Tribology International 36 (2003) 781–789 www.elsevier.com/locate/triboint The Stribeck memorial lecture Bo Jacobson ∗ Machine Elements Division, Department of Mechanical Engineering, Lund University, Box 118, Lund 221 00, Sweden Abstract Stribeck’s publications ‘Kugellager für beliebige Belastungen’ and ‘Die wesentlichen Eigenschaften der Gleit- und Rollenlager’ were remarkable for their time. Many of the findings were revolutionary and are still considered quite modern. The method used by Stribeck to calculate load distribution between the balls within a ball bearing is still used today, otherwise, a full finite element analysis would be required. His measurements and analysis of bearing friction is also astonishingly accurate. Most of the ball-bearing types studied by Stribeck are not in use any more, but the deep-groove ball bearings he investigated were similar enough to be compared with modern deep-groove ball bearings. Stribeck measured the friction coefficient 0.0015 and SKF gives the friction coefficient 0.0015 for deep-groove ball bearings in the catalogue from 1989. For the first time, in the SKF catalogue from 1989, the life calculation method took into account contamination also. Stribeck had stated already 100 years ago that cleanliness was very important for bearing life and function. Stribeck’s investigation of journal bearing friction, as a function of load and speed, was also extremely important, as he showed the possibility of finding a point of minimum friction for lubricated applications. He also showed that the friction for sliding bearings started at high friction at low speeds, decreased to a minimum friction when metal to metal contact stopped, and then increased again at higher speeds, which is the well known ‘Stribeck curve’. 2003 Elsevier Ltd. All rights reserved. Keywords: Friction; Load; Ball bearings; Roller bearings; Journal bearings 1. Introduction It is now 101 and 100 years, respectively, since Richard Stribeck published his famous papers, ‘Kugellager für beliebige Belastungen’ (1901), and ‘Die wesentlichen Eigenshaften der Gleit- und Rollenlager’ (1902) in Zeitschrift des Vereines deutscher Ingenieure [2,3]. The first paper treated the load-carrying capacity of ball bearings brilliantly and the second paper resolved the longstanding dispute over bearing friction characteristics as a function of load, speed and lubrication. Stribeck  was born in Stuttgart in Germany on 7 July 1861. He received his basic education in his hometown where he finished his studies at the Technische Hochschule in Stuttgart. Later, he gained practical experience in various places, including Königsberg. At the age of 27, in 1888, he was back in his hometown, Stuttgart, and was appointed as Professor of Machine ∗ Fax: +46-46222-8504. E-mail address: [email protected] (B. Jacobson). 0301-679X/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0301-679X(03)00094-X Construction at the Building School. Two years later, in 1890, he moved to the Technische Hochschule in Darmstadt. After three years, on 1 April 1893, he moved to the Technische Hochschule in Dresden. As Professor für Maschineningenieurswesen, he gave his inaugural address in Dresden on 6 May 1893 on the subject ‘Progress in the production of steam and in the exploitation of its energy in steam engines during the last 20 years’. Seven weeks later, on 1 July 1893, he went on a sabbatical leave to the United States of America. Later, when he was back in Dresden, in the academic year 1896–1897, he was appointed to the governing body of the newly founded Machines Laboratory I (Strengths). He did not stay there long and moved to Berlin in March 1898. There, he became head of the metallurgical division of the Centralstelle für wissenschaftlich-technische Untersuchungen in Neubabelsberg, Berlin. During the years 1889–1893, when Stribeck worked in Stuttgart and in Darmstadt, he published some 10 scientific papers. This large early output was mainly on giving solutions to the problems of boilers and steam 782 B. Jacobson / Tribology International 36 (2003) 781–789 turbines for marine applications. Only in the last paper in this group, Stribeck dealt with dynamic loading on the main and cross-head bearings of steam engines. That was thus the first time he became involved with tribology and tribological problems. When he was in Dresden, Stribeck studied gears, with particular emphasis on experimental studies of worm gear drives. He experimentally determined the limiting loading for correctly working worm gear drives as a function of load (F) and speed (n). He found that a hyperbola described the function well and that F·n = constant described the combination of load and speed, which could be allowed for any specific drive lubricated with a certain specific oil. In 1897, he published a paper on the consequences of wear of gears. As mentioned above, Stribeck moved in 1898 to Berlin to work as one of the directors of the newly created Centralstelle für wissenschaftlich-technische Untersuchungen in Neubabelsberg, and to head the metallurgical division. There, he undertook and published the findings from his most basic tribological studies between 1898 and 1902. They were in two different areas: the load-carrying capacity of ball bearings and the friction characteristics of plain bearings and radial rolling element bearings. Stribeck applied sound physical principles to his experimental investigations, and used the theoretical background information available at that time. In his very well known study on the load-carrying capacity of ball bearings Stribeck  gave scientific basis for the development of a large industry. He used the Hertzian contact theory, which by then had been known for 20 years, to connect the loads on the different balls to the external load. He then compared the loads on single ball contacts of different geometry, which were needed to give visible plastic deformations. He used three balls in contact, see Fig. 1, a steel plate sandwiched between two balls, and more conforming contacts of the type found in deep-groove ball bearings. Stribeck’s studies, which were commissioned by the Deutsche Waffenund Munionsfabriken, Berlin, were epoch-making in their effect on the ball-bearing industry. Its major impact arose from the analysis of the carefully conducted experiments, see Fig. 2, and the sound appreciation of Hertzian contact theory, together with the presentation of practical formulae in a form suitable for the bearing designer. Stribeck’s approach to the question of loadcarrying capacity of ball bearings was about seven years in advance of similar considerations in gear design. 2. Load-carrying capacity for ball bearings Stribeck’s paper on ball bearings ‘Kugellager für beliebige Belastungen’ was published in Zeitschrift des Vereines deutcher Ingenieure on Saturday 19 January Fig. 1. Test set-up for ball deformation measurements. 1901, as a ‘Mitteilung aus der Zentralstelle für wissenschaftlich- techniche Untersuchungen’. Stribeck stated there that his results were applicable not only to ball bearings, but also to all other types of concentrated contacts of Hertzian type. He used Hertz’ equations for deformation, contact dimension and contact pressure, and applied it to ballbearing geometry. By comparing the permanent deformation left after the unloading, he found that contact pressures could be much higher than the yield strength of the steel, and the elastic deformations were almost halved due to the hydrostatic stress components in the contact centre. He made experiments with three balls in series and a flat or concave plate between two balls to find the allowable load before plastic deformation B. Jacobson / Tribology International 36 (2003) 781–789 783 ing the maximum contact pressure 4.6 GPa for selfaligning ball bearings, 4.2 GPa for other ball bearings and 4 GPa for roller bearings. By measuring the load and ball diameter combination, which just started the plastic deformation, Stribeck found that P / d 2 = k was constant for each geometry type (ball–ball, ball–flat, ball– concave), and that for each steel hardness, the allowable load was proportional to the square of the ball diameter. For the materials he investigated, different geometry gave different k-values between 2 and 10 kg per oneeighth of an inch depending on the groove forms in the rings. 3. Friction for ball bearings One week later, on 26 January 1901, Stribeck published the second half of the paper ‘Ball bearings for varying loads’ (Kugellager für beliebige Belastungen), and there the friction in ball bearings was analysed. He elegantly split the power loss in each contact point into one rolling resistance component and one spinning resistance component, see Fig. 3. By summing up the power loss components, it was obvious that the power loss was proportional to the ratio of ring diameter to ball diameters, or for full complement bearings proportional to the number of balls. The bearings should have a small number of large balls to get low power loss. Stribeck needed to know the load distribution between the balls, and assumed then that only the contact points Fig. 2. Contact deformation shown as a function of load for three types of contact. occurred, see Fig. 2. The geometry balls on balls had sizes 3/80, 1/20, 5/80, 3/40, 7/80, 10 and 1 1/80. For flat between balls, the sizes were 3/80, 1/20, 5/80, 7/80 and 1 1/80. By using linear elasticity and measuring the elastic compression deformations of diameter 16 mm cylinders with 32 mm length, he found that the modulus of elasticity varied slightly between un-hardened, oil hardened and water hardened materials. The difference between the highest and the lowest value was 1.25%, so he used a mean value in his analysis (E = 2,120,000 kg/cm2). Stribeck found, just as predicted by Hertz’ theory, that the elastic deformation was largest for a ball on a ball contact, smaller for a ball on a flat contact and still smaller for concave contacts. His limit of detection of plastic deformation was 0.00025·d, which is 2.5 times as large as the plastic deformation used by ISO before the ISO 76:1987 standard for static load-carrying capacity for rolling element bearings was adopted. Today, the static load-carrying capacity for rolling element bearings is defined by an elastic calculation giv- Fig. 3. Rolling and spinning contacts between ball and race. 784 B. Jacobson / Tribology International 36 (2003) 781–789 were deformed, and the rings had no bending deformations. For a bearing with zero radial play, the load per ball was proportional to cosg 3/2 where the angle g was measured from the ball with the maximum load. Summing up the load components, he found that for 10, 15 and 20 balls in the bearing, the total load-carrying capacity divided with the maximum load on one ball was the number of balls divided with 4.37. To be on the safe side, he gave the famous equation: P0 5 5·P / z (1) where P0 = maximum load on one ball; P = maximum load on one ball; and z = number of balls. For friction calculations, he also found that the sum of the radial forces around the circumference of the bearing was 1.2 times the external load. 4. Experiments with ball bearings Stribeck designed and manufactured a friction torque measurement rig, which automatically compensated for the weight of the different moving parts, see Fig. 4. He was thereby able to measure the small friction with high accuracy. He found that for small amounts of lubricant in the bearings, the friction was independent of the temperature. His experiments were run at 65, 100, 130, 190, 380, 580, 780 and 1150 rpm, starting with the lowest speed. When decreasing the speed from 1150 rpm, Stri- Fig. 4. Friction measurement set-up with compensating counterweight. beck noticed that the friction was lower than during the speed increase despite almost constant temperature. He assumed that the friction decrease was due to running in of the surfaces, as this phenomenon was much stronger for rough surfaces than for polished surfaces, where the friction was not changed by running in. Stribeck ran tests with five different types of contact geometry for ball bearings and found that a deep-groove ball bearing with open osculation had the lowest coefficient of friction, 0.0015, of the tested types, see Fig. 5. For that bearing the largest allowable ball load was 11·d2 kg where d was the ball diameter in eighths of an inch. That shows the material development the last 100 years. The maximum load to avoid plastic deformation then was 3100 N on a diameter 17 mm ball. Today, the ball load is 10,000 N for infinite life. Stribeck also ran endurance tests and detected that also small variations in material hardness had a large influence on life. As soon as a plastically deformed rolling track was visible, the bearing life was short. For good steel hardness, he found the maximum allowable ball load to be P 5 10·d2 kg (d in inches) (2) P 5 100·d2kg (d in cm) (3) when the ring groove radius was 2d / 3. Such good results were only possible when balls and rings were made of good hardened material, and dust and contamination, e.g. forming sand or surface parts from the moulding, were removed from the bearing lubricant, just like for sliding bearings. Fig. 5. Ball bearings with grooved rings similar to modern deepgroove ball bearings. B. Jacobson / Tribology International 36 (2003) 781–789 5. Bearing lubrication One and a half year later, Stribeck published his paper on friction and lubrication for journal bearings and rolling bearings, ‘Die wesentlichen Eigenshaften der Gleitund Rollenlager’, starting on Saturday 6 September 1902, No. 36, of Zeitschrift des Vereines deutscher Ingenieure. He wrote the paper in order to show which bearing type was the best performer under different running conditions, as no hard data were available for journal bearings. No information was available earlier on the different lubrication regimes and their friction coefficients; it was impossible to know which bearing type to choose for different applications. During the investigation, Stribeck not only compared hydrodynamic bearings and ball bearings, but also studied roller bearings. 6. Journal bearings Stribeck had found that not only roughly manufactured bearing surfaces needed to run-in for some time. How fast the running in process could be, was mainly a function of the bearing material. Fastest were some white metals, slightly slower were bearing bronzes and very slow was cast iron. Steel was practically impossible to run-in. The load possible to use during the running in process was also a strong function of the material. White metals could stand the highest running in load, and steel the lowest. For white metals with a yield point of 20 MPa, mean pressures P / (L·d) = 9 MPa were possible to carry. White metals also gave the least wear of the steel shaft, and were therefore considered the best bearing materials. Stribeck also mentioned that a bearing, which had been run-in at a low load, had to run-in again if the load was increased. That is still true, but still not very well known in industry. 7. The lubricant Stribeck saw that the lubricant had a very strong influence on the friction, but also on the allowable load and the safety of the bearing function. If a bearing was run-in with one oil, another oil could start the running in anew or fail the bearing. The best oil found, and used for the tests, was ‘Gasmotorenöl’ delivered from ‘Gasmotorenfabrik Deutz’. The same oil had also been used in the earlier ball-bearing tests. The viscosity at 20 °C was 0.28 Ns/m2, at 40 °C, it was 0.075 Ns/m2, and at 100 °C, the viscosity was 0.012 Ns/m2. The flame point was 180 °C. By comparing the viscosity variation for different temperatures, Stribeck found that the thin Velocite Spindle Oil changed its viscosity in the same way 785 between 20 and 50 °C as a heavy mineral oil between 80 and 110 °C, see Fig. 6. 8. Cast iron Sellers-bearing with ring-lubrication Stribeck’s test bearings were different from most modern journal bearings, in that the bearing width (230 mm) was much larger than the diameter (70 mm), see Fig. 7. This made the bearing sensitive for shaft bending and misalignment. To avoid temperature transients, causing temperatures at different points in the bearing to differ by a few degrees, measurements were made slowly. Steady state temperatures were reached after 2– 3 h of running. That also showed Stribeck that most machines in transient use never would reach the steady state temperature. Stribeck’s experiments clearly indicated that the higher the speed is, the higher is also the bearing load when the minimum coefficient of friction is experienced. When the bearing speed approached zero, all tested loads between 0.25 and 20 kg/cm2 gave the same coefficient of friction 0.14, see Fig. 8. At low speeds, a temperature increase resulted in an increased friction, which was explained as increased metal contact in the bearing. That metal contact also made the friction vary a lot from experiment to experiment. At high speeds, when the oil film was thick and without metal to metal contact, the friction was much more repeatable. At increasing speed above the minimum friction point, the friction increased linearly with the speed, but at higher speeds, the increase was lower due to the increased oil film thickness. Stribeck even registered decreasing friction at increasing speed, when the bearing temperature was allowed to increase at increasing speed and thereby lowered the lubricant viscosity. 9. White-metal bearings The Sellers-bearings were unable to run-in by themselves, but the white-metal bearings were expected to easily run-in without any specific run-in procedure. Different low hardness alloys containing lead, tin and antimony were tested. Their yield points were low, hardly above 20 MPa. The bearing diameter was 70 mm and the bearing length was here 137 mm. The mean pressure for such long bearings was normally below 2.5 MPa and reached only exceptionally 5 MPa pressure. To reach such high pressures in the test set-up, Stribeck halved the bearing length after he had finished the full-length experiments. He then found that the short bearing worked as well as the long one for high speeds, and better than the long one for low speeds. At low film thickness, the long bearing seems to have had problems with edge loading. Stribeck loaded the part of the bear- 786 B. Jacobson / Tribology International 36 (2003) 781–789 Fig. 6. Oil viscosity (°E) as a function of temperature. Fig. 7. Sellers-bearing with ring-lubrication. ing surface containing the lubrication grooves, so the oil film was thinner than if the grooves had been in the unloaded part. 10. The running-in To get a smooth surface fast for the white-metal surface, running in was started at a low load (1.15 MPa) and a low speed (64 rpm). The friction decreased quickly from 0.020 and stabilised at 0.0028 after 18 h. The load was then increased and the running in restarted at 1.9 MPa pressure. The friction stabilised at 0.0022 after 16 h. When the load was increased later to 2.6 MPa, the coefficient of friction was strongly increased, and still after 6 h, it was 0.0044, double the value for lower pressures. After 16 h of running, the bearing was still not runin. The load was then increased to 3.6 MPa for 10 h, but the bearing still did not run-in correctly. When the load then was decreased to2.6 MPa, the bearing worked very well with the coefficient of friction 0.0021. The bearing material (magnoliametalle) worked well and became smoother by the running. The use of a low viscosity oil for the running in process made the surfaces so smooth, that when the bearing later was loaded to 5.1 MPa using a higher viscosity oil, no further running in was taking place. Stribeck also tried to use water as lubricant, but that gave wear and particle production. B. Jacobson / Tribology International 36 (2003) 781–789 Fig. 8. 787 Journal bearing friction as a function of rotational speed for different mean pressures. ‘Stribeck curves’. 11. The run-in bearing lubricated with gas motor oil (gasmotorenöl) When the bearing was so well run-in that no metallic contact occurred for the running conditions tested, Stribeck measured the coefficient of friction as a function of temperature for loads from 0.07 to 7.5 MPa and speeds from 190 to 1100 rpm. The minimum friction was around 0.005 for the highest load and temperature. Stribeck compared the change in viscosity and temperature with the change in friction. He then saw that the friction was not proportional to the viscosity, but the oil film thickness also changed and influenced the friction. The starting friction at zero speed was much higher for the white-metal bearings (0.21–0.24) than for the cast iron bearing (0.14), but for increasing speed, the friction in the white-metal bearing decreased much faster, and the minimum friction was lower than for the cast iron bearing. Even lower friction was found in a smaller bearing with 7.5 MPa load. A comparison between the white-metal bearing and the cast iron bearing showed their different behaviour. The largest difference was in the degree of running in. The polished area in the white-metal bearing was much 788 B. Jacobson / Tribology International 36 (2003) 781–789 larger than the polished area in the cast iron bearing. The conformity between shaft and bearing was thus different for the two bearings after running in. For the same bearing pressure, the bearing performance was very similar for the two bearing materials studied. 12. Roller bearings Stribeck also investigated a number of roller bearings with different types of long cylindrical rollers to compare their friction and load-carrying capacity with ball bearings and hydrodynamic journal bearings. The five bearing types he studied were Laschenrollenlager, bearings with loose tube-formed rollers mounted on small shafts, Kynoch’s roller bearings, Hyatt bearings, and bearings from Mossberg & Granville Mfg. Co. The Laschenrollenlager had loose rollers coupled together 4 by 4 using scissors-like coupling mechanisms at the roller ends. The roller length was about as long as the length along the circumference for one group of four rollers. This caused self-locking by axial motion and turning of the roller group like a self-locking drawer. As Stribeck concluded, ‘Die Konstruktion erwies sich unbrauchbar’ (the design was useless). The other four bearing types were tested extensively, both regarding load-carrying capacity and friction/ power loss. The first bearing type tested had 20 loose rollers with diameter 10 mm and length 90 mm coupled together by two washers having 20 holes around the circumference, one at each side of the bearing. The rollers were ‘extremely accurately manufactured with a diameter variation of only ±0.04 mm’, which is at least 100 times less accurate than modern bearings. The bearing worked well and had a coefficient of friction at high loads of 0.0039, which can be compared with Stribeck’s ball-bearing friction 0.0015. The bearings failed by pitting, probably caused by over-rolling of large numbers of wear particles. The load-carrying capacity of the bearing type was P 5 11·L·d·z / 5 kg (4) where z is the number of rollers; L is the roller length in cm; and d is the roller diameter in cm. This can be compared to Stribeck’s ball-bearing tests, which gave P 5 100·d2·z / 5 kg (5) To give the same load-carrying capacity for a roller bearing and a ball bearing, the roller length had to be 9.1 times longer than the ball diameter if the roller and ball diameters were the same. Kynoch’s roller bearing had a similar geometry, but the long tube-formed rollers were cut into 5–6 pieces giving larger flexibility to accommodate manufacturing errors. The friction was about the same, but the loadcarrying capacity was only 60% of the capacity of the previous bearing type. The Hyatt-roller bearing had also about the same friction but a load-carrying capacity of 85% of the second bearing type. The big problem with the Hyatt-roller bearing was its noise level. Already at 600 rpm ‘ist das Geräusch selbst in einer Schlosserwerkstätte recht störend’ (the bearing noise is really disturbing even in a drop forging shop). The bearings from Mossberg & Granville Mfg. Co. had cages, which surrounded and closed in the rollers with a small gap around most of their circumference. That gave a large hydrodynamic resistance to motion, so its power loss gave very high working temperature at high speed and high friction. The cage did guide the rollers very well though, which gave as a result noise that was the lowest among the roller bearings. Stribeck summed the results up in his Fig. 33, see Fig. 9, where it is obvious that roller bearings had much (2– 10 times) higher friction than ball bearings, but that the starting friction was lower than for sliding bearings. The starting friction, and the steady state high-speed friction, was the same for most of the roller bearing types. The load-carrying capacity for roller bearings was P 5 k·L·d·z / 5 (6) where 6#k#11 for the different bearing types tested. When he compared cast iron journal bearings with roller bearings, only the best roller bearings could reach the high load-carrying capacity of a journal bearing. 13. Conclusions Stribeck’s publications ‘Kugellager für beliebige Belastungen’ and ‘Die wesentlichen Eigenschaften der Gleit- und Rollenlager’ were remarkable for their time. Many of the findings were revolutionary and are still considered quite modern. The method used by Stribeck to calculate load distribution between the balls within a ball bearing is still used today, otherwise, a full finite element analysis would be required. His measurements and analysis of bearing friction is also astonishingly accurate. Most of the ball-bearing types studied by Stribeck are not in use any more, but the deep-groove ball bearings he investigated were similar enough to be compared with modern deep-groove ball bearings. Stribeck measured the friction coefficient 0.0015 and SKF gives the friction coefficient 0.0015 for deep-groove ball bearings in the catalogue from 1989. For the first time, in the SKF catalogue from 1989, the life calculation method that took into account contamination also. Stribeck had stated already 100 years ago B. Jacobson / Tribology International 36 (2003) 781–789 Fig. 9. 789 Comparison of friction for different bearing types. that cleanliness was very important for bearing life and function. Stribeck’s investigation of journal bearing friction, as a function of load and speed, was also extremely important, as he showed the possibility to find a point of minimum friction for lubricated applications. He also showed that the friction for sliding bearings started at high friction at low speeds, decreased to a minimum friction when metal to metal contact stopped, and then increased again at higher speeds, the well known ‘Stribeck curve’. References  Dowson D. History of tribology. London: Longman Group Limited, 1979.  Stribeck R. Kugellager für beliebige Belastungen. Zeitschrift des Vereines deutscher Ingenieure 1901;45(3):73–9 (pt I) & 45(4): 118–125 (pt II).  Stribeck R. Die wesentlischen Eigenschaften der Gleit- und Rollenlager. Zeitschrift des Vereines deutscher Ingenieure 1902; 46(37):1341-1348 (pt I) & 46(38):1432-1438 (pt II) & 46(39) 1463–1470 (pt III).