# On Monitoring Physical and Chemical Degradation and Life Estimation Models for Lubricating Greases

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Empirical Models

## 3. Lubricant Degradation Processes

#### 3.1. Mechanical Degradation

#### 3.1.1. Mechanical Degradation Monitoring

#### 3.1.2. Mechanical Life Estimation Models

#### 3.1.3. Shear Stress Empirical Functions

#### 3.1.4. Shear Stress Analytical Functions

#### 3.2. Chemical Degradation

#### 3.2.1. Chemical Degradation Monitoring Methods

#### 3.2.2. Kinetic Models

- The first-order kinetic model seems to fit well with the oxidation of the lubricant;
- The zero-order kinetic model seems to fit well with the evaporation of the base oil and LMW products;
- The mass fraction of the original oil (MA) decreases almost linearly with time from the first moment of the process;
- The mass fraction of evaporated oil (ME) and evaporated LMW products (MF) increase linearly with time from the first moment of the process;
- The mass fraction of HMW products (MP) increases exponentially with time. There is not any HMW product formation for a while at the beginning of the process. It can be concluded that the oxidation inhibitors’ scarification prevents the polymerization of the radicals in this induction phase; and
- Because of the small size of oil sample, the model neglects the effect of oxygen diffusion. However, the oxidation rate can be limited by the oxygen diffusion mechanism in real applications. Therefore, the model underestimates the life of the lubricant in larger size samples.

_{iso}to the oxidation induction temperature for a scanning run at a heating rate of β:

#### 3.2.3. Chemical Life Estimating Models

_{1}and t

_{2}) at two different temperatures (T

_{1}and T

_{2}) and finding the activation energy for any grease from Equation (49):

_{i}: Induction time in PDSC at test temperature. If t

_{i}> 120, then α = 1.

## 4. Summary and Conclusions

- Mechanical and chemical degradation are important grease degradation mechanisms.
- Mechanical and chemical degradation are irreversible processes.
- Mechanical degradation can be addressed from an energy/entropy point of view.
- Chemical degradation has been studied applying a first-order kinetic model.
- Arrhenius’ law has been used to calculate the activation energy and reaction rate in the applied first-order kinetic model.
- Chemical degradation is controlled by the activation energy provided to grease, and can be studied from an energy/entropy point of view.
- Mechanical and chemical degradation occur simultaneously in real applications.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

c | Concentration |

C | specific dynamic capacity of ball bearing |

D | shaft diameter at bearing seat |

${e}_{rh}\left(t\right)$ | energy density |

${e}_{Rrheo}^{*}$ | apparent rheological energy density |

${E}_{a}$ | activation energy |

HMW | high molecular weight products |

k | reaction rate constant |

${k}_{0}$ | Arrhenius equation prefactor |

${k}^{*}$ | normalized rate constant |

${K}_{G}$ | life parameter |

${K}_{T}$ | temperature factor |

L | grease life |

L_{0} | geometric mean grease life without accounting for either speed or load |

${L}_{40\text{}\xb0\mathrm{C}}$ | grease life when operating at 40 °C |

LMW | low molecular weight products |

M | Mass |

$\overline{M}$ | normalized mass |

N | bearing angular speed |

R | universal gas constant |

S | total half-life subtraction speed factor |

${S}_{G}$ | half-life subtraction speed factor |

${S}_{N}$ | half-life subtraction size factor |

${S}_{W}$ | half-life subtraction load factor |

${t}_{lim}$, ${t}_{\infty}$ | final stable shear stress occurrence time |

${t}_{ind}$ | induction time |

${T}_{ind}$ | induction temperature |

T(t) | temperature function |

W | the radial load |

Z | number of load cycle |

$\alpha $ | shear stress reduction factor |

$\dot{{\rm Y}}$(t) | shear rate function |

τ(t) | shear stress function |

${\tau}_{0}$ | initial shear stress at time zero |

$\tau (\infty ),{\tau}_{lim}$ | final stable shear stress |

ν | base oil viscosity |

f | Frequency |

${\nu}_{40}$ | base oil viscosity at 40 °C |

$\varnothing $ | non-Newtonian behavior number |

Ω | angular velocity |

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**Figure 1.**Guidelines for bearing re-greasing intervals with mild operating conditions [10].

**Figure 4.**Shear stress decrease vs. time for XHP222 grease during a constant shear rate of 2500 1/s and at a constant temperature of 35 °C [13].

**Figure 5.**Spiegel et al. model [22].

**Figure 6.**Micro-oxidation test apparatus [29].

**Figure 7.**Naidu et al. oxidation model [29].

**Figure 8.**Diagram of the reaction scheme [29].

**Figure 10.**Comparison between the model prediction and the experimental data for 185 °C [29].

**Figure 11.**Arrhenius plots for four different greases [33].

**Figure 12.**Linear curve fit to the TGA results based on the assumption of a first-order kinetic model [35].

**Table 1.**Comparison between actual grease life and predicted grease life using Equation (51) [34].

Sample | ASTM D 3527, h | Predicted Grease Life, h | Oil Separation @ 180 °C, % |
---|---|---|---|

A | 151 | 150 | 25.9 |

B | 340 | 368 | 2.9 |

C | 400 | 395 | 4.4 |

D | 240 | 228 | 13.2 |

E | 171 | 191 | 12.0 |

F | 100 | 313 | 82.3 |

G | 192 | 186 | 12.7 |

H | 20 | 200 | 31.8 |

I | 40 | 158 | 52.9 |

J | 287 | 266 | 3.6 |

**Table 2.**Comparison between actual grease life (ASTM D 3527) and predicted grease life using Equation (53) [35].

Sample | Kinetic Life @180 °C, h | ASTM D3527, h | Predicted Grease Life, h |
---|---|---|---|

A | 19.1 | 150 | 167 |

B | 59 | 240 | 240 |

C | 21.2 | 170 | 174 |

D | 0.02 | 20 | 18.6 |

E | 20.7 | 196 | 171 |

F | 4.6 | 100 | 106 |

G | 30 | 192 | 194 |

H | 7.29 | 120 | 123 |

I | 0.25 | 40 | 41 |

J | 108 | 275 | 290 |

Empirical models | [6,7,8,9,10,41,44,45] | ||

Physical Degradation | Mechanical degradation | Monitoring | SEM [13,25,46,47,48] |

Penetration [12,49,50] | |||

Shear stress [13,14] | |||

Shear stress functions | Empirical [14,15,16] | ||

Analytical [13,22] | |||

Mechanical stability [14,17,19,20,46,51,52,53] | |||

Life predicting models [13] | |||

Base oil evaporation [42,48,50] | |||

Base oil separation/Grease leakage [25,42,43] | |||

Contamination [54] | |||

Chemical Degradation | Monitoring | DSC/PDSC [23,30,33,34,35,36,55] | |

FTIR [11,25,47,48,54,55,56,57,58,59,60] | |||

Acid number [25,50,55] | |||

Ruler [55,61,62] | |||

Thermogravimetry [42,63] | |||

gel permeation chromatography [25,29,48] | |||

Kinetic models [23,29,30,33,35,63] | |||

Chemical stability [33,36] | |||

Life predicting models [34,35,63] | |||

Grease Flow | Film thickness measurement [47,54,58,59,64,65,66] | ||

Starvation [54,64,65,66] |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rezasoltani, A.; Khonsari, M.M.
On Monitoring Physical and Chemical Degradation and Life Estimation Models for Lubricating Greases. *Lubricants* **2016**, *4*, 34.
https://doi.org/10.3390/lubricants4030034

**AMA Style**

Rezasoltani A, Khonsari MM.
On Monitoring Physical and Chemical Degradation and Life Estimation Models for Lubricating Greases. *Lubricants*. 2016; 4(3):34.
https://doi.org/10.3390/lubricants4030034

**Chicago/Turabian Style**

Rezasoltani, Asghar, and M. M. Khonsari.
2016. "On Monitoring Physical and Chemical Degradation and Life Estimation Models for Lubricating Greases" *Lubricants* 4, no. 3: 34.
https://doi.org/10.3390/lubricants4030034