Abstract:In this paper, an active design method of meshing line for a spiral bevel gear mechanism with nonrelative sliding is presented. First, the general meshing line equations for a nonrelative sliding transmission mechanism between two orthogonal axes are proposed based on the active design parameters. Then, parametric equations for contact curves on the drive and driven spiral bevel gears are deduced by coordinate transformation of the meshing line equations. Further to this, parametric equations for the tooth sur… Show more
“…The intersecting angles of two angular velocity vectors of above line gears were θ=π and θ=π/2 in Chen et al., 27,28 respectively. It meant that the above pure rolling line gears just illustrated the particular design of pure rolling gears for an arbitrary angle intersecting shafts transmission.…”
Section: Introductionmentioning
confidence: 94%
“…27 If θ=π/2, it changed to be the same spiral bevel gear mechanism as shown in Chen et al. 28 An arbitrary meshing point M was defined on the meshing line K−K . Figure 2.Meshing coordinate systems for the external gearing of an arbitrary angle intersecting shafts.…”
Section: Contact Curves Derivation For a Pure Rolling Line Gear Mechamentioning
confidence: 99%
“…Besides, Chen et al. 28 proposed another kind of line gears, an orthogonal spiral bevel gear mechanism, which were designed for orthogonal shafts transmission with pure rolling meshing based on the active design method of meshing line. Figure 1.A type of line gears for intersecting axes transmission: (a) 3D model; (b) physical photograph.…”
Design of pure rolling line gear mechanisms for an arbitrary angle intersecting shafts was presented in this article. Based on the active design method of meshing line function for orthogonal shafts, three meshing types of conjugated tooth surfaces for an arbitrary angle intersecting shafts were discussed, including the parametric equations of different generatrix circles, the mathematical models of tooth surfaces, and central curves to be constructed, respectively. The validity of the active designed meshing line function was verified according to meshing equations, and the theoretical sliding rations were analyzed to prove pure rolling meshing. Then basic design parameters of pure rolling line gear mechanisms for the geometry design were determined, and the main structural parameters were obtained therefrom. Lastly, three groups of numerical examples were proposed according to mathematical models. Resin samples of line gears were processed by rapid prototyping technology and the kinematic performance of the pure rolling line gear mechanisms were validated. This paper laid the foundation of geometry and parameter design for pure rolling line gear mechanisms for an arbitrary angle intersecting shafts.
“…The intersecting angles of two angular velocity vectors of above line gears were θ=π and θ=π/2 in Chen et al., 27,28 respectively. It meant that the above pure rolling line gears just illustrated the particular design of pure rolling gears for an arbitrary angle intersecting shafts transmission.…”
Section: Introductionmentioning
confidence: 94%
“…27 If θ=π/2, it changed to be the same spiral bevel gear mechanism as shown in Chen et al. 28 An arbitrary meshing point M was defined on the meshing line K−K . Figure 2.Meshing coordinate systems for the external gearing of an arbitrary angle intersecting shafts.…”
Section: Contact Curves Derivation For a Pure Rolling Line Gear Mechamentioning
confidence: 99%
“…Besides, Chen et al. 28 proposed another kind of line gears, an orthogonal spiral bevel gear mechanism, which were designed for orthogonal shafts transmission with pure rolling meshing based on the active design method of meshing line. Figure 1.A type of line gears for intersecting axes transmission: (a) 3D model; (b) physical photograph.…”
Design of pure rolling line gear mechanisms for an arbitrary angle intersecting shafts was presented in this article. Based on the active design method of meshing line function for orthogonal shafts, three meshing types of conjugated tooth surfaces for an arbitrary angle intersecting shafts were discussed, including the parametric equations of different generatrix circles, the mathematical models of tooth surfaces, and central curves to be constructed, respectively. The validity of the active designed meshing line function was verified according to meshing equations, and the theoretical sliding rations were analyzed to prove pure rolling meshing. Then basic design parameters of pure rolling line gear mechanisms for the geometry design were determined, and the main structural parameters were obtained therefrom. Lastly, three groups of numerical examples were proposed according to mathematical models. Resin samples of line gears were processed by rapid prototyping technology and the kinematic performance of the pure rolling line gear mechanisms were validated. This paper laid the foundation of geometry and parameter design for pure rolling line gear mechanisms for an arbitrary angle intersecting shafts.
“…According to an uniform motion of the meshing point M as proposed in literature 16–19 , the law of motion governing the meshing point M along the meshing line K – K can be expressed by where c M is the coefficient of the lineal equation of motion of point M , and t is the motion parameter ( t > 0).…”
Section: Mathematical Models Of Pure Rolling Helical Gear Mechanismsmentioning
confidence: 99%
“…Besides, Chen et al. 16–18 have proposed the active design method of pure rolling gear drives for parallel shafts, orthogonal shafts, and intersecting shafts transmissions. However, the above pure rolling gears are limited by the geometric design where the tooth profiles are generated by generatrices in normal and axial section moving along the calculated contact curves.…”
The geometric design, meshing performance, and mechanical behavior of pure rolling helical gear drives are presented. Parametric equations for contact curves on the pinion and gear are determined by coordinate transformation of the active designed pure rolling meshing line for the whole cycle of meshing. Moreover, parametric equations for the tooth surfaces of helical gears with convex-to-convex meshing type are derived according to the motion of generatrices in the transverse section along the calculated contact curves. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. The meshing performance and mechanical behavior, including contact patterns, loaded function of transmission errors, and variation of stresses for two pitch angles of meshing are compared with those of a reference design of micro-geometry modified involute helical gears. Besides, the influence of basic design parameters on tooth contact analysis and stress analysis is studied. The analysis of the results shows that the proposed pure rolling helical gears have the advantage of reducing the relative sliding between tooth surfaces and the possibility of designing pure rolling helical gears with a small number of teeth, though the contact strength of the surfaces is impaired. However, if the appropriate design parameters and Hermite curve parameters for the fillets are properly evaluated as proposed here, the mechanical behavior of the proposed pure rolling helical gear drive, in terms of contact patterns and variation of bending stresses can be superior to that of the micro-geometry modified involute helical gear drives.
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