A Unified Theory for 3D Gear and Thread Metrology

We propose a unified theory for the metrological treatment of helical machine elements such as cylindrical and conical gears, worms, and screw threads. The main idea is to introduce a universal 3D geometry model for threaded components that provides for distinct parameterization using a unique set of geometry parameters and that offers and a functional description of the transverse profile. Using modern 3D coordinate measuring technology, a holistic evaluation algorithm yields the actual geometry as the result of a high dimensional best-fit procedure and form deviations as corresponding residuals. All determinants and evaluation parameters can then be calculated from the set of actual geometry parameters. By applying certain constraints to the model to be fitted, the novel method can be reduced to the established 2D methods and hence meets demands for the comparison of the two procedures. The results of the novel approach have proven to be very stable and they enable the evaluation of areal measurements with no loss of information.

Reconstitution of the geometric elements of a conic gear

Conical gears are used if the axes of the shafts between which the rotation movement is transmitted are concurrent. The technology of execution of these gears is more demanding, they are more sensitive to the deviations of execution and / or assembly and introduce large axial forces, which complicates, to some extent, the construction of the supports of the wheel support shafts. The straight-toothed conical gears, with relatively simple wheels for technological purposes, are used only at low peripheral speeds (𝑣 < 3 𝑚/𝑠), when step deviations and those of the tooth profiles do not yet produce high dynamic demands and noise. These gears, however, are sensitive to less precise mountings and to deformations, under load, of the support shafts. The calculation of the resistance of the conical gears, in contact and bending, is performed accepting the same calculation assumptions as in the calculation of cylindrical gears with straight teeth. It is, therefore, necessary to make a transition from the conical gear to an imaginary cylindrical gear, called virtual gear, and to find equivalence relations between the two gears - real and virtual.

Strength Analysis of Polymer Conical Gear Wheel Made with 3D Printing Technique

The article deals with the problem of designing conical gears with a curved line contour. The contour of the tooth flank is described by means of a helix and involutions. In the work, a conical gear designed to drive of the lower limb rehabilitation exoskeleton has analysed. Parameters of the conical gearbox have been adapted to design requirements of the exoskeleton. Gear wheels were made with ABS material using 3D printing technique. The article presents the results of strength calculations obtained using the method classical design of the gear wheals described in the norm ISO 6336-1996. In the strength calculations, bending and contact stresses were taken into account. Creating the contour of gears was aided through the gearbox wizard available in Inventor program. The work contains the results of a static tensile test of the material from which the gear wheels were made. In experimental and numerical studies, the orthotropy of the material used was taken into account. The orthogonal values of the Young’s modulus, the Poisson’s ratio and the Kirchhoff’s modulus were determined. The publication also includes partial results of fatigue tests in the area of normal stresses. In the research used to finite element method (FEM), determine of internal loads in the gear. A structure of the FEM model is described in detail. Maximum values of contact pressures determined by use to FEM models have been compared with the results obtained on the basis of Hertz’s formulas. The article presents basic geometrical and strength parameters of the designed gear. The work demonstrates the validity of the material models used. Limitations in the application of the classic method of calculating conical gears made of orthotropic materials have been indicated. The results of analytical and numerical calculations are presented in tabular and graphical form.

The Generation of Conical Gears by a CAD Soft

In this paper we present the modalities to obtain, by a CAD soft, the solids that materialize the conical gears. The procedure is similar to the industrial ones for the cutting of the teeth of the conical gears and it assumes the existence of the generator tool and a raw material. The algorithm of the method permits the obtaining of any gears, no matter the shape of the tooth, its inclination etc. Finally, we present an application for the obtaining of a gear with two wheels with straight teeth.

Contact characteristics of helical conical gears used for V-drive marine transmissions

This article investigates the load-carrying ability of helical conical gears used in transmissions with intersecting and crossed axis for V-drive marine transmission. Mathematical models of helical conical non-involute gears, which can realize line contact, were established on the basis of the conjugated theory. Loaded tooth contact analysis was performed to examine the meshing and bearing contact of the helical conical gear pairs. The contact area was measured in an experiment and compared with theoretical results, and good agreement was observed.