Prediction of life durability in friction for wet clutches of DCT gearboxes

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Prediction of life durability in friction for wet clutches of DCT gearboxes

Lars-Johan Sandström

Mechanical Engineering, master's level 2020

Luleå University of Technology

Department of Engineering Sciences and Mathematics

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Preface

This master thesis is written on the Division of Machine Elements at Lule˚a University of Technology in cooperation with Total. I would like to thank my supervisors Anders Petterson, Kim Berglund and Pär Marklund at Lule˚a Uni- versity of Technology and also Clément Larrière at Total for keeping the project running even when I encountered difficulties.

I would also like to thank Martin Lund and Jan Granstr¨om for taking the time to go through and show how the test rig used in this project was meant to work and sharing valuable information about the test rig.

Lars-Johan Sandstr¨om June 2019, Lule˚a

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Abstract

Many new cars are equipped with automatic transmissions. These gearboxes often have a dual clutch transmission (DCT) that has a built-in wet clutch.

The lubricants used in these gearboxes is often very advanced because it must take care of two systems, the wet clutch and the gears. There is always a strive to make the drain intervals longer. To do this a fundamental understanding of the aging mechanisms inside a DCT must be understood.

This project focuses at the aging of the lubricant and friction material inside the wet clutch. A test rig at Lule˚a University of Technology is redesigned to be able to age this kind of systems. The test rig contains a wet clutch from Volvo Construction Equipment and the redesign focuses mainly on decreasing the oil sump volume to 6 liter and getting the oil sump to be at 100 ^◦C during the tests.

To verify the test rig a test is done that are trying to mimic a test done on a test rig called ZF GK3. The same lubricant, friction material and grove pattern are used as in the test with the ZF GK3. Due to the difference in how the test rigs are built all parameters cannot be held the same during the test. At first the same sliding speed at the mean radius, the average power over an engagement and the oil sump temperature is kept the same. A drop in the static friction can then be seen over time. This was however not the expected behavior. The sliding speed is therefore increased which also increases the average power and transferred energy per engagement. This has also big effects on the temperature inside the clutch. A drop in the coefficient of friction can then be seen at 50 % of the sliding speed which also is seen on the test carried out on the ZF GK3.

This verifies that the test rig can be used for aging of these kind of systems.

The aging that takes place seems to be dependent on the temperature inside the clutch.

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Nomenclature

µ Friction coefficient [-]

ω Rotational speed [rad/s]

Af Friction disc area [m²] Ap Piston area [m²] E Energy [J]

Fs Spring force [N]

Fax Axial force [N]

I Mass moment of inertia [kgm²] k Spring constant [N/m]

N Number of friction interfaces [-]

p Contact pressure [Pa]

p_p Pressure on piston [Pa]

r Radius friction force is acting on [m]

Ri Inner radius of friction disc [m]

Ro Outer radius of friction disc [m]

T Torque [Nm]

v Sliding speed [m/s]

x Displacement [m]

HO• Hydroxy radical R• Alkyl radical RH Hydrocarbon chain RO• Alkyloxy radical ROO• Alkyl peroxy radical ROOH Hydroperoxid O2 Oxygen

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Abbreviations

ATF Automatic Transmission Fluid.

AW Anti wear.

DCT Dual Clutch Transmission.

FM Friction modifiers.

PDK Porsche Doppelkupplungsgetriebe.

VI Viscosity index improvers.

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1 Introduction

In order to reduce the emissions of CO₂, less use of fossil fuels must take place.

The transportation sector is the biggest contributor of these CO₂ emissions [1]. As a result, high demands are therefore placed on manufacturers in the transportation industry to reduce these emissions. The demand for automatic transmissions in cars is also increasing. Many new cars have Dual Clutch Trans- mission (DCT) gearboxes. Compared to an “ordinary” automatic transmission with torque converter and planetary gears the DCT has better efficiency. The implementation of DCTs in cars that runs on fossil fuels is therefore one step in the right direction to reduce the CO2emissions. A DCT can be described as two manual gearboxes, one for even gears and one for odd gears with their re- spective clutch contained in one housing that are controlled automatically [2]. It can therefore always prepare the next gear on the gearbox that are not engaged.

The gear change is then made by engaging the other gearbox while disengaging the first one and therefore the DCT offers fast gear change and good driving characteristics. A principle sketch can be seen in Figure 1.

Input

Dual clutch

Hollow shaft

Output

1 3

5

2 4 6

Figure 1: Principal sketch of a DCT. Red indicates the transmission with odd gears and green with even gears. The dual clutch determines which of the transmission that should be connected to the in going shaft.

Wet clutches are often used in DCT. The clutch and gears are then working in the same lubricated environment. The lubricant has therefore two systems that

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it should serve. This also makes the formulation of the lubricant quite complex.

It is always desired to keep down the drain intervals, the best thing would be to have a “fill-for-life” lubricant that would stop the drain intervals completely.

To do this you have to get a fundamental understanding of the aging of the lubricant and the degradation mechanisms of the friction inside the wet clutch.

1.1 Background of DCTs

Adolphe K´egresse was a French military engineer active in the early 1900’s.

Most people know him for inventing the halftrack. In 1935 he invented the dual clutch transmission and in 1939 he patented his work and the first prototype was tested in a Citroen Traction Avant this year. At the same time automatic transmissions with torque converter were increasing in popularity and was also cheaper than a dual clutch transmission would have been and therefore the concept lay buried for many years [3, 4].

Porsche is one of the first to pick up the concept with the dual clutch transmission again. In the 1980’s Porsche launches the models 956 and 962 with what they call Porsche Doppelkupplungsgetriebe (PDK) which is a DCT. It is a huge success and the Porsche 962 is one of Porsches most successful sportscars of all time [4, 5].

Audi was next to adapt to the DCT but now in another race context. In November 1985 at the Semperit Rally Austria they launched the Audi Quattro S1 with a DCT. Actually, they didn’t build their own, instead they used the Porsche’s PDK. The concept seemed successful and the driver Walter R¨ohrl won 19 minutes ahead of the next competitor [4].

In 2003 Volkswagen released the Golf R32 which was the first production car with a DCT [4]. Porsche introduced the PDK in the Carrera in 2008 and the year after it was also offered in Cayman and Boxster [5]. Since then the DCT has increased in popularity and are offered by many manufacturers, not just in high performance cars. The popularity comes from its fast shift times and better efficiency than an ordinary automatic transmission with torque converter.

1.2 Clutches in DCTs

Wet and dry disc clutches are used in DCTs. The torque is transferred from the input to the output shaft by bringing annular discs in contact under the action of normal force. The friction force between the plates are then transferring the torque. Disc clutches can take a variation in speed between the input and output shaft which often is one of the reasons why they are chosen [6].

Compared to the dry clutch the wet clutch works in a lubricated environment.

The lubricant makes the friction lower in the friction interface compared to the dry clutch. The wet clutches ability to transfer high torques comes from that a multiple set of friction discs are stacked, separated by separator discs forming

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a clutch pack. The clutch pack gives rise to more friction interfaces and higher torque can be transferred [6].

The dry clutch is mainly for low torque applications, up to around 250 Nm. But it has a better efficiency due to no viscous losses [2, 6]. The wet clutch has the advantage that it can be designed for both low and high torque transfer. The lubricant works as a coolant and it can also withstand long engagement times.

It can also be built relatively compact in diameter due to the clutch pack design.

1.3 Purpose

The purpose of this project is to develop a method for evaluating the aging of a wet clutch for the working conditions contained in a DCT.

1.4 Aim

This project is divided in to two parts. The first part is aiming on redesigning the lubrication system on a test rig for wet clutches in Tribolab at Lule˚a University of Technology. The redesign is mainly focusing on getting the test rig to work with a smaller oil volume and which hopefully will speed up the aging process.

In the second part the test rig will be verified. Tests will be performed with lubricants and friction material that is used in DCTs. The results will then tell if the test rig can be used to age this kind of systems.

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2 Wet clutch theory

The main function for a clutch is to transfer torque and rotational speed when desired. A wet clutch consists mainly of friction discs and separator discs and works in a lubricated environment. The friction discs and separator discs are stacked together alternately and can move in the axial direction. Together they build a clutch pack. The friction and separator discs are connected to different shafts. For example, the in going shaft can be connected to the friction discs and the outgoing shaft are connected to the separator discs. This is done by making the friction discs inner splined and the separator discs outer splined or vice versa.

The main difference between a disc clutch and other clutches is that it can take a variation in speed between the ingoing and outgoing shaft under the engagement. When the annular discs are put under the action of normal force the friction force between the discs are transferring the torque from the ingoing to the outgoing shaft. Because of the lubricated environment the friction coefficient in a wet clutch is lower than the corresponding dry disc clutch. The clutch pack design makes it possible to stack multiple discs after each other which gives more friction interfaces and is therefore able to transfer more torque. A conventional dry disc clutch is not based on the clutch pack design. The lubricated environment also provides good cooling and therefore the wet clutch can manage longer engagement times than the dry clutch. Figure 2 shows the clutch pack design and how it looks when it is engaged/disengaged [6, 7].

Input shaft Output shaft

Separator plates Friction discs

(a) Disengaged.

F

(b) Engaged.

Figure 2: Wet clutch engagement

When designing a clutch, the transferred torque is the key parameter. The transferred torque is depending on the pressure that comes from the actuating force shown in Figure 2b, the coefficient of friction, the distance from the shaft that an element of pressure is acting on and the number of friction interfaces.

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Assuming the pressure is equally distributed over all friction surfaces the torque can then be calculated as

T = N Z R_o

Ri

Z 2π 0

µpr²dθdr (1)

where N is the number of friction interfaces, Ri and Roare the inner and outer radius of the friction disc, µ is the coefficient of friction, p is the engagement pressure between the friction lining and the separator disc and r the radius the friction force is acting on [6–8]. When solving the integrals in Equation 1 it can be written like

T = 2

3N πµp(Ro3

− Ri3

) (2)

The pressure can be written as a function of the axial load, Fax and the pres- surized area on the friction disc, Af.

p = Fax

Af

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where the area is

Af = Z R_o

R_i

Z 2π 0

r dθdr = π(Ro2

− Ri2

) (4)

When putting Equation 3 and 4 in 2 the torque can be written as

T =2

3N F_axµR_o³− R_i³

Ro2− Ri2 (5)

and the coefficient of friction as

µ = 3 2

T N Fax

Ro2

− Ri2

R_o³− Ri3 (6)

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2.1 Energy and power in rotating systems

The energy in a rotating system can be defined as

E =1

2Iω² (7)

where I is the mass moment of inertia and ω the rotational speed. The power can then be defined in two ways

P = E

t = T ω (8)

where t is the time on which the energy is consumed and T the torque.

2.2 Friction discs

The friction discs usually consist of a core disc made of hardened carbon steel with friction lining on both sides. There are also friction discs that only has friction lining on one side of the core plate. The other side then works as the separator disc and all the discs are alternated inner and outer splined as usual.

However the difference in heat conductivity between the core disc and friction lining may lead to coning why two sided friction discs are preferred in wet clutch applications [7, 9].

When studying a wet clutch system, the frictional behavior with the lubricant is of great interest and how it varies with sliding speed. A wet clutch usually works with an engagement pressures between 0.1 to 10 MPa and it is only small contact units that are generating the friction in the interface. The friction lining inhibits fluid film and wet clutches are therefore often said to work in the boundary lubrication regime [9–11]. Some functional demands when designing the friction lining is [12]:

Heat and wear resistant

Resistant to mechanical fatigue

Stable friction coefficient over time

Stable µ − v curve

Low drag torque

The separator discs are also made of hardened carbon steel but with no friction lining on. Surface roughness on the separator discs also plays a role in how the durability and wear characteristics will come out [6].

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2.2.1 Friction lining

There are mainly two types of friction lining, paper based and sintered bronze.

Paper based friction lining is very common in DCT transmissions and therefore also in the automotive industry, one reason is their relatively low cost [9].

Paper based friction lining is porous and made of cellulose fibers, synthetic fibers and fillers bounded together with resin. With an adhesive the friction lining can be attached to the steel plates. Either the lining is pressed and cured with a cast with the chosen grove pattern or the paper is cured and the grove pattern are pressed or grinded of afterwards. The durability of the friction lining is very important because in many cases the friction discs are never changed and therefore it determines the life of the machine. By adjusting the content and ratio of each, the durability and friction properties can be set for the desired needs. The resin coated fibers have a diameter of 10 to 50 micrometers and creates a very ruff surface that is a little protrude from the rest of the friction surface. The contact is therefore made of several small contact units that is about 10-20 micrometer. In the end it is about 1-5 % of the total friction lining area that stand for the real contact [6, 10, 12].

The trend is also smaller clutches that should be able to transfer higher torques which leads to high temperatures in the friction interface. Manufactures is therefore adding heat resistant and other functional constituents. By adding synthetic fibers, the heat resistance and fatigue strength is increased. Carbon fibers is for example a good option, but the downside is on the other hand the price. Graphite is also helping to stand against the heat by its lubricity and can prevent thermal breakdown. Fibrous constituents have also been used to prevent compression fatigue. The drawback is that it makes the friction lining denser and less porous. In some Automatic Transmission Fluids (ATFs) there is additives that attacks the cellulose fibers and there mechanical strength is damaged [6, 12].

Sintered-bronze discs are made of a steel core that are covered in bronze powder but also different fillers. They are then sintered in a furnace and after that the grove patterns are pressed into the friction lining. Sintered-bronze discs are often used when high thermal load is expected, for example limited slip differentials where it is continuous sliding over long time periods [6].

Thermal conductivity differs between the two types of friction lining. Paper based friction lining has low thermal conductivity and therefore much of the generated heat will stay int the separator discs. This is not the case for sintered- bronze which has good thermal conductivity. The heat will then be able to go from the separator discs to the friction discs [9].

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2.2.2 Permeability

The permeability of the friction discs is a variable of interest. It says how porous the friction lining is which says how easy lubricant can flow inside the material.

It is the porosity and the grove pattern on the friction lining that helps the lubricant to escape during the engagement and makes short engagement times possible. When the clutch is engaged the lubricant is squeezed into the friction lining, it can be seen as a reservoir. The permeability therefore plays a big role under oil starved conditions. A high porosity is also an suitable way to prevent thermal problems, caution is however necessary because the material also can lose structural strength and resistance to wear when much energy is putted into the engagements. The friction coefficient in the boundary lubrication regime can also be influenced by the porosity of the friction lining. Because the permeability is of great importance in a wet clutch it is also often putted directly into clutch simulations [6, 9, 10, 12].

2.2.3 Grove pattern

There are a wide range of different grove patterns and there is no standardized pattern. As mentioned earlier the groove pattern enables faster engagements because the lubricant can escape easier. The groves also let the lubricant flow through the friction discs when engaged and can fill up the porous friction lining with more lubricant. When there are no groves all the lubricant must flow through the pores which can be difficult if there are high flows. The flow through the friction discs also makes the cooling of the friction discs better when it transports heat away and therefore allows higher engagement energies.

Because it will be a bigger volume between the plates with grove pattern it will also be less drag torque [6, 9]. In Figure 3 the difference between a friction disc with and without grooves are shown.

(a) Friction disc without groove pattern.

(b) Friction disc with groove pattern.

Figure 3: Groove pattern.

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2.3 Lubrication

The lubricant inside a DCT does not only take care of the wet clutch. It also works with the bearings, gears and seals inside the transmission. It often works as a hydraulic oil as well inside the transmission. For example the piston that builds up the pressure inside the clutch can be actuated by hydraulics. The lubricant should have predictable friction characteristics, but it should also

Dissipate heat from contact area

Reduce wear

Prevent contaminants and debris to enter into sensitive systems

Transfer power

Reduce noise, vibrations and harshness

All this is normally done by one lubricant, this makes the composition very complex. The most common one is the ATF which can be recognized by its red color [6, 9, 13].

When analyzing different lubricants for wet clutches the µ − v curve often comes up. It says how the friction coefficient varies with sliding speed inside the clutch.

Here a positive slope is desired, with higher dynamic than static friction which can be seen in Figure 4. This helps in avoiding stick-slip and shudder. A overall high friction coefficient is also wanted for short engagement times. Many have investigated how the slope on the µ − v curve can be positive for a wet clutches but it has never been understood entirely [10, 14].

v μ

Desired behavior

Undesired behavior

Figure 4: Desired (green) and undesired (red) frictional behavior in wet clutch.

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2.3.1 Additives

The lubricants for wet clutches consist of base oil and a large number of additives. It plays a significant role in the clutch frictional behavior. The clutch works mostly in the boundary lubrication regime, and the lubricant also needs to have high sheer stability do to the shear stress from the clutch discs [9, 15].

Frequently used additives in an automatic transmission is Friction modifiers (FM), detergents, dispersants, Anti wear (AW), Viscosity index improvers (VI), pour point depressants, antioxidants, metallic de-activators, anti-rusting agents, seal sweller and foam inhibitors [15].

It is shown that a pure base oil has a negative slope on the µ − v curve. It is also shown that a dry contact has a positive slope. Therefore, the negative slope must come from the base oil. With the addition of organic FMs the coefficient of friction decreases significantly at low sliding speeds and static conditions. They also decrease the friction at higher sliding speeds but not as much. This makes the slope on the µ − v curve positive but less torque is also transferred due to the overall coefficient of friction is lower [10, 11].

The FM consist of long hydrocarbon chains, ten or more carbon atoms with a polar group at the end. It is on the other hand the polar group that says the most of how well the FM works and it can for example consist of carboxylic acids, phosphoric acids, amines and amides. The polar group will attach to the metal surface while the hydrocarbon tail will be orientated perpendicular to the surface and is solubilized in the lubricant. Together they form a layer that is easy to shear which gives the desired slippery surface. When choosing FM you need to regard how the polar group will be absorbed by the friction material but also how it will work with the base oil [15, 16].

As mentioned earlier high friction is desired for short engagements and high torque transfer. Detergents and dispersants can be used to increase the coefficient of friction over all sliding speeds. When FMs and detergents and dispersants are mixed together the µ − v is like the one when only FM is used but now with a higher overall coefficient of friction [10].

Besides giving desirable friction properties the dispersants and detergents helps keeping it clean and therefore gives the parts and the lubricant a longer life.

Detergents consists of a polar head that usually is some organic acid that is attached to a hydrocarbon chain that is soluble in the oil. The detergents gives basicity to the lubricant which helps neutralize acids that can occur. It prevents rust, corrosion and oxidation and retard deposit formation, especially at high temperatures. The choice of detergent and concentration is highly dependent on the application [15, 16].

Dispersants have a surface-active polar head containing oxygen or nitrogen and a hydrocarbon chain that gives oil solubility. They keep sludge and harmful debris dispersed in the oil and therefore it prevents viscosity thickening, filter plugging and wear. In a wet clutch application they will retard the clogging of

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pores by keeping oxidation and thermal by-products suspended in the oil [15, 16].

2.4 Engagement

Wear of paper-based friction materials for wet clutches has been studied since the early 70’s. To do that they had to understand the engagement of a wet clutch and they came up with three engagement phases. There are however no distinct start and end point between the phases.

First is the hydrodynamic squeeze film phase. The friction disc is now coming closer to the separator disc. Lubricant is squeezed over but also through the friction lining. The lubricant is building up a pressure that supports the axial load and there is no contact between the friction disc and separator disc, the behavior can be described as hydrodynamic full film lubrication. The friction coefficient is increasing fast at first. The friction and shear force increase as the fluid film gets thinner and shear velocity increases.

The second phase is the squash film. Asperities makes contact and adhesive friction takes place. Lubricant inside the pores in the friction material is squashed out and a hydrodynamic lift takes place. Mixed lubrication occurs and the load is supported by the asperities and the fluid film. At first the sliding speed is high and the oil film is thin because it is still inside the pores. This leads to high shear force and viscous friction. Later the sliding speed and the forces decreases because the fluid film can be considered constant. The temperature increase leads to decreased viscosity which also leads to decreased hydrodynamic forces.

The hydrodynamic action is dominant while the friction forces decreases. This phase is considered hard to model.

At last the third phase is called the adhesive phase. The full load is now supported by asperity to asperity contact. The hydrodynamic effects are very small, and the clutch is considered to work in the boundary lubrication regime. This is where the clutch works most of the time and it is also where most of the additives in the lubricant are used to get the desired friction behavior. At the end of this phase the sliding speed goes to zero and the friction is static.

In this description of the engagement the permeability is not mentioned, but it will also affect the different phases. For example a high permeability will also mean a larger lubricant reservoir which means that a larger amount of lubricant will be released during the squeeze film phase [6, 17].

2.5 Stick-slip and shudder

When reading about wet clutches the concepts stick slip and shudder often comes up. Stick-slip and shudder can arise under some conditions in wet clutches but can also be an effect of clutch failure. It will affect the comfort and driving experience of the vehicle. The phenomenon can also lead to increased wear on the rest of the drivetrain [18].

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Stick-slip can be described as two surfaces that cycles between rest and motion and a corresponding change in friction force. This is usually described by a higher static friction coefficient than its kinetic counterpart. The friction coefficient can come from advanced functions of sliding speed and sticking time [14, 18, 19].

Shudder are like stick-slip but occur at higher sliding speed and the surfaces does not stick to each other. It can be detected by various torque transfer on the output shaft which can lead to vibrations and noise. The accuracy of the torque transferred is therefore reduced which for example can result in unsmooth gearshifts in a transmission [9, 14, 18].

To avoid stick slip and shudder a positive slope on the µ−v curve is desired with an overall high friction. This means that the friction coefficient should increase with sliding speed [9, 14, 18, 20].

2.6 Degradation

The main purpose of a system containing a wet clutch is the ability to transfer torque. Clutch failure often means that the system lacks the ability to transfer torque in a controlled way. A wet clutch system can be said to have two typical failure modes. Noise and vibration in driveline due to stick-slip or shudder or loss in torque transfer capabilities. The later can yield both a decreased and increased coefficient of friction. This can often be seen when the µ − v curve is studied and is an effect from the degradation of the friction material and lubricant [14, 15].

2.6.1 Material degradation

Material failure can be divided into [15]:

Glazing

The friction material surface will take on a smother and darker look and sometimes even shiny. This can come from depositions from the lubricant and lead to clogging of pores on the friction material. Which then can lead to less adsorption of the lubricant’s additives into the friction material due to loss in porosity. Eventually this leads to bad friction characteristics.

Increased contact area

An increased contact area can come from the wear process or come from too much loading.

Delamination of friction material The friction material delaminates.

Thermal degradation

In paper-based friction material the cellulose fibers can carbonize when temperature reaches 200^◦C or higher.

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Wear

Wear will always appear and is a mechanical degradation.

2.6.2 Lubricant degradation

The degradation mechanism for lubricant can be divided into four categories [15]:

Oxidation

Water contamination

Shear

Thermal degradation

where oxidation is the most common.

Oxidation

The oxidation process can by itself be divided into initiation, propagation, chain branching and termination [15, 16].

Initiation: The initiation reaction a hydrocarbon chain, RH gives two free radicals that are very reactive and therefore short lived, which can be seen in reaction 9. The reaction rate is relatively slow in room temperature but increases hastily with increasing temperature. Shear, UV-light and catalysts such as Fe, Cr and Cu can also speed up the reaction rate.

RH −−→ R• + H• (9)

Propagation: The propagation consists of two reaction. First alkyl radicals, R•

reacts with oxygen and building alkyl peroxy radicals, ROO•.

R• + O2−−→ ROO• (10)

The alkyl peroxy radical, ROO• then reacts with a different hydrocarbon, RH•

and forms a new alkyl radical, R• and hydroperoxid, ROOH like

ROO• + RH• −−→ R• + ROOH (11)

The alkyl radical, R• can now react with oxygen again according to reaction 10 and so on. Reaction 10 has low activation energy and are independent of temperature. Therefore it is reaction 11 that determines the reaction rate of the propagation.

Chain branching: The hydperoxides, ROOH are now divided into free hydroxy radicals, HO• and aloxy radicals, RO•.

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ROOH −−→ HO• + RO• (12) It is first at temperatures of 120^◦C and above the reaction rates become higher because of the high activation energy. The hydroxy and aloxy radicals are on the other hand very reactive and forms ketones and aldehyds.

Termination: Finally in the termination most of the hydroperoxides, ROOH are consumed and the chain reaction will come to an halt which is illustrated in Figure 5.

Rate of oxygen uptakeHydroperoxide concentration

Time

Autoacceleration Autoretardation

Figure 5: Hydroperoxide concentration and rate of oxygen uptake over time [16].

Water contamination

Water contamination in the lubricant can lead to corrosion, erosion, rust, hy- drogen embrittlement and water etching. It may also lead to an accelerating oxidation process [15].

Water contamination can be divided into three phases where phase 2 and 3 are most harmful:

1. Water is dissolved in the lubricant. The water molecules are dispersed evenly in all lubricant.

2. The lubricant has reached its maximum of dissolved water. Microscopic droplets of water are evenly distributed in the lubricant.

3. More water is added, and it will separate from the lubricant which leads to free water in the lubricant.

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Shear

Shear may lead to scission of long molecules. The VIs are often large molecules and therefore exposed to mechanical shear. This may lead to loss in viscosity [15].

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3 Method

The following sections describe the original test rig, the redesigned test rig, the testing procedure and tested materials.

3.1 Test rig

The test rig used in this work has been designed and built by Martin Lund [6, 17]. The test rig has a wet clutch that originates from the transmission of a wheel loader. It has been modified to fit two friction discs and three separator discs.

The rig is equipped with sensors that can continuously measure the actuation pressure on the clutch piston, the torque by a load cell and a torque arm, the rotational speed of the friction discs, the clutch pack thickness and the temperature inside each of the three separator discs. The shaft is driven by an electric motor and allows rotational speeds up 3000 rpm. Engagement pressures has been tested up to 3 MPa. Above pressures of 3 MPa the piston was deformed.

Engagement pressures up to 1.5 MPa should not be a problem for long tests.

The inertia for all the components inside the test rig including the electric motor equals 0.6318 kgm². An extra flywheel can also be mounted which gives a total inertia of 0.7375 kgm².

Inside the clutch a wave spring is mounted to release the pressure on the discs after an engagement. The spring force is therefore subtracted when calculating the axial force acting on the clutch. The spring constant is 48 000 N/m and the axial force is then calculated as

Fax= ppAp− Fs (13)

where Fax is the axial force, pp the pressure on the piston, Ap the piston area and Fs the spring force. The spring force Fsis calculated as

F_s= kx (14)

where k is the spring constant and x is the displacement which is the same as the traveled distance by the piston.

The sample rate on the test rig is 2000 Hz except for the revolution speed that has a sample rate of 100 Hz. This gives a good resolution when analyzing the engagement.

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3.2 Redesign of test rig

The redesign focuses on getting the oil sump volume as small as possible and getting the oil sump temperature up to 100^◦C. This is important for the aging of the wet clutch to take place in a similar way as in the actual application.

Lubrication system for wet clutch: A new oil sump of 6 liter is installed with the outlet that provides the clutch with lubricant on the bottom of the tank. The tank is also prepared with in and outlets from the lid to the old cooling system that runs on tapped water. All in and outlets are submerged so they always will be under the oil surface even if the level in the tank is only 1 liter. In Figure 6 the new oil sump is shown and its additional features.

(a) Full system including cooling system

(b) Tank lid with submerged in and outlets. The return from the rig has a pipe with holes in the bottom to avoid foaming.

(c) New oil sump of 6 liters.

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(d) The tank has an outlet on the bottom for easy drainage.

(e) When the cooling system is plugged in there is an outlet driven by the pump for oil samples indi- cated by the thin black hose.

(f) The flow from the rig can be set to go back to the tank or out for drainage.

(g) The new filter size reduces the filter volume from approximately 1 liter to 0.4 liter.

(h) A check valve is installed to control the flow to the clutch. This makes it possible to control the temperature inside the clutch.

Figure 6: New oil sump and additional features.

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Heaters: To be able to manage a oil sump temperature of 100^◦C three silicone heaters where installed. One under the tank on 400 W, two on the gables of the test rig with a power of 200 W and 300 W each. This sums up to a total power of 900 W. The placement of the heaters can be seen in Figure 7.

(a) Heater of 200 W on gable

(b) Heater of 300 W on gable.

(c) Heater of 400 W under the tank.

Figure 7: Placement of silicone heaters.

The heaters are controlled by a thermostat that senses the temperature in the tank. The thermostat is placed in a housing on the side of the rig, see Figure 8.

Figure 8: Thermostat that are control- ling the heaters.

Insulation: The rig and tank are insulated using cellular rubber isolation with a thickness of 25 mm. The cellular rubber used can withstand temperatures up to 110 ^◦C. Nearest the all the heaters a heat resistant mat is placed that can withstand temperatures up to 1100^◦C The insulation of the rig and oil sump can be seen in Figure 9.

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(a) Heater without insulation.

(b) Heater with heat resistant mat.

(c) Heater with cellular rubber.

(d) Insulation of hole test rig.

Figure 9: Insulation of test rig.

Leakage: There have been problems with leakage between the hydraulic system that pressurizes the clutch and the lubrication system for the clutch. The sealing between the two systems is made by O-rings mounted on the clutch axle. From the beginning it was mounted O-rings by nitrile rubber that is recommended for working temperatures up to 100 ^◦C, which also was the desired working temperature for the tests. By changing the O-rings to thicker O-rings made by Viton that can withstand temperatures up to 200 ^◦C solved this leakage, see Figure 10. The piston inside the clutch was also changed to ensure that no leakage occurred there.

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Figure 10: Heat resistant O-ring made of Viton.

Besides that, the test rig has also been suffering from leakage to the outside which leads to less and less oil in the sump. This was due to the earlier design that has been leading the oil to the outlet of the rig. It was made by sheet metal fastened to the walls. This design was however very hard to seal and therefore it was removed. The oil is now pouring down on the bottom of the test rig and the outlet is rebuilt by a 10 x 80 mm flat iron that is bolted to the gables and bottom of the rig. Before mounting a silicone gasket was placed between. To get the oil to flow to the outlet the whole rig is tilted by approximately 3^◦. An illustration of before and after can be seen in Figure 11.

OUTLET Silicone

Leakage Bottom

Oil

(a) Before.

Silicone Bottom

OUTLET Oil Seal

(b) After.

Figure 11: Section view of rig where leakage occurred.

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3.2.1 Final rig setup

The final rig setup that is used in the tests in this project is shown in Figure 12.

The cooling system is here disconnected because only heating will be needed in these tests. Here it can also be seen that the rig is tilted.

(a) Overview of final setup without cooling system.

(b) Side view of final setup with tilted rig.

Figure 12: Final rig setup.

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3.3 Setting test parameters

When setting the test parameters, it is good to have other tests to mimic. If similar test parameters lead to similar results made in other test rigs it could be seen as a verification that the test rig works as intended. This would also make results coming from the test rig that has not been seen by others more credible.

The starting point when setting the test parameters is a previous test made on a test rig called ZF GK3. ZF GK3 is a standard test rig used in the industry to evaluate the aging and function of wet clutches. When the test is carried out on the ZF GK3 with a low reference lubricant a drop in the dynamic friction can be seen at 50 % of the sliding speed. The coefficient of friction is here decreasing with the number of engagements. This is seen clearly after 12000 engagements on the ZF GK3. This is corresponding to a total energy of 787 MJ that are taken up by the clutch from breaking down the system. This energy is then transferred to the lubricant when cooling down the clutch. The test takes about 48 hours to perform.

Test 1a: When setting the test parameters for Test 1a it is desired to have as many variables equal to the ZF GK3 as possible. Friction discs with the same friction lining and grove pattern is therefore ordered. The size of the friction discs, the number of friction discs and the inertia in the test rig is however not changeable. To make the tests as equal as possible the sliding speed on the mean radius and the mean power per surface area unit is kept the same. The oil sump temperature and volume are also the same.

Test 1b: An more aggressive test cycle is also made where the sliding speed is set to be as high as possible in the rig. This will make the energy per engagement increase to the maximum that the test rig can offer. This will also affect the mean power for the engagements. The rig is never calibrated for a specific mean power here why there not is a specific engagement time. When making this test cycle the engagement pressure is hold at the same level as in Test 1a and the revolution speed is increased. This is made to speed up the aging process.

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3.4 Material

In this section the material used to perform the tests are stated.

3.4.1 Friction material

The friction material is BorgWarner BW 6100 which is paper based. This is the same friction material that was used on the ZF GK3. The groove pattern is based on the same pattern used in the ZF GK3 but adapted to new diameters.

The friction lining thickness is 0.6 mm. In Figure 13 a new friction disc is shown.

(a) The entire friction disc. (b) Close-up.

Figure 13: New friction disc.

3.4.2 Lubricants

The lubricant used in the tests is known to have unfavorable aging properties and will be referred to as a low reference lubricant. The lubricant is available on the market and is designed to operate in a DCT environment.

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3.5 Test matrix

In Table 1 the test matrix is shown. Test 1a is made first and then followed by Test 1b. The lubricant and friction discs are not changed between Test 1a and 1b. The braked energy corresponds to the total energy the clutch has braked down. The duration is the time the test took.

Table 1: Test matrix

Test 1a Test 1b

Lubricant Low reference Low reference

Number of engagements 49549 23250

Braked energy [MJ] 904 846

Speed [rpm] 2124 3000

Engagement time [s] ≈ 1.67 ≈ 2.77

Duration [hours] 280 189

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3.6 Test procedure

The test procedure follows as:

1. Flushing of the clutch lubrication system to clutch with the same type of lubricant that is going to be used under the test.

2. Clean and refill the oil sump with 6 liters of new lubricant.

3. Measure the friction disc and clutch pack thickness with micrometer screw, see Section 3.6.1.

4. Start test.

5. Oil sample of 1.5 dl after 100 engagements. The same volume is replaced with new oil.

6. Stop test.

7. Measurement of clutch pack and friction disc thickness.

8. Oil sample.

3.6.1 Measure clutch pack thickness

The clutch pack is measured by putting it between two steel plates. A light pressure is then applied by a spring. The spring tension is set by the number of revolutions the bolt is set and is kept the same for all measurements. The clutch pack is then measured on nine locations using a micrometer screw and the average thickness is calculated. In Figure 14 it is shown how the clutch pack is mounted between the steel plates.

Figure 14: Measuring the clutch pack.

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4 Results

The results from the tests performed in this thesis are shown in the following sections.

4.1 Test 1, Low reference

Here the results from the tests on the low reference oil is shown. The aging process took longer than expected and therefore the test results are divided into two parts with different test cycles which is shown in Table 1. This was done to speed up the aging process.

4.1.1 Test 1a

Clutch engagement: Figure 15 shows how the axial force, pressure, revolution speed, piston position and torque varies under the engagement.

-0.5 0 0.5 1 1.5 2 2.5

-3 -2 -1 0 1 2 3 4 5 6 7

-60 -40 -20 0 20 40 60 80 100 120 140

Figure 15: Clutch engagement 20 000.

Temperature: In Figure 16 the temperature in the different separator discs and oil sump are shown for engagement 20000. The maximum and mean temperature for all engagements in Test 1a is also shown. The rapid temperature drops in Figure 16b is caused by test rig restarts. It can be seen that the maximum temperature in the center disc is almost 220^◦C in Figure 16a. The maximum temperatures in the separator discs and the average temperature in the oil sump seems to be quite constant during the whole test when looking at Figure 16b.

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0 5 10 15 80

100 120 140 160 180 200 220

(a) Temperatures during engagement 20000.

0 1 2 3 4 5

10⁴ 0

50 100 150 200 250

(b) Maximum and mean temperatures during engagement 1 to 49549.

Figure 16: Temperatures in Test 1a.

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Power: In Figure 17 the power per surface unit is shown for engagement 20000 together with the mean power and maximum power for all engagements in Test 1a. The rapid power drops in Figure 17b and 17c are caused by test rig restarts.

Figure 17a shows how the power is high at the start of the engagement and then decreases during the engagement. In Figure 17b it can be seen that the mean power is first just above 0.75 W/mm²but between 15000 to 20000 engagements a little drop is seen and it then decreases a little. After that it is relatively constant during the rest of Test 1a. In Figure 17c shows that the maximum power during the test is around 2.1 W/mm².

0 0.5 1 1.5

0 0.5 1 1.5 2

(a) Power during engagement 20000.

1 2 3 4

10⁴ 0.45

0.5 0.55 0.6 0.65 0.7 0.75

(b) Mean power during engagement 1 to 49549.

1 2 3 4

10⁴ 1.6

1.8 2 2.2 2.4

(c) Maximum power during engagement 1 to 49549.

Figure 17: Power in Test 1a.

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Coefficient of friction: In Figure 18 the coefficient of friction is shown for engagement 20000 with respect to engagement time and sliding speed. To get a better visualization of how the coefficient of friction varies a moving average is used over 40 data points. In Figure 18b it can be seen that the friction increases with sliding speed.

0 0.5 1 1.5 2

-0.05 0 0.05 0.1 0.15 0.2 0.25

(a) Coefficient of friction with respect to engagement time.

0 5 10 15

-0.05 0 0.05 0.1 0.15 0.2 0.25

(b) Coefficient of friction with respect to sliding speed.

Figure 18: Coefficient of friction under engagement 20000 in Test 1a.

Aging properties

In Figure 19 the coefficient of friction with respect to engagement time and sliding speed is compared for different engagements. In Figure 19a it can been seen that the engagement time increases with the number of engagements. Further- more, the coefficient of friction at the end of the engagement decreases when the number of cycles increases. Figure 19b shows that the coefficient of friction at low sliding speeds decreases as the number of engagements increases.

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0 0.5 1 1.5 2 0

0.05 0.1 0.15 0.2 0.25

0 5 10 15

0 0.05 0.1 0.15 0.2 0.25

Figure 19: Coefficient of friction comparison under Test 1a for the engagements marked in the figures.

In Figure 20 the mean, static, dynamic and maximum coefficient of friction is shown for all engagements in Test 1a. The rapid friction drops seen in the figures are due to test rig restarts. The static friction is defined as the coefficient of friction at a sliding speed of 0.137 m/s. The dynamic friction is taken at 50 % of the sliding speed. In Figure 20a the mean coefficient of friction has a small drop between engagement 15000 and 20000. Besides that the mean friction seems to be quite constant during Test 1a. Figure 20b shows that the static friction decreases slightly during Test 1a. Figure 20c shows that the dynamic friction has a small drop between engagement 15000 and 20000. Besides that it is quite constant during Test 1a. Figure 20d shows that the maximum coefficient of friction is quite constant during Test 1a.

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1 2 3 4 10⁴ 0.08

0.1 0.12 0.14 0.16 0.18

(a) Mean coefficient of friction with respect to the number of engagements.

1 2 3 4

10⁴ 0.08

0.1 0.12 0.14 0.16 0.18

(b) Static coefficient of friction with respect to the number of engagements.

1 2 3 4

10⁴ 0.08

0.1 0.12 0.14 0.16 0.18

(c) Dynamic coefficient of friction with respect to the number of engagements.

1 2 3 4

10⁴ 0.08

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

(d) Maximum coefficient of friction with respect to the number of engagements.

Figure 20: Coefficient of friction during engagement 1 to 49549 in Test 1a.

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4.1.2 Test 1b

Note: Test 1b was started directly after Test 1a and some adjustments of the input parameters in the test rig program needed to be done during the test for the rig to run properly. This can be seen clearly when lock- ing at the power and friction coefficient with respect to the number of engagements. After engagement 56500 all these effects have disappeared and the measured parameters has been stabilized.

Clutch engagement: Figure 21 shows how the axial force, pressure, revolution speed, piston position and torque varies under the engagement. It can be seen that the revolution speed is increased and that the engagement time is longer compared to Test 1a, see Figure 15.

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

-3 -2 -1 0 1 2 3 4 5 6 7

-60 -40 -20 0 20 40 60 80 100 120 140

Figure 21: Clutch engagement 60000.

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Temperature: In Figure 22 the temperature in the different separator discs and oil sump are shown for engagement 60000. The maximum and mean temperature for all engagements in Test 1b is also shown. The rapid temperature drops in Figure 22b is caused by test rig restarts. It can be seen that the maximum temperature in the center disc is almost 300^◦C in Figure 22a. The maximum temperatures in the separator discs and the average temperature in the oil sump seems to be quite constant during the whole test when looking at Figure 22b.

0 5 10 15

100 150 200 250 300

(a) Temperatures during engagement 60000.

5 5.5 6 6.5 7

10⁴ 0

50 100 150 200 250 300

(b) Maximum and mean temperatures during engagement 49550 to 72799.

Figure 22: Temperatures in Test 1b.

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Power: In Figure 23 the power per surface unit is shown for engagement 60000 together with the mean power and maximum power for all engagements in Test 1b. The rapid power drops in Figure 23b and 23c are caused by test rig restarts.

In Figure 23b it can be seen that the mean power is quite unsteady up to approximately 57000 engagements. This is because the test rig program needed to be adjusted during the test when the revolution speed was raised to 3000 rpm in Test 1b. After 64000 engagements the mean power decreases until the end.

Figure 23c shows that the maximum power increases from about engagement 57000 to 60000. It is then quite constant until engagement 71000 where it drops again until the end.

0 0.5 1 1.5 2 2.5

0 0.5 1 1.5 2 2.5 3

(a) Power during engagement 60000.

5 5.5 6 6.5 7

10⁴ 0.65

0.7 0.75 0.8 0.85 0.9 0.95 1

(b) Mean power during engagement 49550 to 72799.

5 5.5 6 6.5 7

10⁴ 2.6

2.8 3 3.2 3.4

(c) Maximum power during engagement 49550 to 72799.

Figure 23: Power in Test 1b.

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Coefficient of friction: In Figure 24 the coefficient of friction is shown for engagement 60000 with respect to engagement time and sliding speed.

0 0.5 1 1.5 2 2.5 3

-0.05 0 0.05 0.1 0.15 0.2 0.25

0 5 10 15 20

0 0.05 0.1 0.15 0.2

Figure 24: Coefficient of friction under engagement 60000 in Test 1b.

Aging properties

In Figure 25 the coefficient of friction with respect to engagement time and sliding speed is compared for different engagements. In Figure 25a it can been seen that the engagement time increases with the number of engagements. Figure 25b shows that the coefficient of friction decreases at 50 % of the sliding speed as the number of engagements increases. For the friction at sliding speeds near zero a small increase can be seen as the number of engagements increases. At the highest sliding speed, it can be seen that the friction for engagement 57000 is lower than the others.

0 0.5 1 1.5 2 2.5 3 3.5

0 0.05 0.1 0.15 0.2 0.25

0 5 10 15 20

0 0.05 0.1 0.15 0.2 0.25

Figure 25: Coefficient of friction comparison under Test 1b for the engagements marked in the figures.

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In Figure 26 the mean, static and dynamic coefficient of friction is shown for all engagements in Test 1b. The rapid friction drops seen in the figures are due to test rig restarts. The static friction is defined as the coefficient of friction at a sliding speed of 0.137 m/s. The dynamic friction is taken at 50 % of the sliding speed. The unstable behavior up to about engagement 56500 comes from the fact that the test rig program needed to be adjusted during Test 1b. This can be seen in all of the plots in Figure 26 In Figure 26a the mean coefficient of friction seems to be quite constant in the beginning but starts to decrease from about engagement 65000 until the end. Figure 20b shows that the static friction increases slightly during Test 1b. Figure 26c shows that the dynamic friction decreases during Test 1b. Figure 26d shows that the maximum friction increases during Test 1b.

5 5.5 6 6.5 7

10⁴ 0.08

0.1 0.12 0.14 0.16 0.18

(a) Mean coefficient of friction with respect to the number of engagements.

5 5.5 6 6.5 7

10⁴ 0.08

0.1 0.12 0.14 0.16 0.18

(b) Static coefficient of friction with respect to the number of engagements.

5 5.5 6 6.5 7

10⁴ 0.08

0.1 0.12 0.14 0.16 0.18

(c) Dynamic coefficient of friction with respect to the number of engagements.

5 5.5 6 6.5 7

10⁴ 0.08

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

(d) Maximum coefficient of friction with respect to the number of engagements.

Figure 26: Coefficient of friction during engagement 49550 to 72799 in Test 1b.

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4.1.3 Test 1, Wear

In Figure 27 the wear on the friction discs is shown with respect to the number of engagements. For Test 1a the wear rate seems linear. In Test 1b the wear rate can be seen to increase rapidly compared to Test 1a.

1 2 3 4 5 6 7

10⁴ -0.35

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0

Figure 27: Wear during engagement 1 to 72799 in Test 1.

Figure 28b shows how the measured wear from the position sensor on the rig differs from before and after measurements of the clutch pack and friction disc thickness. The clutch pack is measured at twelve points from which a mean value is calculated. The friction discs is measured at three point from which a mean value is calculated. It can be seen in Figure 28a that the measured wear on the clutch pack compared to the position sensor gives quite different results.

In Figure 28b it can be seen that the wear differs quite much between the inner, mean and outer radius. The wear on the mean radius seems to agree best with the position sensor.

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0 1 2 3 4 5 6 7 10⁴ -0.4

-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0

(a) Comparison between the wear of the clutch pack measured by the position sensor and the measured clutch pack thickness by a micrometer screw before and after the test. The error bars visualizes ± the standard deviation from the measurements using the micrometer screw.

0 1 2 3 4 5 6 7

10⁴ -0.4

-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0

(b) Comparison between the wear of the clutch pack measured by the position sensor and the measured friction disc thickness before and after using a micrometer screw. The measurements after the test is made on the inner, mean and outer radius of the friction discs. The error bars visualizes ± the standard deviation from the measurements using the micrometer screw.

The wear on the discs varies over the radius and the value from the position sensor agrees best with the value measured on the mean radius.

Figure 28: Comparison between the measured wear by the position sensor and the measured values using a micrometer screw.

4.1.4 Test 1, Friction discs

In Figure 29 and 30 the friction discs can be seen after Test 1. It can be seen that the surfaces against the center disc which is the hottest has more wear than the other surfaces. The surfaces against the center disc has also more wear on the inner radius where no grove patterns is left compared to the outer radius.

The surfaces seems to get slightly darker as the maximum temperature that they have been exposed to increases.

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(a) The entire disc, placed in contact with the outer separator disc.

(b) Close-up, placed in contact with the outer separator disc. Maximum temperature in Test 1b approximately 170^◦C.

(c) The entire disc, placed in contact with the center separator disc.

(d) Close-up, placed in contact with the center separator disc. Maximum temperature in Test 1b approximately 300^◦C.

Figure 29: Outer friction disc after Test 1.

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(a) The entire disc, placed in contact with the center separator disc.

(b) Close-up, placed in contact with the center separator disc. Maximum temperature in Test 1b approximately 300^◦C.

(c) The entire disc, placed in contact with the inner separator disc.

(d) Close-up, placed in contact with the inner separator disc. Maximum temperature in Test 1b approximately 210^◦C.

Figure 30: Inner friction disc after Test 1.

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5 Discussion

In Test 1a the mean power can be seen to be around 0.75 W/mm², see Figure 17 and when looking at the test parameters in Table ?? the desired value was 0.6975 W/mm². This means that the test rig has been calibrated correctly and the average power is in the right range. When looking at how the coefficient of friction varies with respect to engagement time and sliding speed in Figure 19 a drop in friction can be seen at low sliding speeds which corresponds to the end of the engagement. This would mean that there would be a drop in the static friction. This is seen more clearly in Figure 20b. It is however not the real static coefficient of friction because it is measured under a sliding motion, but it gives an idea of how it varies with the number of engagements. The real static friction should be measured at zero sliding speed, but then no torque is transferred in these tests so it cannot be seen. Another type of test must be made to see the real static friction. The engagement time is also increasing with the number of engagements in Figure 19a. This would indicate that the mean coefficient of friction would decrease. A small decrease in the mean friction can be seen between engagement 16000 and 19000 in Figure 20a. Otherwise the coefficient of friction is quite constant during Test 1a, the same drop can be seen in the dynamic friction when looking closely but it is very small. The difference in engagement time will follow the same behavior as mean coefficient of friction and the mean power. A decrease in mean friction and mean power indicates longer engagement times. By considering this the engagement time varies a little but it can also be said to be quite constant during Test 1a. The drop in friction, mainly the static does not give the µ − v curve an undesired behavior because the static friction is lower than the dynamic and therefore the risk of stick-slip and shudder are still low. The lower static friction levels observed for Test 1a can therefore be due to running-in the wet clutch system.

In Test 1b there had to be some calibrations of the test cycle during the test, but this was settled after engagement 56500. Therefore, the behavior of the different variables is mainly studied after this. Due to the increased revolution speed to 3000 rpm the kinetic energy in each engagement is almost twice the energy as in Test 1a. An increase in average power can also be seen in Figure 23b when comparing with Test 1a. It can also be seen that the mean power decreases with the number of engagements which corresponds to longer engagement times and a decreasing coefficient of friction. The maximum power on the other hand can almost be seen to increase in Figure 23c towards the end. When looking at how the coefficient of friction varies with respect to engagement time and sliding speed in Figure 25 the behavior differs from that seen in Test 1a. Here the static and maximum coefficient of friction seen at low and the maximum sliding speed looks more like they are increasing with the number of engagements.

The friction at 50 % of the sliding speed rather seems to decrease with the number of engagements. In Figure 26 it can be seen more clearly how the mean and dynamic friction at 50 % of the sliding speed decreases with the number of engagements. The static and maximum friction are on the other hand increasing

Prediction of life durability in friction for wet clutches of DCT gearboxes