Geometric design using undercutting and pointing conditions for a curve-face gear

Abstract

Curve-face gear drive is a new type of variable transmission ratio gear pair between the intersecting axes based on the face gear pair. And tooth width is one of the main geometrical factors of curve-face gear which affects the intensity of tooth root. This article uses the method of boundary function and geometric approximate evaluation to investigate the undercutting and pointing conditions of curve-face gear considering the tooth profile difference. The equations of tooth profile distribution angle and engagement angle are derived using the coordinate transformation theory. On this basis, the equations of the theoretic undercutting and pointing conditions are deduced, and the undercutting inner diameter and pointing outer diameter of the tooth profile are simulated using mathematical software. Then, the corresponding phenomenon of undercutting and pointing of curve-face gear are analyzed. In the end, the feasibility of the theoretical calculation is received by the experiment of curve-face gear.

The Mathematical Model of Curve-Face Gear and Time-Varying Meshing Characteristics of Compound Transmission

“…It is worth noting that, the surfaces of the curve-face gear and cylindrical gear with the same specification as the shaper are also in line contact in the process of meshing. Besides, according to the conditions of undercutting and pointing, the determination of tooth width of curve-face gears has been discussed in detail in our previous research [42], so those won't be covered again here.…”

“…Instead of the simulation processing by non-circular shaper in previous researches with SolidWorks [41], this method fills the blank of mathematical modeling of curve-face gear tooth surface. Based on meshing of general curve-face gear pair in line contact [42], the contact and slip characteristics of tooth surface, and the motion characteristics of compound transmission are also analyzed. This work provides a theoretical basis for the subsequent processing of curve-face surface gear by standard shaper and the design of the spatial finite helical motion of the curve-face gear compound transmission with variable transmission ratio.…”

Meshing characteristics of a sphere–face gear pair with variable shaft angle

“…Then, a numerically controlled machining model was established by transforming adjustment parameters from the cutter-tilt milling machine to a common multi-axis numerical control machine. Lin and colleagues [10][11][12] presented an orthogonal fluctuating gear ratio face gear pair, which comprises a non-circular pinion and a curve-face gear. Based on the mathematical model, they investigated the undercutting and pointing conditions, tooth contact and transmission errors of the curve-face gear pair.…”

Modelling, design and analysis of offset, non-orthogonal and profile-shifted face gear drives

“…Stadtfeld, 12 Tang et al, 13 Wang et al 14,15 and Shen et al 16 have done some important work on the precision machining methods of face gear to meet the tough requirements of high-power applications, including hobbing, milling, honing and grinding. In addition, a new type of face gear drive consisting of a non-circular gear and a curve-face gear with intersecting axes was proposed by Lin and colleagues, 17,18 which integrated the features of curve-face gear and non-cylindrical gear and achieved variable ratio transmission of power and motion.…”