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林业科学 ›› 2019, Vol. 55 ›› Issue (3): 134-140.doi: 10.11707/j.1001-7488.20190315

• 论文与研究报告 • 上一篇    下一篇

竹材旋切的数学模型建立与理论分析

刘九庆1, 张贺1, 马岩1, 范芯蕊1, 杨春梅1, 周玉成2   

  1. 1. 东北林业大学机电工程学院 哈尔滨 150040;
    2. 山东建筑大学信息与电气工程学院 济南 250101
  • 收稿日期:2017-08-01 修回日期:2018-01-23 出版日期:2019-03-25 发布日期:2019-04-17
  • 基金资助:
    中央高校基本科研业务费专项资金(2572016EBC3);哈尔滨市应用技术研究与开发项目(2016RQYXJ015)。

Mathematical Model Establishment and Theoretical Analysis of Bamboo Rotation Cutting

Liu Jiuqing1, Zhang He1, Ma Yan1, Fan Xinrui1, Yang Chunmei1, Zhou Yucheng2   

  1. 1. College of Mechanical and Electrical Engineering, Northeast Forestry University Harbin 150040;
    2. College of Information and Electrical Engineering, Shandong Jianzhu University Jinan 250101
  • Received:2017-08-01 Revised:2018-01-23 Online:2019-03-25 Published:2019-04-17

摘要: [目的]为加工出等厚连续的整张竹单板,减小竹材无卡轴旋切机加工竹材选取的局限性,扩大旋切设备的应用范围,提高竹材旋切的整体出材率和成品率,提出一种以"对数螺旋线"为基础的新型旋切曲线数学模型,并计算竹单板的理论出材率,分析讨论所建立模型是否适用于无卡轴竹材旋切机的使用。[方法]对旋切机2种旋切曲线进行数学建模,利用Matlab软件对传统无卡轴旋切理论"阿基米德螺旋线"的数学模型及改进的旋切曲线数学模型(呈椭圆形的"对数螺旋线"旋切曲线)进行仿真分析,建立待加工竹材段的三维模型,结合Matlab仿真结果,对竹材旋切出材率公式进行推导。[结果]通过Matlab仿真结果可知,"阿基米德螺旋线"为圆形螺旋线,由于竹材横截面不规则且近似为椭圆形,壁薄,旋成圆形后,竹材壁厚加工余量小,圆形螺旋线旋切曲线并不完全适用于加工自然生长的竹材,存在加工竹单板易碎、形状不整等缺陷;改进后的"对数螺旋线"旋切曲线呈椭圆形,旋切曲线贴近竹材实际形状,可以保证相邻螺旋线距离误差精确度在许可范围内,模型更加适用于竹单板旋切。数学模型参数可以根据竹材内外径大小实时调整,缩小竹材选取局限性。对推导出的出材率数学模型进行分析,得出竹材的材率η与竹段长度L无关,但应注意长度、壁厚和尖削度的相互影响。[结论]改进后的旋切曲线数学模型以"对数螺旋线"为基础,在旋切竹材时单板厚度误差小,旋切效率更高,具有很高的可靠性和加工精度。在满足加工要求的前提下,为保证竹材出材率、旋切效率、旋切质量等具体要求,加工竹段长度L应在0.8~1 m,竹材壁厚大于10 mm,尖削度小于3~4 mm·m-1。新的旋切模型的建立可提升竹材的整体利用率,拓宽加工范围,为竹材旋切设备设计提供基础理论,对无卡轴竹材旋切加工提出一个新的发展方向。

关键词: 无卡轴旋切, 竹材旋切, 阿基米德螺线, 对数螺线, 出材率

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

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