# Analytical mathematical modeling of the torque caused by the laundry

• OussamaSscn
There is a lot of real-world complications in this problem. The impact of the "beaters" with clothes, the relationship between the water and the clothes, the rapidity of the change of direction and speed of the spin, etc. I am afraid that the only realistic way to proceed is experimental.

#### OussamaSscn

TL;DR Summary
analytical mathematical modelling of the torque caused by the laundry and water in a washing machine drum
Hello my dear physicists,
I'm trying to model the varied generated (needed)Torque to rotate a washing machine Drum during a Washing Process
so i assumed that the Model has as Input the target vilocity and as an Output the new needed torque to rotate the Drum(to be as a input for the motor model), depending on what is happening inside the drum.
The main final Goal is to simulate the consumed Power by the motor
My questions are :
1)If anyone can help me about this Topic with recommended Documents, ideas ..etc i will be very thankfull
2)inside the Drum there is Water, causing a Torque, I think depending on the water density and the friction with the inner wall of the Drum. so how can I calculte the Torque caused by the Water ?
3)during the Washing process, the Target Speed is relative low (about 45rpm) which makes the clothing lifted up to certain angle and then falling down. I could calculate the limit angle of lifting and the"flight"time and the landing angle of the clothing assuming that the clothing is a one point mass , how can I generalize this equations on a continium of Mass of clothing occupying a certain Volume of the Drum depending on its density and friction properties ? how can i calculate the Torque caused by this Motion ? (I'm not asking for an exact solution, but any idea or notice what could help)
3)during spinning process the clothing still attached on the inner wall of the drum but with random distribution causing an unbalanced Load and a uniformily distributed Load, so how can I determine the Torque in this case ?
Attached is a picture explaining a little bit

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There is a lot of real-world complications in this problem. The impact of the "beaters" with clothes, the relationship between the water and the clothes, the rapidity of the change of direction and speed of the spin, etc. I am afraid that the only realistic way to proceed is experimental.

OussamaSscn and jrmichler
@OussamaSscn
Welcome to PF.
Are you analysing a top loader with a central agitator, or a water efficient front loaded machine ?

OussamaSscn
1. The energy is almost all consumed by continuously lifting the soaking wet clothes and there is no recovery of energy from their subsequent fall.
2. Assuming all of the wet clothes are lifted 0.5m per rev at 1 rev /sec then this consumes 5 watts lifting each kg of wet clothes in the drum
3. The drum contains ~30l of water (almost all absorbed into clothes repeatedly ) so when running the motor must supply 150 W of useable mechanical power at 1rps.
4. I believe this estimate is consistent with the size (1/3-1/2 HP) motors seen in these units
So maybe the estimate is not so complicated (I really didn't "cheat")!

OussamaSscn
FactChecker said:
There is a lot of real-world complications in this problem. The impact of the "beaters" with clothes, the relationship between the water and the clothes, the rapidity of the change of direction and speed of the spin, etc. I am afraid that the only realistic way to proceed is experimental.
Experimental is unfortunately not an option,

Baluncore said:
@OussamaSscn
Welcome to PF.
Are you analysing a top loader with a central agitator, or a water efficient front loaded machine ?
Hallo and thank you for replying,
It is a front loaded machine
Three lifters are on the inner wall of the drum

hutchphd said:
1. The energy is almost all consumed by continuously lifting the soaking wet clothes and there is no recovery of energy from their subsequent fall.
2. Assuming all of the wet clothes are lifted 0.5m per rev at 1 rev /sec then this consumes 5 watts lifting each kg of wet clothes in the drum
3. The drum contains ~30l of water (almost all absorbed into clothes repeatedly ) so when running the motor must supply 150 W of useable mechanical power at 1rps.
4. I believe this estimate is consistent with the size (1/3-1/2 HP) motors seen in these units
So maybe the estimate is not so complicated (I really didn't "cheat")!