The use of "a fan belt" is a direct reference to a machine that has worn out from too much use.  The image of the woman being conditioned to possess "good nature" is one that reflects a constant demand to be nothing other than "good natured."  In this light, the Piercy suggests that the socialization of women is one that treats them as objects, constantly needing them until they are of no use and disposed when they are no longer useful or productive.  This connects to her overall idea that modern women who are constructed as "Barbie Dolls" are products of a patriarchy that seeks to dehumanize and objectify women, using them for specific ends and then discarding them when those ends are met:  "In 'Barbie Doll' the girlchild fulfills the patriarchal prescription for obedience by destroying herself. She perpetuates patriarchal power in death by being transformed into someone she could not be in life."  In constructing women's perception in this manner, the use of the "fan belt" is a reminder that all machines have a life span, and when they reach a certain point of extended use, all machines die out.