**BY**Willy Goellner, Advanced Machine & Engineering Co.

o not let resonance destroy your sawing machine and ruin efficiency within your shop. Learn how to test resonance and prevent a catastrophic outcome.

What is resonance? How do I prevent resonance from ruining my machine?

Resonance occurs when a vibratory system is subject to an external pulsing force and the excitation frequency is the same as the natural frequency of the system. When this happens, and there is no damping in the system, amplitude continues to grow infinitely. Typically, machines are designed with some damping in the system so that the amplitude reaches a finite peak value. Without proper damping, the displacements can escalate to a point where the system can no longer support its function, and this can lead to complete destruction of the system.

A saw machine base, normally built with a heavy casting or weldment, has a certain natural frequency depending on mass and stiffness. Experienced machine designers will try to create a sufficient spread between the natural frequencies of the base structure and the exciting frequency. But even in the case of minor resonance, the tool life will be affected.

The problem can be significantly reduced by filling the base with a compound, which dissipates vibration energy as thermal energy to dampen the system. Consider the tool, in this case, a circular carbide-tipped saw blade. These blades are very stiff in the cutting direction (torsional stiffness), but laterally, 90 degrees to the blade plane, the blades are very weak.

On the other hand, the harder the carbide tooth, the more brittle it becomes and, of course, brittle materials are debilitated by vibration forces. Smaller diameter saw blades are not as challenged, because the vibration amplitudes are smaller and the natural frequency is higher. The amplitudes of the vibration increase proportionally with the blade diameter, so the larger the saw blade, the more challenging it becomes to suppress the vibration amplitudes.

History teaches some great examples of how important the knowledge of resonance is. In 1940, the Tacoma Narrows Bridge collapsed due to strong wind that caused the bridge to vibrate in a torsional resonance mode.

**Experimental Modal Analysis**(Impact Test): In this test, you strike the blade with an impact hammer. Accelerometers will track the transfer function with the help of a data acquisition device (DAQ). Hint: If you don’t have a DAQ available, you can also use an oscilloscope and track the signal transformation (Fast Fourier Transformation) in Excel. As a result, you can see the lowest natural frequency, for example at 23Hz.

**Finite Element Modal Analysis:**The equations that arise from the modal analysis are the same that can be found when solving eigenvalue problems.

Every eigenvalue (natural frequency) has a corresponding eigenvector (mode shape).

The end result is very close to the measurement of 23Hz.

This mode, which is represented by node diameter 2 and node circle 0, is one which causes most damage to the teeth.

Because we know the methods to obtain the natural frequency of the blade, we can compare it with the tooth pass frequency of the blade.

Modern engineering aids, like data acquisition devices (DAQ) and finite element analysis (FEA) features in CAD software, are used to uncover issues during the design of industrial machinery.

A solid knowledge of the dangers of resonance allows you to know the important parameters that need to be adjusted to benefit from longer tool life and higher productivity.

Experienced machine designers analyze all vibration sources using stabilizing and damping aids to improve the sawing process.