#
The Impact of Lubricant Film Thickness and Ball Bearings Failures^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Empirical Equations for ${L}_{10}$ Life

## 3. Tribological Predictions of ${L}_{10}$ Life

## 4. First Parametric Study

## 5. Second Parametric Study

## 6. Conclusions

## Supplementary Materials

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

${L}_{10}$ | Number of revolutions before 10% chance of failure |

SKF | Svenska Kullagerfabriken |

RMS | Root Mean Square |

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**Figure 1.**Calculated values of the ${L}_{10}$ life for the Timken 29348 roller bearing, utilizing theoretical Equation (25) and empirical Equation (1), all for a parametric series of loads, speeds, and lubricant temperatures. The data are placed in the order the parametric sample was conducted on the X-axis. The parametric study was conducted for a temperature ranging between 20 ${}^{\circ}$C and 300 ${}^{\circ}$C (112.2355 cSt to 1.0648 cSt), in increments of 10 ${}^{\circ}$C; an equivalent axial load of 1–100% (in 1% increments) of the 2040 kN dynamic load ${C}_{a1}$; and a bearing speed of 1000–15,000 RPM, in increments of 500 RPM.

**Table 1.**Dimensions of Timken Spherical Roller Bearings, used in the parametric study described in Section 5. The average radius of the roller race ${R}_{R}$ (m) is the half the average of variables ${d}_{b}$, H, E, and D, where ${R}_{R}=\frac{{d}_{b}+H+E+D}{8}$.

Model | d (mm) | ${\mathit{C}}_{\mathit{a}1}$ (kN) | ${\mathit{d}}_{\mathit{b}}$ (mm) | H (mm) | E (mm) | D (mm) | |
---|---|---|---|---|---|---|---|

1 | 29418 | 90 | 820 | 98.9 | 148 | 137 | 190 |

2 | 29320 | 100 | 462 | 108.1 | 141 | 134 | 170 |

3 | 29420 | 100 | 1020 | 108.8 | 164 | 151 | 210 |

4 | 29322 | 110 | 604 | 118.6 | 157 | 149 | 190 |

5 | 29422 | 110 | 1200 | 120.3 | 180 | 167 | 230 |

6 | 29324 | 120 | 768 | 128.5 | 172 | 163 | 210 |

7 | 29424 | 120 | 1390 | 131.6 | 197 | 182 | 250 |

8 | 29326 | 130 | 852 | 140.3 | 186 | 177 | 225 |

9 | 29426 | 130 | 1600 | 142.4 | 213 | 197 | 270 |

10 | 29328 | 140 | 970 | 148.9 | 199 | 188 | 240 |

11 | 29428 | 140 | 1640 | 152.8 | 223 | 207 | 280 |

12 | 29330 | 150 | 993 | 159.5 | 209 | 198 | 250 |

13 | 29430 | 150 | 1860 | 163.5 | 238 | 222 | 300 |

14 | 29332 | 160 | 1190 | 170.5 | 225 | 213 | 270 |

15 | 29432 | 160 | 2100 | 175 | 255 | 237 | 320 |

16 | 29334 | 170 | 1230 | 179.2 | 235 | 223 | 280 |

17 | 29434 | 170 | 2380 | 184.8 | 270 | 251 | 340 |

18 | 29336 | 180 | 1430 | 190.7 | 251 | 238 | 300 |

19 | 29436 | 180 | 2660 | 197.6 | 286 | 267 | 360 |

20 | 29338 | 190 | 1620 | 202.2 | 268 | 253 | 320 |

21 | 29438 | 190 | 3040 | 205.5 | 303 | 281 | 380 |

22 | 29340 | 200 | 1880 | 213.3 | 284 | 269 | 340 |

23 | 29440 | 200 | 3210 | 217 | 317 | 295 | 400 |

24 | 29344 | 220 | 1950 | 231.6 | 303 | 288 | 360 |

25 | 29444 | 220 | 3350 | 237.8 | 339 | 317 | 420 |

26 | 29348 | 240 | 2040 | 251.9 | 323 | 308 | 380 |

27 | 29448 | 240 | 3410 | 259 | 360 | 338 | 440 |

28 | 29352 | 260 | 2580 | 275.7 | 356 | 340 | 420 |

29 | 29452 | 260 | 4160 | 279.2 | 391 | 367 | 480 |

30 | 29356 | 280 | 2580 | 296.8 | 376 | 360 | 440 |

31 | 29456 | 280 | 4920 | 300.6 | 423 | 397 | 520 |

32 | 29360 | 300 | 3150 | 315.6 | 407 | 388 | 480 |

33 | 29460 | 300 | 4990 | 321.1 | 443 | 418 | 540 |

34 | 29364 | 320 | 2830 | 333.3 | 427 | 407 | 500 |

35 | 29464 | 320 | 5155 | 320 | 469 | 444 | 580 |

36 | 29368 | 340 | 3120 | 365.8 | 463 | 443 | 540 |

37 | 29468 | 340 | 5922 | 340 | 500 | 473 | 620 |

38 | 29372 | 360 | 3632 | 360 | 476 | 457 | 560 |

39 | 29472 | 360 | 5440 | 360 | 528 | 498 | 640 |

40 | 29376 | 380 | 4295 | 380 | 507 | 486 | 600 |

41 | 29476 | 380 | 6493 | 380 | 546.1 | 518 | 670 |

42 | 29380 | 400 | 3850 | 400 | 534 | 510 | 620 |

43 | 29480 | 400 | 7333 | 400 | 577.1 | 547 | 710 |

44 | 29284 | 420 | 2682 | 420 | 513.1 | 498 | 580 |

45 | 29384 | 420 | 4040 | 420 | 561 | 537 | 650 |

46 | 29484 | 420 | 6780 | 420 | 608 | 576 | 730 |

47 | 29388 | 440 | 4530 | 440 | 585 | 561 | 680 |

48 | 29488 | 440 | 8606 | 440 | 635 | 602 | 780 |

49 | 29392 | 460 | 4820 | 460 | 614 | 589 | 710 |

50 | 29492 | 460 | 8120 | 460 | 666 | 631 | 800 |

51 | 29396 | 480 | 4820 | 480 | 635 | 610 | 730 |

52 | 29496 | 480 | 9320 | 480 | 700 | 662 | 850 |

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**MDPI and ACS Style**

Marko, M.D.
The Impact of Lubricant Film Thickness and Ball Bearings Failures. *Lubricants* **2019**, *7*, 48.
https://doi.org/10.3390/lubricants7060048

**AMA Style**

Marko MD.
The Impact of Lubricant Film Thickness and Ball Bearings Failures. *Lubricants*. 2019; 7(6):48.
https://doi.org/10.3390/lubricants7060048

**Chicago/Turabian Style**

Marko, Matthew David.
2019. "The Impact of Lubricant Film Thickness and Ball Bearings Failures" *Lubricants* 7, no. 6: 48.
https://doi.org/10.3390/lubricants7060048