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

Hoang Long

Advances in Science and Technology. Research Journal

2024

Vol. 18, no 4

347-354

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.

Gear fault diagnosis and industrial applications

Combet F.

Diagnostyka

2012

nr 1(61)

9-12

This paper introduces the concept of a gear profile, which is the polar representation of the time synchronous averaged vibration signal computed on the rotation period of a pinion. A gear profile provides an attractive visual representation of the meshing efforts on the individual teeth for each of the gears present in a gearbox. It is mostly useful for the detection of local tooth faults (cracks, pitting) or shaft eccentricity faults. Its computation however presents some pitfalls as some parameters need to be selected with care: choice of the mesh harmonic to demodulate, filter bandwidth, signal duration for the time averaging. We propose some practical rules on how to select them. The amplitude and frequency modulation functions of the profile can then be computed, and the amount of the modulation may be quantified by some parameters. We also present a case where the electrical currant measurement can be very helpful for gear fault diagnosis. The technique is illustrated on a few industrial cases.