On the design of external involute gears

A theoretical investigation of the stresses in external involute helical gears has been carried out. Geometrical conditions are given and the load distribution along and between the gear teeth in contact is calculated. With this load distribution, contact pressure and fillet tensile and compression stresses are calculated. The influence bending functions, used to calculate the load distribution, and the fillet stresses are calculated by the finite element method. Results are presented for the contact pressure and fillet stresses as functions of the number of teeth and the helix angle

A Parametric Analysis of the Gear Surface Roughness After Hobbing

Hobbing is a common manufacturing method when producing helical, involute gears. In order to give the manufactured gear a controlled surface smoothness, a method to, very accurately, determine the achieved surface geometry is needed. In this report, the cutting surfaces of the tool, of which the cutting edges are the boundaries, are assumed to be plane in arbitrary directions. They are mathematically described using parametric and analytically differentiable functions. These functions give the possibility to determine the geometry of the three-dimensional surface of the manufactured gear, without any additional numeric approximations. By comparing this surface with the smooth surface of an ideal gear, the roughness of the surface can be determined. An example is given in which the surface topology and the characteristic surface roughness parameters are determined

A dynamic analysis of the oscillations in a chain drive

A model is presented in which the oscillations, and the forces thus produced, in a chain drive, working at moderate and high speed, can be calculated. Since the outer system affects the result it has been necessary to include this in the model. The mass of the chain is included in the model and both the gravitational forces and the inertia forces in the chain are taken into account. The elasticity in the links is included. The sprockets are connected by two spans, both of which have to be included in the model to fulfill the equilibrium equations for the rollers in contact with the sprockets. The position of the chain is given by the geometric conditions as well as the equilibrium condition. On the slack side a chain tensioner is used to reduce the tansverse oscillation, which occur at higher speeds

A method for calculating contact pressure and tip contact in spur gear sets with manufacturing errors

To investigate how manufacturing errors affect the gear set, a method is developed to calculate the contact stress of a gear set with pitch and involute incline errors. The method is parametric, and a hybrid model is used to model the gear stiffness. Contact outside the line of action is considered.A numerical example is used to show how manufacturing errors can change the contact pressure and cause tip contact, in spite of tip relief, resulting in high contact pressure. A threshold for maximum allowable torque of the gear set due to the specified errors is found

A dynamic model to determine vibrations in involute helical gears

A method to determine the dynamic load between two rotating elastic helical gears is presented. The stiffness of the gear teeth is calculated using the finite element method and includes the contribution from the elliptic distributed tooth load. To make sure that the new incoming contacts which are the main excitation source are properly simulated, the necessary deformation of the gears is determined by using the true geometry and positions of the gears for every time step of the dynamic calculation. This allows the contact to be positioned outside the plane of action. A numerical example is presented with figures that show the behaviour of the dynamic transmission error as well as the variation of the contact pressure due to the dynamic load for different rotational speeds

A general approach for determining dynamic forces in spur gears

A model is presented taking into account off line-of-action, non linear wheel stiffness by using the finite element method, and elasticity coupling between the gear teeth. The contact points are determined by searching the common normal using the undeformed, but otherwise true theoretical, tooth shapes where the teeth have a tip rounding to prevent contact singularity in off-line-of-action points. A comparative study is included, which shows the important influence of the elastic coupling and off line-of-action