陈水胜,孔加超,陈梦婷,周世棠.基于瓦楞辊齿廓啮合理论的运动学方程[J].包装工程,2019,40(7):168-173.
CHEN Shui-sheng,KONG Jia-chao,CHEN Meng-ting,ZHOU Shi-tang.Kinematics Equation Based on the Tooth Profile Meshing Theory of Corrugated Roller[J].Packaging Engineering,2019,40(7):168-173. |
| 基于瓦楞辊齿廓啮合理论的运动学方程 |
| Kinematics Equation Based on the Tooth Profile Meshing Theory of Corrugated Roller |
| 投稿时间：2018-12-24 修订日期：2019-04-10 |
| DOI：10.19554/j.cnki.1001-3563.2019.07.025 |
| 中文关键词: 瓦楞辊 啮合 加权拟牛顿法 运动学方程 楞型 图谱 尺度参数 |
| 英文关键词: corrugated roller mesh weighted quasi Newton method kinematics equation corrugated type diagram corrugated scale parameters |
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| 中文摘要: |
| 目的 为了优化瓦楞辊的齿形结构，研究瓦楞辊各齿廓啮合点的运动学方程，并对其啮合非线性方程组求解，得到运动学分析图谱。方法 利用微分几何和相对运动学原理建立齿廓函数，采用加权拟牛顿法，并编制相应计算程序，对各齿廓啮合点运动学方程进行求解。结果 通过计算实例，将U，V和UV型瓦楞辊各类楞型的原始参数代入啮合方程计算，得到一一对应的运动学性能分析图谱。该图谱显示瓦楞纸板成型时，瓦楞辊齿廓啮合引起的中心距变化规律一致，仅是对称于不同的分度角坐标轴，满足传动比i=φ2/φ1=?1，且满足齿形侧楞平行条件，φ2?φ1=180°，即两切线平行时为啮合的交替点。结论 该图谱揭示了楞型尺度参数与瓦楞辊工作时转角速度、中心距变化加速度和位移的关系，并能评价各类楞型运动性能的优劣，给瓦楞辊的设计制造与误差分析提供了依据，特别是为其运动学、动力学和加工原理分析奠定了理论基础。 |
| 英文摘要: |
| The work aims to study kinematics equations of tooth profile meshing point and solve the nonlinear equations of meshing to obtain the analysis diagram of kinematics performance in the optimization of corrugated roller tooth structure. Based on differential geometry and principle of relative kinematics, the tooth profile functions were established and the Weighed Quasi Newton method was used to solve the kinematics equations of tooth profile meshing point with the calculation program. Through the calculation example, the original parameters of U, V and UV corrugated rollers were substituted into the meshing equation for calculation, and the analysis diagram of kinematics performance was obtained. The diagram showed that the variation of center distance caused by the meshing of the tooth profile of corrugated roller was consistent when the corrugated board was formed and was only symmetric on the different indexing angle coordinate axis and in conformity with transmission ratio, i=φ2/φ1=?1 and the parallel conditions of side-corrugated tooth profile: φ2?φ1=180°, namely the meshing alternating points when the two tangents were parallel. The diagram reveals the relation between corrugated scale parameters with the angular velocity of the corrugated roller at work, acceleration and displacement of variation in center distance and evaluates the kinematic performance of various types of corrugated rollers, thus providing the basis for error analysis and design calculation of corrugated roller, and laying a theoretical foundation for the analysis of kinematics, dynamics and machining principle specially. |
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