Polygonal turning

Polygonal shaft/collar connections have many advantages, but producing these cross-sections has always been a highly demanding and fairly unproductive process. Polygon turning changes this. With this innovative process, outer and inner polygons with a widely differing number of vertices and various shapes can be produced easily, highly productively, and extremely precisely by turning, without the need for complex special fixtures. Even twisted polygons are possible.

When using the innovative polygon turning process, the tools are almost as large as the inner polygon itself and are accordingly stable. Programming is very easy and is also supported by the INDEX polygon turning cycle.  Thanks to the continuous cut, polygon turning is suitable for both soft and hard machining. The process can be used on all INDEX and TRAUB machines.

These types of polygon have also been standardized since November 2021.

Process kinematics

In terms of shape, these polygons are hypotrochoids. These are roulettes that are created when a circle rolls around an inner circle. A 3/4/5-sided polygon is also called an H3/H4/H5 profile. Some of us may still be familiar with such curves from childhood: the flower-like patterns that are created when drawing with a spirograph are also hypotrochoids.

Polygon turning makes use of the spirograph principle. Here, the tool and the workpiece rotate in the same direction (e.g., tool CW and workpiece CCW, or vice versa). The polygon is ultimately created because the tool rotates faster than the workpiece and because the two axes are offset from each other by the eccentricity.


INDEX machine tool


This type of polygonal shaft/collar connection has been standardized in DIN 3689-1 “Shaft to collar connection - Hypotrochoidal H-profiles - Part 1: Geometry and dimensions” since November 2021.

According to this standard, a polygon profile with three sides and a minimum circumscribed/maximum inscribed circle diameter of
da = 22 mm and di = 18 mm
is designated as follows:

H3 – 22 x 18

“Polygons are extremely reliable and very durable, especially for shaft/collar connections. With the INDEX polygon turning cycle, we have created a tool that allows us to provide our customers with excellent support.”

Dr. Volker Sellmeier is Head of Technology Development at INDEX


Case Study

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INDEX bevel gear cutting