# Accelerated Reliability Demonstration Test

A

#### Apan

Hello, I am new to reliability and I am trying to define test time for 2 AC motors with 0 failures, demonstrated reliability of 0.9 and CL of 0.9. I do not have history data for the Weibull shape parameter, so I assumed 3, because my plan is to increase the duty 28.8 times and this will lead to wear out failures eventually.
The time the reliability is demonstrated for is 26280 hours (3 years). I calculated that if tested at normal stress level the test time should be 58317 hours. With the linear acceleration factor for the duty of 28.8, the test time would become 2025 hours. Is that correct? Or my line of thinking is totally wrong?
My next intention is to combine the increased duty with increased load (deliberately slowing the shaft) and I am not sure how to go about that. I'd appreciate any help.

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#### Miner

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I verified your calculations of 58317 hours under normal stresses and of 2025 hours for a duty cycle acceleration factor of 28.8. One caveat to these is that other stressors do not increase along with the duty cycle. Specifically, the temperature of the motor. Otherwise, you will have another acceleration factor for the increased temperature, which would follow the Arrhenius model.

Regarding the increased load, do you mean how to physically accomplish the increased load (i.e, using a dyne), or how to incorporate this into your demonstration test calculations? If the load is purely torsional, you will have increased current and temperatures, which will impact the motor's insulation and possibly the bearing grease. If you have axial or radial load components in addition to the torsional load, you will have corresponding loads on the bearings. The increased temperature may be modeled using the Arrhenius model, and the increased current using the inverse power model.

A

#### Apan

Thank you, Miner. The motor is driving a propeller that stirs ground coffee with water. So I would say the load is strictly torsional. I measured the current and it remains the same with or without load, so it looks safe to assume that the only other acceleration factor would be the increased temperature. My struggle now would be how to incorporate the Arrhenius model into the calculations for the reliability demonstration test. How do I find the activation energy? Thank you.

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#### Miner

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Most propeller stirrers would also put an axial thrust load on the bearings. While it may be small, do not overlook it as I would assume the motor and bearings are equally small for this application.

The only way to determine the activation energy precisely is through experimentation. However, there has been some research published on this. An activation energy between 0.5 - 0.6 eV is fairly typical. You can also use the 10 degree C rule where the life is reduced by 50% for every 10 degrees C above the normal operating temperature. AF = 2 ^ [(T1 - T0)/10], where T1 is the elevated temperature and T0 is the normal operating temperature.

I recommend that you read up on degradation testing. You could potentially measure the change in leakage current or of temperature rise to predict a failure time well in advance of the actual failure. This can dramatically reduce the time to test.

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