Design method of a novel variable speed ratio line gear mechanism

Based on the space curve meshing theory, a novel noncircular line gear mechanism was advanced, namely, this paper presented a design method of the variable speed ratio noncircular line gear with coplanar axes. Firstly, the universal contact curve equations of the constant speed ratio and variable speed ratio line teeth were established. After the constraint equations of the rotating angle of the driving and driven variable speed ratio noncircular line gears were analyzed and established, the relationship between the rotating angle of the driven variable speed ratio noncircular line gear and the parameter t in the VSR area was assumed to be a piecewise fourth-order curve. Then, the contact curve equations of the variable speed ratio noncircular line gears were derived, and the entity models of variable speed ratio noncircular line gears were built. The prototypes of the parallel axis and intersecting axis variable speed ratio noncircular line gears were manufactured by Stereo Lithography Apparatus, and the speed ratios were measured on the kinematic test rig. The kinematic and finite element analysis results demonstrate that the relationship between the rotating angle of the driven variable speed ratio noncircular line gear and the parameter t conforms to the designed function and the noncircular line teeth smoothly achieve the preset VSR transmission. The proposed design method is helpful to design the variable speed ratio noncircular line gears with lower theoretical sliding rate and wider variation range of the speed ratio; consequently, the designed variable speed ratio noncircular line gears have better applicability in specific variable speed ratio applications.

Virtual pole method applied at the profiling of the gear shaped cutter tool for generating a K-type bore

The “virtual pole” method allows profiling of the cutting tools that generate by rolling. This mode of generation is advantageous in terms of the accuracy of the geometric shape obtained. The mentioned method combines the analytical accuracy of profiling with a simplified calculation mode, compared to the established algorithms. The paper presents an application made on the basis of the “virtual pole” method, for the profiling of the gear shaped tool, designed to generate the bore of a bush with a K-profile. Based on this methodology, in house software was developed for the type of profile mentioned above. The program allows the numerical and graphical representation of the profile to be generated, the contact curve and the profile of the generating tool.

Cartan ribbonization and a topological inspection

We develop the concept of Cartan ribbons together with a rolling-based method to ribbonize and approximate any given surface in space by intrinsically flat ribbons. The rolling requires that the geodesic curvature along the contact curve on the surface agrees with the geodesic curvature of the corresponding Cartan development curve. Essentially, this follows from the orientational alignment of the two co-moving Darboux frames during rolling. Using closed contact centre curves, we obtain closed approximating Cartan ribbons that contribute zero to the total curvature integral of the ribbonization. This paves the way for a particularly simple topological inspection—it is reduced to the question of how the ribbons organize their edges relative to each other. The Gauss–Bonnet theorem leads to this topological inspection of the vertices. Finally, we display two examples of ribbonizations of surfaces, namely of a torus using two ribbons and of an ellipsoid using closed curvature lines as centre curves for the ribbons.

GEOMETRIC CONSTRAINTS AND INTERFERENCE-PROOF CONDITIONS OF HELIX-CURVE MESHING-WHEEL MECHANISM

In some recent publications, a gear mechanism named Space-Curve Meshing-Wheel (SCMW) has been proposed by the present authors. This paper presents the geometry of the Helix-Curve Meshing-Wheel (HCMW), the most common SCMW at present. The driven contact curve equation is optimized by removing a redundant length parameter. Then, both geometric constraints and interference-proof conditions are calculated in the following three aspects: contact curves, HCMW pair and HCMW train. A parameter selection of a novel reducer with HCMW trains is shown as a practical example. The theories in this paper are mainly applied to determine the feasibility range of the geometric parameters within the HCMW, and provide foundation to its industrial standardized production.

Parametric Study of Meshing Characteristics With Respect to Different Meshing Rollers of the Antibacklash Double-Roller Enveloping Worm Gear

Roller shapes play a very critical role in the performance of antibacklash double-roller enveloping hourglass worm (ADEHW) gears; however, their influence is seldom reported in the literature. Based on the theories of differential geometry and gear meshing, this paper presents generic models of meshing characteristics for ADEHW gears, including both the contact curve and the tooth profile. We present different meshing functions and their derivatives with respect to each drive type and their associated roller shapes. We also compare the effects of contact curve, tooth profile, tooth undercutting, lubrication angle, induced normal curvature, and autorotation angle in order to design the most optimal tooth profile for the ADEHW gear. Finite element analysis was also conducted in order to minimize the contact stresses as a function of the roller type. Our results show that a spherical roller has the smallest value among the three available meshing roller shapes but is the most difficult design to procure. A cylindrical roller, however, incurs the greatest contact stress.

How to Model a Bonded Joint

The problem is considered of a semi-infinite plane region bonded to a rigid region, with the boundary of contact being in the shape of a cosine curve. It is shown that, when a rigid displacement is applied to the boundary of the elastic region, there is a particular value of the amplitude of the contact curve that minimizes the sum of the strain energy and adhesion energy.