1 Motivation and Background Lubrication is a key technology for sustainability as it is requested in the Brundtland Report [1]: „Humanity has the ability to make development sustainable - to ensure that it meets the needs of the present without compromising the ability of future generations to meet their own needs.“ Lubrication reduces friction and, therefore, saves energy. This reduces the carbon footprint of any mechanical operation. Even more important is the reduction of wear. This enhances the lifetime of any lubricated machine part and, therefore, saves the resources required for production of the lubricated part. At the same time lubricants require resources themselves. Lubricants are mostly based on petroleum oils, a very precious resource. Oil production, refining and processing requires energy. The carbon footprint of mineral based lubricants may very roughly be assumed to be approx. two kg of CO 2 per kg of lubricant. Therefore, the application of lubricants should always be sustainable itself, lubricants should never be wasted. They should not be exchanged long before the service life is over and the re-lubrication rate should not over-lubricate the machine part. This requires methods to predict the service life and the re-lubrication rate. Aus Wissenschaft und Forschung 19 Tribologie + Schmierungstechnik · 69. Jahrgang · eOnly Sonderausgabe 1/ 2022 DOI 10.24053/ TuS-2022-0027 A practical Approach to predict Service Life and Re-lubrication Rate of Grease in Rolling Bearings Frank Reichmann* Lubrication is crucial for a sustainable operation of any machinery. A sustainable application of lubricants requires the avoidance of any waste, lubricants should not be exchanged long before their service life has ended. This refers especially to those applications where high operation temperatures are reducing the service life and require a huge consumption of lubricants. Therefore, to fulfil the requirement of sustainability a prediction of the service life at elevated temperatures is crucial. At elevated temperatures the service life of lubricants is limited by thermal aging. This results from a chemical reaction of components of the grease with the oxygen of the ambient air. Such a process follows the Arrhenius equation of chemical kinetics and is given by a straight line in a so-called Arrhenius plot. The slope of the line in the Arrhenius plot is given by the activation energy E A . The FAG FE9 test run is a typical method to assess the service life of a lubricating grease in bearings at elevated temperatures. The test is performed at the upper temperature limit of the grease and gives the service life at this maximum temperature. Once the activation energy E A is available the service life at any other temperature may be calculated. Since the temperature of Abstract * Frank Reichmann CARL BECHEM GMBH, Hagen, Germany the FE9 test run is usually the upper temperature limit the operation temperature is usually lower. Once the calculation start from a high temperature in direction a lower temperature low figures of activation energy E A are resulting in conservative service lives, as it is displayed in in this paper. In case of high figures of the activation energy E A the calculated service life becomes too high what may result in bearing failures. With FE9 test runs at different temperatures an activation energy E A = 75 kJ/ mol was found for a reference grease. Laboratory methods to determine the activation energy do usually result is much higher figures. For example, HP-DSC test with this reference grease resulted in an activation energy E A > 100 kJ/ mol, mostly it was even E A > 120 kJ/ mol. Such a result will lead to unrealistic high calculated service lives. An activation energy of E A = 75 kJ/ mol is basically a proper assumption for the calculation of service life of most greases. Generally it is always recommended to estimate a low activation energy. Keywords thermal aging, Arrhenius equation of chemical kinetics, FAG FE9 test run 3 Aging Aging may occur as mechanical aging or thermal aging. Mechanical aging is the continuous degradation of the lubricant due to shear stresses. Thermal aging results from a chemical reaction of components of the grease with the oxygen of the ambient air. This reaction is temperature-driven. 3.1 Mechanical Aging Many bearing manufacturers have published charts [2, 3] where the service life or re-lubrication rate of greases is a function of the so-called speed factor. The speed factor results from the speed and the size of the bearing and may additionally include a factor representing the type of bearing. Another approach [4] suggests the calculation of service life based on the shelf life of the grease, its speed limit and a simple inverse proportional equation depending on the speed factor. The speed limit may be measured on an adequate test rig such like the FAG WS22 spindle bearing test rig. 3.2 Long Term Temperature ϑ LT All the above mentioned approaches have in common to exclude thermal effects on aging since they represent aging processes at a lower temperature level only. Usually an upper temperature limit for the validity is defined. Once the operation temperature of the bearing exceeds this temperature limit a drastic reduction of the service life needs to be considered. Only an operation below this temperature limit allows a long term service of the grease. Therefore, the temperature limit introduced here shall be called long term temperature ϑ LT from now on. Bearing manufacturers [2, 3] often suggest to consider half of the service life of the grease for each 15 K above the long term temperature. This is a significant impact on the service live. Only 45 K above the long term temperature will leave just 12.5 % of the service life. 3.3 Chemical Kinetics The thermal aging of greases is a chemical reaction and, therefore, should follow the Arrhenius equation of chemical kinetics. According to the common approaches [5] the Arrhenius equation gives the dependence of the rate constant k of a chemical reaction on the temperature T of the reaction. (1) In equation (1) k 0 is the pre-exponential factor and a constant for each chemical reaction. E A is the activation enerk = k 0 exp RT E A - Aus Wissenschaft und Forschung 20 Tribologie + Schmierungstechnik · 69. Jahrgang · eOnly Sonderausgabe 1/ 2022 DOI 10.24053/ TuS-2022-0027 This refers especially to applications where short service life requires high consumption rates. Typically, high operation temperatures are the key factor to shorten the service life of lubricants drastically. Therefore, to fulfil the requirements of sustainability a prediction of the service life at elevated temperatures is crucial. Only very rough procedures are available to predict the service life of greases in rolling bearings. These procedures do often include a number of parameters that are to be estimated only. Therefore, based on the estimations almost any result may be achieved. Furthermore, basic data to follow these procedures are not available and there are no references given how to generate them. Lately there have been a lot of activities to investigate the physical and chemical influences on service life of lubricants in general. Some approaches include the Arrhenius equation that is widely applied in chemical kinetics. Herewith a simple approach for prediction of service life of greases in rolling bearing is introduced, that considers the latest results of these activities. 2 Mechanisms limiting Service Life It is usually the limit of the service life that is asking for re-lubrication. Therefore, usually the re-lubrication rate is given by the service life of the lubricant. The following mechanisms may limit the service life of greases in rolling bearings: • Loss • Contamination • Aging Loss may be evaporation but is rather more likely leakage. Contamination may occur from the ingress of dust. The particles are often abrasive and, therefore, may reduce the service life. Loss and contamination may occur simultaneously, for example in cases of water wash-out, when the water enters the bearing, contaminates the grease and washes it out at the same time. Nevertheless, in any way re-lubrication rates are to be selected to compensate losses and to avoid contamination. Mostly the required re-lubrication rates are high enough to ensure aging is not determining for the service life at all. However, for perfectly sealed bearings there will be neither loss nor contamination. Under the aspects of sustainability this situation is definitely preferable since this will allow an application of the grease until it has aged. This will reduce any waste of grease to the minimum since, as mentioned above, aging is supposed to be the most lengthy mechanism limiting the service life of bearings. gy for the reaction and R is universal gas constant with Depending on the rate constant k the time t required for a certain reaction will be longer or shorter. It is (2) and with equation (1) this results in: (3) C includes several constants introduced so far. In a so-called Arrhenius plot the natural logarithm of the time required for a chemical reaction ln t is dispayed versus the inverse temperature 1/ T. According to equation (3) this should follow a straight line. 3.4 Arrhenius Plots for Grease Aging According to Matzke et al [6] the aging of greases may be well described by the Arrhenius equation. Matzke has carried out experiments with the RapidOxy tester from Anton Paar GmbH. Grease samples of about 0.5 g are heated in an autoclave under pure oxygen to the testing temperature. With the heat the pressure increases inside of the closed chamber. Afterwards a steady decrease of the pressure was observed which is assumed to result from a chemical reaction between grease and oxygen. At a certain point of time the pressure drops drastically. Matzke assumes this point to correspond to the nearly full depletion of the antioxidant and the beginning oxidation of base oil and thickener. This was repeated with different temperatures and the variables of temperature and time to the pressure drop were displayed in an Arrhenius plot. This was matching quite well a straight line. Therefore, it is proven that thermal aging of greases follows an Arrhenius equation. From the slope of the line the activation energy E A of the aging reaction may be found. 4 FAG FE9 Test Run According to DIN 51825 [7] the FAG FE9 test defines the upper service temperature of greases for bearings in a temperature range from 120 °C upwards. Therefore, this test is quite common and results are available for most greases for bearings. 4.1 Test Run and Results For the FE9 Test 5 rolling bearings are operated with the tested grease at a pre-set temperature. The time of operation until the bearings fail is measured. For each test run there are now 5 times of operation until failure of the bearings. k . t = const ln t = + C RT E A R = 8.314 J/ (mol K). The statistic according to Weibull [8] is rather common to analyse lifetimes. Here an exponential function is applied to describe the statistical distribution of lifetimes. By variation of parameters the function may be adjusted to match the measured lifetimes as good as possible. Once adjusted, the failure probability after any time of operation may be found from the function. In the same way any time to reach a certain failure probabability may be found with the function. Typically the statistical operation time to reach the failure probability of 10 %, this is the F10 value, or to reach the statistical failure probability of 50 %, the F50 value is considered. 4.2 Upper Service Temperature ϑ u According to DIN 51825 [7] the upper service temperature ϑ u for greases in bearings is the highest temperature where a 50 % failure probability is not reached before an operation time of 100 hours. This refers to upper service temperatures ϑ u ≥ 120 °C and corresponds to the following condition: (4) with Typically the upper service temperature is defined in discrete steps of 20 °C starting from 120 °C. FE9 tests ask for a certain effort. To reach F50(ϑ u ) ≥ 100 h some of the bearings may operate more than a week. Therefore, FE9 test runs are usually only conducted at the upper service temperature of the corresponding grease. Higher temperatures are usually not relevant since the lifetime of the grease becomes too short for any technical application. Lower temperatures are of strong technical relevance but the time for each test will increase drastically for lower temperatures. Remembering the suggestion of bearing manufacturers [2, 3] to consider half of the service life of the grease for each 15 K above the long term temperature we finally end up with a figure of F50 ≥ 800 h for a test at 45 °C below the upper service temperature. 4.3 Activation Energy from FE9 Test For one grease of Messrs. Carl Bechem GmbH there have been several FE9 test results available over a temperature range of 60 °C. These test result are to be found below in Table 1. Based on the figures of table 1 an Arrhenius plot with F10 and F50 values is given in Figure 1. According to this plot the thermal aging of greases in rolling bearings is well described by the common Arrhenius equation. u ) 100 h u 120 °C Aus Wissenschaft und Forschung 21 Tribologie + Schmierungstechnik · 69. Jahrgang · eOnly Sonderausgabe 1/ 2022 DOI 10.24053/ TuS-2022-0027 Arrhenius equation with E A = 75 kJ/ mol at lower temperatures close to the temperature the long term temperature ϑ LT the calculation starts from. Going to higher temperatures the difference increases and becomes huge. In any way the 10 K rule results in lower lifetimes and, therefore, is more conservative compared to the 15 K rule or E A = 75 kJ/ mol. However, using the Arrhenius equation with much higher activation energy of E A = 120 kJ/ mol for example will lead to even more conservative results. Nevertheless, mostly the calculation will follow the other direction from high temperature to low temperature. As mentioned earlier the upper service temperature ϑ u is tested rather frequently and, therefore, results from FE9 runs at these high temperatures should be available. For our reference grease where the activation energy was found to be E A = 75 kJ/ mol Figure 3 gives the example of a calculation from from high temperatures to low temperatures. In this case we may even start our calculation from a testing temperature above the upper service temperature ϑ u where the lifetime of the grease was Aus Wissenschaft und Forschung 22 Tribologie + Schmierungstechnik · 69. Jahrgang · eOnly Sonderausgabe 1/ 2022 DOI 10.24053/ TuS-2022-0027 From the slopes in figure 1 an average activation energy of approximately E A = 75 kJ/ mol may be found. 5 Grease Life at elevated Temperatures Elevated temperatures are temperatures ϑ ≥ ϑ LT where the equation (3) of Arrhenius is valid or the rough 15 K rule suggested by the bearing manufacturers [2, 3] may be applied. Once the service life of the grease at any particular elevated temperature is known and, furthermore, the activation energy E A of the grease is available the service live at any other temperature ϑ ≥ ϑ LT may be calculated. In Figure 2 the example of a calculation is given once a low temperature, probably the long term temperature ϑ LT , is known. This example refers to the previously introduced reference grease where an activation energy of E A = 75 kJ/ mol was found from several FE9 runs. The Arrhenius equation with this activation energy differs quite clearly from the commonly recommended 15 K rule. Once a 10 K rule is applied this comes rather close to the Table 1: Results of FE9 test [4] Figure 1: Arrhenius plot from FE9 results [4] Figure 2: Calculation from low to high temperature only F50 = 24 h. Now a rather good matching between Arrhenius with E A = 75 kJ/ mol and the 15 K rule is found. Furthermore, both approaches are providing much more conservative figures compared to the 10 K rule that appeared to be better before once we discussed the other direction. A much higher activation energy of E A = 120 kJ/ mol, that used to result in the most conservative figures before, now leads to the highest lifetimes. Therefore, in this example the 15 K rule appears to be a proper tool for a rough assumption of the service life of greases under elevated temperatures. Furthermore, the Arrhenius equation with E A = 75 kJ/ mol matches quite well with this commonly suggested 15 K rule based on long experience. Using the more scientific approach of the Arrhenius equation it is recommendable to calculate with a low activation energy of E A = 75 kJ/ mol or even lower. 6 Determination of the Activation Energy The activation energy that has been found from several FE9 tests seems to match quite well with the common and long established 15 K rule. Nevertheless, characteristics of greases may vary and, therefore, a more scientific approach with a variable parameter should be preferred. Such an approach is given with the Arrhenius equation with a specific activation energy for every grease. To find activation energies from FE9 test runs as it has been demonstrated above seems to provide reliable figures but is an enormous effort and, therefore, not practicable. This is why recently there have been severals attempts to find activation energy of greases in lab scale test with less effort. 6.1 Activation Energy from HP-DSC Tests The Differential Scanning Calorimeter (DSC) is a fundamental tool in thermal analysis and uses a feedback loop to maintain a sample material at a set temperature while measuring the power needed to do this against a reference furnace [9]. It may be applied to assess the reactivity of a material under a reactive gas, mostly oxygen or air. For activation of this reaction the test is running at temperatures of 190 to 240 °C. To avoid evaporation of volatile matter from the material and to shorten the testing time the tests are often conducted under high gas pressure. This is called High Pressure DSC (HP-DSC). To measure the activation energy with a HP-DSC the sample is heated to the testing temperature under an inert gas, generally nitrogen. Afterwards the sample is flushed with reactive gas, oxygen or air, and after a certain time an exothermal reaction of sample and gas is detected by a lower energy demand to keep the testing temperature. Running this test at different temperatures creates pairs of temperature and time that may be displayed in an Arrhenius plot. As it was discussed earlier already, the activation energy E A is to be found from the slope in the plot. 6.2 Comparison of Results In section 4.3 an activation energy of E A = 75 kJ/ mol has been found from FE9 tests for a reference grease. Two samples of the same product have been taken to detect the activation energy in the HP-DSC as well. Both samples have been tested with pure oxygen under a pressure of p Ox = 5 bar and p Ox = 10 bar. The results of the tests are to be found in Table 2. Generally, the results are in a range of 120 to 130 kJ/ mol. Only the 1 st test under p Ox = 5 bar is clearly lower with an activation energy of E A = 87.8 kJ/ mol. In the 2 nd test under p Ox = 5 bar an activation energy of E A = 127.7 kJ/ mol is found what is very close to the result under p Ox = 10 bar. Therefore, it may be assumed Aus Wissenschaft und Forschung 23 Tribologie + Schmierungstechnik · 69. Jahrgang · eOnly Sonderausgabe 1/ 2022 DOI 10.24053/ TuS-2022-0027 Figure 3: Calculation from high to low temperature Table 2: Activation energy from HP-DSC Most probably this correlation will refer to only one temperature. Therefore, it is suggested to search for a correlation between activation energies from lab tests and bearing tests to cover a wider range of temperatures. 8 Reference [1] United Nations: Report of the World Commission on Environment and Development, Note by the Sectretary- General General Assembly, Fourty-second session, 4 th of August, 1987 [2] Schaffler Technologies GmbH & Co. KG: Rolling Bearing, Issued: 2014, April [3] SKF: Hauptkatalog, Druckschrift 6000/ 2 DE, November 2012, SKF Gruppe, 2012 [4] Frank Reichmann: Vorstellung eines allgemeinen Verfahrens zur Bestimmung der Gebrauchsdauer von Schmierfetten in Wälzlagern, Tribologie und Schmierungstechnik, 67. Jahrgang, 5-6/ 2020 [5] Manfred Baerns, Hans Hofmann, Albert Renken: Chemische Reaktionstechnik, Georg Thieme Verlag Stuttgart, New York, 1987 [6] Markus Matzke, Gerd Dornhöfer, Jörg Schöfer: Quantitatively-accelerated testing of grease oxidation - a parameter study with the RapidOxy, 60. Tribologie-Fachtagung der Gesellschaft für Tribologie e.V., Göttingen, September 2019 [7] DIN 51825: Schmierstoffe, Schmierfette K - Einteilung und Anforderungen, DIN Deutsches Institut für Normung e.V., Beuth Verlag GmbH, Berlin, 2004 [8] Dubbel, Taschenbuch für den Maschinenbau: 16. Auflage, Springer Verlag Berlin, Heidelberg, New York, London, Paris, Tokyo, 1987 [9] PerkinElmer, Inc.: 20 Common Questions about DSC, PerkinElmer, Inc., 2013 [10] In-Sik Rhee: Prediction of high temperature grease life using a decomposition kinetic model, 76 th NLGI annual meeting, Tucson, AZ, 2009 Aus Wissenschaft und Forschung 24 Tribologie + Schmierungstechnik · 69. Jahrgang · eOnly Sonderausgabe 1/ 2022 DOI 10.24053/ TuS-2022-0027 that the single low figure of E A = 87.8 kJ/ mol is a mismeasurement. Finally, it may be concluded that the activation energies found from the HP-DSC are significantly higher compared to the activation energy found from the FE9 test. 7 Conclusion and Outlook Currently there is no way known for a fast and simple measurement of a reliable figure of the activation energy E A . The only reliable procedure is to run FE9 tests at different temperatures. This, of course, is laborious and time-consuming. Therefore, a conservative assumption of the activation energy is the best way at present. Based on experience a figure of E A = 75 kJ/ mol or lower appears to be a good guess. Nevertheless, guessing this important parameter should not be the standard in future since more accurate calculations are required to optimise sustainability of the lubrication. Therefore, the efforts should be continued to find proper lab method to detect activation energies for grease aging. A very promising approach is the introduction of a formula to transfer the activation energy measured by means of RapidOxy tester or HP-DSC test to the conditions of a bearing. Such an approach has been introduced by Rhee [10]. Rhee has applied a thermogravimetric analyser (TGA) to analyse the kinetic properties of ten greases and calculated the grease life at 180 °C. The lifetime of the greases in the bearing test acc. to ASTM D3527 was also tested at 180 °C a huge difference to the calculated lifetime was found. This confirms the findings published in this paper. However, Rhee found a correlation between calculated and measured lifetime.