In the sawing process, one of the major challenges is the vibration and noise generated by the saw blade. A commonly used method to reduce these issues is to cut appropriate slots into the blade. This paper aims to provide a mathematical foundation for the design of slotted saw blades and the re-use of blades with radial root cracks. By treating radial slots and radial cracks as equivalent, we analyze their impact on the blade's vibration characteristics using finite element analysis.
To begin with, we examine the natural vibration modes of a standard circular saw blade. The blade has an outer diameter of 1.0 m, thickness of 0.006 m, clamping ratio of 0.5, Young’s modulus of 2.058 × 10¹¹ N/m², Poisson’s ratio of 0.3, and density of 7.8 × 10³ kg/m³. Due to its axial symmetry, only half of the blade was modeled. It was divided into 90 quadrilateral elements and 114 nodes (5 radial divisions, 18 circumferential divisions). The model was analyzed using SAP6, and the results were post-processed using a custom program to identify vibration modes, denoted by (m, n), where m is the number of nodal circles and n is the number of nodal diameters.
To evaluate the effect of mesh density, the model was refined to 180 elements (222 nodes) and 360 elements (407 nodes). The natural frequencies calculated under different mesh densities were compared with the exact solution. As shown in Table 1, the lower-order natural frequencies are consistent across all mesh densities, indicating that a mesh of 90 elements is sufficient for practical applications.
Next, we analyzed the vibration characteristics of saw blades with radial slots. These slots, up to 1 mm wide and uniformly distributed, can represent radial root cracks. We created a model with 180 elements and 216 nodes. By varying the slot length and number, we calculated the natural frequencies and identified the mode shapes. As seen in Table 2, the presence of slots causes some originally coincident frequencies to split. The frequency decreases gradually as the slot length increases, but the drop remains below 10% when the slot length is less than 20% of the blade radius.
Moreover, increasing the number of slots generally leads to a slight decrease in natural frequencies, though this trend is not always consistent. The position of the node diameter and the relative placement of the blade remain fixed, which helps prevent the formation of stationary waves at critical speeds.
In conclusion, the introduction of radial slots allows for better energy distribution during excitation, reducing vibration intensity. The vibration modes depend on the number and distribution of the slots. When the slot length-to-radius ratio is less than 0.2, the reduction in natural frequency is minimal, so there is no need to worry about significant loss of bending stiffness. Blades with small radial cracks can still be used after proper drilling and balancing. This study provides valuable insights for improving the performance and longevity of saw blades.
Double-sided Poly Ribbed V Belt,Double-sided Poly Ribbed V-belt,Double Sided Poly Ribbed V Belts,Double Sided Poly Ribbed Belt
Zhoushan Aosheng Auto Transmission Belt Manufacturing Co., Ltd. , https://www.aoshengbelt.com