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I want to minimize a backlash on the Ball Screw.
For THK Precision Ball Screw, five ranges of axial clearance are available.
  G0: Axial clearance is 0 or less
  GT: Axial clearance is between 0 and 0.005
  G1: Axial clearance is between 0 and 0.01
  G2: Axial clearance is between 0 and 0.02
  G3: Axial clearance is between 0 and 0.05

We recommend G0 (axial clearance of 0 or less) if you want to minimize the backlash.

However, note that G0 axial clearance is not available for some models that work under high loads.
Contact THK for details.