Mathematical model for design and analysis of power skiving tool for involute gear cutting

• Power skiving can efficiently produces accuracy gears; particularly internal gears.
• This paper proposes a comprehensive methodology for designing power skiving tools.
• The conjugate surface theory and full-field angle analysis are applied.
• A mathematical model of the virtual-conjugate-surface and rake surfaces is derived.
• The working rake and clearance angles are investigated base on ISO-standards.

Power skiving is an efficient means of producing high accuracy gears; particularly internal gears. However, the literature lacks a systematic mathematical model for the design and analysis of such tools. Accordingly, the present study proposes a comprehensive yet straightforward methodology for the design of resharpening power skiving tools based on conjugate surface theory and full-field angle analysis. The proposed methodology has three important features. First, mathematical models of the virtual-conjugate-surface and rake surfaces are derived, and thus the cutting edges can be obtained. Second, the power skiving is modeled by transformation matrices, and the normal/tangent vectors of the relative surface can be explicitly obtained. As a result, the working rake and clearance angles can be investigated in accordance with recommended ISO-standards. Finally, a method is prescribed for determining the working rake angles, clearance angles and wedge angles of the cutter based on the ISO-defined reference planes. Utilizing this method, a simple technique is proposed for redesigning the power skiving tool so as to avoid negative working clearance angles. The results of the illustrative example are shown that the proposed approach provides a comprehensive, simple and versatile technique for modeling a wide range of power skiving tool design features.