Polygon connection

Spline connection compared to polygon connection.

The polygon connection is a machine element that is often found in mechanical engineering . Due to its characteristic polygon shape it is assigned to the so-called non-circular connections. It is one of the releasable or movable connections . They are mainly used with impact loads. The basic shape is usually the triangle or square . It can be used as a shaft-hub connection, for example as an alternative to other profile shaft connections (splined shaft connection). The dimensions of polygon profiles are categorized according to DIN 32711 for the P3G profile (triangle) and according to DIN 32712 for the P4C profile (square).

interpretation

Polygon connection P3G on a shaft stub.

The connection is mathematically checked for the permissible surface pressure of the material. The following applies to the P3G profile:

${\displaystyle p_{m}\approx {\frac {K_{A}\cdot T_{nenn}}{l'\cdot \left(0,75\cdot \pi \cdot e_{1}\cdot d_{1}+0,05\cdot d_{1}^{2}\right)}}\leq p_{zul}}$

The following applies to the P4C profile:

${\displaystyle p_{m}\approx {\frac {K_{A}\cdot T_{nenn}}{l'\cdot \left(\pi \cdot e_{r}\cdot d_{r}+0,05\cdot d_{r}^{2}\right)}}\leq p_{zul}}$

With:

• ${\displaystyle T}$: nominal torque to be transmitted
• ${\displaystyle K_{A}}$: Application factor
• ${\displaystyle e_{r}={\frac {d_{1}-d_{2}}{4}}}$: calculated eccentric size
• ${\displaystyle d_{r}=d_{2}+2\cdot e_{r}}$: calculated theoretical diameter
• ${\displaystyle d_{1},d_{2},e_{1}}$: Profile sizes according to DIN 32711, DIN 32712
• ${\displaystyle l'}$: load-bearing profile length
• ${\displaystyle p_{zul}}$: permissible surface pressure

In addition , the cross-section stressed by torsion , bending , tension and pressure must also be checked in accordance with the recognized rules of technology .

advantages

• very low notch effect
• Self-centering (flank-centered)
• very high torques can be transmitted
• good dynamic properties (very smooth running)
• easy construction
• Space saving

disadvantage

• high surface pressure
• radial forces (explosive forces on the hub)
• expensive compared to a feather key
• Dimensioning
• Difficult storage and manufacture

swell

• Wittel, Jannasch, Voßiek, Spura: Roloff / Matek machine elements . 23rd edition. Springer Vieweg, Wiesbaden 2017, ISBN 978-3-658-17895-6 .
• Wittel, Jannasch, Voßiek, Spura: Roloff / Matek machine elements collection of formulas . 14th edition. Springer Vieweg, Wiesbaden 2018, ISBN 978-3-658-19899-2 .