A New Envelope Computational Method for Meshing Heliacal Gears Profiling Applied to Air Compressor Screw Pair

Abstract

The theory of enveloping, which determines the envelope to a family of surfaces, the meshing equations of kinematics pairs, including pinion and gear, cutting toll and gear, is widely used in Mechanical Engineering. This paper presents a new envelope computational method for profiling the meshing gear pair. It uses the normal projection of the instantaneous relative rotation axis of the kinematic pair onto the pinion surface to generate the contact line and then automatically computes geometric data of this contact line to create the gear tooth surface. As the profile complexity, the reverse engineering of compressor screw pair was a typical proper example to verify and clarify the proposed method. The method can generate the meshing surface pair with high accuracy: the 3D comparison average error of the surfaces generated by the proposed method and the Boolean method is 0.004 mm, and their RMS error is 0.01 mm. The novel idea of the proposed method is that the contact line, which is used to calculate gear surface, is created easier than solving complex meshing equations, which most previous work used. The proposed method in detail with an algorithm can be used as well for reverse engineering of air compressor screw pair as for parallel axixes heliacal gear pair

Keywords

• gear profile
• compressor screw
• contact line
• meshing condition
• envelope theory