Study On Design Theory Of Skew Line Gear

Line gear, as an innovative gear, is first proposed by Prof. Chen Yangzhi. In previous studies, many progresses on line gear have been made such as design theory, manufacturing technology, strength calculation, reducer design and applications. However, these research results are concentrated on the line gear pair with two vertical cross axes or two arbitrary angle axes on the same plane. The line gear pair with two vertical cross axes is named as vertical line gear pair; and the line gear pair with two arbitrary angle axes is named as arbitrary intersecting line gear pair. In this paper, the skew line gear pair with two skewed axes(skew line gear pair or SLGP, for short) is proposed and its design theory is studied.Line gear is an innovative gear based on the space curve meshing theory with the advantages such as small size, convenient design, and easy processing, whose applications are focused on micro or small mechanical transmission field. In this paper, the study contents include the basic design formulae of a SLGP, the calculation formulae of the design parameters for a SLGP, the contact ratio of a SLGP, the sliding ratio of a SLGP and the design formulae of the basic wheel of a SLGP oriented to additive manufacturing technology.1. The basic design formulae of a SLGP. First, space curve meshing equations of a SLGP are established. The equations of the driving contact curve, the driven contact curve, the driving line tooth center curve and the driven line tooth center curve are subsequently deduced and derived. Using space circular helix as the driving contact curve of a SLGP, the equations of the driven contact curve, driving line tooth center curve and driven line tooth center curve are simplified. According to these fundamental design equations, the examples are illustrated in detail and simulated by using the Pro/E software. The prototype samples with 135° alternate angle were manufactured of 316 L stainless steel by Selective Laser Melting technology and an experiment was carried out to test their kinematic performance. The experimental result verified the accuracy of the deduced fundamental equations for a SLGP.2. Design criteria and fundamental design parameters formulae for a SLGP. By studying the equations of the driving and driven contact curves for the skew line gear pair, their geometric characteristics are deduced. The geometric interference is analyzed between the driving and driven line teeth of a SLGP at the non-meshing point during the mesh process. Afterwards, a supplementary design criterion is proposed for proofing the geometric interference, and the selection criteria and calculation formulae of fundamental design parameters for a SLGP are subsequently derived. Finally, the design examples are illustrated and their kinematics characteristics are simulated in the Pro/E software to verify the accuracy of the design criteria and fundamental design parameters formulae for a SLGP.3. Studying on a contact ratio for a SLGP. A design formula of a contact ratio for a SLGP is deduced according to the contact ratio of the arbitrary intersecting line gear pair, and eight influencing parameters are found. The influences of eight parameters on contact ratio for a SLGP are studied. And the calculation and selection of the fundamental design parameters for a SLGP are deduced to ensure the contact ratio of a SLGP is more than 1. Moreover, two types of interferences between the driving and the driven line teeth are discussed, then these geometric parameter formulae for the interference-proof conditions are deduced, and design formulae of a maximum line tooth number for the driving line gear are derived by different interference-proof conditions.4. Studying on the sliding rate of a SLGP with two vertical skewed axes. First of all, according to the definition of the sliding rate of an arbitrary intersecting line gear pair, the design formulae of sliding rates for a SLGP are defined and deduced. Then, by deciding the values of the sliding rates at the initial, middle and terminal meshing points and the varying pattern of the sliding rate of a SLGP with two vertical skewed axes, the characteristics of the sliding rate are obtained. Finally, the design formulae of helix radius of driving contact curve are deduced on basis of the allowable value of sliding rate and verified by means of the simulation in Matlab.5. The design formulae of basic wheels for a SLGP oriented to additive manufacturing technology. First, the expressions of meshing forces on the line teeth of a SLGP are deduced; by taking their line teeth as a cantilever beam, the deformations and stresses of a SLGP are analyzed by Ansys Workbench, and the result showed they only can transmit in a smaller load. Second, a hollow truncated cone with ribbed slab is optimized as the driven line gear wheel structure with a design objective of using fewer materials; then, the parameters standardization formulae of the driven line gear wheel are deduced by stiffness and strength analyses. Third, the calculation formulae of the driving line gear wheel are deduced according to the strength and stiffness criterion. Finally, the design case and statics simulation by Workbench show the detail design of a SLGP with one-tooth driving line gear in conventional powered transmission field.