1 Introduction

Modern gear boxes in airplane applications, like geared turbofans, have to be designed to meet the ever-increasing demands for reduction of frictional losses as well as weight. Consequently, applications more often use low viscosity oils and component sizes are reduced altogether. These requirements cause major challenges as high contact pressures are combined with very high pitch line velocities. That increases the risk of scuffing and catastrophic termination of lifetime. Moreover, weight saving strategies, resulting in a lack of secondary lubrication systems and operating modes like negative g, additionally add up loss of lubrication (LOL) conditions to the gear contact.

Therefore, alternative materials and coatings or surface machining procedures are required to enhance future gear box resilience against scuffing during LOL conditions at high operating velocities. As prototype tests on gear boxes [1] are costly and time-consuming, they have to be limited to a few promising variants. More abstract model tests are less complex and allow the screening of a larger number of design variants than full gear-box tests. FZG gear test rigs are applied to assess friction [2] or scuffing [3, 4]. In addition, twin-disc test configurations are frequently used to study gear contacts on a fundamental level [5, 6]. Transferability and comparison of results between gear test rigs and twin-disc rigs is not trivial and in the focus of various studies by, e.g. Castro et al. [7].

Usually twin-disc test rigs focus on entrainment velocity ranges between 0.5 m/s and 8 m/s and with maximum slide-to-roll ratios of 50%, which results in sliding velocities of only 0.15 m/s to 4 m/s [6, 7]. Higher velocities are rarely realized on available twin-disc test rigs with a few exceptions such as in the following publications. Patching et al. [8] published coefficient of friction values and start of scuffing on a twin-disc tests at up to 21 m/s entrainment velocity under fully lubricated conditions and a recently published work by Handschuh et al. [9] on a rig operating at up to 50 m/s entrainment velocity. However, modern gear applications, especially in aerospace, operate under much higher velocities [9, 10], and that increases the need for data at high velocities. Additionally, these applications come along with higher lubricant temperatures than the often published ranges between 40 °C and 90 °C [6].

Published literature on scuffing usually reports studies on continuously lubricated systems and examines parameters that lead to scuffing such as overload cycles on twin-disc test rigs [8, 11, 12], gear tests [12] as well as on ball-on-disc rigs [13]. Increasing the slide-to-roll ratio to provoke scuffing in a ball-on-disc configuration is used to build up simulation models for scuffing such as in [13]. On the other hand, there is a limited number of studies under LOL conditions on twin-disc test rigs [14]. Riggs et al. [4] compared different lubricants and surface roughness in LOL conditions with a ball-on-disc configuration that could spin the ball and control entrainment and sliding velocity up slide-to-roll ratios of 100% but limited to 16 m/s entrainment velocity. Similar studies on a ball-on-disc test rig were used as pre-tests prior to full gear tests by Kozachyn et al. [15], who focused on a benchmark of coatings and Berkebile et al. [16], who studied time of failure in a ball on disc configuration for different steels. Kozachyn et al. [15] combined the ball-on-disc tests with full scale FZG tests in LOL conditions. Gear tests studies under LOL conditions published by [3, 17] focus on the test methodology itself, but lack physical based explanations on the observed results.

The current study is part of a larger undertaking to characterize the effect of high velocities on friction, temperature, and the behaviour during LOL conditions at high entrainment velocities that correlate to pitch line velocities of 80 m/s for a type C FZG gear. The project part presented in this work is focusing on the friction behaviour on a twin-disc configuration during continuous and LOL conditions of two transversally ground discs, jet lubricated with a typical turbine oil and heated up to 120 °C. The paper presents a specially designed twin-disc test rig, which enables tests at entrainment velocities of up to 80 m/s along with high-pressure, high-temperature jet-lubrication. Subsequent chapters present the elaborated test procedure for LOL conditions as well as selective tests with superfinished discs. The experimental results on a wide range of lubricant injection temperatures, normal pressures, entrainment velocities as well as slide-to-roll ratios are consolidated with mixed EHL simulations to identify the key influencing parameters for stability of friction during continuous lubrication and the robustness against LOL conditions.

2 Aim of the investigation

The aim of the current study is to detect the key influencing parameters on friction level in continuous lubrication mode and on time of failure in LOL mode under high-speed conditions in a twin-disc configuration. In contrast to gear contacts that offer integrated effects along the line of contact but impair root-cause analysis of observed change of friction behaviour, a model test such as the twin-disc test presents the option to assess parameters separately and thus rank the effects of potential design variations.

The test rig and the testing procedures elaborated in the current work are intended to be used for further benchmark studies on material, coating, or machining variants for gear applications. Within the presented scope focussing on transversally ground surfaces a preliminary comparison with superfinished surfaces was performed.

3 Materials and investigated topographies

The steel used in the current study was the AISI 9310. It is carburizing steel which has high hardenability, high core hardness together with high fatigue strength. It is a standard steel used for critical aircraft engine gears due to its good ductility properties combined with good weldability and machining properties. The discs were carburized to a hardening depth of 1 mm. The hardness at the surface was in a range between 600 and 850 HV0.05 according to hardness profiles determined in metallic cross sections, cut perpendicular to the testing surface.

The applied lubricant Aeroshell Turbine oil 500 (MIL-PRF-23699, class STD, NATO Code O‑156) is a synthetic base oil with an ester component and antioxidative additives. Its viscosity properties are given in Table 1.

Table 1 Lubricant properties of Aeroshell 500
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The 3D surface topographies of the discs, measured with an Alicona Infinite Focus G5 with focus variation at a magnification of 200 x, were defined by two different machining processes: transversal grinding and superfinishing. Their respective roughness parameters are given in Table 2. The simulations enable additional studies of circumferential griding pattern by rotating the measured surface numerically. The roughness parameters of this rotated surface topography in direction of the lubricant flow are also given in Table 2.

Table 2 Surface roughness parameters of transversally and circumferentially ground as well as superfinished surfaces measured with focus variation
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4 Transfer of gear loading conditions to a twin-disc configuration

4.1 Loading conditions

The tests were carried out at operating conditions deduced from the gear mesh calculation for load stage LS9, which is specified by a pinion torque of 302 Nm and a wheel torque of 453 Nm. Based on calculation with the software KISSsoft®, the maxi-mum Hertzian contact pressure and sliding velocity vs combinations along the line of contact for a slightly modified type C gear were determined, shown in Fig. 1.

Fig. 1
figure 1

Maximum Hertzian contact pressures and sliding velocities vs derived for the modified type C gear flank. The colours each represent another pitch line velocity of the gear (vt = blue:20 m/s, red: 40 m/s, grey: 60 m/s, yellow: 80 m/s)

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The high pitch line velocities vt of interest were in a range of vt = 20 m/s up to 80 m/s. These calculated parameters were transferred to entrainment velocities, sliding veloc-ities and contact pressures for the twin-disc test rig. To cover a range of contact conditions in the gear along the line of contact, combinations of three contact pressure levels and three pitch line velocities vt were chosen and transferred to entrainment velocities ve = 0.5(v1+v2) of the discs:

  • vt = 20 m/s → ve = 8 m/s,

  • vt = 60 m/s → ve = 23 m/s,

  • vt = 80 m/s → ve = 30 m/s.

4.2 Disc samples

The discs manufactured for the twin-disc test rig had a diameter of 200 mm to widen the range of achievable velocities. The grinding pattern orientation of the discs was chosen to be transversally ground, oriented parallel to the disc axis, which makes the grinding grooves oriented perpendicular to the lubricant inlet flow direction, here the entrainment flow direction respectively. This correlates to the grinding pattern orientation on a gear flank.

The decision for a cylindrical disc geometry was driven by manufacturing limitations precluding a transversal grinding pattern on crowned discs. The discs were designed to narrow down from 20 mm in the center to a width of 10 mm and a contact length b, as indicated in the sketch in Fig. 2. To reduce the edge effects, which come along with cylindrical samples and line contacts, rounded edges were machined on the thinner disc. The final width of b was 2.8 mm (upper quartile 2.9 mm, lower quartile 2.4 mm) that enabled the required 1600 MPa contact pressure. This presents a compromise between aspect ratio of the contact and large disc diameters enabling significantly increased velocities.

Fig. 2
figure 2

a Schematic of twin-disc test rig depicting the main components; b detail of the disc contact showing the widths of the lower disc (10 mm), the upper disc (b = 2.8 mm), and the distance of the temperature sensor from the surface (4 mm); c 3D drawing of the bearing blocks and the oil box with the nozzle and the drainage; d detailed 3D drawing of the oil box and the nozzle with the injection jet

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5 Test rig and test conditions

5.1 Test rig and measurement devices

The tests were executed on a twin-disc test rig which was configured to enable very high velocities, both entrainment and sliding velocities. The employed test rig (Fig. 2) was designed to enable entrainment velocities up to ve = 80 m/s—well above velocities of ve = 8 m/s, which are often reported as the highest tested entrainment velocity at twin-disc rigs in literature. For a type C FZG gear ve = 8 m/s correlates to a pitch line velocity of only 20 m/s.

Figure 2a shows a schematic of the test rig. In the centre it illustrates the oil box that encloses the two vertically aligned discs. Each disc is connected to an axis supported by a bearing block. Separate engines drive each disc independently. Transition belts for accelerating the disc speeds are applied for each engine and are indicated by the dashed lines. The lower disc, its bearing block and engine are mounted on a movable table. The normal force on the tribological contact is applied by pushing this movable table upwards. The load is applied pneumatically and can be set seamlessly up to 15 kN. The friction torque is measured at the upper shaft. For the determination of the coefficient of friction the torque measured for unloaded rotation was subtracted to consider the torque loss in the bearings and the drive belt transmission system.

Figure 2b shows the tribological contact between the two discs in detail. Figure 2c is a 3D drawing of the bearing blocks and the box with the injection nozzle placed in the centre of the box. The latter one is also illustrated in Fig. 2d, which depicts the oil injection jet into the tribological contact. The flow rate was set to 2.2 l/min. To provide the whole width of the contact with lubricant, a fan nozzle was installed for the injection with a nominal horizontal spray angle of 2°. The drainage of the oil box indicated in Fig. 2c transports the oil from the box back into the oil tank (not shown in the figures). The drainage consists of two outlets to enable drainage via gravity and additionally by sucking with a pump. This ensures that no lubricant remains in the box during LOL experiments. The lubricant is supplied into the contact by means of a pump via the feed line into an injection nozzle.

The higher velocities of up to 80 m/s were realized by the transition belt system on both shafts of the rig as well as with large disc diameters of 200 mm. The feasible sliding velocities are directly linked to the friction torque evolving in the contact, which are limited by the torque limits of the test rig engines. Therefore, no general values can be stated. The two engines which drive each disc separately work in a master-slave configuration.

The applied oil circuit can supply lubricant with a high injection temperature of up to 180 °C. Temperature limits largely depend on the lubricant itself. With the Aeroshell 500 used in the current study, screening tests up to 150 °C were possible. The focus of the experimental test has been set to 120 °C. This provided some temperature span for safety and allows the lubricant to heat up due to friction below the evaporation point of 185 °C.

The temperature of the thinner disc was measured 4 mm below the contact area with Type K thermocouples, which transmitted the signal contactless via a transmitter at the end of the rotation shaft.

5.2 Testing parameters and procedures

In Table 3 the investigated parameter combinations are listed. For some parameter combinations not all three pressure levels have been studied due to the limited number of samples. The rotational direction of the discs was adjusted to the same direction as the direction of the oil flow injected by the inlet nozzle.

Table 3 Testing parameters of the twin-disc test rig for continuously lubricated conditions and limiting sliding velocities vs for stable friction condition. The transversally ground discs are indicated by “g”, the super-finished discs by “sf”
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After a pure rolling phase at 0% slide-to-roll ratio (SRR), the testing protocol follows a stepwise increase of the SRR, usually in 5% steps. The SRR was increased as long as the CoF at each step did reach a stable value. Each SRR step was maintained until a stop criterium—to protect the test rig from damage—was reached.

Stop criteria were defined as:

  • steep increase of the friction torque, reaching the torque limit of the rig. Depending on the rotational speed of the engine and the duration of the loading the maximal torque limit of 100 Nm can be exceeded for a short period of time or decrease at high rotational engine speeds according to the engine characteristics.

  • high disc temperatures T ≥ 150 °C, which led to smoke formation of the lubricant.

  • maximum LOL time of 15 min, provided no other changes of the torque, temperature or rig was observed

    In any case the time till reaching the respective shut-off criterium was address as time of failure (TOF).

5.3 Procedures for continuous lubrication conditions

At all test conditions which resulted in stable friction conditions the coefficient of friction (CoF) was determined by calculating its average over 10 min test duration. These average CoF values were used to analyse the dependency of the CoF on entrainment velocity, sliding velocity and contact pressure.

During continuous lubrication, the SRR was increased in 5% steps. A change in SRR can lead to a run-in behaviour of the CoF or to a continuing increase. If the CoF over time runs into a plateau at a stable level, then this level was taken as the “stable CoF” value, provided the CoF signal did fulfil the criterion for stability

$$\frac{\mathrm{CoF}\_ \mathrm{Q_{3}}-\mathrm{CoF}\_ \mathrm{Q_{1}}}{\mathrm{CoF}_{\text{median}}}< 0.1{,}$$
(1)

where CoF_Q3 refers to the upper quartile, CoF_Q1 to the lower quantile and CoFmedian to the median value of all recorded CoF values at the respective SRR.

Table 3 shows the maximum sliding velocity that proved to fulfil the criterium for stability of the friction over time in the performed experiments.

5.4 Procedures for loss of lubrication (LOL) experiments

Temporary and permanent LOL tests (oil-off tests) were performed at the highest possible SRR step with stable friction conditions. Under LOL conditions the time of absence of lubricant supplied by the inlet nozzle was varied. Permanent oil-off tests were run without oil until a shut off criterium was reached. The duration until that shut off criterium was reached, was identified as TOF. The temporary oil-off consisted of a series of increasing time spans where the oil-inlet nozzle was closed, each followed by a continuously lubricated phase to allow the system to regain stable conditions. The oil-off duration was extended from initially 20 s oil-off to 60 s and 135 s to eventually permanent oil-off. In cases which did not allow the full 60 s or full 135 s as temporary oil-off the respective maximum duration was taken as the permanent oil-off case of this parameter combination.

6 Mixed Friction and EHL simulation model

The EHL simulation model is based on the quasi-stationary Reynolds equation

$$\nabla \cdot \left(\frac{h^{3}}{12\upeta }\nabla p\right)-v_{e}\nabla h=0{,}$$
(2)

describing the relation between lubrication gap h and lubricant pressure p for given entrainment speed ve and viscosity η(p). In addition, a strongly coupled elastic problem is solved to incorporate the elastic deformations of the solids. The expected loads make it necessary to extend Eq. (2) to the mixed lubrication regime. Based on the work presented in [18, 19], a homogenization method [20] is used to obtain flow factors A, B and an asperity contact pressure pA. These flow factors are calculated in a non-dimensional form using a scaling parameter hr, usually chosen as arithmetic mean of the measured surface roughness h1. Utilizing \(A\in R^{2\times 2}\) and \(B\in R^{2}\), the resulting homogenized Reynolds equation reads

$$\nabla \cdot \left(\frac{{h}_{r}^{3}}{\upeta \left(p\right)}A\nabla p\right)-12v_{e}h_{r}\nabla B=0.$$
(3)

The pressure dependence of the viscosity is modelled using the Roelands equation [21, 22]

$$\upeta \left(p\right)=\eta _{0}\left(\frac{\eta _{0}}{\eta _{r}}\right)^{{\left(1+\frac{p}{p_{r}}\right)^{z}}-1}{,}$$
(4)

with the dynamic viscosity at ambient pressure η0, the coefficients \(\eta _{r}=6.31\cdot 10^{-5}\,\mathrm{Pa}\cdot \mathrm{s}\) and \(p_{r}=0.196\,\mathrm{GPa}\), the dimensionless parameter

$$\mathrm{z}=\frac{\upalpha p_{r}}{\ln \left(\eta _{0}\right)-\ln \left(\eta _{r}\right)}$$
(5)

and a positive parameter \(\upalpha =10^{-8}\mathrm{P}\mathrm{a}^{-1}\) describing the rate of change of the viscosity with respect to the pressure.

The strongly coupled problem consisting of the homogenized Reynolds equation and the elasticity problem is implemented within an EHL simulation package developed by AC2T research GmbH in cooperation with CERBSim GmbH. This specialized package for mixed EHL simulations is based on the mesh generator Netgen [23] and the finite element software NGSolve [24, 25], which are both open-source software packages. They are combined using their Python interfaces, allowing to keep the whole simulation workflow within one framework, which simplifies the implementation of parameter studies and the post-processing of the results. The outstanding feature of this combination of open-source software and customized code development offers vast potential for increasing simulation speed and improved accuracy of the simulation results due to the high order discretization spaces.

A section of the full 3D disc model is given in Fig. 3. The whole FEM model consists of two full size discs, discretized with 10,714 tetrahedral elements and local refinement to 0.1 mm in the area of contact. To cover the expected edge effects, the element size is further reduced to 0.05 mm along the edges of the contact area. The simulation results in this study have been performed with third order continuous finite elements. The disc width was chosen to be equal to the median value of all discs for the experimental test series, which was only 2.8 mm due to some variation in machining production. The normal contact pressure was set to 1000 MPa, 1300 MPa, and 1600 MPa to allow comparisons with the experiment. Figure 3 schematically depicts the evaluation method used for the EHL results in the next section, where the lubrication gap and pressure results were either evaluated across the disc sample width, which is a cutting plane normal to the flow direction, or parallel to the flow direction in the middle of the disc width.

Fig. 3
figure 3

Finite element mesh and a representative solution of the lubrication gap h, indicating the cross-sections parallel and normal to the entrainment flow direction

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A 3D image of the measured topographies (details and roughness values in Table 2 in chapter 3) of the ground and superfinished surfaces are shown in Figs. 4 and 5, respectively. They were numerically applied to both discs to reflect the experimental test, which always used a pair of equally machined discs. For each surface topography a representative subdomain of about 1 mm2 was selected. The combined surface topography h1 is given by the difference of the surface roughness height of the selection subdomain of the disc surface and its copy, which was flipped around the y‑axis. This mimics the contact of two discs with the same surface finish. For the resulting arithmetic means hr of the function h1, we obtain hr = 2.15 µm for transversally ground, hr = 2.23 µm for circumferentially ground and hr = 1.23 µm for superfinish. The homogenized lubrication gap h, as output of the mixed EHL simulation, is defined as strictly non-negative function, which indicates contact of the asperities for values below hr. For simplicity, the homogenized lubrication gap is denoted as lubrication gap h in the remainder of the paper.

Fig. 4
figure 4

Measured 3D topography of the transversally ground disc surface

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Fig. 5
figure 5

Measured 3D topography of the superfinished disc surface

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7 Results and discussion of frictional behaviour under continuous lubrication and LOL conditions

7.1 Experimental and simulation results for continuous lubrication

7.1.1 Experimentally determined friction coefficient level

The CoF values were determined experimentally at the parameter combinations derived from loadings in the line of contact at the gear described in chapter 5.2. Figure 6a to d show the values that were assessed to be stable, which means that the friction coefficient behaviour fulfils the criterion of stable friction defined in chapter 5.3. The tests in Fig. 6a and b were run with 8 m/s entrainment velocity ve, but the oil temperatures were different being 60 °C in Fig. 6a and 120 °C in Fig. 6b. Therefore, the oil viscosity was higher for the tests in image section Fig. 6a.

Fig. 6
figure 6

Stable CoF as function of vs at different ve and oil temperatures; a ve = 8 m/s, T = 60 °C; b ve = 8 m/s, T = 120 °C; c ve = 23 m/s, T = 120 °C; d ve = 8 m/s, T = 120 °C

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On average the CoF values for 60 °C are lower than for 120 °C. This could be explained by a larger lubrication gap height for the higher oil viscosity, reducing the CoF in mixed lubrication regime. Furthermore, image section Fig. 6a depicts the tendency of decreasing CoF values with increasing sliding velocities, which indicates increasing lubricant gap with increasing sliding velocity. Tests in Fig. 6b–d were all run at 120 °C but with different entrainment velocities ve of 8 m/s, 23 m/s and 30 m/s, respectively.

The limiting SRR for stable friction condition decreased with increasing entrainment velocity, but in absolute values the corresponding sliding velocity was observed to be at about 4.5 m/s. Deviations are attributed to scatter of the measurement data. This limit could be explained by the amount of frictional heat generated in the studied system that reached a critical value close to 4.5 m/s sliding velocity. Consequently, resulting in critical surface temperatures and scuffing, followed by surface roughening which itself increases friction torque successively.

7.1.2 Mixed-EHL simulation results on lubrication gap and pressure

The surface topography and the orientation of the machining pattern strongly influences the lubrication gap height and its shape, which will be discussed in this section. First, two orientations of the grinding pattern are compared—see Fig. 7 followed by a comparison of two different machining processes, keeping the transversally ground orientation according to the real machined samples for the experiments. The surface topographies and their orientation with respect to the flow direction in the experiments are shown in Figs. 4 and 5.

Fig. 7
figure 7

Ground surface topography indicating the orientation of the grinding pattern. The solid arrow corresponds to the transversally ground orientation used in the experiments and the dashed arrow to a grinding direction parallel to the flow direction

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Influence of grinding direction

Grinding grooves oriented parallel to the flow direction lead to a more evenly distributed gap height across the width of the nominally 2.8 mm wide line contact for all entrainment velocities ve (see Figs. 8 and 9). The maximum gap heights in the middle are on equal levels for 120 °C and the standard ve = 8 m/s. Yet, for higher entrainment velocities the gap height is substantially lower for the parallel grinding pattern. This difference seems to decrease in its relative values (15% compared to 30% at 120 °C) when the inlet temperature is decreased to 60 °C, though the absolute values are naturally much higher for lower inlet temperatures.

Fig. 8
figure 8

Lubrication gap across the sample width, normal to the flow direction for grinding direction normal and parallel to lubricant flow

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Fig. 9
figure 9

Lubrication gap in flow direction for grinding direction normal and parallel to lubricant flow

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The simulation of the two different grinding directions cannot be compared to experimental results as those have been decided to focus on grinding directions normal to the inlet flow. However, the simulation illustrates the tendencies and indicates the differences between those two variants in numbers to assess the difference of machining directions for the lubrication gap results. In fact, there is a difference in characteristics besides the difference in numbers as the typical EHL pressure peak hardly shows for the 120 °C cases in the parallel grinding variant but is does show markedly for all simulated cases for the transversally ground variant, as shown in Fig. 9.

Furthermore, the simulation results illustrate a much more pronounced edge effect for the transversally ground variant, which explains to a certain degree the operational challenges involved in the execution of twin-disc line contact experiments with such short contact length as in the current study.

Influence of surface topography—superfinished versus ground

A well-chosen parameter combination was performed on the only pair of discs in the superfinished condition. So, simulation provided a means to study the topography effect in more detail virtually. The mixed EHL simulation model does, first of all, show a pronounced difference for the two topographies with respect to lubricant pressure and lubrication gap height distribution for the experimentally executed tests at 120 °C inlet temperature and ve = 30 m/s at a vs = 3 m/s (Fig. 10). The lubricant in the ground surface gap cannot bear the same amount of pressure as the superfinished version even though its gap height is only at 0.65 µm compared to 0.85 µm for the ground version (both evaluated at the centre point in Fig. 9). Qualitatively the same can be observed for lower inlet-temperatures, which is implemented by an increased lubricant viscosity, but the load carrying capacity of the lubricant becomes indistinguishable. The curves across the disc width for 60 °C inlet temperature of ground and superfinished surface largely overlap and can consequently not be distinguished in Fig. 10.

Fig. 10
figure 10

Lubricant pressure, asperity pressure, lubrication gap in flow direction at an entrainment velocity of 30 m/s and 1000 MPa contact pressure

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The pronounced difference in the experimentally determined coefficient of friction between the ground (CoF = 0.0222) and superfinished (CoF = 0.0137) version can be explained with the simulation results with respect to the asperity pressure distribution in Figs. 10 and 11. The transversally ground surface shows significantly higher and laterally much larger extension of the asperity pressure, which basically shows the regions of solid-solid contact. Both surface variants are in mixed lubrication condition for 120 °C or 60 °C injection temperature and ve = 30 m/s. Yet, the ground surface appears to be even further away from hydrodynamic conditions than the superfinished one and even in continuously lubricated conditions at seemingly rather moderate sliding velocities of 3.0 m/s the friction is dominated by asperity contact. These results indicate that not the absolute gap widths are most relevant for the friction but rather the load carrying capacity of the lubricant in the gap.

Fig. 11
figure 11

3D asperity pressure contact distribution over the whole contact area for a transversally ground b superfinished surfaces at 1000 MPa, ve = 30 m/s, injection temperature 120 °C

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The topography influence seems to become more relevant for higher lubricant inlet temperatures. It has to be considered that the entrainment velocity does have a similar effect on the lubricant gap. Particularly higher entrainment velocities increase the lubricant pressure and thus its load carrying capabilities which reduces the asperity contact by increasing the gap height. As a consequence, the topography becomes less relevant at high entrainment velocities.

Within the studied parameter range, the comparison of all key parameters in Fig. 12 indicates that entrainment velocity and lubricant injection temperature have the most prominent influence on the central lubrication gap height. At higher entrainment velocities, the influence of lubricant temperature is more pronounced, but it is still significant for the lowest studied entrainment velocity. As the slope of gap height increase is steeper for lower injection temperatures, the differences in gap heights upon change of lubricant temperature becomes largest for the highest entrainment velocity. In comparison, the gap decrease due to loading pressure increase is relatively small.

Fig. 12
figure 12

Central lubrication gap as a function of ve given for 60 °C and 120 °C inlet temperature and three pressure levels (indicated by symbol shape). Results for transversally ground surface are depicted with full symbols, for superfinished surface in open symbols

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Figure 12 further illustrates the effect of topography changes from a transversally ground to a superfinished surface. The open symbols show reduced gap heights for superfinished surfaces for all conditions compared to the transversally ground surface represented by full symbols. Nevertheless, the overall asperity contact is lower for superfinished ones as the lubricant pressure in the gap is higher (see Fig. 10 exemplarily for 30 m/s at 120 °C).

7.2 Results of friction behaviour under LOL conditions

All LOL tests discussed in this paper were performed with an oil-inlet temperature of 120 °C in continuous mode. As the time to reach thermal stability of the test setup—including the test rig, the oil circuit, and the discs—is rather high, initial temperatures of the discs at the start of LOL conditions could not be kept identical for each test but were set in a range of 80 °C to 100 °C starting disc temperature. Therefore, absolute temperature levels are to be compared with great care only. The qualitative conclusions which can be drawn from the results within the range of the testing study are as follows. Note that all subplots in the Figs. 13, 14, 15, 16, 17, 18 and 19 show the CoF on the primary Y‑axis and the disc temperature (4 mm beneath the contact) on the secondary Y‑axis on the right-hand side. Scales are identical within one experiment for all subplots but adapted for the sake of clarity for each experiment. Solid lines illustrate the data before and during the LOL events, while the dashed lines refer to the data after each LOL step.

Fig. 13
figure 13

LOL test of transversally ground discs at ve = 8 m/s, vs = 1.2 m/s, 1000 MPa with succession of three temporary and a permanent oil-off test. Each LOL period starts at time 0 s

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7.2.1 LOL condition—influence of entrainment and sliding velocity and pressure

The influence of the entrainment velocity is illustrated by the Figs. 13 and 14 where entrainment velocity is increased from 8 m/s to 30 m/s and both LOL tests have been performed at a SRR of 15% and a contact pressure of 1000 MPa. Both parameter combinations allowed a full sequence of 20 s, 60 s and 135 s temporary oil-offs, which all led to the CoF and disc temperature of the prior continuous level. Considerable differences can be observed regarding the friction behaviour during the temporary oil-offs, which is especially pronounced during the longest period of 135 s. The higher entrainment velocity resulted in a distinctly larger increase of friction. Note, that the continuous friction levels are higher for the test at lower entrainment velocity of 8 m/s, so the maximum friction level at the end of the 135 s LOL period is higher for 8 m/s than for 30 m/s, despite higher relative changes.

Fig. 14
figure 14

LOL test of transversally ground discs at ve = 30 m/s, vs = 4.5 m/s, 1000 MPa with succession of three temporary and a permanent oil-off test. Each LOL period starts at time 0 s

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During the permanent oil-off phase the 8 m/s test did not exhibit further increase of friction but rather remained at the level reached already during the 135 s duration of lubrication absence. After an unstable behaviour, the friction coefficient even decreased by 15% to about 0.04 and this phase could be maintained for a comparatively long time which is also reflected in the disc temperature that reached a plateau value of 117 °C. The recorded TOF was 900 s, which was in fact the maximal time criterium for a manual shut-off, provided no obvious changes could be observed by the operator. Contrary, the high entrainment velocity test reduced the TOF to 272 s due to a fulfilment of the maximum torque and maximum disc temperature criterium. During the LOL phase for the ve = 30 m/s test, the friction increase also does exhibit a decreased slope after an initial phase, however, the friction still increases steadily until a nearly instantaneous increase of torque led to an abrupt temperature increase and manual shut off for safety reasons. Although future LOL tests at ve = 8 m/s should run longer than 15 min, the present observations still clearly show a significant influence of the entrainment velocity at equal SRR, here 15%.

The influence of contact pressure can be illustrated for two tests performed at an entrainment velocity of 23 m/s and a SRR of 10%, one at 1000 MPa (Fig. 15), the other at 1600 MPa (Fig. 16). The increase of contact pressure which is accompanied with an increase of the generated friction power led to a drastically reduced TOF from 1264 s to 35 s. Again, the initial friction level in the continuous phase is different, which can also be attributed to the increased contact pressure and the thus decreased lubrication gap height (s. section above). However, the friction behaviour in the 1000 MPa experiment shows a deceleration of the increase of CoF after about the first 100 s. Then the system seems to be capable of preserving functionality for a very long time until suddenly, there is an instantaneous increase which calls the maximum friction torque shut-off criterium.

Fig. 15
figure 15

LOL test of transversally ground discs at ve = 23 m/s, vs = 2.3 m/s, 1000 MPa with succession of three temporary and a permanent oil-off test. Each LOL period starts at time 0 s. Here the critical torque limit was approximately 45 Nm

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Fig. 16
figure 16

LOL test of transversally ground discs at ve = 23 m/s, vs = 2.3 m/s, 1600 MPa with one temporary and a permanent oil-off test. Each LOL period starts at time 0 s. Here the critical torque limit was approximately 45 Nm

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This behaviour can be explained by the following hypothesis: a residual amount of lubricant is adhering to the surface and can sustain in the initial period of LOL. Once it is consumed, the asperity tips touch and the surface begins to roughen up. Thus, friction increases and becomes more unsteady. This condition appears to be maintained for some time until the surface becomes so rough that local asperity pressures become high enough for scuffing to occur, which results in this instantaneous torque increase. As the measured torque increase comes along with a likewise disc temperature increase, it can be concluded that also the surface temperature rises. Critical surface temperatures are numerously described as one criterium for scuffing initiation in simulation models e.g., in one for point contacts in [13].

On the other hand, for a 1600 MPa experiment at ve = 23 m/s (Fig. 16), the friction versus time trend exhibits a marked kink at about 5 s. Apparently, there is no intermediate phase and once the centrifugal forces removed all adhering lubricant residuals, scuffing sets on immediately. The detected maximum CoF and maximum temperature values are very sensitive to the reaction time of the operator as well as those of the sensor system of the test rig. Therefore, the maximum values are to be interpreted qualitatively. In future, of course tests with statistically sufficient repetitions would also allow comparison of respective CoFmax and Tmax values with this testing protocol.

The influence of pressure was also studied at an entrainment velocity of 8 m/s which showed a substantially different picture and fortifies the key influence of the entrainment velocity on the frictional behaviour during oil-off conditions. Figure 17 shows the 1600 MPa test with its temporary oil-off tests followed by a 690 s duration of a permanent oil-off. Although this TOF is clearly much lower than the 900 s for the 1000 MPa, the qualitative trend of the friction, after lubrication supply is shut-off, is equal: After an initial steep increase of friction, there is a decrease of the slope and the signal becomes more scattered, which is interpreted as a phase with substantial surface roughening, followed by a marked decrease of friction. The differences between a 1000 MPa and a 1600 MPa loading are observable in the disc temperatures. The higher contact pressure case results in yet increasing disc temperatures. Whereas the 1000 MPa case seems to lay on an equilibrium point, where temperature increase due to increasing frictional power and temperature decrease due to cooling of the sample side surfaces levels out and results in a constant disc temperature for a substantially long time (Fig. 13). Only the 1600 MPa loading condition (Fig. 17) called the torque shut-off criterium due to instantaneous friction torque increase, which is interpreted as scuffing. The low load case was manually shut-off after reaching the maximum time criterium.

Fig. 17
figure 17

LOL test of transversally ground discs at ve = 8 m/s, vs = 1.2 m/s, 1600 MPa with succession of three temporary and a permanent oil-off test. Each LOL period starts at time 0 s. Here the critical torque limit was approximately 100 Nm

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To sum up, at lower entrainment velocities the frictional behaviour during LOL exhibits a decrease torque which comes along with moderate or even no further disc temperature increase. Higher entrainment velocities result in immediate scuffing or—depending on the acting contact pressure—exhibit an intermediate phase with slower, but steady increase of friction.

7.2.2 Permanent LOL conditions and time of failure—influence of topography

The topographies superfinished (Fig. 18) and transversally ground (Fig. 19) were compared in LOL experiments at otherwise identical conditions, which were as follows: ve = 30 m/s, vs = 3.0 m/s, p = 1300 MPa.

Fig. 18
figure 18

LOL test of superfinished discs at ve = 30 m/s, vs = 3.0 m/s, 1300 MPa with succession of three temporary and a permanent oil-off test. Each LOL period starts at time 0 s

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Fig. 19
figure 19

LOL test of transversally ground discs at ve = 30 m/s, vs = 3.0 m/s, 1300 MPa with succession of one temporary and a permanent oil-off test. Each LOL period starts at time 0 s

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The topography shows two effects, once it determines the level of the CoF in the continuous mode, which is substantially lower for the superfinished surface being only at 0.0137 prior to LOL tests and is 0.0222 for the ground surface. This on the one hand leads to more friction energy introduced into the contact of the ground surface. A temporary oil-off of 60 s was possible with both surface topographies. The results clearly show a qualitatively different behaviour and a much higher robustness against oil-off for the superfinished surface as a 135 s LOL test and a permanent one lasting nearly 250 s were feasible, but the ground surface terminated after 35 s under LOL conditions. Both called the maximum torque shut-off criterium. Due to the limited number of tests a comparison of absolute values is not yet supported by the results.

The surface in the contact area was studied in SEM images and the cross sections with light microscopy as given in Fig. 20, which also illustrate the difference between ground and superfinished surfaces. The ground sample shows a higher degree of roughening after a continious test, followed by LOL tests, than the superfinished sample exposed to nominally the same loading parameters. Legit post-test roughness measurements were impossible as the required minimum measurement length would not be available. The small disc widths were further narrowed by the edge effects mentioned above.

Fig. 20
figure 20

SEM images of wear tracks after continuous and LOL tests of an initially a transversally ground b superfinished surface. c Light microscopy image of the micro-structure of a ground sample after LOL. Stereo images of wear tracks: d ground and e superfinished surface

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The detailed SEM images in Fig. 20a, b show sections of the scuffing features. The corresponding light mircoscopy image in Fig. 20c shows a representative image of the scuffing features for the samples of the current study. Figure 20d, e show the corresponding stereo images of the ground and superfinished version and illustrate the significant differences of the runway after equal LOL tests.

On the top SEM views scuffing shows through pits of fractured surface areas and residuals of torn off material, prior welded together in the contact spots. In the cross sections these areas reveal to consist of distinct patches of white etching layer, with a depth of 5–10 µm. Number and lateral extension of these white etching layer patches differ, but they never cover the whole wear track. They sometimes show cracks as clear signs of embrittlement. TEM images would be required to narrow down the origin of the white etching layer which could be caused by thermal overheating or by extremenly high deformation. It is most likely a combination of both.

Beneath the white etching zone, a highly deformed martensite structure can be perceived on some locations in the light microscopy. The SEM top views back up the interpretation of highly deformed martensite as they show that also plastic shear deformation of material occurs, leading to flattening of the initially ground surface, presumably in lower loaded regions of the contact. The superfinished surface exhibits more of these features generated by large shear and less features clearly indicating scuffing. However, there is no correlation between the applied operating conditions and the microstructural changes, e.g. the amount or areal extent of the observed white etching layer patches.

8 Conclusion

In this paper a new experimental twin-disc test rig was designed to operate at high entrainment velocity up to 80 m/s and high normal loads up to 15 kN, corresponding to a maximum contact pressure of 2000 MPa for the presented geometry, and at lubricant injection temperatures of up to 180 °C. The test rig enables studying fully lubricated conditions at constant CoF levels as well as temporary and permanent loss of lubrication (LOL) experiments, in which the lubricant inlet supply is shut off.

The current study used Aeroshell 500 and transversally ground, case hardened AISI9130 discs to set up an experimental procedure for continuously lubricated and LOL tests as well as to elaborate the limits of stable friction behaviour and time of failure (TOF) during LOL.

Parameter variations under full lubrication showed that entrainment velocity has a significant influence on the steady state friction level. With an increase in entrainment velocity from 8 to 30 m/s, the friction level decreased from about 0.3 to 0.2. In contrast, increasing the SRR hardly affects the CoF under stable friction conditions. The limit for stable friction is determined by the absolute value of the sliding velocity and was found to be approximately 4.5 m/s. This could be explained by the critical heat generated within the contact zone at this sliding velocity leading to unstable friction conditions in the studied system. Simulation results obtained with a mixed EHL model confirmed and complemented the observations, showing larger lubrication gaps and significantly lower asperity pressure at high entrainment velocities. Low injection temperatures had a similar effect as high entrainment velocities, increasing the lubrication gap, lubricant pressure and decreasing the friction level.

LOL conditions performed at stable conditions of the continuous lubrication mode at 120 °C resulted in a drastic reduction of the TOF by two orders of magnitude, upon an increase from 1000 MPa to 1600 MPa. The initiation of scuffing during LOL appears to be guided by a critical frictional power density in the contact, which is influenced by contact pressure and sliding velocity.

In both lubrication modes the surface topography has a highly significant influence, affecting the level of CoF and resilience against LOL conditions. Under the same conditions of 1300 MPa load, entrainment velocity of 23 m/s, and 10% SRR, the superfinished surface demonstrated a TOF of 214 s, while the transversally ground surface ended LOL after 35 s.

Future studies aim to make full use of test capabilities with a lubricant with higher scuffing resistance, focusing on the influences of surface finishing and coating on the friction behaviour.