So I have two dimensions in my data warehouse:
dim_machine
-------------
machine_key
machine_name
machine_type
dim_tool
------------
tool_key
tool_name
machine_type
What I want to make sure of is the machine_type field in both dimensions has the same data. Should I create a third dimension to snowflake between the two or is there another alternative?
I'm not sure exactly what problem you're trying to solve? This sounds like something that you would simply build into the ETL process: for both dimensions, map your source data to the same target list of machine types. If a new value appears that has no mapping, raise an error (or set a default placeholder value and review the data later).
A completely different option would be a "mini-dimension" (Kimball's term), that holds all possible machine/tool combinations. If two dimensions are closely related and often used together in searches then it can be useful way to consolidate and simplify them. But even then, I assume you will be checking and cleaning the source data to conform the machine types.