The contact angles formed at the position of each ball in ball screws are conventionally assumed to be a constant value in determination of contact stiffness. In this study, instead of being treated as pre-assumed constants, the contact angle is formulated as functions of the position angle of balls to reflect their distribution dependent on the operation condition and design parameters. After establishing a proper transformed coordinate system according to the ball screw mechanism, the variable contact angles and normal forces of the ball screw are predicted. Then the contact stiffness obtained by numerical calculations is validated by experiment and several characteristics arising from the variable contact angle will be discussed.
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