Understanding Washing Machine Vibration?
I have noticed on several occasions on different brands and types of top loading semi-automatic Washing Machines (picture attached below) that when I use the dryer part exclusively (i.e., with an empty washing bucket, the left side bucket in the picture below being empty),
- it starts with mild vibration,
- then a terrible disastrous vibration as if all the components are going to fall out and
- then as the bucket inside the dryer speeds up further, it goes back to mild vibration.

I don’t know if my analysis is correct but I feel that it is the classical case of whirling of shaft phenomena at play here. Initially, there is mild vibration, then, when it is near the first critical speed, it starts vibrating violently (the amplitude is quite high because of resonant condition) and finally when it overcomes the critical speed, it goes on to vibrate in a normal manner.
Mathematical Note on Critical Speed of Shaft
In the case of filled washing bucket, we don’t get violent vibration when the dryer is turned on (in most cases which I have encountered) and I think it is because of critical speed (omega) = sqrt (stiffness/mass). When the mass is higher, the critical speed is much less and the motor overcomes the first critical speed very quickly and then it never encounters violent vibration.
I know my analysis is very rudimentary because I am not accounting for the way mass is distributed overall and if in the case of filled washing bucket, the additional mass changes the stiffness constant or not but I would appreciate if someone could throw a little more light on this phenomena.

