Circular Saw Stability–A Theoretical Approach

The tensioning of circular saws is done to improve their stability under operating conditions. The total potential energy of a saw blade is composed of four components 1) bending stiffness, 2) thermal gradients, 3) angular (rotational) velocity, and 4) tensioning stresses. If any of these four items increases, the total potential energy increases and the blade becomes more stable. Conversely, any decrease in energy will make the blade less stable. Saw blade vibrations are composed of a combination of specific amplitude distributions and corresponding frequencies of vibration. Resonance occurs when the frequency of oscillation of an external force is equal to one of the structural natural frequencies (usually the lowest). The lowest natural frequency of a saw is called the fundamental frequency. The fundamental frequency of a saw becomes lower with thinner blades and thermal stresses. If the blade fundamental decreases into the frequency range of the oscillating external forces, resonance occurs. A blade is optimally tensioned if the fundamental frequency of oscillation is as large as possible for the specified operating conditions. The total potential energy and the fundamental frequency always increase and decrease at the same time. Of the four energy components, bending strain and rotational strain are the simplest. An increase in blade thickness increases the bending strain energy and if a thick enough blade is used, resonance can be avoided. An obvious disadvantage is a thicker kerf. Angular rotation increases the fundamental frequency and is always a stabilizing effect. Thermal stress is due to radial temperature gradients and may increase or decrease blade natural frequencies. Tensile stresses increase the fundamental frequency while compressive stresses decrease it. In practice, resonance difficulties are often associated with a decrease in the fundamental frequency caused by heating of the blade. Tensioning, like thermal stress, may cause some natural frequencies to increase and others to decrease. The problem is to tension so the fundamental is as large as possible. Experimental data show that tensioning stresses and thermal stresses have an opposite effect on the blade potential energy. and natural frequencies. Therefore, tensioning can improve the stability of a heated blade. If the blade is not heated, tensioning will decrease the fundamental. An example is given showing how the effect of tensioning on the fundamental frequency can be computed.

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