Chip fractal geometry and loading characteristics of sinusoidal multi-cutters in hack-sawing process

This work proposed a sinusoidal-type discrete analytic geometry model and derives sinusoidal serrated chip loading characteristics equation for the simulation of the hack-saw reciprocating mechanism by the cutter analytic geometry. The chip loading with different wavelength units in hack-sawing process are studied. The factors affecting chip loading of unit wave, namely the length of the wavelength, the cutters numbers of unit wavelength, saw blade thickness, the equivalent cutting depth per tooth, the cutting overlap-area ratio per cutter edge, the pitch per each cutter, the cutting overlap-area factor, and the proportional factor of sinusoidal amplitude are investigated. The effects of sinusoidal cutter arrangement on chip loading are simulated by the chip loading equations. It is found that the maximum chip loading is always in the front of the cutters, which is at either the peak or the trough of different phase, while the numbers of wavelength unit is 3, 5, 7 and 40, respectively. The chip loading characteristics depend on the convolution of chip loading function, the cutter order window function and the cutter interval function. The simulated results from the established cutting force model for sinusoidal multi-cutters agree well with the experimental measurements. The wear location and failure types of cutters could be predicted for in hack-sawing process.