Development of a piston expander for Rankine cycles: Tribological challenges



Rankine cycles using piston expanders are a promising technology for waste heat recovery in heavy-duty vehicles. Piston expanders present tribological challenges however, as they must operate reliably at high temperature and with little or no lubrication. An axial piston expander using a swashplate mechanism was designed and operated with a vapor of ethanol and water comprising small amounts of PAG oil. Three tribological topics which were addressed during the development of the machine are presented:

The contact between the piston ring and the cylinder liner: Experimental investigations of tribo-materials under various pressurized hot vapor conditions in the SRV® sealed tribometer at the BAM laboratory in Berlin were conducted. Sb-impregnated carbon against Cronidur®30 or against DLC-coated Cronidur®30 were tested and showed the lowest coefficient of friction when in ethanol vapor.

The contact between the shoe and the swashplate: A model of the lubrication conditions in the contact was developed using the finite volumes method and experimental characterization of the boundary regime in a shoe- on-disc setup was carried out at the QUARTZ laboratory in Paris.

The contact between the valve rocker and the cam: An analytical model using M’Ewen equations was used to evaluate the location of highest stress in the contact, for different coefficient of friction.

A description of those challenges, the strategies carried out to find solutions, and the results obtained are reported here.




Faced with upcoming stringent regulations regarding CO2 targets and with increasing customer requests to reduce their operating costs, the truck industry sees in waste heat recovery systems (WHRS) a credible answer, which can be integrated in the existing value chain of heavy-duty OEMs. The targets in the European Union by the regulation EU/2019/1242 are expressed as a percentage reduction of emissions compared to EU average in the reference period (1 July 2019–30 June 2020) of 15% reduction from 2025 onwards and of 30% from 2030 onwards. The average fuel economy of class 7 and class 8 (18-wheeler) heavy trucks in the United States and Canada based on data collected between 2016 and 2017 depicted an average miles per gallon range between 4.51 mpg and 6.47 mpg. It is relevant to address heavy duty trucks with WHRS as only approximately 40% of the primary energy is converted into mechanical power, the residual part being released to the environment as heat (Seher, 2012).

WHRS are yet very complex systems which need to provide enough fuel economy to achieve acceptable environmental benefits and return on investment. Their impact on the vehicle must be minimal in terms of volume and weight and they must operate at high temperature while remaining long-lasting and ideally maintenance-free.


Various types of WHRS relevant to the automotive and heavy-duty markets have been investigated in the last 15 years, such as thermoelectric, turbo-compound, Stirling and Rankine cycles (Legros, 2014). Rankine cycles recently emerged as the most promising candidate and is favored by the industry’s stakeholders (Grelet, 2017) (Grelet, 2015) (Reiche, 2019) (Fouquet, 2017). Such Rankine cycles rely on extracting mechanical power from a working fluid evaporated in a heat exchanger placed in the exhaust line of a truck. The key components of an integrated Rankine cycle WHRS are shown in Figure 1.

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Figure 1: Main components of a Rankine Waste Heat Recovery System for trucks (Darmedru, 2017)

Implementation of WHRS based on a Rankine cycle could lead to a 4 to 5% fuel economy, and thus contributes to CO2 emissions reduction. Early concepts on WHRS relied on hot steam (G. Buschmann, 2001) (R. Freymann, 2012) as a highly calorific working medium. Using ethanol as the working fluid allows a Rankine cycle at lower operating temperatures adapted to Diesel exhaust gases. Moreover, pure ethanol freezes at -144°C and can lower the freezing point of water when a mixture is used.


Rankine cycles can be operated with various types of expanders (Guillaume, 2019) but piston expanders are a particularly promising technology for trucks, when mechanical re-injection of the recovered power to the internal combustion engine (ICE) is desirable.

EXOES has developed a piston expander (A. Darmedru, 2013), which is mechanically connected to the ICE, re-injecting torque to save fuel. A high pressure superheated vapor is generated in the evaporator from the heat of the hot exhaust gases. This vapor is then fed to the piston expander where inlet valves distribute it to 3 single acting pistons at their top

dead center. During expansion, the temperature and pressure of the vapor decrease, and it leaves the machine through exhaust ports arranged at the bottom dead center of the pistons. This saturated vapor flows to a condenser and turns into liquid. The existing cooling circuit of the ICE is used for condensing the vapor to avoid an additional front radiator. Once liquified, the working fluid is pumped back to the evaporator by means of a high-pressure gear pump. The working fluid circulates in a closed and sealed circuit. An exploded view of the piston expander is shown in Figure 2, and Table 1 presents its main characteristics. After several iterations over the years, a very simple and robust mechanical design has been reached (Figure 3).

Figure 2: Exploded view of EXOES’ piston expander for WHRS

Characteristics Typical values or range
Speed range 1000 – 4500 RPM
Maximum shaft power 12 kW
Maximum inlet pressure 40 barA
Outlet pressure 1 – 4 barA
Transmission Freewheel

Table 1: Main characteristics of EXOES’ piston expander

Figure 3: Key components of EXOES’ expander EVE-T2 (Daccord, 2017)

The conversion of the reciprocating motion of the pistons into shaft rotation is done by means of a swashplate, a concept known from hydraulic motors. This technology has been chosen as it allows for a good compactness and does not require balancing, which provides weight savings.

For reasons related to efficiency, costs, corrosion and ambient temperature (freezing), a mixture of water and ethanol was chosen as working fluid, typically around 90 %.-wt. ethanol and 10 wt.-% of water. Although the only component requiring proper lubrication is the expander, preventing the lubricant from leaving the expander revealed to be too challenging and having oil circulating with the working fluid could not be avoided. The oil circulation rate (OCR) affects the efficiency of the WHRS (Daccord, 2017).

The high temperature of the incoming vapor, around 220°C, makes the use of liquid lubricants challenging. In consequence, the tribo-systems formed by moving parts in direct contact with the incoming vapor (e.g. valves and pistons) operate unlubricated or under deficient lubrication.

Many studies address the thermodynamic sizing and various configurations of Rankine cycles, but none covers the multiple and diverse tribological challenges encountered in the development of a piston expander. Solving them is yet necessary for achieving the targeted efficiency and reliability.

The objective of the research reported here, was to find tribological solutions for a low-wear and low-friction piston expander. This work focused on three major tribo-systems: piston ring-cylinder liner, piston shoe – swashplate, and valve rocker – cam, operating with a unique lubrication concept of lubricant-loaded high-temperature vapor.

Perspective on the tribological challenges

The selected working fluid, a mixture of ethanol and water, is not generally considered as an efficient lubricant because the backbones of hydrocarbon compounds are cracked by steam. Addition of a synthetic lubricant in the flow of vapor was therefore decided. While expanding in the cylinders, the vapor cools down, thereby also cooling the lubricant. The various parts of the expansion machine are therefore provided with a lubricant having different viscosities and thus different lubricating properties. The lubricant was selected such that its highest viscosity would be when in contact with the swashplate, assumed to be the location of highest frictional dissipation.

Piston ring – Cylinder liner

The working fluid entering the cylinders comprises a very little amount of oil with insufficient viscosity and flow rate to provide hydrodynamic fluid film formation between the piston ring and the cylinder liner. The approach chosen was therefore to consider the piston ring – cylinder liner contact as deprived of oil lubrication. Any lubricating effect of the oil would be considered as a bonus. The materials for the piston rings and cylinder liner would thus need to show low friction and low wear under hot vapor lubrication. These considerations oriented the selection and later tests of various candidate materials.

The tribo-elements operate under the lubrication regime of dry friction or boundary lubrication resulting from an interaction of the surface with water and ethanol. Tribo-materials, like antimony impregnated carbon against MgO-ZrO2 or Al2O3, providing low friction and low wear in hot steam vapor were identified previously (Woydt, 2004) (R. Wäsche, 2019). Very low coefficients of friction of ~0,01 at 400°C in steam were associated to the tribo-oxidative formation of reaction layers composed of Zr(OH)4 or aluminum hydroxides (Al(OH)3 [Gibbsite] or α-Al(OH)3 [Bayerite] or α-AlO(OH) [Boehmite].

Tests of ceramic materials and hard coatings in liquid ethanol or water are reported in the literature, generally in relation with the use of ethanol as an alternative fuel for internal combustion engines. Sasaki (Sasaki, 1992) had in a systematic study illuminated that the coefficients of friction of alumina (or zirconia) sliding couples can be lowered by polar fluids, like oxygenates (ethanol, dipropylene glycol, acetic acid, etc.). Various investigations at room temperature demonstrated a lower friction of various ceramic materials, CrN against Si3N4 (Bandeira, 2013), Cr3C2-NiCr against TiO2 (Li, 1998), self- mated Ti3SiC2 (W. Hai, 2013), in liquid ethanol compared to liquid water or in air. Reported friction coefficients ranged from 0.5-0.8 under dry friction to 0.15-0.2 in liquid ethanol. Little tribological data is yet available about friction in ethanol vapor.

Reciprocating sliding tests of α-alumina couples in ball-on-disk geometry (Woydt, 2004) showed that the wear rates in hot steam at 200°C were similar to those observed at room temperature (with relative humidity of about 40-50 %). In hot steam environment the friction was lowest compared to all other tested conditions. Tribo-chemistry between the material´s surface and the steam is a viable lubrication mechanism. On the other hand, all materials must be steam degradation resistant.

Under the operating conditions of EXOES’ piston expander, the objective of the tribological investigations on the piston ring – cylinder liner was to obtain a coefficient of friction below 0.1 and to achieve a wear rate below 10-7 mm3/N.m.

Piston shoe – Swashplate

The work generated during the expansion of the vapor is transferred to the swashplate through the base of the piston which comprises a socket housing for two half-balls (shoes), sliding on the swashplate (Figure 4). Multiple contacts occur between the swashplate and the piston: convex surface of the shoe on the concave surface of the socket, planar surface of the shoe on the planar surface of the swashplate, and socket housing (bridge) on the side of the swashplate. The contact in the bridge was not studied during the development, because of the small normal force, and lack of experimental failures in this area. At the opposite, the contact between the shoe and the swashplate has been extensively studied.

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Figure 4: Contacts in the area where the piston connects to the swashplate

A swashplate cannot be lubricated by forced-fed lubrication and must rely on pure spraying. Investigations related to the tribology of the piston shoe – swashplate contact have been made in the field of refrigeration compressors, either under oil-lubricated conditions (Mitsuhiro Fukuta, 2010) (Tadashi Hotta, 2004), starved lubrication conditions (H. K. Yoon, 1999) and even in oil-less conditions (Seung Min Yeo, 2021) (T.A. Solzac, 2006). For refrigeration compressors lubricated by circulating oil mixed with the refrigerant, and depending on the OCR, speed and pressure, minimum oil film thicknesses between 0.5 and 4 µm were reported, with coefficients of friction below 0.02. In oil-less or starved lubrication conditions, two approaches are usually proposed: either to use hard coatings on the swashplate, such as DLC or WC/C, or to use soft polymeric coatings such as PTFE or PEEK. The shoe is almost always made of hard steel. Polymeric coatings are reported to provide lower coefficients of friction, definitively below 0.1, while hard coatings provide coefficients of friction between 0.1 and 0.2 in the studied conditions. Hard coatings are nevertheless more resistant to scuffing which is critical for a swashplate.

Those investigations focused on the experimental evaluation of the friction, oil film thickness, and wear rate of various combinations of materials, fluids, and operating conditions. A theoretical approach of the hydrodynamic lubrication conditions was proposed for a swashplate compressor shoe having a dimple (Yasuhiro Kondoh, 2006).

Valve rocker – Cam

The valvetrain of the expander comprises 2 cams and 6 valves and is located inside the cylinder head area, near the top dead center of the pistons. Both cams are secured to the shaft of the expander which is rotated thanks to the action of the pistons on the swashplate. One cam actuates 3 inlet valves, another cam controls 3 exhaust valves (see Figure 5). Although most of the vapor is exhausted at the bottom dead center of the pistons, an exhaust valve remains open while the piston travels toward the top dead center, to limit the recompression of vapor.

In some versions of the expander, a trochoidal pump is provided at the end of the shaft and carries lubricant from the crankcase (housing of the swashplate) to the valvetrain.

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Figure 5: Valvetrain of the piston expander

The contacts between the cam and the valve rocker, and the valve rocker and the valve tip are critical in a Rankine expander where a short inlet angle (high efficiency) is associated with a high angular speed (high compactness). Inertia of the valve must be balanced with a stiff spring, inducing high contact pressures.

The hot and diluted lubricant is unable to ensure a proper lubrication in this elasto-hydrodynamic lubrication conditions, and coatings have been applied to both the valve tip (CrN), valve rocker (DLC) and cam (DLC), all having a thickness of 3µm. It was therefore important to verify that the stress induced under the surface of the parts was not too high in the region where the coatings bond to the substrates. The sub-surface stress in valvetrains has been already widely studied,

including with a focus on the tribology of coatings (Lindholm, 2004) but most approaches consider that the contacts in the valvetrain are well lubricated and therefore assume or calculate coefficients of friction which are low and therefore do not impact the position of the sub-surface stresses much. Moreover, finite element models are generally used (Folęga, 2012) although analytical calculations could already provide useful results when taking friction into account.

The following work focuses on the contact between the valve rocker and the cam.

The objective of the research program presented here was to find solutions to the aforementioned tribological challenges:

  • Selecting an appropriate couple of materials for the piston ring and cylinder liner
  • Designing piston shoes and swashplate that would bear the load without leading to seizure
  • Ensuring the thickness of coatings applied in the valve rocker – cam contact comply with the location of maximum stress

Method and materials


The specifications of the Rankine cycle induce key requirements for the properties of the lubricant and the design:

The lubricant should withstand frequent, though short, peak temperatures (the walls of the evaporator can reach 300°C).

  • The products generated by the degradation of the lubricant should not deteriorate the heat transfer (no soot deposits).
  • The lubricant should be miscible with the liquid phase of the working fluid to avoid emulsions and oil traps.
  • The lubricant should have a “sufficient” viscosity.
  • The crankcase of the expander should act as a 2-phase separator by retaining most of the lubricant.
  • The crankcase must be kept above the boiling point of the working fluid, so that the liquid inside the crankcase is mostly the lubricant itself (with some vapor dissolved in it).

A polyalkyleneglycol-based (PAG) base oil was selected and adapted to meet those requirements. In particular, this oil has an exceptional viscosity tolerance to water contamination, which allows limiting the consequence of dilution by the working fluid. The kinematic viscosity of the lubricant at 40°C against dilution is shown in Figure 6. The very high intrinsic viscosity index of VI= 237 of the anhydrous PAG retains well the viscosity over temperature and by dilution with water.

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Figure 6: Effect of oil dilution on the kinematic viscosity of PAG (measured according to ASTM D445)

It has been found experimentally that an oil circulation rate of about 10 %.-wt. represents a good compromise regarding efficiency, design complexity, and safe lubrication (Daccord, 2017).

The mixture comprising the liquid lubricant and the vaporized working fluid enters the expander at around 220°C, and the oil therefore provides only little to no hydrodynamic lubrication to the piston ring due to the effect of temperature on the viscosity. Expansion of the working fluid induces an increase of the viscosity. The formation of liquid droplets of working fluid when reaching a saturation state does not affect substantially the viscosity of the oil. Then the oil flows to the crankcase and lubricates the swashplate. The crankcase is designed such that oil can settle in it, thereby acting as an oil pan. Part of the oil is circulated to the valve/cam system through an internal pump. Part of the oil leaves the expander and circulates with the working fluid.

Figure 7 shows the simulated distribution of friction losses within the expander, which were experimentally calibrated. The mechanical efficiency of the expander is about 92% (Darmedru, 2017).

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Figure 7: Distribution of friction losses within the expander at 2400 RPM, with a 25 bar inlet pressure, 1 bar outlet pressure and 20K superheat at the inlet

Contact between the piston rings and the cylinder liner

For this topic, polished discs (Ra 0.004 µm to Ra 0.012 µm) made of nitrogen alloyed and martensitic Cronidur®30 (DIN 1.4108, X30CrMoN15-1) with a diameter of 24 mm, a height of 7.9 mm were selected to represent the cylinder liner. The Cronidur®30 is a suited candidate for hot steam, as it can be heat treated to 60 HRC, has an excellent corrosion resistance and its annealing temperature is above 400°C.

A 10 µm-thick DLC coating from InnerArmor by Sub-One Technology was applied to one side of the discs, because the process offers high deposition rates and enables coating thicknesses of up to 50 µm deposited on inner surfaces. In consequence, such a DLC-type coating may also enhance the protection against hot vapors (steam, ethanol). The indentation hardness by Berkovich indenter (CSM, 45 Hz, 2 nm) for a penetration depth of 300 nm was HIT= 12.08±1.2 GPa with an indentation modulus of EIT=109.4±6.4 GPa. A Raman spectroscopy indicated that this DLC-type film was composed of sp² and sp³ hydridized carbon. The present sample is likely a DLC-type film rather than a ta-C type film.

Cylindrical samples of antimony-impregnated carbon were used as upper specimen to represent the piston ring. The dimension of the cylinders was 8mm in length with a diameter of 6mm.

One test involved the addition of oil that was deposited on the disc prior to testing. Water soluble polyalkylene glycol (diethyleneglycol initiated EO/PO (2:1)) with a calculated kinematic viscosity of 7.6 mm²/s (anhydrous) at the test temperature of 180°C was used.

A new hot steam tribometer shown in Figure 8 was used, in which it is possible to conduct tests under pressurized vapor conditions and high temperatures. This sealed tribometer is of SRV® type and the test conditions chosen are presented in Table 2. The carbon cylinders were loaded against the discs, the initial maximum Hertz contact pressure reached at test start was P0max= 259 MPa. The cylinders oscillated on the discs under an inclination angle of 10° such as described in DIN51834, part 4. The contact geometry is illustrated in Figure 9. Test duration was set to 3 h and 30 minutes.

Test parameters
Temperature 180°C
Stroke 2000 µm
Frequency 25 Hz
Average velocity 0.100 m/s
Test number Description Initial disc roughness Ra




1 Hot laboratory air 0.009 100
2 Water vapor 0.012 150
3 Water / ethanol vapor mixture (50/50 wt.%) 0.004 147
4 Ethanol vapor 0.012 150
5 Ethanol vapor with oil 0.007 175
6 Ethanol vapor with DLC coated disc 0.176 100

Table 2: Test conditions for the assessment of friction and wear of the piston rings/cylinder liner contact

Figure 8: Sealed SRV® Tribometer at the BAM laboratory

Figure 9: Contact geometry

Friction coefficients were recorded continuously during the tests as well as load, frequency, stroke, temperature, and gas pressure. The wear volumes of the cylinders were determined by measuring the wear scar width and planimetric wear by stylus profilometry at the end of each test. Wear rates were calculated from the wear volumes divided by sliding distance and normal load.

Contact between the swashplate and the shoe

The contact between the swashplate and the shoe was first addressed theoretically, through the evaluation of the oil thickness in the contact. Figure 10 presents a schematic illustration of the swashplate – shoe contact with notations used in the model.

Figure 10: Schematic illustration of the planar contact between the swashplate and the shoe

The shoes are made of 100Cr6 ball bearing steel, while the swashplate is coated with diamond-like carbon (DLC). This combination protects against wear under mixed lubrication regime, which can occur in many probable situations such as high lubricant temperature, high dilution of working medium, low rotational speed or high load, as per the classic Stribeck- type curve approach (Figure 11).

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Figure 11: Stribeck-type curve defining different lubrication regimes encountered in the swashplate-shoe contact

The two contacts related to the shoe have been modeled but only the plane/plane contact is reported here. The goal of the model was to:

  • Evaluate the influence of viscosity on the lubricant film thickness,
  • Assess the influence of design and operation parameters such as speed, pressure, diameter of the shoe, sliding radius etc.,
  • Provide a tool to estimate the friction generated in the swashplate.

Modeling the swashplate-shoe lubrication in the hydrodynamic regime was carried out through solving the Reynolds equation (Equation 1) with a finite volume approach in Matlab™. Due to the very low roughness of the swashplate, the relationship for thin viscous film does not take the statistical effect of roughness into account.

Equation 1: General expression of Reynolds equation

A rectangular domain has been considered, with a zero-pressure assumption outside of the contact (i.e. outside of the orange area in Figure 12).

Figure 12: Domain considered for the calculation

The following assumptions and simplifications were made for solving the Reynolds equation, and increase the calculation speed:

  • Viscosity is considered isotropic,
  • Small angles approximation is made,
  • No cavitation is taken into account,
  • The friction between the convex top of the shoe and the concave socket of the piston is neglected.

The calculation strategy presented in Figure 13 allows calculating the minimum oil film thickness in the contact. Various operation points of the piston expander, accounting for various situations (starting, nominal operation, full power), were simulated. In those situations, the expander experiences different speeds and pressures, thereby changing the oil film thickness.

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Figure 13: Simulation strategy for calculating the minimum oil thickness between the swashplate and the shoe

Contact between the valve rocker and cam

Hertz’ equations provide the stress of each points located on the contact surface, for z=0 (Figure 14), and the stress in the parts, along the contact axis (x=0 and y=0). Moreover, Hertz’ equations apply to static contacts while in the piston expander, the contact between the valve rocker and the cam is dynamic: load varies within one revolution while velocity can change according to the expander’s speed.

Assessing the location of the maximum stress in the contact was carried out using the approach of M’Ewen (M’Ewen, 1949), who proposed an extension of Hertz’ model when friction exists between the parts in contact, i.e. when a tangential load (FT) is created between the surfaces in relative motion. The friction coefficient is defined in Equation 2:

The analysis was carried out by assuming that the actual configuration, comprising thin coatings, could be approximated to a massive homogeneous and isotropic body, given that the Young’s modulus and Poisson coefficient of the coatings are close to those of the steel substrate.

Figure 14: Classic Hertz representation of a cylinder on plane contact

The value of the shear stress according to Tresca was calculated under dynamic conditions (subscript D), i.e. when a normal load (subscript N) and tangential load (subscript T) apply on the contact due to friction between the surfaces (Equation 3).

For z≠0:

Thus, the shear stress is:



The maximal shear stress at each point in the (x,z) plane can now be calculated.

This description works with or without friction, and we can therefore verify that, for µ = 0 ; = 0 ; = 0:

  • The maximum shear stress is found for = 0.78
  • The value of maximum shear stress is 1 ≈ 0.3

Those results are similar to those provided by Hertz’s theory.


Contact between the piston rings and the cylinder

The friction coefficients of antimony-impregnated carbon against Cronidur®30 and Cronidur®30 coated with DLC under various conditions are illuminated in Figure 15. It can be seen that the friction is important in air and lowest in ethanol vapor. The presence of PAG oil or the coating with DLC film does not seem to have a significant impact on the friction in ethanol vapor. The obtained coefficient of friction, lower than 0.1, fulfills the design requirement.

Figure 15: Coefficient of friction for each configuration

Figure 16 emphasizes that vapor greatly favors a reduction of the wear rates on the various specimens. By comparison between the test with water vapor and ethanol vapor, we do not observe any correlation between low coefficient of friction and low wear rate in a vapor environment. Indeed, water seems to reduce wear but not friction whereas ethanol provides a low friction with a slightly higher wear rate. The addition of PAG oil or the use of DLC coating can help to reduce the wear in ethanol vapor.

Figure 16: Wear rate for each configuration

Characterization of materials and worn surfaces was done consequently, through optical microscopy (Olympus SZX7TR), Laser confocal microscopy (Olympus LEXT OLS4100) and scanning electron microscopy (Zeiss EVO50). In particular, roughness measurements were performed with Olympus LEXT OLS4100. The following picture (Figure 17) shows the carbon cylinders under optical microscopy (x12.5).

Figure 17: Optical microscopic view (x12.5) of the wear scars on the cylinders run in (1) hot air, (2) water vapor, (3) ethanol/water vapor, (4) ethanol vapor, (5) ethanol vapor with oil and (6) ethanol vapor oscillated against DLC coated discs.

The wear track on the Cronidur®30 disc of test n°4 in ethanol vapor is shown in Figure 18.

Figure 18: Optical microscopy of wear track on the Cronidur®30 disc, from friction with the carbon cylinder n°4.

Given the shape of the specimens representing the piston ring in the test, the contact pressure is greatest at the beginning of the test and decreases over time as material is worn out. Figure 19 shows the worn volume over time for the test in ethanol vapor, as well as the calculated P*V factor (contact pressure times velocity).

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Figure 19: Measurement of the worn volume of a cylinder during a test in ethanol vapor

We can observe two wear regimes, depending on the P*V value (green curve):

  • At the beginning (blue curve), above a given P*V value, the specimen experiences severe wear at an average wear rate of 10-6 mm3/N.m.
  • Once a P*V value of 2.4 has been reached, wear slows down (red curve) and stabilizes at an average rate of 2.10-8 mm3/N.m.

This expected behavior provided a useful input for the design of the piston rings whose geometry was determined to keep the P*V factor below the maximum measured value for most of the piston stroke, thereby benefiting from a low wear rate satisfying the initial requirement.

In conclusion, we observed that both the friction coefficients and the wear rates were lowest in the vapors compared to dry friction. The friction coefficient was lowest when friction occurred in ethanol vapor. In particular, the coefficient of friction observed in ethanol vapor is much lower than those reported for ceramic materials or coatings in liquid ethanol. The low friction in ethanol vapor could be assigned to favorable tribo-chemical reactions. Further work is needed to identify potential lubricious oxides involved.

Regarding the experimental results both in terms of friction and wear, the couple antimony-impregnated carbon and Cronidur®30 seems a good candidate for parts experiencing high temperature friction in a WHRS piston expander working with vapor of ethanol and water. The lack of oil can be compensated successfully by using those materials.

Contact between the swashplate and the shoe

The results of the simulation of the oil film between the swashplate and the shoe are now presented.

Comparing the minimum oil thickness h0 with the composite root mean square roughness of the swashplate and shoe surfaces Rq* allows evaluating an oil film parameter λ = ℎ0/Rq* . The design was oriented such that λ>3 with the hydrodynamic lubrication regime. The very low surface roughness of DLC in the range of Rq~ 20 nm favors the lubricating film formation. Figure 20 presents a typical pressure profile in the contact for a nominal operation of the expander.

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Figure 20: Oil pressure profile between the swashplate and the shoe

The calculation of the friction force (Equation 4) is then used to determine the coefficient of friction (Equation 5) when a normal load Fpiston is applied on the shoe.

Three effects influencing the dynamic viscosity of the oil have been taken into consideration as much as possible:

  • Dilution by working fluid (the actual viscosity, measured with working fluid dilution, was taken as reference)
  • Effect of pressure by means of Barus’s equation; the pressure-viscosity coefficient was determined by the PAG supplier.
  • Effect of temperature due to heat generation in the contact, by means of Reynolds’ equation; 20% of the heat generated in the contact due to friction is considered to increase the temperature of the oil, given the ratio of thermal effusivities of the materials.

The outgasing of working fluid due to the temperature increase was not taken into account.

The results of the simulation for two operating points are presented in Figure 21. Both configurations (A & B) were simulated with an incoming steam at 225°C and exhaust pressure of 2 barA. In configuration (A) the incoming steam pressure is 45 barA and the rotation speed 1500 RPM, representing a challenging situation (e.g. uphill driving). The calculated average coefficient of friction in configuration (A) is µ = 0.008. In configuration (B), the incoming steam pressure is 30 barA and the rotation speed 3000 RPM, representative of a typical highway cruising. The calculated average coefficient of friction in configuration (B) is µ = 0.003.

Figure 21: Simulation results for two operating conditions of the expander

In parallel, experimental investigations of the swashplate-shoe contact have been carried out:

  • At EXOES, where the piston expander has been tested and the swashplate and shoes examined on a regular basis.
  • At the QUARTZ laboratory in Paris, where tests on an adapted pin-on-disc tribometer have been performed (Figures 22 and 23).

The QUARTZ tribometer allowed to simulate the swashplate-shoe friction in oil up to 140°C, with a load generating up to 7.3 MPa and a speed between 0.001 and 2 m/s (L. Havet, 2001). The shoe was made in ball bearing steel 100Cr6 and the swashplate was represented by a Z38CDV5 (X37CrMoV5-1) disc coated with DLC.

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Figure 22: Pin-on-disc tribometer adapted to test friction between the swashplate and the shoe in hot oil

Figure 23: Test parts used to represent the swashplate and the shoe

19 tests on the tribometer have been carried out and the following conclusions can be shared:

  • The tests allowed to plot a Stribeck curve highlighting various lubrication regimes (Figure 24).
  • The lowest coefficient of friction measured was 0.001, in a region with Hersey numbers close to those expected during nominal operation of the piston expander.
  • Five wear tests were performed, under extreme conditions of very low speed (8 mm/s), high load (7.3 MPa) and high temperature oil (140°C). Under these conditions, a low wear rate of Kv~110-7 mm3/(Nm) was measured for the shoe, while the disc hardly showed any wear.

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Figure 24: Experimental Stribeck-type curve of the swashplate-shoe lubrication obtained at the QUARTZ laboratory

The results of the initial simulations and the later experiments, whether on the adapted tribometer or with the expander prototype have confirmed that very low coefficients of friction can be reached under the challenging conditions of the crankcase of the expander, combined with a relatively safe oil thickness. The tests also confirmed the relevance of the materials selected for this contact, which did not lead to seizure or scuffing.

Contact between the valve rocker and cam

The equations presented in section 2.4 were used to calculate the shear stress on a grid representing the (x,z) plane within the material. The results are depicted using Microsoft Excel where each of the 30.000 cells of the grid was populated with a calculated value and colored accordingly. This technique allowed using an analytical approach instead of finite elements simulations. The following graphs in Figure 25 show the relationship between the position of the maximum shear stress and the coefficient of friction, with the load data of the expander valvetrain.

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Figure 25: Displacement of the location of the maximum shear stress due to increasing friction coefficient

We can observe that the location of the zone of maximum shear stress shifts toward the surface and opposite to the direction of motion. Also, the maximum shear stress increases with the coefficient of friction. From a static condition (μ = 0) to a sliding condition under high friction (μ = 0.4), the value of the shear stress increases by 50%.

It was estimated that the interface between the DLC layer (3 µm) and the substrate (steel grade 1.2343), or between the CrN layer (4 µm) and the substrate (steel grade 1.4871) would experience acceptable stress up to a coefficient of friction of 0.3. Regarding the nature of the two coatings in contact and considering the presence of small amount of oil, the contact was deemed safe.

Assuming a worst-case scenario of μ = 0.4, the stress within the steel of the valve rocker would vary during a revolution between a maximum value of ~200 MPa and a minimum value of ~70 MPa. Assuming a fatigue strength of the material at 50% of its UTS (780 MPa), no initiation of sub-surface cracks should occur during the lifetime of this component.

Long term reliability testing of the piston expander of more than 108 cycles did not reveal premature wear of the valvetrain and thereby confirmed the theoretical conclusions.


Facing difficult tribological challenges during the development of its piston expander technology, EXOES relied on an approach combining advanced simulation of the tribological contacts at stake, and extensive experimental testing both at the component level and at the system level. This strategy was successful in reaching the high reliability targets desirable for a piston expander used to recover heat from long-haul trucks.

Water-ethanol vapors usually exert a low lubricity on the common tribo-systems, but beneficial tribo-chemical interactions between the surfaces and the gaseous working fluid, parsimonious use of a carefully selected oil, and appropriate design can result in a well operating and durable equipment.


Thiébaut Kientz¹*, Mathias Woydt², Jean-Louis Ligier3, François Robbe-Valoire4

¹ Capax Infiniti SAS, 13 rue Chapon, F-75003 Paris, France; ² MaTriLub, D-12203 Berlin, Germany; 3HEIG-VD, CH-1401 Yverdon-les-Bains, Switzerland; 4Quartz, 3 rue Fernand Hainaut, F-93407 Saint-Ouen, France; *Corresponding author: [email protected]


Many thanks are addressed to Prof. Dr. François Robbe-Valoire, Supméca – Institut Supérieur de Mécanique de Paris, (QUARTZ) engineering laboratory of mechanical systems and materials, FR-93407 Saint-Ouen, France, for performing the tribometric test campaign. Mr. Manfred Hartelt of BAM is gratefully acknowledged for executing the tribological tests in hot steam.


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