Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis

Abstract

A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.

Generalised non-dimensional multi-parametric involute spur gear design model considering manufacturability and geometrical compatibility

“…for the influence of module [7,13], addendum [14][15][16][17][18][19][20][21][22], profile modification [23][24][25][26][27][28][29] tooth thickness [30][31][32][33][34][35][36], dedendum [37][38][39][40][41][42], cutter tip radius [43][44][45][46], pressure angle [47][48][49][50][51][52][53][54], etc, but without considering the simultaneous manipulation of other design parameters as well, typically assigning standard values to the latter. Additionally, many researchers have investigated the influences of each design parameter for different applications such as contact analysis [55][56][57][58][59]…”

Nonrelative sliding gear mechanism based on function-oriented design of meshing line functions for parallel axes transmission

“…where T is the helix angle parameter. The parametric equations of equations (15) and (16) indicate that the contact curves for parallel axes transmission with uniformly accelerated motion of meshing points are both varying-pitch cylindrical helixes, respectively.…”

“…Then, Chen and colleagues 14,15 further developed the conjugated curves meshing theory including the selection of arbitrary contact vector directions, design of new circular arc tooth profiles, 16 geometric and contact characteristics of tubular meshing tooth surfaces, [17][18][19] and sliding ratio analysis for conjugated curve gears. 20 Figure 1 shows a general design of tooth profiles for the abovementioned two types of meshing theories.…”

Theoretical and experimental analyses of spiral bevel gears with two contact paths

“…In this model, n was determined as the reference design pressure angle in the process of generating the pinion. From equations (17) and (18), it could be found that after n is determined, n lp is also determined.…”

“…Mo and Zhang 16 investigated the influence of machining parameters on the tooth profiles of bevel gears and obtained the true tooth surfaces in their research. To simplify the designing process of point contact gears, Chen et al [17][18][19] presented the so-called spatial conjugate curve meshing theory. This theory uses curves instead of surfaces as the basic meshing elements.…”