Abstract: [Objective] In order to produce the whole bamboo veneer with equal and continuous thickness, reducethe limitation of material selection by bamboo no-card axis rotary cutting machine, expandthe application range of rotary cutting equipment, and improvethe overall turnout percentage and yield rate of bamboo rotary cutting, in this paper, a mathematical model of a new rotary cutting curve based on "logarithmic spiral" is proposed, and the theoretical turnoutrate of bamboo veneer is calculated. The fitness of established model for the use of the no-card axis bamboo rotary cutting machine was also analyzed.[Method] Mathematical model of the two rotary cutting curves were built.Then the mathematical model of the traditional no-card axis rotary cutting theory "Archimedes spiral" and the improved mathematical model of the rotary cutting curve (elliptical "logarithmic spiral" curve) was simulated and analyzed by using Matlab. Finally, the three-dimensional model of the bamboo segment to be processed is established. Combined with the simulation result of Matlab, the formula of the bamboo cutting yield rate is deduced, and the mathematical formula for calculating the yield rate is obtained.[Result] According to the simulation result of Matlab, the "Archimedean spiral" is a circular spiral. Since the cross section of the bamboo is irregular and approximately elliptical, the wall is thin, and after being rounded, the machining margin of the bamboo wall-thickness becomes smaller, the circular spiral curve is not completely suitable for the processing of natural growth bamboo,and defects such as fragile and irregular shape of the processed bamboo veneer occured.The improved "logarithmic spiral"shows the elliptical curve and the cutting curve is similar to the actual shape of the bamboo, which can ensure that the accuracy of the adjacent spiral distance error is within the allowable range, and the model is more suitable for the rotary cutting of the bamboo veneer. The mathematical model parameters can be adjusted in real time according to the size of the inner and outer diameter of the bamboo during processing, which reduces the limitations of bamboo selection.Through the mathematical model analysis of the turnout percentage, it is concluded that the turnout percentage(η) of bamboo is independent of the length (L) of the bamboo segment, and the influence of length, wall thickness and sharpness are analyzed, which can provide reference and theoretical basisfor actual processing and production.[Conclusion] The improved mathematical model of the rotary cutting curve is based on the "logarithmic spiral". When the bamboo is rotated, the thickness error of the veneer is small, the rotary cutting efficiency is high, and the reliability and processing precision are also high. Under the premise of meeting the processing requirements, in order to ensure the bamboo material yield rate, rotary cutting efficiency, rotary cutting quality and other specific requirements, the length of the processed bamboo segment L is required to be about 0.8-1 m. The wall thickness of the bamboo is more than 10 mm, and the sharpness is less than 3-4 mm·m^-1. The establishment of the new rotary cutting model has improved the overall utilization rate of bamboo and broadened the processing range. It provides a basic theory for the design of bamboo rotary cutting equipment, and proposes a new development direction for the bamboo cutting processing without card shaft.

Key words: no-card axis rotary cutting machine, bamboo-wood rotary cutting, Archimedean spiral, logarithmic spiral, turnout percentage