Abstract
To improve the stability and accuracy of non-circular gear transmission, a beveloid non-circular gear transmission scheme was developed to reduce the meshing impact and achieve backlash adjustment. When using the beveloid rack as the medium, the instantaneous contact line of the beveloid non-circular gear pair was shown to be a straight line, and the tooth surface was shown to be a ruled surface based on the transmission relationship between the rack centerline and the non-circular pitch curve. The zero-modification method was employed to develop the beveloid non-circular gear. Further, the generation method for the tooth profile of the modified non-circular gear was reviewed, and a digital solid model was developed for the beveloid non-circular gear. The physical contact simulation method was used to analyze the meshing backlash, and the influence of the axial displacement adjustment on the meshing backlash of the gear pair was obtained. By considering a pair of beveloid elliptic gears as an example, machining and transmission experiments were conducted, with results showing smooth gear-pair meshing and the anticipated backlash adjustment effect.
Highlights
A non-circular gear exhibits a non-linear displacement relationship via meshing motion
A beveloid noncircular gear pair scheme was designed based on the design concept of a beveloid cylindrical gear to improve the transmission accuracy and stability of noncircular gears
The beveloid spur noncircular gears can be used for backlash adjustment
Summary
A non-circular gear exhibits a non-linear displacement relationship via meshing motion. The gear pair can adjust the meshing backlash by axial relative displacement by linearly changing the modification coefficient of each section along the direction of the gear axis; this is suitable for transmission with precise transmission requirements. Using the zero modification design method, the beveloid noncircular gear can be constructed and the modification coefficient of the driving gear can be changed from 2x1 to x2 along the gear axis direction, whereas the driven gear can be changed from x1 to 2x2 along the gear axis direction Both the driving gear and the driven gear have a noncircular cone shape and equal center distance, and equal gear ratio transmission can be realized in each section of the axial direction. The transformation matrix M21 of the coordinate system S1 to S2 is an inverse matrix of M12, as follows:
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