FINISHING THE CONCAVE SHAPE OF THE WORM THREAD

ABSTRACT

The aim of this work was to improve the accuracy of the concave profile worm thread by using a new generating surface of grinding wheel. To support the geometrical and technological optimization, the current article describes how we produced a smooth and accurately finished tool that will provide maximum line of contact between the tool and the worm with minimum stress concentration at any point. The present study proposed grinding the thread with grinding wheel having a curvature profile in the axial plane in the form of an arc of hyperbola. The generating equation of the tool profile and its arrangement with respect to the worm during grinding were determined.     

MODIFICATION OF GEOMETRY AND TECHNOLOGY OF CYLINDRICAL WORMS

The objective of this research is to develop a new method of grinding process that can efficiently make concave profile of the worm thread smooth. The grinding is carried out using a wheel with curvature profile in the axial plane in the form of an arc of logarithmic spiral. The proposed method will provide maximum line of contact between the tool and the worm with minimum stress concentration at any point. The generating equation of the grinding tool profile and its arrangement with respect to the worm during thread grinding were determined.     

MODIFICATION OF GEOMETRY AND TECHNOLOGY OF CYLINDRICAL WORMS

The objective of this research is to develop a new method of grinding process that can efficiently make concave profile of the worm thread smooth. The grinding is carried out using a wheel with curvature profile in the axial plane in the form of an arc of logarithmic spiral. The proposed method will provide maximum line of contact between the tool and the worm with minimum stress concentration at any point. The generating equation of the grinding tool profile and its arrangement with respect to the worm during thread grinding were determined.     

磨削TI蜗杆的砂轮廓形

TI蜗杆由渐开线斜齿轮包络形成,与斜齿轮组成一种环面蜗杆传动.TI蜗杆传动推广应用的关键制造技术是解决蜗杆齿面的精确磨削问题,即确定出与磨削方法相对应的砂轮廓形.分析TI蜗杆传动运动关系和TI蜗杆产形面特点,将对TI蜗杆的磨削转化为成形砂轮磨削渐开线螺旋面的问题.依据齿轮啮合理论,推导出砂轮磨削渐开线螺旋面的啮合方程,依此得到精确磨削TI蜗杆的砂轮轴断面廓形.     

基于多体系统理论的螺纹磨削研究

将多体系统运动建模方法应用到数控螺纹磨床建模中,建立机床、工件和砂轮的运动关系,推导出多线砂轮磨削螺纹的加工方程。开发螺纹磨削仿真软件,获得螺纹磨削加工G代码,在磨削螺纹的生产中取得了很好的效果。     

基于VERICUT的ZC1蜗杆磨削仿真技术

基于磨削啮合原理建立ZC1蜗杆磨削过程的数学模型。根据空间坐标转换与啮合原理推导出砂轮轴向截形方程,借助MATLAB软件计算砂轮截形,生成其离散点数据,并在SolidWorks平台下建立砂轮与磨削机床几何模型。在VERICUT平台中编制数控程序进行仿真磨削加工,提取蜗杆截形,并测量虚拟误差,分析了磨削过程中当交错角变化时蜗杆截形的误差变化趋势,为ZC1蜗杆的精密磨削加工提供新思路。     

ZK蜗杆齿形误差及其控制方法的研究

首次建立了包含砂轮修整参数的ZK蜗杆数学模型,分析了当砂轮半径发生变化时,m、z_1、d_1对蜗杆齿形误差的影响规律,给出了计算ZK蜗杆齿形误差的经验公式。提出了ZK蜗杆磨削过程中砂轮的智能化修整原理,实现了根据砂轮半径的变化对砂轮廓形的自动修整。     

SELECTION OF GEOMETRIC PARAMETERS OF GEAR AND GRINDING WHEEL TO ENSURE MAXIMUM GEAR TOOTH PROFILE ACCURACY

An analysis of possibilities for the selection of gear and tool geometry parameters is presented to reduce tooth profile errors during the grinding of gears by double tapered wheel (Hofler or Niles method), double wheel generating (Maag method) and by worm wheel techniques (Reishauer method). The selection of gear and tool geometry parameters is based on the analysis of the grid diagram of a gear and a rack. Formulas and graphs are presented for the selection of the pressure angle, module, and addendum of the rack-tool. The experimental results of the grinding of gears confirm the theoretical analysis.     

Grinding of the inner thread without tilt of the tool spindle

A mathematical model of the grinding process for an inner step thread with an abrasive wheel without tilt of the tool spindle is described. The problem of calculation of a shape of a curvilinear part of the profile of the grinding wheel and simulation of thread processing is solved for the evaluation of a possibility of cutting this thread with the required accuracy using a tool of a certain diameter. Examples of calculation of the process parameters for grinding various types of inner thread are shown.     

SELECTION OF GEOMETRIC PARAMETERS OF GEAR AND GRINDING WHEEL TO ENSURE MAXIMUM GEAR TOOTH PROFILE ACCURACY

ABSTRACT

An analysis of possibilities for the selection of gear and tool geometry parameters is presented to reduce tooth profile errors during the grinding of gears by double tapered wheel (Hofler or Niles method), double wheel generating (Maag method) and by worm wheel techniques (Reishauer method). The selection of gear and tool geometry parameters is based on the analysis of the grid diagram of a gear and a rack. Formulas and graphs are presented for the selection of the pressure angle, module, and addendum of the rack-tool. The experimental results of the grinding of gears confirm the theoretical analysis.     

Stress analysis in worm gears with ground concave worm profile

Stress analysis by a finite element method is carried out in the worm and the gear of a cylindrical worm gear drive with a concave worm profile, ground by a grinding wheel of double arc profile. A computer program, based on finite elements, is developed for the calculation of stress distributions in the worm thread and the gear tooth. By using this program, the influence of the design parameters of the worm gear drive and of the load position on stresses have been investigated. On the basis of the obtained results, by using regression analysis and interpolation functions, equations for the calculation of stresses in the worm thread and in the gear tooth have been derived.     

A profile dressing method for grinding worm used for helical gear with higher order modification profile

In the case of generation grinding of the higher order modification gear surface, there are main problems such as difficulty in solving the 3D meshing equations and complexity of expressing the profile of grinding worm. In this study, an indirect generating method is proposed to calculate the profile of grinding worm by applying a virtual rack-cutter (VRC) between the grinding worm and the work gear. The grinding worm dressing experiments were processed by using a ball-nose diamond wheel. According to the results of tooth profile deviation measurement, the tooth profile modification curve is coincident with the predesigned modification curve. Compared with the gear without modification, vibration experiments show that the basic frequency, double frequency, and triple frequency decreased simultaneously, which verified the correctness of calculation and effectiveness of dressing for the profile curve of the grinding worm.     

双导程ZN蜗杆修缘成形磨削研究

双导程ZN蜗杆(又称法向直廓蜗杆)修缘的精密加工需要研究一种成形磨削方法。传统的蜗杆修缘磨削方法是根据加工经验对砂轮进行手工修形,加工效率低且难以实现高精度的齿形修缘磨削。为此,以ZN蜗杆修缘齿形的成形磨削为目标,在蜗杆法平面引入齿形修缘分析,建立ZN蜗杆修缘齿形的数学模型,依据空间啮合原理计算出蜗杆磨削的成形砂轮截形,并利用数控砂轮修整装置修整砂轮。为验证蜗杆修缘的成形磨削效果,选用实际生产中的某一双导程ZN蜗杆,在自主研制的数控砂轮修整系统和工厂的蜗杆磨床上进行试验,经过对成形磨削砂轮计算、修整和蜗杆磨削,结果表明,磨削蜗杆的修缘量满足预期设计要求,蜗杆齿形精度达到6级。表明该方法可用于双导程ZN蜗杆修缘的高精度成形磨削。     

Displacements in worm gears with ground concave worm profile

A computer program based on finite elements has been used for the calculation of displacements in the worm and the gear of a cylindrical worm gear drive with concave worm profile, ground by a grinding wheel of double arc profile. The influence of the design parameters of the worm gear drive and of the load position on displacements has been investigated. On the basis of the obtained results, by using regression analysis and interpolation functions, equations for an easy calculation of displacements in the worm thread and in the gear tooth have been derived.     

用于磨削面齿轮的蜗杆砂轮修整方法研究

为了实现面齿轮磨齿加工,采用包络原理对面齿轮磨削蜗杆砂轮齿形进行设计,并对蜗杆砂轮的修整方法进行研究.建立了蜗杆砂轮齿面的包络坐标系;给出了蜗杆砂轮产形面方程;推导了蜗杆砂轮齿廓的曲面方程,利用Matlab软件对蜗杆砂轮齿廓进行了仿真,根据面齿轮磨削蜗杆砂轮的齿面生成原理,给出了修整工具的齿廓形状、齿宽限制以及修整工具...     

磨齿产生中凹齿形的机理与防止措施

针对蜗杆砂轮磨齿机产生中凹齿形的问题,研究了蜗杆砂轮与工件的接触状态,分析了中凹齿形产生的机理.当重合度不是整数时,表明啮合过程中啮合齿面的对数在变化.啮合齿面的对数的变化会在齿面的法向方向产生一个交变力,这个交变力就是产生中凹齿形的主要原因.提出了防止中凹齿形产生的措施.     

Undercutting and interference for thread form grinding with a tilt angle

In the form grinding that is widely used to produce precision threads, screws, and gears, the grinding wheel profile is usually calculated from a given tooth profile and the so-called equation of meshing. However, in the presence of undercutting or secondary enveloping, the grinding wheel calculated cannot be guaranteed to produce the desired thread profile. Therefore, this paper proposes a geometric approach to determining the grinding wheel profile and the conditions to avoid undercutting by means of the tilt grinding wheel axis. Specifically, we calculate the thread’s profile based on its relationship to each transverse plane of the grinding wheel in the form grinding process. The grinding wheel profile on each transverse plane is then determined using the shortest distance from all the thread profile points to the grinding wheel revolution axis. Obtaining these distances allows derivation of a formula to calculate the minimum tilt angle that avoids undercutting. This proposed geometric approach is numerically more stable than the conventional equations of meshing, and the derivation of the undercutting equation is straightforward and easy to understand.     

螺旋槽螺纹铣刀的磨削砂轮设计

针对螺旋槽螺纹铣刀在磨削加工时内外侧磨削量不同的问题,通过齿形的数学建模和分析计算,提出了其磨削砂轮的修正量计算公式.同时编制了砂轮设计程序,实现了从螺纹铣刀参数到其磨削砂轮参数的自动转换.通过 AutoCAD 和 SolidWorks 应用开发,可以自动生成砂轮的二维图和三维模型.本文提出的方法可以提高螺纹铣刀磨削砂...     

Grinding of high-lead and gothic-arc profile ball-nuts with free quill-inclination

A method for gothic-arc ball-nut grinding is presented. The gothic-arc is a combined curve of two arcs with the same radius and shifted centers. Generally, gothic-arcs are manufactured by form grinding; the grinding wheel is formed into the gothic-arc and is tilted at the lead angle of the thread. In ball-nut grinding, which is internal grinding, interference between quill (wheel shaft) and internal surface of a workpiece limits the length of the ball-nut. In the presented method, the quill is tilted independently of the lead angle so as not to contact the internal surface of the workpiece. Instead, the wheel is formed into an optimum profile with which the nut obtains a gothic-arc profile. The procedure of finding the optimum wheel profile is presented. Grinding simulation showed that the gothic-arc thread is obtained accurately by the method, though a part of the thread surface is not a perfect gothic-arc. This method allows the use of large-diameter wheels to manufacture high-lead ball-nuts.     

硬质合金精密滚剃刀齿形制造新技术

给出了用双曲线拟合滚剃刀渐开线蜗杆法剖面齿形新技术，提出了锥面砂轮按斜直线进行修整，能够获得砂轮轴截面为双曲线形状。按此技术修整砂轮，通过对滚剃刀渐形线蜗杆的圆磨，有效地提高了滚剃刀齿形精度。