What failed?
Based on her experience with centrifuge, Lily quickly realized it was most likely due to the malfunction of the safety device on the lid, which we later found out to be a lid switch (see a picture of the stand alone lid switch assembly below) . It was validated: when she used a screw driver to push on the switch assembly, the washing machine started running! I unscrewed the assembly main body from the washer's frame and squeezed it everywhere, and put it back in - the washer could work normally.
However the washer stopped working again the following week. I turned off the washing machine (for Safety!!) and removed the lid switch from the frame again. Upon investigation, it turned out that the plastic case of the working unit fractured. I searched http://www.repairclinic.com/ (note - I used this website to identify the failed part in my dryer previously) and eventually found out the part is officially called lid switch Assembly. We decided to replace the part.
After I identified the part, I went back to look at it again. When I squeezed the fractured part back together, and turned on the washer, it ran again. So I used steel wire to tie the fractured part together and then wrap the bundled part with duct tapes. The washing machine worked fine that week.
Why did it fail?
Typically this part should not fail. I thought about the cause of the failure, and quickly determined that it was due to the fact that we let the lid close on its free fall after loading laundry; in applied mechanics terminology, it is the impact of pin (on the lid) to the lid switch which caused the fracture and shortened the life of the part. The impact force is much larger than static force. If we close the lid all the way by hand, the max force on the lid switch would be just half its weight, the lid switch should last very long time.
With this understanding, we started a new rule right away - close the washing machine washer's and dryer's lids/covers gently by hand. With this practice, the washer has been working for a month without any problem. I expect that my temporary fix should be a permanent fix with gentle closing of the lid. We will not replace the lid switch after all!
Quantitative Failure Analysis
I was wondering how much higher the force would be due to free fall impact than statically closing it. So I did a hand calculation from Newtonian mechanics and preformed a simulation to show the dynamic process.
The lid (cover) is modeled as flat plate which can freely rotate at one side (the triangle symbol in the following figure).
Based on conservation of energy, we have the following relations - basically it is that the potential energy of the vertical lid equals to the (rotational)kinetic energy when the lid is horizontal (close position)
When the lid (D=18 inch) free falls to horizontal position right before it hit the lid, its angular velocity is 8.01radians/second or 459 deg/second! It takes a lot of force to stop the lid with high angular velocity in a very short time. If I assume that the lid would be stopped in 0.001 second (both plate and lid switch are assumed to be rigid), then the impact force would be 250 times of the static force.
A simulation that model the lid as steel, and the lid switch as a rigid block, showed the impact force is 165times the static force (half weight of the cover). Since both lid and lid switch are deformable objects, and the solid spring on the lid switch actually deforms a lot when pressed, or in other words, not all of the potential energy is converted into kinetic energy, some of it is conveted into strain(deformation) energy. The force amplification is estimated to be more close to 100.
Note: This is the first time I performed a quantitative failure analysis outside my professional work. Hindsight, I think tha it would be helpful to show that high school physics (newtonian mechanis) can be used to solve real world daily life problems.
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