Naoya Kato

Analysis of Rotational-Angle Difference Between Gears for Gear Noise Under Transient State Using Hilbert Transform

The authors developed a useful analysis method of the rotational-angle of gear under transient state using the Hilbert Transform because the conventional method was not available under the transient state. Here, under the transient state the gear revolution speed was changed from 600r/min to 2000r/min in 0.35 seconds. A key technology of this method was that Hilbert Transform method, which used to be applicable only for steady data was improved so that it could treat transient data. Hence, the following procedures were developed. 1. The rotation of gear-teeth was detected by a gap-sensor pair, which can cancel the measuring error due to fluctuation of gear shaft. 2. The frequency of such signals varied significantly by the gear-revolution speed. Transient gear-teeth detection signals obtained at a constant sampling rate were converted to almost-constant frequency signals over the data series axis using a trigger pulse obtained per gear revolution. These converted signals were named the quasi-steady signals. 3. By analysis of quasi-steady signals with the Hilbert Transform, phase-angle of gear-teeth rotation was obtained. Here, value of rotational-angle of gear is given as dividing the value in phase-angle by the number of gear-teeth. What is new with this analysis method was the adoption of a conversion process into quasi-steady signals, and through such conversion, accuracy of the analysis was improved to be smaller than 3 degrees phase-angle, even under immediate acceleration of 1400r/min gear revolution speed within 0.35 seconds. On a gear-tooth, which is deformed by transfer torque loaded during meshing period and restored repeatedly, problems of reliability and noise cannot be avoided. Especially under the transient state, because the deformation of gear-teeth changes immediately, abnormal noise may become obvious. This technology is the key to solving these problems of development, by clarifying the rotational-phase-angle difference between meshing gears under the actual operation state. This paper will report on how the gear noise during acceleration is generated. By using this developed method, it has become clear that the noise is generated by the worsening of the gears meshing-performance due to elastic deformation of gear-teeth caused by gear transfer torque.