8 1
Piston speed [m/s]
Oil film thickness [µm]
Series A (T2 chargestroke)
Test 1 Test 2 Test 3
Figure 1. Series A at chargestroke.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Piston speed [m/s]
Oil film thickness [µm]]
Series A
(T2 chargestroke simplified)
Test 1 Test 2 Test 3
Figure 2. Series A at chargestroke simplified.
