Their surface of the action and line of contact depend completely on the obligue angle, normal profile and relative-io-pitch-plane position of the counterpart rack, but not on the pitch diameter of the helical gear.

By the aid of the analysis of spatial geometric relationships among gear, hobbing cutter and rack, the tooth generating theory of conical involute gear and the calculation formulae of geometrical parameters are investigated.

The mathematical models for asymmetric helical gears can be provided by the application of two imaginary rack cutters.

This article discovers several characters possessed while the helical gear is engaged with its counterpart rack. It's clearly pointed out that the engagement of helical gear with its counterpart rack belongs to line-contact mesh. Their surface of the action and line of contact depend completely on the obligue angle, normal profile and relative-io-pitch-plane position of the counterpart rack, but not on the pitch diameter of the helical gear. At the same time, the concrete methods which solve conjugate profile...

This article discovers several characters possessed while the helical gear is engaged with its counterpart rack. It's clearly pointed out that the engagement of helical gear with its counterpart rack belongs to line-contact mesh. Their surface of the action and line of contact depend completely on the obligue angle, normal profile and relative-io-pitch-plane position of the counterpart rack, but not on the pitch diameter of the helical gear. At the same time, the concrete methods which solve conjugate profile of the helical gear and define the tooth profile of the hob basic worm. Thus some principles, such as the principle of the envelope line, the principle of the common normal etc, which are applied to plane engagement can be applied to space engagement-the engagement of crossed helical gear pair. As a result, the process solving problems is simplitied to a certain degree.

A theory of hobbing involute conical gears on a hobber with a horizontal feed motion is described in the light of the gear engagement principle.The relations among some important parameters of the imaginary rack shaper cutter and the generated gear are analyzed,and the design method of a change speed train mainly composed of intersected involute conical gears is considered in detail.It has many special advantages such as many speed degrees...

A theory of hobbing involute conical gears on a hobber with a horizontal feed motion is described in the light of the gear engagement principle.The relations among some important parameters of the imaginary rack shaper cutter and the generated gear are analyzed,and the design method of a change speed train mainly composed of intersected involute conical gears is considered in detail.It has many special advantages such as many speed degrees only with a few gears,adjustable gear clearance by changing position of the gear along with their axes respectively.Because in designing this kind of train it is very important how to minimize the volumn and size and how to maximize the changable speed degrees and the difference between the highest degree and the lowest degree.A practical method is provided to control some key parameters to reach these goals.The present theory is proved correct and the method is shown practical by tests of a sample change speed train.

The gear hobbing of conical involute gear is a complex generating motion with doubledegree of freedom. Based on the theory of tooth enveloping for multi-degree of freedom, the relative motion between cutter and gear and the generating mechanism of imaginary rack are analyzed, thus, the existence of imaginary rack is proved, and its tooth shape is obtained. By the aid of the analysis of spatial geometric relationships among gear, hobbing cutter and rack, the tooth generating theory of conical involute gear and...

The gear hobbing of conical involute gear is a complex generating motion with doubledegree of freedom. Based on the theory of tooth enveloping for multi-degree of freedom, the relative motion between cutter and gear and the generating mechanism of imaginary rack are analyzed, thus, the existence of imaginary rack is proved, and its tooth shape is obtained. By the aid of the analysis of spatial geometric relationships among gear, hobbing cutter and rack, the tooth generating theory of conical involute gear and the calculation formulae of geometrical parameters are investigated. The results are helpful to hobbing machining of conical involute gears and to the other processing methods that have the similar generating motion.