Sensor integrating plain bearings: design of an energy-autonomous, temperature-based condition monitoring system

Plain bearings are increasingly being used under mixed friction, resulting in a higher risk of wear-induced failure. Therefore, the relevance of condition monitoring is increasing, which can enable the early detection of wear inducing conditions. The presented work focuses on the development of an energy-autonomous, temperature-based condition monitoring system for plain bearings. The components of the condition monitoring system are to be integrated directly into the machine element and operating data to be transmitted wirelessly. The fundamental monitoring approach pursued, is the in-operando calculation of the lubrication gap height via the standardized Gümbel-curve based on the temperature map in the plain bearing. If the gap height undercuts a critical threshold, the plain bearing will operate in mixed friction. Thus, representing a potentially wear-causing operating point. The energy required for operating the system is harvested thermoelectrically within the plain bearing via thermo-generators, which use the temperature gradients in the plain bearing during operation. In this work, the simulative evaluation of the harvestable energy will be presented. The usable temperature difference will be determined for varying positioning of the energy harvester. The results obtained allow the subsequent manufacture of a first Sensor integrating Machine Element (SiME)-prototype. In this context a feasible setup regarding the types and number of sensors as well as a microcontroller for processing the measured data will be defined with respect to the harvestable energy. Furthermore, the principle for temperature-based gap height determination will be introduced, applied for different operating points and compared to simulative results.


Introduction
Condition monitoring of machine elements is of essential importance for advancing digitalization in mechanical engineering. With the help of condition monitoring, critical operating states and the development of damages in early stages can ideally be detected in-operando. Resultantly, machines can be maintained needs-based, resulting in lower downtime and subsequently lower capitalized losses [1]. The bearing is one of the most failure-prone parts on the system level. For instance, approximately 50% of all failures in electrical machines are due to bearing failures [2].
Common monitoring systems for plain bearings, such as costly wired inductive displacement sensors, are currently retrofitted to the plain bearings [3]. Temperature measurement is a low-cost monitoring method for plain bearings. Sustaining mixed and solid-state friction causes an abrupt temperature increase in the load zone close to the running surface [4]. In real applications, the placement of thermo sensors in the load zone is often not possible due to external power cabling, which reduces the sensitivity of the thermo sensors regarding friction development. Resultantly damage cannot always be detected reliably or only at an advanced stage. Therefore, the standard temperature measurement is not well suited for condition monitoring and early stage damage detection [5].
Plain bearing systems that utilize sensor technology in industrial applications can be classified as Sensor carrying Machine Elements (ScMe) according to Vorwerk-Handing et al. [6]. Those systems are characterized by an external wired power supply, which does not allow a practicable installation in multi-axis rotating system assemblies, such as planetary gearboxes in wind turbines. Therefore, there is a need for condition monitoring systems, that can be incorporated directly into the machine element plain bearing. The aspired solution should allow an integration into the existing system with minimal influence. In order to fulfill this requirement, the sensor system should work autarkic. Naumann defines autarkic sensors system as units which fulfill its function independently of any permanently installed cabling [7]. For realizing this concept, the external wiring of the energy supply has to be substituted. To meet this criterion, the energy supply of the sensor system needs to be integrated directly into the machine element. The en-ergy for operating an autarkic system can be harvested by utilizing one or more physical effects from the surrounding environment. Furthermore, the wiring for information transfer has to be eliminated. This challenge can be met by using wireless data transmission technology. The resulting unit is classifiable as a Sensor-Integrated Machine Element (SiME) by [8].
Since microcontrollers require a voltage of several volts in order to process measurement data and provide them for wireless transmission, the implementation of a DC-DC converter is necessary to operate an energy-autonomous sensor system. The efficiency of energy converters (e.g. DC-DC) has rapidly increased recently and is further optimized for energy harvesting solutions like thermo generators (TEG), piezoelectric modules or solar cells [9]. On the other hand the power consumption of electronic circuits and system is steadily decreasing [10]. This enables deriving the energy from the framework conditions occurring in the environment like heat, light or motion, which can be used to supply the energy required for powering electronic devices.
Thermal energy harvesting is a promising method for capturing energy in processes by using temperature differences and converting them to electrical energy [11]. TEG are devices that utilize occurring temperature differences and convert those temperature gradients into electricity based on the thermoelectrical effects [12][13][14].Thermal energy harvesting is an emerging technology, which is increasingly explored and further developed regarding its efficiency and reliability [15][16][17][18][19]. This also includes the low-level heat range, in which the TEGs are able to harvest energy at occurring temperature differences of a few Kelvin [20,21]. For some applications, energy harvesting can completely eliminate the need for an external power supply [22]. Figure 1 displays the schematic structure of a TEG.
The Seiko Thermic watch represents a prominent example for the successful application of an energy-autonomous, commercially available electronic device powered by a thermoelectrically generated energy supply [24]. The watch utilizes a TEG, which converts heat from the human wrist into electrical energy. The installed generator is capable of deploying a power of at least 1.5 μW with a temperature gradient in the range of 1-3 K, which is sufficient for operating the watch. K Fig. 1 Schematic structure of a Thermoelectrical Generator [23] In plain bearings heat is available in the form of waste heat produced by rotational, kinematic movement of the shaft relative to the plain bearing resulting in friction. With regard to the application of thermoelectric energy generation in plain bearings, one challenge is the relatively low temperature gradients occurring within the plain bearing. In the range of low level-heat and small thermal gradients the output voltages of TEG are usually beneath the minimum required input voltage to supply a wireless communication module [24,25]. The output voltages of TEG are situated in the range of 50 mV per K, depending on the number of series-connected dices within the TEG [26]. Furthermore, an energy buffer can be deployed, which stores surplus electrical energy. Surplus energy is generated at times when the energy production exceeds the consumption of the entire system. At times of increased energy consumption, the energy storage can compensate for the deficit. Possible storage elements for autonomous systems are rechargeable batteries and high value capacitors [26].
In addition to increasing efficiency of TEG, the power consumption of wireless communication sensors has been reduced largely due to the field of ultra-low-power-electronics [27]. RFID (Radio-Frequency Identification) technologies, including the well-known NFC (Near Field Communication) standard, represent an energy-efficient transmission standard. Communication sensors that utilize RFID for data transmission are usually in a deep sleep state for 99.9% of their operation time, only waking up for data communication. The period of the sensor's awake phase is only a few milliseconds. Subsequently the average power consumption of wireless sensors has been reduced to below 10 μW [28].
In the layout of hydrodynamical plain bearing, DIN standard 31652 represents an established calculation method for determining operational safe conditions [29][30][31][32]. The calculation method is based on the hydrodynamical characteristics from the numerical solution of Reynolds' differential equation. In an iterative calculation model, the hydrodynamic condition of fully separation of the surfaces through a lubricant film is aimed for. DIN 31652-2 includes Gümbel-curves, which utilize simplifications of Reynolds' differential equation [33]. The Gümbel-curves represent a di-agrammatic solution illustrating the relationship between the misalignment angle and the relative eccentricity of the shaft within the plain bearing. Therefore, the relative eccentricity of the shaft and thus the minimum lubrication gap height within the contact can be calculated from the Gümbel-curves, if the shaft misalignment angle is known. The misalignment angle in turn, directly correlates with radial position of the maximum temperature occurring on the running surface of the bearing [3]. This relation will be tested initially for the temperature-based calculation of the lubrication gap height based on an established design guideline for hydrodynamical plain bearings.

Objective and approach
The presented work addresses initial challenges on the way to developing a sensor integrating plain bearing. In this work, the simulative evaluation of the thermoelectrically harvestable energy will be presented. The usable temperature difference will be determined for varying positioning of a TEG within the plain bearing. The principle for temperature-based gap height determination will be presented, applied for different operating points and compared to simulative results. The whole concept of the condition monitoring system to be developed is presented in depth in [3].
In Chap. 3 the simulative investigation of the harvestable energy within the plain bearing system will be presented. For this purpose, a coupled multibody-simulation (MBS) and thermo-elastohydrodynamic (TEHD) model of plain bearing test rig is created in the software AVL Excite Power Unit. The determined temperature map of the oil film will be transferred on a FEM-model of the test rig in Abaqus. In the FEM-model a Thermogenerator will be placed directly into the plain bearing volume. A heat transfer analysis will be performed for different positions of the TEG within the bearing. If the mean temperature difference between the cold and hot sides of the TEG is known, an energy budget can be drawn up from measurement data captured for a TEG and DC-DC converter. Based on the determined energy budget a feasible setup regarding the type and num- ber of operable thermo sensors for the temperature field determination near the running surface and type of microcontroller is determined. In Chap. 4 the temperature-based oil gap height will be calculated based on the Gümbel-curve for varying operation conditions. The calculated values will be compared to the results from the MBS-TEHD analysis concluded and the deviation of the gap height results will be analyzed. Finally, a conclusion of the results presented will be drawn.

Model layout
For the investigations, a submodel of a plain bearing test rig, which will be used for future experimental examinations, was created. During the test, the plain bearing to be tested is positioned in a friction scale. The test force is applied to the plain bearing via the friction scale. The frictional torque occurring in the bearing is recorded metrologically via a load cell connected to the friction scale. The test plain bearing is made of the bronze alloy CuSn12Ni2-C (approx. 85% copper and 12% tin [34]). The test bearing has an inner diameter of D = 120 mm and a width of B = 30 mm. In the test bearing a mineral oil of class ISO VG 320 is selected. The test rig shaft is supported by two roller bearings, which are located in bearing housings connected to the machine bed. The drive of the shaft is realized via a coupling using an electric motor.
The model of the drive train has been built in commercially available software AVL Excite Power Unit as a coupled TEHD-MBS. The TEHD modeling of the test plain bearing is able to simulate the mechanic as well as the thermal interactions among the lubricant film and the lubricated solid parts [35]. The modeling for the simulative determination of the usable temperature differences for thermoelectrical energy harvesting was carried out in four steps: 1) Modeling of the drivetrain subsystem by simplifying an existing test rig model in a CAD software (Inventor Professional 2018) and discretization of the relevant component geometries and calculation of stiffness matrices (Abaqus CAE 2019), 2) application of boundary conditions as well as definition of contact conditions (AVL Excite Power Unit 2022 R1). Finally, 3) the thermal boundary conditions of the TEHD contact are applied to the subsystem friction scale + plain bearing with an integrated TEG and 4) the useable temperature difference for the TEG is determined (Abaqus CAE 2019). Figure 2 illustrates the tool chain used and the sub models created.
For completeness it should be mentioned that the calculation of the temperature in the lubricant gap can be performed by using the EHD + T methodology [36]. In the EHD + T methodology, the heat flows are calculated and are applied to an FE model of the assembly in a consecutive step to calculate the resulting temperatures on the surfaces of the bearing and shaft. Subsequently a series of iteration steps is run through EHD + T and FE simulations until a thermal steady-state is reached. The resulting effort within the EHD + T method is significantly higher than for the TEHD calculation. In the TEHD method the temperature map in the lubricant gap is calculated directly from the heat conduction of the shaft and plain bearing. The TEHD method is not able to consider complex structures for the heat conduction calculation, the plain bearing and surrounding friction scale are depicted as layered discs. In the TEHD analysis the parameters inner and outer diameter of each layer, the width and the heat transfer on the surface areas are assignable. Sous showed that the results of a TEHD calculation of a comparable test rig correspond adequately with measurements on the test rig [36]. Therefore, the TEHD calculation method was applied to gain an initial insight into the usable temperature differences for energy harvesting within the plain bearing. In the TEHD model, the plain bearing with surrounding friction scale and the shaft shoulder at the level of the TEHD contact were modeled (see Fig. 2b)). Since the support bearings and the further shaft shoulders (see Fig. 2a)) in the TEHD calculation have no significant influence on the temperature map on the running track of the test bearing, they were not considered to reduce the calculation time.

Simulative results
In the simulations conducted the thermal steady-state was analyzed. Since the oil feed temperature Toil,In has the largest influence on the resulting temperature level in the oil film, it was varied in four steps (Toil,In = 40°C, 50°C, 60°C, 70°C).
In the experimental test rig setup, the lubricating oil is fed back to the test bearing after filtering. Therefore, the oil gradually heats up over time. In addition, an external heating of the lubrication fluid via heating cartridge is available. The two lower selected oil feed temperatures correspond to the usual temperatures that are measurable in experimental investigations without additional heating of the oil. The process input variables "shaft circumferential speed v" and "specific bearing pressure p" significantly influence the temperature differences occurring locally in the lubrication gap, which are relevant for the temperature-based displacement angle determination. However, compared to Toil,in, the influence of for v and p on global temperature level of the lubrication fluid is relatively small. Therefore, constant values for the circumferential speed and specific pressure were selected for the simulations (v = 1 m/s, p = 10 MPa).
The values for v and p were chosen subcritical to achieve a state of liquid friction. The resulting temperature maps on the running track, which were calculated in Excite Power Unit using TEHD method, are displayed in Fig. 3 The temperature maps are shown for the respective steady-state condition over the bearing width (B = 30 mm) and the bearing angle ϕ.
From the temperature distribution shown, it can be observed that there is a relatively homogeneous temperature distribution in the lubrication gap. Wear at the edges can be observed, which results in local temperature increases  The maximum temperature difference within the lubrication gap is about Tgap = 6 K for the simulation parameters investigated. After reaching the temperature maxima in the load zone, the temperature level then is, according to expectations, decreasing over ϕ to the minimum temperature at the lubrication groove at ϕ = 360°-0°. In a final step, the temperature maps determined were transferred on a FEM model (see Fig. 2). In the subsequent heat transfer analysis, the plain bearing including the surrounding friction scale as well as a TEG, which was integrated into the plain bearing volume, were modeled. The components were modeled considering their material properties as well as their interactions with the surrounding area. The TEG was placed in three different positions within the plain bearing. Thermal simulations were performed for these positions to identify the temperature differences occurring between the hot and cold sides of the TEG in each case. The three different positioning of the TEG are shown in Fig. 4 The viewing angles shown are based on the motor side.
In all three arrangement positions, the TEGs were arranged at a bearing angle of ϕ = 135°. The selected angle ensures that the temperature field range relevant for the temperature measurement setup is not disturbed by the TEG. At standstill, the displacement angle of the shaft is β = 0°( ϕ = 180°). For the temperature-based displacement angle TEG,min,Pos2 = 6.13 K P = 16.5 mW determination, the sensor system must be placed in this area (ϕ ≥ 180°) without being influenced by the TEG (e.g. changed heat flux). With an increase in v, β increases for the considered rotational direction. The TEG modelled, has a width and depth of 25 mm each as well as a height of 4.7 mm. The TEG uses bismuth telluride (BiTe) conductors for the n-and p-type dices, which are connected in series using copper platelets. The copper platelets are in turn connected to ceramic plates (see schematic structure in Fig. 1).
In the first arrangement (see Fig. 4a), the TEG is placed close to the running track at a distance of one millimeter from the running surface. In the second arrangement (see Fig. 4b), the TEG is aligned flush with the end face of the plain bearing and is in contact with the front face of the friction scale. In the third arrangement, the TEG is positioned aligned with the opposite end face of the bearing (Fig. 4a). Here, an air contact occurs with a cavity on the motor side inside the friction scale. The material properties of the components used for the thermal analysis are listed in Table 1.
For the modeling of the convective heat transfer between the solid and the fluid (surrounding air), heat transfer coefficients from the literature were used, which are listed in Table 2. The position of each coefficient used is shown Fig. 5.
The contact of the Al2O3-plates with the plain bearing and the friction balance was realized as a tie constraint in the FE analysis. In the experimental investigations, ther-mal paste is to be applied to the ceramic plates. Thermal paste with a higher conductivity than the Al2O3 is commercially available [48], therefore a tie constraint was considered appropriate. The applicability of the tie constraint will be examined in a feasibility study. The contact between the bearing and friction scale was modelled as a surfaceto-surface contact. To estimate the thermal conduction of the surface contacts, characteristic values of a steel-copper contact were used as an approximation. The characteristic values used originate from a paper by Fletcher, which analyzed the contact conductance for varying material pairings as a function of the contact pressure [47]. For the contact at the outer shell surface of the bearing to the friction balance, a uniform pressure of 10 MPa was assumed. During operation, the bearing is secured against relative axial movement by a circlip. The pressure between the end face of the bearing and the contact surface with the friction scale at the front was assumed to be 10 -3 MPa. The resulting contact conductance coefficients are given in Table 2. The feasibility will be examined in following experimental studies. For the subsequent definition of a condition monitoring setup that can be operated by using thermoelectrically generated energy, the average temperature occurring on the contact surface to the adjacent component/fluid of the hot as well as cold side was determined. The average temperature differences TTEG between the hot and cold sides are shown in Table 3 below for the three different positioning of the TEG and oil feed temperatures Toil,in considered. Table 3 displays, that with a higher oil feed temperature Toil,in and a higher temperature gradient to the ambient, larger usable TTEG are associated. In the comparison of the usable TTEG with varied positioning, it can be observed that the highest TTEG occurs in position 2. The lowest temperature difference at an oil supply temperature Toil,in = 313.15 K (40°C) is TTEG,Pos2 = 6.13 K at positioning 2. For this value a conclusion regarding the thermoelectrically generatable power in an oil-lubricated plain bearing in operation, based on own measurement data of a commercially available TEG was drawn.

Energy budget determination
The TEG considered was the model "TEG1-30-30-2.1/100" that is designed for energy harvesting from low-level heat sources [49]. In Fig. 6 the generatable power output of the TEG over TTEG is depicted. The orange dots represent the individual measurement points. The blue trend line represents the modeled power by a quadratic function.
Based on the characteristic curve shown, a harvestable energy of at least 16.5 mW is expectable at the minimal TTEG of 6.13 K in positioning 2. Since the output voltage of the thermoelectric generator is significantly lower than the minimum voltage of the electronic components, it must be raised with the aid of a DC-DC converter. For this purpose, the DC-DC-Converter "LTC3106" is used as a reference [50]. It is designed for energy harvesting, which results in a particularly low minimum input voltage. The converter also supports the connection of an external energy storage to buffer excess energy and backup the loads in case of power shortage. Within the expected electrical power range of the thermoelectric generator of approximately 1 to 50 mW, depending on the available temperature difference, the efficiency of the LTC3106 is uniformly above 60%. The order of magnitude of the electrical power available to the circuit is therefore maintained. However, the maximum output power of DC-DC converters is generally dependent on the input voltage. For example, according to the LTC3106  . 7 Gümbel-curve-minimum oil gap height for the bearing geometry investigated datasheet, only 15 mW can be converted at an input voltage of 0.3 V, regardless of the available current. This must be considered in addition to the efficiency when designing the power supply. For the minimal TTEG of 6.13 K in position 2 the resulting usable energy at the voltage to operate a condition monitoring setup is 9.95 mW.
To estimate the expected energy consumption of a condition monitoring setup, the following off-the-shelf components are assumed as the reference design. The temperature distribution will initially be measured using six LM73 sensors [51]. This widely used sensor offers sufficiently high temperature resolution and relative accuracy and already integrates all the required circuitry. The temperature values are to be retrieved and subsequently processed using a microcontroller. Since there are no special requirements for computing power and transmission protocol, the use of the popular atmega328p is suggested [52]. It offers a wide supply voltage range and a medium power consumption depending on the operating mode, which makes it well suited for this estimation.
Since data transmission only takes place sporadically or in an emergency case, the energy required for this purpose can be accumulated over a longer period of time and can therefore be neglected for the purpose of estimating the order of magnitude here. In order to determine the expected energy consumption of the whole system, the time interval of the temperature measurement is of decisive importance, since the energy consumption of the components presented here differs by 2 to 3 orders of magnitude between active and idle state. In the following, a time interval of one second is assumed. The expected consumption results from the following: Temperature Sensors LM73 P TS = 6 .0.300 mA 0.1s + 0.002 mA 0.9s/ 3.3V=1s The required energy in normal operation is therefore in the order of several milliwatts (4.23 mW). With the energy budget determined beforehand, generated thermo-electrically in the plain bearing, the defined setup would be permanently operable.
It should be noted here that the accuracy of this calculation is only an estimate of the order of magnitude, and may deviate from the later implementation by even larger factors. On the one hand, storage and conversion losses will increase the consumption in a real implementation, on the other hand, presumably occurring operational gaps, e.g. during the measurements, can still be exploited for further energy savings.

Temperature-based oil gap height determination via Gümbel-curve
An operation-safe dimensioning of hydrodynamic plain bearings in steady-state mode is described in DIN-stan-dard 31652-1 [30]. The calculation of the radial plain bearing is performed using the hydrodynamic parameters from the numerical solution of the Reynolds' differential equation [53] for finite bearing width. The integration of the Reynolds' differential equation provides the pressure curve in circumferential and width directions. Based on the pressure curves dimensionless similarity quantities are calculatable for the characteristic values of interest (e.g. frictional behavior, misalignment angle, Sommerfeld number). However, the analytical solving of the equation for calculating the pressure and temperature distribution is mathematically complex [33]. An exact, analytical solution is not possible in most cases. Therefore, numerical or graphical methods are usually used in dimensioning of hydrodynamic plain bearing. In the majority of publications only single parameter values are calculated, which are only approximately usable in many practical applications. For many discrete values one has to rely on the interpolation of results, which are mostly available in the form of curves or tables [33]. In DIN standard 31652, numerical solutions of the Reynolds' equation are likewise used and provided to the user in graphical and tabular form for the determination relevant operating characteristics of plain bearings [30][31][32].
The hydrodynamic and thus operation-safe condition is achieved when the minimum oi film height hOil,min is higher than a threshold oil gap height, which primarily depends on the surface roughness [30,54,55]. This ensures that there is no solid contact or mixed friction condition. In Fig. 7 the Gümbel-curve as well as the eccentricity ε and related minimum oil gap height hOil,min over the misalignment angle β are displayed for the bearing geometry investigated (β = φ -180°).
To test the quality of the Gümbel-curve, the gap height calculated via the Gümbel-curve was compared with the respective simulated gap height for varying simulation parameters. The MBS model presented in Chap. 3 was used for the investigation. The ramp-up process was modeled starting from the stationary shaft until the steady-state was reached. The shaft circumferential speed v and specific pressure p were kept constant within the individual simulations. The minimal gap height and the displacement angle were determined for each of the operating states passed through up to the steady state. The minimum gap height was determined via the correlation of the Gümbel-curve and the simulated displacement angle β. This was done by linear interpolation between the values shown in Fig. 7. In Fig. 8, the curves of the minimum gap height until the steady-state condition is reached, as determined by the Gümbel-curve, are plotted in solid lines against the simulative determined gap height curves in dashed lines.
For the investigations, comparisons were made in a fullfactorial simulation plan in which the input variables circumferential speed ( v = 1; 2 m/s), specific pressure (p= 5; 10 MPa) and oil feed temperature (Toil,in = 303.15; 343.15 K) were varied in two steps each. The comparison shows that the minimum gap height is represented with high accuracy via the Gümbel-curve in the steady state for the simulations conducted. After the run-up, the average deviation is in the sub-micron range. In the preceding ramp-up process, it can be seen that the hoil,min-values interpolated over the Gümbelcurve rise earlier compared to the simulated values. The maximum is reached at an earlier point in time for the interpolated curves and is on a higher level. After the maximum has been reached, the interpolated curve decreases and aligns with the simulated lubrication gap height. From the results, it is evident that the temperature-based lubrication gap height determination via the Gümbel-curve offers high accuracy to simulated results in the steady state. For transient operating conditions, the quality by which the oil gap height can be determined via the temperature field must be examined. The planned temperature field measurement near the running surface provides a further monitoring parameter in the planned concept. With the occurrence of mixed and solid friction, the temperature in the running surface rises abruptly. Once a temperature limit value is exceeded, the system can additionally transmit a critical operating state.

Conclusion and outlook
A simplified MBS-TEHD simulation model of a plain bearing test rig was set up. In this model, the temperature distribution occurring on the running track of the plain bearing was calculated for varying oil supply temperatures. The resulting temperature fields in the oil gap of the bearing were transferred on the plain bearing and the volume of the surrounding structure in a subsequent step in an FE analysis. In the FE analysis, a thermo generator was integrated into the plain bearing at varying positions and the temperature differences between the hot and cold side of the Thermogenerator (TEG) were analyzed. In the investigations, the usable temperature differences were in a range of TTEG = 6-13 K.
Based on the determined TTEG, the expected thermoelectrically harvestable energy was determined using measurement data of one TEG. An energy budget was defined considering the efficiency of a DC-DC converter. With an available energy budget of 9.95 mW at the lowest determined TTEG, the energy demand of a monitoring setup consisting of six digital temperature sensors as well as a microcontroller is met. By using several TEGs connected in series, it may be possible to further increase the harvestable energy. In addition, the monitoring setup shows potential for the further reduction of the energy consumption. This can be achieved by exploiting occurring operational gaps, e.g. during the measurements.
Furthermore, the methodology of the temperature-based lubrication gap calculation was investigated. If the displacement angle of the shaft in the bearing is known, it is possible to calculate the lubrication gap height via the correlation of the Gümbel-curve.
For run-up processes to achieve steady-state conditions, the gap heights determined by the analogy of the Gümbelcurve were compared to the simulated gap heights. Under varying rotational speed, oil feed temperature and specific pressure, a high level of correspondence was achieved in the steady-state. Accordingly, the Gümbel-curve methodology represents a promising approach for temperature-based lubrication gap calculation based on the displacement angle. However, it is necessary to examine whether the methodology can be transferred to operation under highly varying conditions, such as start-stop motions.
The results obtained in this work represent a first step towards the creation of an energy-autonomous, temperaturebased condition monitoring system for plain bearing. The harvestable energy determined by simulation will be evaluated in future investigations on a test rig. Furthermore, experimental investigations will be carried out with regard to the thermal measurement of the displacement angle. A microcontroller, which models the relationship of the Gümbelcurve, will be integrated into the plain bearing and the lu-brication gap height will be determined in operando. The determined values are subsequently evaluated and validated by measuring the lubrication gap height using inductive displacement sensors. By implementing wireless interfaces for data transmission, the autonomous operation of a condition monitoring system fully integrated into the plain bearing, is aimed for.
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