Effects of rack-cutter parabolic modification on loaded contact characteristics for crossed beveloid gears with misalignments

Based on the generation concept of beveloid gears, a novel design approach with parabolic modification is introduced in this paper. The equation of normal section of parabolic modified rack-cutter is derived, and the generating procedure of beveloid gears with parabolic modification is proposed. Therefore, the mathematical model of parabolic modified beveloid gears is obtained. Thereafter, the solid models of beveloid gear pair with and without parabolic modification are developed in the CAD software. Based on the installation condition, the mesh model considering misalignments is established. Then, the loaded tooth contact analysis (LTCA) is performed, and the effects of load and misalignments on the general beveloid gear pair and parabolic modified beveloid gear pair are discussed. Also, the contact pressure, transmission error, contact pattern and tooth root stress are investigated. Results show that under the same load, parabolic modification can reduce the maximum value of contact force and tooth root stress of beveloid pinion. Meanwhile, it can reduce the peak to peak value of transmission error and change the shape of contact pattern from wave mode to parallelogram. Under shaft angle error and offset error, the location of contact pattern and maximum value of tooth root stress move to the heel and toe side, while the axial position error of pinion and gear only slightly affects the contact performance. After parabolic modification, the peak to peak value of transmission error and the maximum value of tooth root stress of beveloid gear pair reduced are reduced significantly under misalignments.