Cutting Force Fluctuation Suppression and Error Homogenization of Noncircular Gear Hobbing Based on the Tool Shifting Method

The current research on noncircular hobbing mainly focuses on the linkage model and motion realization.However,the intermittent cutting characteristics of hobbing would increase uncertainties in the manufacturing process.In this paper,a hobbing machining model with tool-shifting characteristics was proposed to solve the problems of cutting force fluctuation and inconsistency of tooth profile envelope accuracy at different positions of the pitch curve in noncircular gear hobbing.Based on the unit cutting force coefficient method,the undeformed chip volume generated by interrupted cutting was used to characterize the fluctuation trend of the hobbing force.The fluctuation characteristics of the cutting force generated by different hobbing models were compared and analyzed.Using the equivalent gear tooth and hob slotting numbers,an analysis model of the tooth profile envelope error of the noncircular gear was constructed.Subsequently,the tooth profile envelope errors at different positions of the pitch curve were compared and analyzed based on the constructed model.The transmission structure of the electronic gearbox was constructed based on the proposed hobbing model,and the hobbing experiment was conducted based on the selfdeveloped noncircular gear CNC hobbing system.This paper proposes a hobbing method that can effectively suppress the fluctuation of the peak and whole circumference cutting force and reduce the maximum envelope error of the whole circumference gear teeth.

Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken through some countries,and is in the stage of deep application research.Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China,the noncircular gear CVT is still in the preliminary exploration and research stage.The linear functional noncircular gear pair,whose transmission ratio is a linear function in the working section,to realize continuously variable transmission was the research object in this paper.According to the required transmission ratio in the working section,the transmission ratio function in the non-working section was constructed by using a polynomial.And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair.In addition,for improving the stability and bearing capacity of gear transmission,the noncircular gear pair transmission with high contact ratio was designed.Furthermore,the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile,from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment.Finally,an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

DESIGN OF NONCIRCULAR GEARS WITH DISCONTINUOUS PITCH CURVE

When the noncircular gear pair is applied to the continuously variable transmission （CVT） with gear, the transmission ratio function is discontinuous. In accordance with this unique characteristic, a new approach to design and analyze noncircular gears with discontinuous pitch curve is proposed. The design courses of various noncircular gear pairs with discontinuous pitch curve are unified based on the numerical algorithm of spline fitting and ＂fairing boundary condition＂. According to the particularity of discontinuous pitch curve, the rules and procedures for teeth distribution are recommended. It is explained in detail why the undercut is formed and how to manage the undercut based on meshing principle.In addition, the calculation formulas for each tooth profile segment are also derived. If the tooth profile data are calculated, the measurement and the incision process for noncircular gear can be conducted and the CAD simulation can be achieved easily. To ensure the continuity of the transmission, the transmission interference of the tooth which is located at the pitch curve joint point is managed by utilizing Bezier curve with CAD software. And the contact ratio of gear pair is obtained. The case study shows that this approach is successful and opens up a new way for the design of noncircular gear.

Design of Vegetable Pot Seedling Pick‑up Mechanism with Planetary Gear Train

It has been challenging to design seedling pick-up mechanism based on given key points and trajectories,because it involves dimensional synthesis and rod length optimization.In this paper,the dimensional synthesis of seedling pickup mechanism with planetary gear train was studied based on the data of given key points and the trajectory of the endpoint of seedling pick-up mechanism.Given the positions and orientations requirements of the five key points,the study first conducted a dimensional synthesis of the linkage size and center of rotation.The next steps were to select a reasonable solution and optimize the data values based on the ideal seedling trajectory.The link motion was driven by the planetary gear train of the two-stage gear.Four pitch curves of noncircular gears were obtained by calculating and distributing the transmission ratio according to the data.For the pitch curve with two convex points,the tooth profile design method of incomplete noncircular gear was applied.The seedling pick-up mechanism was tested by a virtual prototype and a physical prototype designed with the obtained parameter values.The results were consistent with the theoretical design requirements,confirming that the mechanism meets the expected requirements for picking seedlings up.This paper presents a new design method of vegetable pot seedling pick-up mechanism for an automatic vegetable transplanter.

非圆间歇齿轮的节曲线设计及其周转缺陷的最速回转修复

针对非圆齿轮不能实现单向连续回转的问题,提出了一种等时间歇的N叶任意非圆齿轮节曲线的设计方法。通过分析节曲线的设计过程,将节曲线分为功能型和非功能型2类,其中,功能型节曲线用于满足任意给定的传动要求,非功能型节曲线用于补偿功能型节曲线以修复周转缺陷。为了提高非圆间歇齿轮的传动效率,基于变分原理构建了一种非功能型节曲线设计的最速回转修复模型,研究了该模型的实现机理。以功能型节曲线的边界条件为依据,利用欧拉-拉格朗日方程推导了该模型的解析解,给出了与其共轭的外啮合和内啮合非圆齿轮的节曲线方程。数值实例验证了该非圆间歇齿轮设计方法的实用性和最速回转修复模型的有效性。

高阶变性椭圆锥齿轮传动模式设计与分析

高阶变性椭圆锥齿轮是球面大端节曲线为高阶椭圆或变性椭圆的非圆锥齿轮。针对目前非圆锥齿轮的设计与分析方法较繁复的问题,根据齿轮空间啮合原理,提出一种仿真加工获得高阶变性椭圆锥齿轮齿形的方法。模拟加工刀具与高阶变性椭圆锥齿轮的节曲线作纯滚动的齿形生成过程,推导出齿形形成过程中的运动参数,并对其节曲线、齿顶曲线及齿根曲线进行设计。重点分析高阶椭圆锥齿轮与变性椭圆锥齿轮齿廓的传动模式及其运动学特性,建立以高阶变性椭圆为基础的椭圆锥齿轮族的仿真模型,统一各种椭圆锥齿轮的传动模式及其设计过程,获得高阶变性椭圆锥齿轮齿廓在传动过程中的运动变化规律及齿轮副匹配模式的通式。通过试验验证该仿真加工获得高阶变性椭圆锥齿轮齿形的方法的正确性。此齿形获得方法可推广应用到任意球面节曲线形状及任意轴间夹角的非圆锥齿轮,从而实现非圆锥齿轮的通用参数化设计。

叶片差速泵偏心圆-非圆齿轮驱动系统的研究

叶片差速泵是一种新型容积泵,它由偏心圆一非圆齿轮驱动系统、泵壳及同轴安装于泵壳内的两个叶轮组成,利用不等速转动的两个叶轮相邻叶片之间周期性张开、闭合来实现密闭容积变化进而完成排液及吸液过程,两叶轮的张合运动由两对偏心圆-非圆齿轮驱动实现。根据偏心圆-非圆齿轮传动的节曲线封闭条件,以及叶片闭合时偏心圆-非圆齿轮的转角关系求出偏心圆-非圆齿轮传动的相对偏心率ε和相对中心距d,进而设计出偏心圆-非圆齿轮的节曲线。通过偏心圆-非圆齿轮的传动分析,确定了叶片的理论最大张开角θmax、理论叶片角γ和配液孔的理论张角β。根据叶片差速泵工作时叶片不干涉条件和配液孔不连通条件确定了实际叶片角γ0和配液孔实际张角β0。

常见的凸封闭节曲线非圆齿轮副设计

根据非圆齿轮的啮合原理,针对椭圆、偏心圆和巴斯噶蜗线等几种常见的凸封闭节曲线及其共轭的非圆齿轮,推导了节曲线的计算公式,并可利用计算机进行精确求解和某些特性参数的修正计算。对三类齿轮副的传动性能和设计制造方面的优缺点进行了对比分析,为其后续设计和制造提供依据。

非圆斜齿轮滚切加工CNC联动控制方案

分析了传统滚齿机不宜加工非圆斜齿轮的原因。针对用数控滚齿机滚切加工非圆斜齿轮的动轴线变传动比的复杂运动几何关系 ,综合运用螺旋齿啮合原理和工具斜齿条法 ,设计出非圆斜齿轮滚切加工的 4种CNC联动控制方案 ,经推证它们是四坐标联动或五坐标联动。给出了非圆斜齿轮滚切加工CNC联动控制的一般原理图。

外啮合非圆齿轮加工模型及根切特性研究

根据范成法加工外啮合非圆齿轮时刀具和齿轮节曲线间的位置关系,提出了插齿加工的数学模型.在分析范成加工外啮合非圆齿轮不根切的模数、偏心率取值范围的基础上,根据所建模型将加工外啮合非圆齿轮的范成过程用计算机进行了动态图形仿真.根据仿真图形结果可以分析和判断所加工的非圆齿轮的齿形特征,从而为设计和制造节曲线封闭型外啮合非圆齿轮提供了一种直观的判断方法.

基于包络特征的非圆齿轮齿廓计算方法研究

依据齿条刀具范成法加工非圆齿轮的原理,建立了计算机仿真加工中的刀具与齿坯间运动学模型;通过对仿真齿条刀具加工中齿廓形成过程的分析,提出了一种基于齿廓特征点的齿廓描述方法;根据齿廓的形成规律,提出了齿廓特征点、齿根圆、齿根过渡曲线和齿顶圆等全部齿廓数据的计算算法,并利用该算法编写了椭圆齿轮齿廓计算程序,该程序可直接用于线切割等数控加工设备加工。采用该方法设计加工出的椭圆齿轮已成功应用于所研制的插秧机分插机构样机及其试验台中,从而验证了该方法的可行性。

基于MATLAB的非圆齿轮副齿廓算法研究

根据展成法加工齿轮的原理和变位思路设计非圆齿轮齿廓。阐述了精确计算一对外凸节曲线非圆齿轮副齿廓数据的数值算法,并提出依据主动轮节曲线自动优化非圆齿轮副中心距和计算从动轮节曲线的方法。主从动非圆齿轮齿廓的啮合曲线部分分别由同一齿条刀具不同侧包络而成,确保啮合时无间隙。通过齿条刀具沿两齿轮旋转中心连线偏离节曲线改变变位量,消除根切,实现非零变位。采用该方法设计加工出的非圆齿轮已应用于实际样机中,确保该方法的可行性。

变性椭圆齿轮连杆机构的运动特性及齿轮副设计

为获得非圆齿轮组合机构特定的运动输出,针对变性椭圆齿轮特性系数对机构运动规律和齿轮参数设计的影响进行了系统的研究。首先在推导了变性椭圆齿轮节曲线和机构执行构件速度与位移计算公式的基础上,对偏心率、变性阶数和曲柄初始角等参数对机构输出运动的影响进行了详细的讨论。其次,根据一对变性椭圆齿轮副参数相同的要求,提出了相应的设计原则和方法。理论研究与试验结果表明,利用对机构特性系数的选择和调整,可以在得到符合基本设计条件的变性椭圆齿轮的同时,实现机构预期的运动要求。

内啮合非圆齿轮加工的数学模型及图形仿真

根据范成法加工内啮合非圆齿轮时刀具和齿轮节曲线间的位置关系,建立了插齿加工的数学模型,分析了加工非圆齿轮时其节曲线为凸的条件。根据所建模型和节曲线为凸的条件,将加工内啮合非圆齿轮的范成过程用计算机进行了动态图形仿真。根据图形仿真结果,可以分析和判断所加工非圆齿轮的齿形特征,为设计和制造节曲线封闭型内啮合非圆齿轮提供了直观的判断方法。

非圆齿轮的成形砂轮展成磨削原理

提出了用成形砂轮展成磨削法磨削非圆齿轮的方法,并给出了利用该原理进行数控加工数据计算的方法。把成形砂轮看作插齿刀的一个刀齿,就可以利用非圆齿轮插齿加工过程中齿廓成形原理,推导出非圆齿轮齿廓的成形砂轮展成磨削方法,同时讨论了按这一原理磨齿时需要的运动及数控机床结构。这种磨削原理不仅可以应用于节曲线外凸的非圆齿轮,而且可以应用于磨削带内凹节曲线的外非圆齿轮及内非圆齿轮。解决了非圆齿轮硬齿面无法精加工的难题,使非圆齿轮应用于精度要求高的场合成为可能。

高阶椭圆锥齿轮齿形设计与加工

根据齿轮空间啮合原理,分析了范成法生成高阶椭圆锥齿轮齿廓过程中,范成刀具的空间走刀位置;建立了高阶椭圆锥齿轮齿廓的数学模型,推导出了高阶椭圆锥齿轮的齿面方程,得到了高阶椭圆锥齿轮副的虚拟实体及装配模型;探讨了采用五轴联动数控机床加工高阶椭圆锥齿轮的方法,通过高阶椭圆锥齿轮的加工与啮合试验,对高阶椭圆锥齿轮理论传动比与实际传动比进行了对比分析,验证了范成法生成高阶椭圆锥齿轮齿廓模型的正确性,以及采用五轴数控机床加工高阶椭圆锥齿轮的可行性。

基于插齿数值计算模型的非圆齿轮根切分析

提出了一种判断非圆齿轮任意齿廓是否发生根切的精确方法。该方法首先从非圆齿轮齿廓数值计算模型出发,计算出齿廓在节曲线法向等距线上的一系列点和形成这些点的对应插齿刀齿廓上的点,然后利用齿廓啮合基本定律对非圆齿轮齿廓根切进行理论分析,最后将插齿数字模型和根切产生的原理综合起来,得出判断各个齿是否发生根切的精确方法,并首次对齿廓的根切程度提出了量化计算方法。根据这些方法可以在设计阶段对非圆齿轮根切缺陷进行校验和评价。

高阶椭圆锥齿轮泵的流量特性

针对齿轮泵的变量功能及非圆锥齿轮的应用,提出了一种新型相交轴变量齿轮泵——高阶椭圆锥齿轮泵.该齿轮泵是以高阶椭圆锥齿轮为工作转子的非圆锥齿轮泵.根据齿轮的空间啮合原理,给出了其工作转子高阶椭圆锥齿轮副的齿形生成方法.基于该种齿轮特殊的运动学特性,分析了高阶椭圆锥齿轮泵的传动特性,并对其工作结构进行了设计.依据球面微分理论,推导出了高阶椭圆锥齿轮泵的平均理论流量公式、瞬时流量公式以及流量脉动公式,同时分析了高阶椭圆锥齿轮的偏心率、阶数等参数对其流量特性的影响.在同等参数模型及工况条件下,将对高阶椭圆锥齿轮泵的平均理论流量、瞬时流量及其变量范围与圆柱齿轮泵和非圆柱齿轮泵的流量特性进行了对比分析,获得了该锥齿轮泵在同等条件下排量最大、变量范围最大的特点.

急回机构中非圆齿轮节曲线的设计

提出了一种以非圆齿轮为前置机构的急回机构。将非圆齿轮节曲线的设计分为等速行程和过渡行程两段进行讨论,通过对所得三种传动比函数的比较,确认了两种较为理想的传动比函数。使所设计机构能实现输出件在工作区间内完全等速,且具有较好的急回特性,比传统的六杆急回机构能更好地满足实际应用中的不同需求。

Pascal蜗线型齿轮滚切插补算法对比

根据Pascal蜗线型齿轮滚切加工模型推导出Pascal蜗线型齿轮滚切插补算法,探讨了不同插补算法中程序段弧长和机床运动轴的变化规律.同时,为了对比程序段弧长的均匀性,提出了程序段弧长均匀度的概念.实例结果表明,在最小曲率半径处,工件等极角插补程序段弧长最长,工件等转角插补程序段弧长变换较为平稳,工件等弧长插补程序段弧长相等;3种插补算法程序段的弧长均匀度由小到大依次为工件等弧长插补、工件等转角插补和工件等极角插补;采用工件等极角插补算法时机床运动轴无一恒定,不便于控制,采用工件等转角插补算法的滚刀控制复杂,而工件等弧长插补算法较为实用.