1. Introduction
Although polymer materials have been found in almost all machinery for decades, they have only recently become a significant role in power-transmitting machine elements such as spur gears. Technical polymers such as thermoplastics are able to meet the requirements for low noise emission through damping, lightweight design, cost-effective manufacturing and also load-carrying capacity when combined with liquid lubrication. The design of such systems is still a subject of research.
Liquid lubrication reduces friction and wear during contact and removes detrimental heat. Elastohydrodynamically lubricated (EHL) contacts with technical polymers feature approximately one order of magnitude lower contact pressures than steel, which results from the much lower stiffness (approximately two orders of magnitude). As a result, the fluid viscosity increases enough to form a lubricating film between the contact surfaces and remains low enough to reach a very low fluid friction level. The heat generated due to shearing is thus also low and is shown to be in the range of the compression heating according to Vicente et al. [
1] as well as Ziegltrum et al. [
2]. EHL contacts with technical polymers operate in a transition region between the soft and hard EHL regime, e.g., [
3,
4,
5], and they may reach fluid friction in the range of superlubricity (µ < 0.01) as shown by Reitschuster et al. [
6].
The complex and possibly nonlinear dependencies of the material properties of polymers on temperature, humidity, age, loading frequency, and chemical surroundings affect the tribological behavior (Dominghaus [
7]) and therefore the design of power-transmitting machine elements. For example, Putignano and Dini [
8] show experimentally that the viscoelastic behavior of polymers may cause a pressure maximum at the contact inlet and a film thickness shrinkage at the contact outlet, depending on the operating conditions and the coupling between fluid flow and solid response. This behavior can also result in additional hysteresis friction in the polymer solid, as shown by a strong increase in bulk temperature under pure rolling conditions by Reitschuster et al. [
6].
In situ measurements of local quantities in an EHL contact such as the pressure and temperature profiles can offer insights into the complex behavior of polymers during the operation of power-transmitting machine elements. Several in situ measurement principles exist for studying local quantities in EHL contacts [
9]. Optical in situ measurement principles are often used. Turchina et al. [
10] were among the first to use infrared technology at an optical EHL tribometer to measure contact temperature. The measurement principle has been further developed, especially in the lateral resolution, e.g., by Reddyhoff et al. [
11], and it is even possible to measure three-dimensional temperature distribution in the EHL contact (Lu et al. [
12]). In addition to temperature measurements using infrared technologies, pressure via Raman microspectroscopy (Jubault et al. [
13]) and film thickness using white light interferometry can also be measured. Very few studies have considered technical polymers. Marx, Guegan, and Spikes [
14] applied the measurement principle to soft EHL contacts with thermoplastics using polymethylmethacrylate (PMMA) and polyurethane (PU). In addition, Putignano and Dini [
8] measured film thickness in an EHL contact with PMMA. All optical in situ measurements require at least one transparent counter body coated with a semi-reflective layer [
9].
As a further in situ measurement principle, thin-film sensors can be used to measure temperature, pressure, and film thickness. The pioneering publications are from the early 1960s. Crook et al. [
15] were among the first to apply evaporated metallic thin-film sensors to measure the film thickness in EHL contacts based on the capacitive method. Kanel et al. [
16] used the pronounced piezoresistive properties of manganin to measure contact pressure using thin-film sensors. Orcutt as well as Chen and Orcutt [
17,
18] measured the contact temperature with thin-film sensors made of titanium having pronounced thermoresistive properties. Building on these works, numerous authors have applied thin-film sensors for pressure and temperature measurement in hard EHL contacts. The spatial resolution in particular has improved rapidly. Hamilton and Moore [
19] resolved the second pressure maximum experimentally. Safa, Anderson, and Leather [
20] reduced the active width of a thin-film sensor to 1 µm, thus allowing a high resolution of the second pressure maximum.
Given that the electrical resistance of metallic thin films always depends on pressure and temperature, a mutual interference exists which influences the target value to be measured. Especially with regard to temperature measurements, the influence of contact pressure is not negligible. Ebner et al. [
21] report a correction of up to 12 K for platinum thin-film sensors at a maximum contact pressure of 1000 MPa. Numerically calculated pressure profiles were used for pressure correction. In order to align the pressure correction signal, they used the peak concept from Dauber [
22] under the assumption of a simultaneous appearance of the second pressure maximum and the maximum contact temperature.
Safa [
23] and Baumann [
24] developed a twin-layered thin-film sensor made of manganin and titanium. The interference from pressure on the temperature signal of these sensors was able to be reduced by up to 90%, but it is limited due to the complex control of the layer thickness during deposition. Emmrich et al. [
25] recently developed thin-film sensors embedded in surface coatings to increase durability and enable measurements under mixed lubrication. Since the surface coatings typically exhibit a lower thermal effusivity than steel, high damping of the measured temperature can occur. Numerical calculations of the temperature distribution in coated EHL contacts from, e.g., Ziegltrum et al. [
2] revealed strong temperature gradients within surface coatings. Hofmann et al. [
26] applied thin-film sensors to dry lubricated soft-coated rolling-sliding contacts. Beyond rolling–sliding contacts, thin-film sensors have also been investigated for temperature measurement, e.g., in cutting tools [
27]. No studies were found, which applied thin-film sensors in EHL contacts with technical polymers.
Technical polymers such as thermoplastics have very different material properties compared to steel. The material behavior can exhibit complex dependencies, and its effect and relevance in EHL contacts is the subject of research. Thin-film sensors are a proven in situ measuring method in hard EHL contacts, but they have yet not been applied to EHL contacts with technical polymers. The objective of this study is to characterize the operating behavior of EHL contacts with polyetheretherketone (PEEK) as a selected thermoplastic polymer by applying thermo- and piezoresistive thin-film sensor technology. The effects and relevance of the thermoplastic material properties of PEEK will be discussed in the context of pressure and temperature measurements.
2. Materials and Methods
Thin-film sensor technology is applied in order to measure pressure and temperature in EHL contacts with thermoplastic polymers. The thermo- and piezoresistive concepts only depend on the material properties of the thin-film sensor, thus making the measurand independent of the polymer material properties. PEEK is selected as a promising high-performance polymer for, e.g., power-transmitting gears. The following sections present the twin-disk tribometer, test specimens, and thin-film sensors considered, as well as the operating conditions and experimental procedure.
2.1. Twin-Disk Tribometer
The experiments are performed on a twin-disk tribometer, which was also used for thin-film sensor measurements in hard EHL contacts by Ebner et al. [
21] and in dry lubricated contacts by Hofmann et al. [
26].
Figure 1 shows a schematic of the mechanical layout of the twin-disk tribometer considered. The following description and formulations are mainly based on Ebner et al. [
21].
The upper and lower disk are pressed-fitted onto shafts, which are individually driven by two three-phase motors. Traction drives mounted between the motor and the driving shafts enable the continuous variation of surface velocities
v1 (upper disk) and
v2 (lower disk). The sum velocity
, sliding velocity
vg, slip ratio
s, and slide-to-roll ratio SRR are defined in Equations (1) to (4).
The normal force FN during disk contact is continuously applied by a load spring via a pivot arm where the lower disk is mounted. The upper disk is mounted in a skid, which is attached to the frame by thin steel sheets. The skid is supported laterally by a load cell so that the friction force FR in the disk contact for slip ratio s 0% can be measured as a reaction force with hardly any skid displacement. The upper disk v1 is thereby faster than the lower disk v2. The normal force FN, friction force FR, surface velocities v1 and v2, and the bulk temperature of the test disk 5 mm below the surface are measured. An injection lubrication unit is used for conditioning the oil temperature and oil volume. The lubricant is injected directly into the contact inlet with the oil temperature at a volume flow of = 1.5 L/min. In order to provide an evenly distributed load during line contact of the disks, a contact print on pressure indicating sensor film (Fujifilm Prescale®) is carefully evaluated before each test, and any misalignment is corrected mechanically.
2.2. Test Specimens and Material Data
An electrically insulating ceramic sensor disk made of zirconium dioxide (ZrO
2) is used as the upper disk in all of the experiments. The thin-film sensors described in
Section 2.3 are applied to its surface. The lower test disk is made of PEEK or case-hardened steel 16MnCr5 (AISI5115) for reference measurements. The material pairing ZrO
2/PEEK refers to thermoplastic EHL contact, and the material pairing ZrO
2/steel refers to steel EHL contact. The PEEK test disk is injection-molded around a perforated steel inlay, as described by Reitschuster et al. [
6]. PEEK was chosen as a promising material for power-transmitting machine elements because it exhibits stable material properties over a wide range of temperatures [
7].
Figure 2 shows a schematic representation of each test and sensor disk. The disks have a diameter of 80 mm and a width of 5 mm or 20 mm, respectively.
All surfaces are mechanically polished to a mean arithmetic surface roughness Ra
0.03 µm. Roughness measurements were performed in the axial direction by the profile method according to DIN EN ISO 13565-1 to 13565-3, with a measured length of
Lt = 4.0 mm and a cut-off wavelength of
= 0.08 mm.
Table 1 clarifies the mechanical and thermophysical properties of the test and sensor disks considered.
2.3. Thin-Film Sensors
Thin-film sensors are applied on ceramic sensor disks by means of process photolithography for masking and ion beam sputtering for the deposition process. The manufacturing process is described in detail by Ebner et al. [
21].
Figure 3 shows the typical layout of the thin-film sensors applied at a total layer thickness
dA of between 100 and 150 nm in order to minimize the sensor influence on the contact quantities [
31].
Given its high sensitivity to temperature and low sensitivity to pressure, platinum is used for the temperature measurements. To increase the adhesion between the thin-film sensor and the ceramic sensor disk, a titanium layer of approximately 40 nm was applied at NMI Reutlingen, Reutlingen, Germany. The width
l2 of the active part of the thin-film sensor is approximately 20 µm. The ohmic resistance of a platinum thin-film sensor in the manufacturing state is in the range of
R = 120
. Given its high sensitivity to pressure and weak sensitivity to temperature, chromium is used for the pressure measurements. The sensor was manufactured in cooperation with NMI Reutlingen, Reutlingen, Germany. The width
l2 of the active part of the thin-film sensor is approximately 30 µm. The ohmic resistance in the manufacturing state is in the range of
R = 1000
, which enables a higher supply voltage of the measurement chain [
32] and thus improves the signal-to-noise ratio. Note that the electrical properties of thin chromium films depend on the geometry and the deposition process.
The correlation between the resistance change
of thin-film sensors due to temperature
and pressure
can be expressed by
with
as the temperature coefficient and
as the pressure coefficient. The ratio
k between the temperature- and pressure-dependent resistance change can be used to evaluate the suitability of a sensor material for pressure or temperature measurement. Note that this suitability depends on both the material properties and the absolute increases in temperature and pressure. The latter increase is particularly influenced by the contact type as well as the operating conditions conducted.
A ratio of
k 1 is suitable for temperature measurements, and
k 1 is suitable for pressure measurements. The temperature coefficients for the thin-film sensors were derived by way of calibration in a tempered oil bath with the lubricant considered (cf.
Section 2.4). In addition to the ohmic resistance, the output voltage of the amplifier was also tracked for the platinum sensor to exclude thermoelectric effects between the titanium adhesion layer. The pressure coefficient for the platinum sensor was derived by nearly steady roll-overs at the twin-disk tribometer as reported, e.g., in Emmrich et al. [
25]. The pressure coefficient of the chromium sensor was derived based on the equilibrium of integrated contact pressure over the sensor distance and external load
FN (see, e.g., Hamilton and Moore [
19]). Pressure profiles at pure rolling were chosen in order to minimize the influence of temperature on resistance change. Note that this method is only suitable for pressure sensors given the low interference of temperature on sensor resistance. The resulting temperature and pressure coefficients of the thin-film sensors are summarized in
Table 2.
Based on the temperature and pressure coefficients,
Figure 4 shows the ratio
k as a function of the absolute pressure
p and temperature change
T. In this case,
p and
T are adapted to the expected changes in the thermoplastic EHL contact with ZrO
2/PEEK.
Regarding the investigated material pairing and operating conditions (cf.
Section 2.4), the platinum thin-film sensor for temperature and chromium thin-film sensor for pressure measurement demonstrate satisfactory suitability in terms of the measured temperatures and pressures (cf.
Section 3). The platinum thin-film sensor
k exhibits its minimum of
k = 2.97 at w = 150 N/mm,
= 8 m/s and pure rolling (
s = 0%), and the chromium thin-film senor has its maximum of
k = 0.39 at
w = 100 N/mm,
= 12 m/s and
s = 50%. This result supports the application of thin-film sensor technology on thermoplastic contacts. Note that the temperature and pressure scales are nearly identical within soft and hard EHL contacts (cf.
Section 3.3), thus resulting in a comparable
k ratio.
2.4. Operating Conditions and Lubricant
Table 3 illustrates the operating conditions considered, which are derived from the kinematic conditions typical of plastic gears, e.g., Illenberger, Tobie, and Stahl [
33]. The slip ratios
s considered corresponds to an SRR of between 0 and 0.66.
Mineral oil (ISO VG 100) with 4% sulfur–phosphorus-based extreme-pressure (EP) additive Anglamol A99 is used as lubricant, the main properties of which are described in
Table 4 [
34].
The lubrication regime was estimated based on the relative film thickness
according to Niemann et al. [
35] and at the minimum film thickness h
m according to Myers et al. [
3] for the PEEK test disk and Dowson and Higginson [
36] for the steel test disk. Fluid film lubrication with
>> 2 is observed in all of the operating conditions considered. To classify EHL contacts, Johnson [
37] introduced a viscosity (g
1) and elasticity parameter (g
3), depending on the material and lubricant properties as well as the operating conditions. Therefore, given g
1 = {35.2–109.6} and g
3 = {10.3–28.1}, the thermoplastic EHL contact ZrO
2/PEEK considered operates in the transition regime. In the reference steel EHL contact ZrO
2/steel, the viscosity parameter g
1 range is g
1 = {44.6–80.9}, and the elasticity parameter range is g
3 = {2.3–3.5}. Hence, it operates in the rigid piezoviscous regime.
2.5. Experimental Procedure and Evaluation
The measurement chain is calibrated at room temperature before each test sequence. The kinematic conditions are initially adjusted for each operating point at the twin-disk tribometer, with the sensor and test disks separated from each other. When the bulk temperature of the test disk is basically quasi-stationary, the normal load FN is applied, and eight roll-overs are tracked at a sampling rate of 2 MS/s. This procedure is repeated once, resulting in 16 recorded roll-overs for every operating point. As a result, all of the pressure and temperature profiles described in this study represent a mean value of 16 signals. Each test sequence is started at = 8 m/s and pure rolling (s = 0%). After increasing the slip ratio up to s = 50%, the procedure is repeated for = 12 m/s and 16 m/s. The tribometer is cooled down to room temperature, and the measurement chain is calibrated again when conducting a different line load w.
Every single signal is filtered using a low-pass filter, whereby the cut-off frequency is adapted to the sensor width
l2 based on the formulations of Marko [
38]. To better visualize the various speeds and slip ratios, the time is converted to the sensor disk distance
x. Regarding the contact temperature measurements, the temperature rise is in reference to the minimum temperature measured before the contact zone (cf.
Section 3.2.1). As a result, the heat generation due to shearing of the lubricant in the inlet and contact zone, as well as due to compression, are able to be compared and related to the operating conditions under consideration. The surface temperature
of the sensor disk is able to be obtained during conditioning. Note that this is only possible in operating conditions under full film lubrication and no sensor wear. The latter would result in resistance change and hence pseudo temperature rise.