**5. Conclusions**

ASTM D2596 was developed with an understanding that seizure prevention by EP lubricants is largely affected by factors like actual load, ball diameter, sliding speed, lubricant temperature and friction that were directly accountable for changes in local temperature. Therefore, it makes sense that these parameters were well described in the standard. However, this study shows that


**Author Contributions:** Conceptualization, D.H.V.; methodology, D.H.V., D.P. and S.K.J.; software, A.D.; validation, D.H.V., D.P. and S.K.J.; formal analysis, D.H.V., D.P. and S.K.J.; investigation, D.H.V., D.P. and S.K.J.; resources, A.D.; data curation, D.H.V., D.P. and S.K.J.; writing—original draft preparation, D.H.V.; writing—review and editing, D.P.; visualization, D.H.V.; supervision, D.H.V. and D.P.; project administration, D.H.V.; funding acquisition, A.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

#### **Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank Channabasappa from Kluber Lubrication (Mysore, India) for helping us in selection of high weld load greases and Fabio Alemanno from Ducom Instruments for creating the graphical abstract.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. Calculation of Actual Load, Sliding Speed and Coefficient of Friction in Four-Ball Tester**

#### *Appendix A.1. Calculation of Subtended Angle in Four Ball Tetrahedral Configuration via CAD Method*

For calculating the contact radius of the ball interface, we must know the vertical contact angle, (θ) subtended between the top ball and the bottom three balls. Refer to the image for details. The angle is derived via 3d CAD-based assembly measurements.

Details of the steps used to arrive at the angle are illustrated in the images on the right-hand side.

The first image shows a typical 4-ball assembly as it manifests on a four ball testerHere all the four balls are of identical diameters and measure 12.7 mm.

A cut section view is generated exactly with the center of two balls taken simultaneously. One being the top ball which is held in the collet and the other one is one of the balls which are locked in the ball pot.

A sketch is generated using the references created in the assembly model. The halfangle (*θ*) here is measured at 35.26◦, which is the angle of contact with respect to the axis of rotation and the direction in which the normal load (*N*) is applied.

**Figure A1.** Illustration of four ball assembly in four-ball tester.

*Appendix A.2. Correlating Applied Test Load, P, with the Local Normal Resultant Force, N, on the Balls*

From Section 1, we know that the vertical angle subtended at the contact points of the ball is 35.26◦ (*θ*). Knowing this, we can correlate the test load, *P*, applied to the assembly with the resultant force, *N*, at the contact. The following steps are used for this:

$$P = \cos(35.26^\circ) \times N$$

$$P = 0.8164N$$

1.2247*P*

*N* =

or:

where, *P* is the applied load during a test.

#### *Appendix A.3. Measurement of Frictional Torque and Local Frictional Forces, on the Ball*

The frictional torque (*FT*) is measured using a module which consists of a load cell and arm attached to the ball pot and displayed on controller. Using the displayed value, we calculate:

$$FT = f \times r$$

where, *f* is the frictional force between the contacting balls or:

$$f = FT/r$$

$$f = FT/0.00366$$

$$f = 272.929 \times FT$$

where, *r* = distance on contact of ball from center (in m):

> *r* = sin 35.26 × (diameter of the ball/2)

> > *r* = 0.577 × (0.0127/2) *r =* 0.577 × 0.00635 = 0.00366 m

*Appendix A.4. Measurement of Sliding Velocity at the Initial Contact for ASTM D4172 Test*

The distance between the central axis of rotation of the top ball and the point of contact between any of the bottom three balls, *r*, was calculated in Section 3.

Knowing '*r*', the sliding velocity at the point of contact can be calculated as:

$$v = \frac{2\pi rN}{60}$$

where *v* = sliding speed in m/s, *r* = distance between ball contact and central axis, in m, *N* = speed of rotation in RPM. For ASTM D2266, *N* = 1770 RPM. From FBT tetrahedral geometry, *d* = 0.00366. Hence, sliding speed *v* = (2 × *PI* × 0.00366 × 1770)/60 = 0.678 m/s.

*Appendix A.5. Calculation of Coefficient of Friction Using Applied Load, P, and Measured Friction Torque, FT*

Moving on, the coefficient of friction—CoF (*μ*) is calculated by using the formula:

$$\mu = f/N$$

where, *f* is the frictional force between the contacting balls, *N* is the resultant load between the contacting balls.

Now, with the information and derivations from Appendices A.1–A.3, we can calculate CoF:

$$\mu = 272.929 \text{FT}/1.2247 \text{P}$$

Therefore, CoF at the ball contact can be calculated with the following formula:

$$\mu = 222.854 \times FT/P$$
