There is something wrong with either your shop wiring or my understanding of how you are describing it. A sub panel is not bonded because you never want an interrupted neutral fault to use the ground circuit as a substitute. The ground circuit in the shop should go all the way to the main breaker panel and be bonded there. A ground rod is not at all a substitute for a dedicated conductor between each machine or load and the main panel bonded ground. This circuit goes through the sub panel without being grounded to the sub panel, the ground buss bar is isolated from the panel and is not bonded. In any case, if there are any 110 loads on a 220 machine, it is best to use 4 wire conductor to have both a ground and a dedicated neutral.