Study on milling surface roughness of a milling cutter with the cutter blade arranged according to phyllotactic pattern

Based on the principle of phyllotaxy arrangement in biology, a milling cutter with blade arranged according to phyllotactic pattern was designed. In order to investigate the influence of the phyllotaxy coefficient h and growth angle β on the machined surface roughness Ra, the mathematical equation of the cutting edge of the milling cutter was firstly constructed, then the motion equation of milling was established, and finally the kinematic simulation of the milling process was carried out, and the influence law of the phyllotaxy coefficient h and growth angle β on the surface roughness was obtained. The results show that: changing the phyllotaxy coefficient h and the growth angle β have a large influence on the machined surface roughness Ra, in which the surface roughness Ra is the smallest when the growth angle β is 137.508°, that is, the golden angle of the biological phyllotaxy arrangement; when the case of the growth angle β is fixed, the value of the surface roughness Ra gradually increases with the phyllotaxy coefficient h.