"What micron filter should be used to filter a 220 gear oil? We are looking into getting a filter cart to filter the oil while the machine is running."

First, determine the optimum target cleanliness level for that specific gearbox, and the do not forget to ensure adequate breathers are fitted, as any attempts at clean-up will be lost quickly. A few tips on filter carts:

First, ensure that for each type of lubricant in use, there is a dedicated filter cart to avoid cross contamination of fluids. 

Second, because this is fluid power generating device, ensure it complies with all the safety requirements and has a pressure venting safety valve in the event of dead-heading the pump. 

Third, ensure the cart includes a by-pass loop to the filters, and incorporates a sampling connector for the use of online instruments or bottle sampling. The design (pump and filter selection) of filter carts is dependent on two factors; the lubricant's viscosity grade, and the temperature at which the cart will be used. A higher viscosity, such as an ISO VG 220 oil, will require a lower flow rate in the pump to avoid high differential pressures across the filter. But this will be affected by the ambient and operating temperatures.

While the use of quick connectors allow the cart to be used while the gearbox is operating (this is the optimum filtering condition), the lubricant's viscosity will also be affected by the ambient temperatures, so if this is located outdoors, assume the worst case winter temperature when looking at the viscosity issue. Of course, slowing the flow rate to avoid high differential pressures will increase the time to filter the box, and depending on the Beta ratio, the rule of thumb is to allow the volume of the gearbox to circulate seven times through the filter for effective clean-up. For example, a gearbox with 50L sump capacity and a filter cart with a 10L/min flow rate will take five minutes for one pass and approximately 35 minutes to clean up. Keep in mind the flow rate versus the time available for filtering.

As to the filter rating, experience has shown a 10 micron filter capable of achieving better than ISO 17/15/12. However, if your optimum target cleanliness level is lower than this, consider a 6 micron filter. There are various ways to strike an optimum balance between flow rate and filter rating, and this includes the possibility of putting several filters in parallel to increase the flow area. As a simple guide, the differential pressure can be halved by doubling the length of the element or putting two elements in parallel. 3 micron filters will work with ISO VG 220 oils, but check the temperature conditions, and whether your target cleanliness levels require such fine filters. The cost of these elements should be considered.