Contour Quality Evaluation of the Toroidal Cutter

A toroidal cutter is an effective tool for use in the machining of freeform surfaces. Its contact point on the machined surface creates a second-order continuous curvature, thus the scallop height is decreasing if the cutter axis is inclined at a suitable angle against the machined surface. However, few studies address the evaluation of the contour quality produced by this kind of cutter. The geometry of a toroidal cutter includes a cylindrical shank, cutting body, and a toroidal surface. These components may deviate from the ideal geometry, resulting in contour errors. Therefore, it is very important to evaluate the radius of the cutting body and the toroidal surface based on the axis of the minimal circumscribed cylinder. This paper first presents a reliable model to determine the axis of the minimal circumscribed cylinder (MCC) of the cutter shank, from measured data. Then, based on the determined axis, the radius of the cutting body is calculated, and finally the minimal circumscribed toroidal surface (MCTS) of the revolving surface of the corner arc is investigated. An illustrative example is given to verify the validity of this modelling methodology. This work provides a basis for evaluating the actual contour quality for this kind of rotating cutter. The method illustrated here can also be used for error evaluation for other kinds of cutter with a single shank having multiple cutting edges.     

Models for evaluating the contour quality of revolving cutter with involute generator

The toroid-shaped helical cutter with an involute generator is a precision tool used in the machining of involute helical gears. Taking the axis of the minimum circumscribed cylinder of the measured points on the cylinder shank as the datum axis, this paper provides models of the minimum circumscribed involute revolving surface and the minimum circumscribed toroid-shaped revolving surface. This paper also presents models for evaluating the contour quality of a toroid-shaped cutter with an involute generator. The validity and accuracy of these models are confirmed by worked examples.     

Study on the Form Error Evaluation Model of a Conical-Shank Ball-End Milling Cutter

This paper presents a complete form error evaluation model of a conical-shank ball-end cutter. The complete conical-shank ball-end cutter comprises three major revolving portions including the conical shank, cylindrical section, and spherical head. By using the central line of the minimum circumscribed conical shank as a datum axis and employing profile data measured directly from cutter surfaces, the proposed evaluation method systematically computes the exact revolving envelopes of the conical shank, cylindrical part, and spherical part separately, and then combines them. One application example is presented to illustrate the effectiveness of the proposed modelling method. This paper provides a simple, logical, and precise method for the quality evaluation of a special rotating cutter and can be further extended for use in the quality assessment of various complicated cutters.     

Evaluation of Contour Quality in Sampling Inspection of Two Drill Types

This paper introduces the differences in quality evaluation for the sampling inspection of drills with taper or cylindrical shanks. For a drill with a taper shank, the datum axis is taken to be the axis of the minimum circumscribed cone, whereas for a drill with a cylindrical shank, the datum axis is taken to be the axis of the minimum circumscribed cylinder. The features that are common to both drill types are the definition of the minimum circumscribed cylinder of the cylinder part with helical grooves and the minimum circumscribed univalent hyperboloid based upon the datum axes given above. This paper presents all the necessary supporting models, illustrated and verified by examples, for the evaluation of actual contour quality for these two drill types which are comprised of compound surfaces.     

A precision design and NC manufacturing model for concave-arc ball-end cutters

Having first defined the helical angle as the angle between the cutting edge and the axis of rotation of the cutter, this paper then presents design models for producing the cutting edge and groove of a ball-end cutter with concave-arc generator. The relative feed speeds of the grinding wheel in the radial and axial directions during NC machining of the cutter are derived based upon a given speed of rotation. The feed speed of the grinding wheel in the radial direction is modified according to the cross section of the groove that passes through the center of the cutter sphere. The paper presents a method for manufacturing a concave-arc ball-end (CABE) cutter using a 2-axis NC machine. The models that are used to calculate the actual obtained groove and the computer simulation method are also included. To further enhance the accuracy of the mathematical models, a compensatory machining process that eliminates residual profile on the revolving surface is presented. This paper provides a valuable reference for the design and machining of this cutter type.     

Design and NC Machining of Concave-Arc Ball-End Milling Cutters

The paper presents a geometric modelling approach for the precision design and NC machining of a concave-arc ball-end milling (CABEM) cutter which is an important tool for mould-making industries. This paper presents systematic models of the cutting edge, helical groove, and grinding wheel design for the NC machining of a CABEM cutter. Both the normal to the revolving axis and the tangent to the groove, are used to derive the required precision sectional profiles of the grinding wheel. In compliance with the maximal sectional radius of the cutter, the profile of the groove section and both the radial and axial cutting speeds of the grinding wheel are computed in sequence. Using the computer simulation results of the groove actually obtained, this paper proposes a method to resolve the problems of the residual revolving surface and the narrow cutting edge strip. This paper is intended to serve as a reference for the design and NC machining of cutters of this type .     

斜航式法向圆弧螺旋锥齿轮的参数化有限元建模

给出了斜航式法向圆弧螺旋锥齿轮的参数化建模方法。推导了在CAD/CAE软件中建立齿轮齿面的方程,解决了建模过程中由于齿面复杂而引起的技术难点。利用ANSYS软件的APDL语言生成齿轮轮廓的主要关键点,结合实体造型功能建立生成齿轮模型的宏文件,完成参数化程序建立。最后,给出了一对齿轮的实体模型以及基于实体模型建立的有限元模型。     

Kinematic errors on helical gear of triple circular-arc teeth

Two imaginary skew rack cutter curves with stepped triple circular-arc teeth are presented in this paper. A helical gear pair that includes the gear and pinion surfaces was generated by using two matched imaginary skew rack cutter surfaces. The mathematical models of the helical gear pair with stepped triple circular-arc teeth were developed based on theory of gearing. With the use of these models, the analysis of kinematic errors can be illustrated and evaluated by computer programming and tooth contact analysis (TCA). The assembly errors used had several kinds: ideal assembly errors, vertical misalignment angles, horizontal misalignment angles, manufacturing errors of helical angles, and center distance deviation. TCA revealed that the sensitivity of horizontal misalignment angles was lower than that of manufacturing errors of helix angles but higher than that of vertical misalignment angles.     

特种回转面刀具螺旋槽的通用几何模型

针对数控磨削螺旋槽的特点 ,提出了基于一般特种回转面刀具刀刃曲线和刀面截形的螺旋槽通用几何模型。该模型采用统一的形式表示螺旋槽 ,为特种回转面刀具的设计和数控加工提供了理论基础。该模型也适用于其它类型的回转刀具     

Discussion on the problems related to NC machining of toroid-shaped taper cutter with constant angle between cutting edge and the cutter axis

Defining the helical angle as the angle between the cutting edge and revolving axis of the cutter presents the designing models of the cutting edge and helical groove of a toroid shaped taper cutter. Under the condition of a certain revolving speed, the relative radial and axial feeding speeds of the grinding wheel in two-axis NC machining of the cutter are deduced. The models for calculating the actual obtained groove and the simulation-method of computer are also provided.The surface near to the top of the end cutter has no helical cutting edges and infinite feeding speeds of NC machine. It is necessary to adopt a supplementary cutting edge. A supplementary cutting edge is designed as a cutting edge with a constant pitch. This paper provides valuable reference for the design and NC machining of this kind of toroid shaped taper cutter.     

圆弧刃刀具切削时理论粗糙度的计算

在圆弧刃刀具切削直线廓形时理论粗糙度计算的基础上，着重研究圆弧刃刀具切削圆弧廓形时理论粗糙度的计算方法。研究表明，工件已加工表面理论粗糙度取决于工件已加工表面的廓形、刀具切削刃形状和刀具切削运动方式，优化选取刀刃半径和刀具进给量后，可以有效地减小理论粗糙度值并提高切削效率。     

基于传递矩阵法的微细刀具临界转速分析

针对某微细刀具的实际结构特征,利用传递矩阵法计算了该微细刀具在不同刀尖质量、不同刀柄悬伸长度和不同刀径锥角下的临界转速,分析了刀柄悬伸长度和刀径锥角对微细刀具临界转速的影响规律。分析结果表明,刀柄的悬伸长度是影响微细刀具临界转速的主要因素。当转速接近临界转速时,可通过调节刀柄的悬伸长度改变微细刀具的临界转速,使切削加工处于安全的转速范围内。     

导弹天线罩廓形误差评定研究

为实现对导弹天线罩这类薄壁复杂回转体进行测量,研制了导弹天线罩几何参数测量仪.就测量数据的误差处理,探讨了应用鞍点规划的方法对天线罩廓形误差进行评定、给出了评定的线性鞍点规划模型、评定的最小条件,以及具体的操作方法.     

Geometric modeling and grinder design for toroid-cone shaped cutters

This paper presents a set of mathematical models for the design and manufacture of the helical flute and cutting-edge curve of a toroid-cone shaped revolving cutter. The study not only considers the section profile and relative feeding velocities of the grinding wheel used in the NC machining of the cutter, but also addresses the deviation of the cutting-edge curve, the residual material which exists between adjacent flutes, and the lack of cutter land. Through a process of numerical simulation, a compensation technique is developed which reduces the residual material and rebuilds the missing land. The accuracy of the theoretical models is verified by means of an experimental machining test using a WALTER CNC grinding machine. The experimental results are in good agreement with those predicted theoretically, thereby confirming the accuracy and reliability of the proposed models. This study serves as a valuable reference for researchers investigating the NC machining of cutters with special forms.     

曲面加工靠模曲线的计算

用仿形工艺加工曲面零件时,仿形靠模的形状并非与曲面零件的形状一致,也不是简单的放大或缩小。针对这一问题,以仿形车削圆弧回转面的靠模为例,首先讨论靠模触头滚轮中心的运动轨迹,再求出滚轮圆族外包络线的运动轨迹,最后得出靠模曲线形状的计算方法。     

球面加工非圆靠模的计算

用仿形工艺加工曲面零件时,仿形靠模的形状并非与曲面零件的形状一致,也不是简单的放大或缩小.针对这一问题,以仿形车削回转球面的靠模为例,首先讨论出靠模触头滚轮中心的运动轨迹,再求出滚轮圆族外包络线的运动轨迹,最后得出靠模曲线形状的计算方法.     

基于仿增量算法的圆度误差快速准确评定

提出按最小外接圆法和最小区域法评定圆度误差的仿增量算法.将工件轮廓看作一个点集,并在其中建立可以确定圆(环)的子集.若子集确定的圆(环)包容原点集,则可得到相应的圆度误差;否则每次给子集增加一个在包容区域外的点构成新子集,确定包容新子集的圆(环)并去掉其中不在圆(环)边界上的点.证明了该算法是单调收敛的.同时还提出以按最小外接圆法评定圆度误差时在包容边界上的点为最小区域法初值的新思路.该算法概念清楚、模型简单,易于在计算机上实现.几个实际零件圆度误差的评定验证了算法不仅正确,而且结果准确,耗时极少.     

Research on the design and manufacturing of an outer cycloid slotting cutter

Outer cycloid gears are used widely in many instruments and machines. The outer cycloid slotting cutter is an important cutting tool used in the manufacturing of this type of gear. In the process of design, the ideal outer cycloid cutter is one where a cylindrical surface takes the tooth profile of the outer cycloid as the directrix. However, during the manufacturing process, it is used as a cutter and therefore a cutting edge is required. As a result, it will be seen that the processes of design and usage of the outer cycloid cutter are not the same. The range of the qualified length of tooth is deduced in this paper by using the mid-point and mid-line method. This paper also presents the associated outer cycloid slotting cutter design and manufacturing models so that the modelling accuracy and the necessary relief angles of the top cutting edge and side cutting edge can be ensured. This paper is intended as a reference to be used in the manufacture and application of this type of slotting cutter.     

HSK工具系统结构特点分析

HSK（空心短圆锥柄）最突出的特点就是按照DIN69893具有的轴向面夹紧机制,实现了机床主轴与刀具在锥面接触的同时还增加了在端面的接触,即过定位配合,从而避免了刀具在高速回转时的轴向串动,并保证了重复定位精度。由于HSK刀柄是采用中空式结构,使得刀柄锥面能够产生一定的弹性变形,所以当机床主轴在高速回转时,HSK刀柄锥面能够保持与机床主轴锥面的紧密可靠接触。HSK刀柄采用1：10锥度,有利于刀柄与主轴连接时产生自锁,使得夹紧更为可靠。     

法向圆弧锥齿轮加工干涉研究

法向圆弧锥齿轮是基于Bertrand共轭原理发展起来的一种新型传动形式,除具有优良的传动性能,还具有良好的工艺性,十分便于采用指状或盘状铣刀进行成型法加工。研究了一对共轭法向圆弧锥齿轮廓面的诱导曲率特征,给出了曲率轴在法向圆弧共轭曲面干涉判断中的应用,以曲率轴为手段研究了齿廓加工时不发生曲率干涉和过切干涉的条件,提供了一种铣刀盘直径的近似求法。