Problem

 To determine how a washing machine spin cycle works, as well as how the modern day spin cycle is self-balancing.

Interesting Phenomena

 You are washing your clothes in your mom’s old washing machine and when it gets to the spin cycle you start to hear loud thuds coming from inside the washing machine.  What causes this problem and what do you do to fix it?  You open the lid and rearrange the load in an attempt to make the load better balanced. Why is it when you do your laundry at the laundry mat you don’t have to worry about balancing your clothes?  The answer to these questions is proven through the use of some simple properties of dynamics, Eulers 1st and 2nd laws.

Analysis

 Euler’s 1st and 2nd laws can easily explain the dynamics of a washing machine spin cycle.

Sigma Fc =  Sigma m_Ia_I                    1st Law
Sigma Mp =  r_cp x (Sigma m_Ia_I)       2nd law
 

In Euler’s  1st law the force is what pushes your clothes to the exterior of the basket then the force pushes the water in your clothes out of your clothes and through the holes in the washing machine basket.

Sigma Fc = m[ac + (alpha_b/g x r_ci) + (w_b/g x w_b/g x r_ci)]

Sigma Fc = m[ r_ciw_b/g² ]î

If the load is balanced, i.e. all the point masses at the exterior of the basket are equal.  Then the   Sigma Fc = 0 due to the fact that the forces induced by point masses at 180^o from each other will cancel each other out.

Now let us suppose that the point masses on the outside of the basket are not equal.  This will lead to the Sigma Fc <=> 0.   This in turn leads to a moment around the base of the basket, which causes the basket to wobble .  This can be seen from the drawing.

Sigma Fc = Sigma m_Ia_I  <=> 0

Sigma Mp = Sigma r_CP x Sigma m_Ia_I
 

                                         Top View                                                                                                         Side View

Now for a self-balancing washing machine springs are inserted in a circular pattern around a point lower than ‘P’.  These springs create forces and moments that counteract any forces and moments that could be created at ‘P’ by an unbalanced load.  The exact spring constants would be determined by the engineer for the required application.
 
 
 

Applications

The theory behind spinning an unbalanced load can be applied to many other applications in the engineering world.  One example would be car wheels.  When you get new tires put on your wheels the wheels are placed in a balancing machine which tells the mechanic were to add weight to the rim of the wheel to balance the wheel.  If you didn’t get your tires balanced your car would shake and pull from the unbalanced forces created in the wheel.  Another example is of turbine blades.  When turbine blades are made they are not made perfectly balanced and the have to be ground in places to balance them.  If the blades weren’t balanced they would break the shaft that they were mounted on and destroy the turbine.

Conclusion

In the preceding analysis it can be concluded that an older washing machine with an unbalanced load creates noise from the basket rattling around in the steel frame.  The basket rattles around due to the moment created at the base by the unequal forces created by the unbalanced load.   But with the simple addition of the springs at the base of the washing machine it can be shown how a self-balancing washing machine works.

References

McGill, David J. and King, Wilton W.  An Introduction to Dynamics   PWS 1995