TPT September 2017

AR T I C L E

Advanced Machine & Engineering/AMSAW

Key calculations for maximising tool life in carbide saws By Christian Mayrhofer, Manager R&D, AME, and Willy Goellner, AME

Theoretical analysis, calculation and practical identification

This has been done for a simple one-stage gear train with four inertias and three degrees of freedom since inertia two and inertia three are coupled with the ratio. After having modelled up the system in this fashion the dynamic equilibrium of the forces can be formulated for the free body diagrams.

Torsional vibrations are hard to measure because of the rotating elements (gears, shafts) that are inside a closed gear case and not easily accessible. However, knowing the exciting torque, passing through the gear train and the gear data, critical vibrations such as resonance can be calculated and analysed. The following calculations and theoretical analysis are perhaps boring for most individuals dealing with carbide saws, but they show that much can be theoretically analysed, where practical limitations exist. A well experienced carbide saw specialist will be able to analyse torsional vibration from the noise level, the cut surfaces, and the form of the chips. He will, however, have difficulty pinpointing where the trouble starts and what to change in order to solve the problems. In every gear train torsional vibrations and torsional natural frequencies can cause significant problems if not addressed properly. One approach to realise basic effects and parameters is to discretise every shaft in stiff inertias and massless torsional springs which connect these inertias.

The result is the following set of differential equations which has the structure:

With the concept of eigenvalues and eigenvectors the natural frequencies and corresponding mode shapes can be calculated.

The determinant is set equal 0 and values below are used to calculate λ 2 . Example values based on a simplified portion of an AMSAW gearbox:

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SEPTEMBER 2017