Advanced Tooth Contact Simulation of spiral bevel and hypoid gears.

Tooth Contact Analyses (TCA) for hypoid and spiral bevel gears.

Software provided by

Direct Digital Simulation (DDS) method was used for tooth contact analyzes on spiral bevel and hypoid gears.

MP1000 METSO gear tooth cut by Perfect Mold specification MP1000 METSO gear tooth cut by Perfect Mold, Addisom, IL, USA

This gear and the mating pinion have been mapped on a CMM for reverce engineering of the tooth surfaces

MP1000 METSO gear set reverse engineered mathematical models

Tooth contact has been simulated on software provided by

MP1000 METSO gear set tooth contact TCA

Tooth contact on drive side found to be less than perfect.

MP1000 METSO gear set tooth contact TCA

Tooth contact on coast side was good.

Below are some more calculation results obtained with help of DDS method using software from

1. Gear cutting machine summaries are used as input data for calculation of gear and pinion tooth surface geometry.

Spiral Bevel gear tooth surface.

DDS method produces more data for 3-dimentional graphic presentation compare to other methods. The calculation results are presented as 3-d models with high resolution. The resolution and quality of graphical outputs are often underestimated. DDS software provides high quality 3-dimentional calculation results in a form of a CAD model, which can be used in existing CAD programs like CATIA or Pro/Engineer.


2. Tooth Contact Analyzes (TCA).

The new method calculates distances between the meshing surfaces in each of a large number of points in order to provide a high quality representation of the combined tooth contact. The theoretical coordinates of the points on the tooth surface are calculated by using the gear cutting machine summary. The real coordinates can be measured on a CMM (reverse engineering). The theoretical or the real coordinates can be loaded to the TCA software for mathematical simulation of the tooth contact.

Spiral Bevel gear tooth contact.

The distance between surfaces is shown in different colors. The colors are set in rainbow sequence. The red color in set in the point where the distance between the surfaces is equal to 0.

Spiral Bevel gear tooth 3d computer model.

With DDS it is easy to show the 3-dimentional models of the gear tooth in rendering or in wire frame. The gear, the pinion and the contact pattern can be seen in one assembly in the same time. The image below has the gear tooth surface shown in 67% of transparency so it is easy to see both surfaces on the same image.

Spiral Bevel gear and pinion tooth surfaces in contact.

The image of the contact pattern shown above (elementary contact) is not the same contact patterns that one can see on a real gear set after the gears were rotated and the contact moved over the tooth surface. The image below shows the contact simulation on gear set that was rotated – combined contact. The combined contact pattern is calculated as a sum of the elementary contacts on different angular positions of the gears. Different increments of rotation can be selected in order to obtain different images of the combined contact.

Tooth contact pattern.

Tooth contact pattern.

Tooth contact pattern.


Because of the high resolution of the DDS method it becomes posibble to calculate areas covered by different colors on the 3-dimentional contact model.

Contact data. Gap in (mm) and area in sq. mm.

The following outputs can be helpful for gear noise, lubrication and driving effitiency analyzes.

Spiral Bevel gear tooth sliding.

The black lines on the picture are tangent to the gear tooth surface. Each line represents direction and value of sliding velocities between gear and pinion tooth surfaces.

Approach of surfaces.

The red lines show approaching velocity vectors of the pinion tooth surface to the gear tooth surface.

The driving efficiency can be calculated very accurate for each angular position of the rotating gears. The author calculates the driving efficiency as a sum of driving efficiency calculated on each cell on the gear tooth surface. DDS method allows to calculate sliding direction and friction on each cell of the tooth surface and for each position of the rotating gears. While the author has been conducting the driving efficiency calculation for different designs of spiral bevel and hypoid gears, different methods of improving of driving efficiency have been discovered.

Developed by Dr. Stepan V. Lunin in 2001

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