Experimental Analysis of Resistive Lubricant Film Thickness with Circular Contact Area

Rolling element bearing is one of the most important component of the mechanical machineries. The continuous presence of lubricant between the ball & races enhances the life of bearing. Online condition monitoring is presently done by vibration signature analysis, ultrasound, acoustic emission & use of strain gauges. These methods are either complex or costly. A novel online condition monitoring method is used which involves continuous measurement of electrical resistance between the inner and outer race of rolling element bearing, which is indicative of load as well as speed. This resistance is direct measure of lubricants presence between ball and race. A new parameter from this based on Hertz contact theory is defined as Resistive Lubricant Film Thickness (RFT) obtained from experimental analysis of bearing 6307 with lubricant SAE 40. KeywordRolling element bearing, Resistive lubricant film thickness (RFT), Resistivity, Bearing resistance.

The numerical simulation of a steel ball on glass disc contact was performed by Jiaxin Zhao [11] and the results were compared with the experimental results. And it is reported that the numerical model can be used as a valid tool in studying the start up condition in elastohydrodynamic lubrication under different contact situations with different lubricant properties. A numerical solution of isothermal elastohydrodynamic conjunction for concentrated contact of elastic bodies under the elliptical point contact condition is given by D Jalali-Vahid [12] and it is reported that the lubricant film thickness decreases with increase in load.
[13] has carried out an investigation to study the reflection of ultrasonic waves from the lubricated contact between a sliding steel ball and a at steel disc when substantial solid contact occurs. He has correlated the liquid film stiffness and Solid contact stiffness with the lubricant film thickness. it is reported that the stiffness increases with increase in load and decreases with increase in film thickness, reflection coefficient and speed. An approach has been investigated by R. S. Dwyer-Joyce [14] in which the response of a lubricant -film to an ultrasonic pulse is used to determine the film thickness and it is reported that the film thickness increases with increase in speed of the bearing.
The method for the measurement of the film thickness and condition monitoring used in the past are expensive so an inexpensive online condition monitoring of the bearing based on Resistance method is developed by Matharu et.al [15][16][17][18][19] [23]. Electrical resistivity of the lubricant is used for the calculation of Resistive lubricant film thickness (RFT), and is calculated experimentally by Dewangan et.al [24] using the design of experiment. Also analytically elliptical and circular contact area for the bearing 6007, 6207, 6307 & 6407 has been calculated using the Hertz concept by Dewangan et.al [25]. Resistive lubricant film thickness (RFT) is calculated experimentally by Dewangan et.al [26] for the bearing 6207 & 6307 considering the elliptical and circular contact area. Dewangan et.al [27] is also used Artificial Neural Network to calculate the elliptical contact area.
In the present work bearing 6307 & lubricant SAE 40 is selected for the experimentation. Two parameters Load and speed has been chosen for taking the reading of Voltage drop between the bearing ball and race. Readings of the Voltage drop between the ball and race is taken at the Load of 40 kg, 60 kg, 80 kg & 100 kg and at a speed of 800 rpm, 1000 rpm, 1200 rpm & 1400 rpm.

Definitions
Bearing Resistance (R T )-It is the electrical resistance of the lubricant trapped between the ball and races of the bearing. Resistive Lubricant film thickness (RFT)-It is a indicative lubricant film thickness formed between the heaviest loaded ball and race of the ball bearing.

II. METHODOLOGY
For a ball bearing, the Resistive lubricant film thickness (RFT) based on Hertz contact theory for circular contact area between ball and races is estimated by Matharu et. al [15,16]

Determination of Circular Contact Area
Bearing 6307 has been selected for experimentation and the Load on heavily loaded ball can be calculated by Striback's equation Q act = 40 kg Q = 0.543Q act ⨉9.81 = 0.543⨉40⨉9.81 = 213.07 N ρ = 37.65x10 10 Ω-mm (from other experiment, not discussed here) Now the circular contact area shown below is calculated for inner and outer race.  1940.82 10 37.65 10 3.516 ⨉ 10 mm Calculations for remaining readings are also done but not shown here, it is graphically represented in Fig. 2-5.

V. RESULTS AND DISCUSSION
An ultrasound method is used by I. Křupka et.al.
[8] and reported that the lubricant film thickness increases with the increase in speed. The same result is also observed by R. S. Dwyer-Joyce [14] using the interferometry method. The present experimental setup is based on the resistance method to observe the RFT, and it is calculated for each combination of speed and load selected, and is varying from 0.3516 µm to 0.6505 µm. Obtained results are summarized in Fig. 2-5