Characteristics of Stribeck s Curve of Hydrodynamic Lubrication Using Experimental Values and Modified Petroff s Equation

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1 Characteristics of Stribeck s Curve of Hydrodynamic Lubrication Using Experimental Values and Modified Petroff s Equation Daniel Joel Amine 1, Oryina Mbaadega Injor 2 and Peter Obinna Ekeanyanwu 3 1,2,3 Mechanical Engineering Department, University of Agriculture, Makurdi, Nigeria. jdpamine@gmail.com Article Received: 9 October 217 Article Accepted: 29 November 217 Article Published: 16 December 217 AB ST R ACT The effect of different slot sizes and orientations on journal bearing performance was investigated. Sixteen sliding bearings locally produced in a foundry and grouped based on groove sizes of.15m,.2m, and.25m; and orientation at angles of 2o, 4o, and 7o were investigated. The bearings were fixed one after the other in a hub and a shaft was inserted through them at each given time with one end fixed to the jaw of a lathe machine. This was allowed to run for 5 mins using oil lubricant of 2ml applied at intervals for various speeds of (4, 85, 125, 26) rev/min with thermocouple clipped by the bearing which read lubricant temperature and pressure. Results showed that between speeds of 4-85 (rev/min), sliding surfaces of the bearing and shaft were practically in direct contact and friction was at its highest level. At speeds of (rev/min), lower friction levels were achieved through the use of mixed lubrication, where the sliding surfaces were partially separated by the lubricant. While at speeds above 125 (rev/min), the minimum of the friction coefficient was reached in conformity with Stribeck curves at the critical value of the duty parameter, which was the dividing line between the mixed and hydrodynamic lubrication zones. Keywords: Boundary Lubrication, Coefficient Of Friction, Hydrodynamic Lubrication Zones and Stribeck Curve. 1. INTRODUCTION Bearings are metallic objects with specially designed surface upon which another metal (journal) rolls. It is designed to reduce friction by supporting radial loads and often used when load is light and motion is relatively continuous, such as in crank shaft [1]. The study of journal bearing in mechanical engineering is of paramount importance because of the functional role it plays in control of friction between wheels and shafts of machines and automobiles. The reliability and efficiency of machine components is greatly affected by friction and wear. However, power supplied from power sources such as motors, engines and generators can be lost through friction and wear in the various interacting surfaces of a machine, regardless of its scale. Such interacting surfaces can be found in mechanical components such as bearings, gears, bushings, pistons, and seals [2]. Historically, early bearings had surfaces of wood or leather lubricated with animal fat so as to reduce friction, but recent studies have shown that improved form of bearings can be obtained from research [3]. One of such is that journal bearings made up of metallic alloys with inserted grooves/slots which contain oil during motion of shaft or wheels to enhance lubrication and reduce wear of contact surface by formation of oil film, can be designed and produced. These grooves are either introduced in a bearing axially, radially or at an angle [4]. Various groove patterns used in the industry includes; straight axial, circular or radial, axial and circular, butterfly groove, single loop, double loop, and a lot more. However the choice of type of groove depends on the direction of applied load, whether it is in one direction or varies considerably. Therefore one size of groove and orientation that will be suitable for one application may not be suitable for another. The most important factor that should be considered in groove size and orientation should be service conditions; low coefficient of friction, low temperature increase and high pressure [4]. Once these factors are taken into consideration, wear of the bearing material will be highly minimized. 231 P a g e Website:

2 There are works claiming that journal bearings with grooves or cavities in mating surfaces show, under some conditions, better properties than standard ones with smooth-surface mating components [5, 6, 7]. This view is also considered right by some researchers studying the hydrodynamic lubrication of slide bearings. It follows from the previous works of [8, 9] on the initial modelling of a spiral-grooved journal bearing that, under some circumstances, the journal grooves may enhance the bearing load capacity compared with a smooth journal bearing. In high-speed rotational machines, the lubricant shear stresses induce important (non-negligible) temperature increase. Thus, the thermal considerations play an important role in the analysis of bearings [1]. However, premature bearing failure is as a result of several causes including; dirt, insufficient lubrication, misalignment, overloading, corrosion, false brinelling, overheating and improper finish [11]. Hydrodynamic bearings wear very slowly as wear occurs during start-up and shut-down, when the speed is too low to produce sufficient fluid pressure to support the bearing surfaces on a lubricant film [12]. The concept of slots came as a result of the need to combat friction, reduce wear and enhance life span of bearing by increasing productivity and reducing mean machine down time. These slots are located in bearing through different methods in accordance to design and purpose in machine assembly. To ascertain the size of the groove for better performance, [13] made a comparison for non-dimensional load for different groove angles, and observed that the load carrying capacity was slightly higher with 1 groove angle in comparison with and 3 in case of two axial groove bearings. The rise in bearing temperature increases or decreases bearing clearance, and the variation in thermal coefficient of different material used may also result to clearance increase thereby reducing load capacity. Frictional heat can be removed by conduction through the bearing components or by oil flow [14]. Advancements in oil-surface interaction understanding may allow better fundamental-based selection of both lubricants and components materials where Stribeck curves are used [15, 16]. 2. MATERIALS AND METHODS 2.1 Materials The materials used in this research work included; Fifteen (15) sliding bearings with mating surfaces having a composition (Tin-base babbitts of 89% Sn, 8% Pb and 3% Cu), Lathe machine (Harrison 6), Oil lubricants (SAE 2W 5), Thermocouple (type k), Oil pressure gauge (-4 bars), Hub, Shaft (15.97 mm diameter and 3 mm length), Injection syringe for introducing a specific quantity of oil into the system, and 5 mm hose connected from the lower part of the bearing to the pressure gauge. 2.2 Methods The sliding surface tin-based bearings were locally produced from a local foundry with dimensions; 16 mm diameter and 36 mm length using l d ratio of 2.25, where 2.25 l d 1 for safe condition [Robert, 4]. The bearings were further grouped based on groove size and orientation as follows; One non-split journal bearing without slot, split journal bearings with radial slots of different sizes, split journal bearings with axial slots of different sizes, and split journal bearings with inclined slots of different sizes and orientation. 232 P a g e Website:

3 A shaft of.3 m length and.1597 m diameter was machined from mild steel to test run the performance of the bearing. Lathe machine (Harrison 6) was used to produce spindle speed of shaft for the test run. The hub was produced locally to house the bearing in order to avoid vibration during the test run. Standard engine oil (SAE 2W-5) was used and the volume at each test run was 2 ml. Injection syringe with calibration was used to introduce 5 ml of the lubricant for each test run. Thermocouple (type k) was clamped to the body of the bearing and the temperature read at the stop of the machine. A.5 m hose was connected from the lower base of the bearing. The experimental process took place after experimental setup has been put in place, and bearing assembled. Each bearing was run one at a time at various speed of 4, 85, 125 to 26 (rpm) in the following order; 1. Non split journal bearings without slots. 2. Three split journal bearings with radial slots of different sizes. 3. Three split journal bearings with axial slots of different sizes 4. Six split journal bearings with inclined slots of different sizes and orientations grouped into three starting from the first three inclined at, next 4 and the third group at 7 respectively. The bearings were fixed one after the other in a hub and the shaft inserted through them at each given time with one end fixed on the jaw of a lathe and allowed to run on the bearing for 5 min using oil of 2 ml. After a period of 5 minutes, the machine was put to a stop and thermocouple clipped on the body of the bearing to read temperature immediately. The same was done for pressure but with an oil pressure gauge permanently clamped at the base centre hole of the bearing. However, the phenomenon of bearing friction as explained by Petroff using the Petroff equation on the assumption that the shaft is concentric defines groups of dimensionless parameters, and the coefficient of friction predicted turns out to be quite good even when the shaft is not concentric, as shown in Equation 1. f=2π^2 [μnr pc]..eqtn 1 Where f- coefficient of friction μ- absolute viscosity N- speed (rev/min) r- shaft radius p- pressure c- diametric clearance Petroff s equation was modified based on data available from this research work as follows; Slot length.1 m Slot width.5 m Slot depth (.15,.2 and.25) m Bearing inner diameter.16 m Shaft diameter.1597 m Clearance.3 m 233 P a g e Website:

4 The length occupied is the entire length of the bearing, which was 36 mm with width of 16 mm and the thickness equals the minimum film thickness h_o=.25d Where, D- Bearing diameter =.16 m. Hence, h_o=.25.16=.4 m Total volume of oil on the bearing surface = Total surface volume + Total slot volume Surface volume = = m 3 Slot volume at different depths of.15 m,.2 m,.25 m is as thus; For.15 m, = = m 3 For.2 m, = = m 3 For.25 m, = = m 3 Total volume when slot is at depth of.15 m = = m 3 increase in volume % increase as a result of presence of slot = original volume = = m 3 Hence, the new Petroff s equation becomes, 1 f = 2π 2 μnr pc( ).. Eqtn 2 Total volume when slot is at depth of.2 m = = m 3 % increase = = m 3 Hence, the new Petroff s equation becomes, f = 2π 2 μnr pc( ).. Eqtn 3 Total volume when slot is at depth of.25 m = = m 3 % increase = = m 3 Thus the new Petroff s equation becomes; f = 2π 2 μnr pc( )..Eqtn P a g e Website:

5 Coefficient of Friction (f) (x1-6 ) Coefficient of Friction (f) (1-6 ) 3. RESULTS Data obtained from various experimental tests carried out on the characteristics of Stribeck s curve of hydrodynamic lubrication using experimental values and modified Petroff s equation are presented in the figures 1-6 below. The figures show dependence of bearing coefficient of friction on bearing modulus/somerfield number DEGREE 4 DEGREE 7 DEGREE Bearing Modulus(1-6 ) Fig. 1. Curve of coefficient of friction versus bearing modulus at depth of.15m DEGREES 4 DEGREES 7 DEGREES Bearing Modulus(x1-6 ) Fig. 2. Curve of coefficient of friction versus bearing modulus at depth of.2m 235 P a g e Website:

6 Coefficient of friction (f) (x1-6 ) Coefficient of Friction (f) (x1-6 ) Bearing Modulus(x1-6 ) 2 DEGREES 4 DEGREES 7 DEGREES Fig. 3. Curve of coefficient of friction versus bearing modulus at depth of.25m Bearing Modulus(x1-6 ) 2 DEGREES 4 DEGREES 7 DEGREES Fig. 4. Curve of coefficient of friction versus bearing modulus at depth of.15m for the modification of Petroff s equation. 236 P a g e Website:

7 Coefficient of friction (f) (x1-6 ) Coefficient of friction (f) (x1-6 ) DEGREES 4 DEGREES 7 DEGREES Bearing modulus(x1-6 ) Fig. 5. Curve of coefficient of friction versus bearing modulus at depth of.2m for the modification of Petroff s equation DEGREES 4 DEGREES 7 DEGREES Bearing Modulus(x1-6 ) Fig. 6. Curve of coefficient of friction versus bearing modulus at depth of.25m for the modification of Petroff s equation. 4. DISCUSSION Results showed that there was usual initial high value of coefficient of friction between bearing and journal at the start of machine, and this value dropped as the bearing modulus value increased. Thus, as the value of the bearing modulus increased, the value of the coefficient of friction dropped, after the initial high rise in value. This was an indication that the work done was in line with outlined principles of lubrication and had given more insight that slot (groove) inclusion in a journal bearing actually increases the rate of drop of value of coefficient of friction in 237 P a g e Website:

8 bearing during actual service life. At depth of.15m, according to Fig1, bearings with inclined slot showed better performance especially with slot inclined at 7o. This was seen when its curve was closer to that of the stribeck s curve, followed by 2o, 4o, axial, radial and then non-split. Same also was applicable in Fig 2, where inclined slot at 4o gave a curve exactly like that of the stribeck s curve. It was also the same as in Fig 3 where 2o inclinations gave a better result of curve taking almost the same shape as that of the stribeck s curve. In comparison with non-split bearings without grooves and split bearings with grooves, it was deduced that those with slots showed better performance, in terms of drop in coefficient of friction than those without slots. Using coefficient of friction as performance index to analyze bearings with slots, with a view to ascertaining which of them has less value of coefficient of friction, it was observed that bearings with slots having higher angles of inclination, performed better than others, beginning at 7o,to 4o and to 2o [13]. Practically, bearings with higher lubricant retaining ability in them will produce less friction than those with less lubricant. However, curves produced when Petroff s equation was modeled, as seen in Fig 4-6 were also closer to the Stribeck s curve of hydrodynamic lubrication according to the results obtained which showed that the curves were better at depth of.15m and.25m. 5. CONCLUSION Result of characteristics of stribeck s curve of hydrodynamic lubrication using experimental values and modified petroff s equation showed that all the curves produced took the same shape as that of the stribeck s with some having better shape at depth of.15m and.25m. ACKNOWLEDGEMENT This work was carried out in collaboration between all authors. Author JDA designed the study and supervised the experiments. Authors OMI and POE wrote the protocol and wrote the first draft of the manuscript and managed literature searches. All authors read and approved the final manuscript. The authors also acknowledge the staff of the mechanical workshop in the department for their assistance. COMPETING INTERESTS Authors have declared that no competing interests exist. REFERENCES [1] Z. Szeri, Fluid film lubrication, 2nd edition, Cambridge University Press, London, 211. [2] R. L. Jackson, J. Lei, Hydrodynamically Lubricated and Grooved Biomimetic Self-Adapting Surfaces. Journal of Functional Biomaterials, vol. 5, (214), pp [3] Bushan, Principles and application of tribology. John Willey and Sons Inc., New York, [4] K. Dmitri, Mechanisms of Wear, 5th edition, John Wiley & Sons, New York, P a g e Website:

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