A Non-Arrhenius Model for Mechanism Consistency Checking in Accelerated Degradation Tests
Abstract
:1. Introduction
1.1. A Brief Introduction to the Accelerated Lifetime and Degradation Tests
1.2. Literature Review
- A non-Arrhenius model is proposed to portray the degradation behavior of electromagnetic relays under ADT. The model is based on the theory of the crystal vibration energy of the material of the spring. As compared to the conventional Arrhenius-based degradation model, EFM is able to better capture the temperature characteristics of coefficients in the degradation model (TCCDM) over a much wide temperature range (see Figure 3).
- A procedure for degradation mechanism consistency checking is devised. The procedure leverages the statistical hypothesis (i.e., the test), and checks whether the parameter characterizing the degradation mechanism changes or not over temperature. Analytic expressions of the partial derivatives to the likelihood function are derived, and the Bayesian information criterion is employed to compare EFM- and Arrhenius-based degradation models.
- The proposed model can be used to explain the degradation of a wide range of materials and components, such as the capacitor or rubber.
2. Mathematical Description of the Arrhenius Model
- The temperature characteristics of degradation parameters (TCDPs) (e.g., the force of the spring over temperature) align with the shape that the Arrhenius model prescribes.
- The temperature characteristics of coefficients in the degradation model (TCCDM) (e.g., d only changes with temperature) align with the shape of TCDP.
3. Theory of the EFM
3.1. Temperature Characteristics Based on Crystal Vibration Energy
3.2. Comparison of the Arrhenius Model and EFM
4. Procedure for Mechanism Consistency Checking
- Establish a degradation model;
- Define a criterion for mechanism consistency checking.
4.1. Degradation Model
4.2. Criteria for Mechanism Consistency Checking
4.3. Parameter Estimation
5. Case Study on the Degradation of Electromagnetic Relays
5.1. Stress Relaxation as the Degradation Parameter
5.2. Loss of Spring Force as the Degradation Parameter
6. Discussion
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Accelerated Model | Parameters | ||||
---|---|---|---|---|---|
Arrhenius model | A | - | - | - | |
- | - | - | |||
- | - | - | |||
- | - | - | |||
- | - | - | |||
- | - | - | |||
- | - | - | |||
EFM | - | - | - | ||
- | - | - | |||
- | - | - | |||
b | - | - | - | ||
- | - | - | |||
- | - | - | |||
- | - | - | |||
- | - | - | |||
- | - | - | |||
Accelerated Model | Outcome | ||||
---|---|---|---|---|---|
Arrhenius model | Reject | ||||
EFM | Retain |
Temperature | Time | Force Loss | Degradation Rate | Arrhenius | EFM |
---|---|---|---|---|---|
(K) | (h) | (N) | (N/h) | ||
3456 | |||||
3216 | |||||
3456 | |||||
3456 | |||||
3456 |
Model | BIC | ||
---|---|---|---|
Arrhenius | −91.11 | ||
EFM | −91.72 |
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You, J.; Fu, R.; Liang, H.; Lin, Y. A Non-Arrhenius Model for Mechanism Consistency Checking in Accelerated Degradation Tests. Actuators 2023, 12, 319. https://doi.org/10.3390/act12080319
You J, Fu R, Liang H, Lin Y. A Non-Arrhenius Model for Mechanism Consistency Checking in Accelerated Degradation Tests. Actuators. 2023; 12(8):319. https://doi.org/10.3390/act12080319
Chicago/Turabian StyleYou, Jiaxin, Rao Fu, Huimin Liang, and Yigang Lin. 2023. "A Non-Arrhenius Model for Mechanism Consistency Checking in Accelerated Degradation Tests" Actuators 12, no. 8: 319. https://doi.org/10.3390/act12080319