Models for evaluating the revolving cutter profile of circular-arc end mills

This paper presents models for defining the minimum circumscribed cylinder (MCC) of the cutter shank, the minimum circumscribed circular-arc-type revolving surface (MCCRS) and the minimum circumscribed corner arc revolving surface (MCCARS) with a spiral groove. A systematic modeling procedure is presented for the assessment of the contour quality of the circular-arc end milling (CAEM) cutters with a cylindrical shank. The axis of the MCC of the cylindrical shank of a revolving cutter with a circular-arc generator curve and a corner radius is taken as the datum line. The profile tolerances and errors are estimated. The presented models are all illustrated and verified by example. This approach can be generalized to a cutter with more than two circular arcs in its shape profile. The paper provides a valuable reference for the evaluation of the actual contour quality of this type of revolving cutter.     

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.     

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.     

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.     

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.     

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.     

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 .     

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.     

交错轴变速比渐开线斜齿轮——齿条传动的啮合分析与加工

在交错轴变速比渐开线斜齿轮－齿条传动中,其变速比功能是通过一个渐开线斜齿轮和一个特殊的斜齿条之间的啮合来实现的,齿条呼个齿郭沿齿长及齿高方向均呈不相同的复杂曲线状。本文建立了该运动的运动几何模型,在啮合分析的基础上,导出了斜齿郭方程,完成了复杂齿条的几何造型。并将复杂的斜齿条齿廓当作自由曲面来处理,提出并实现了一种有别于传统的展成法的新的齿条加工方法。     

圆弧齿线圆柱齿轮的参数计算及选择

圆弧齿线圆柱齿轮是一种新型齿轮,１９８６年在布鲁塞尔第３５届国际新技术贸易展览会上展出。它的特点是：轮齿与其分度圆柱面的交线在分度圆柱面所展开的矩形中为圆弧;而且在齿宽中央截面内为渐开线齿形。本文推导了这种新型齿轮的齿面方程、重合度、压力角、齿宽系数计算公式;给出了其几何尺寸计算公式表;并论证了其特性参数：刀盘半径、齿宽系数、模数及齿数的选择原则。     

基于Pro／Engineer标准渐开线斜齿圆柱齿轮参数化设计

介绍了一种基Pro/E渐开线斜齿圆柱齿轮的精确参数化建模的方法.利用软件中的程序和关系,实现了斜齿圆柱齿轮的参数化建模,仅改变齿轮的相关参数就能快速生成新齿轮,从而极大地提高设计效率.     

特种回转铣刀球头部分的加工方案

讨论了带球头的特种回转铣刀的制造难点 ,提出了解决该加工难点的非数控加工法、新定义方和三轴联动加工方案及其对应的数学模型 ,为研究和加工球头回转铣刀提供了参考     

基于Pro/E的非对称渐开线斜齿圆柱齿轮参数化设计及应力分析

非对称渐开线斜齿圆柱齿轮作为一种新型的齿轮,目前对其还没有展开详细的研究。从齿轮范成法加工角度出发,根据齿条型刀具上各曲线部分参数,推导求得非对称渐开线斜齿圆柱齿轮端面主动侧、从动侧的渐开线、齿根过渡曲线方程。以轮齿端面曲线方程为基础,结合三维造型软件Pro/E,建立出非对称渐开线斜齿圆柱齿轮的三维模型。由于建立后的齿轮模型已经参数化,通过更改基本参数,可以快速生成需求的齿轮。同时,以建立的模型为基础,结合有限元分析软件,对对称与非对称渐开线斜齿圆柱齿轮两个特殊啮合位置的轮齿齿根弯曲强度进行了分析、比较。     

径向剃齿刀修形的优化设计

根据啮合原理推导径向剃齿刀齿面方程,计算其法向修形量,根据齿条展成渐开线齿面原理,建立砂轮磨削剃齿刀齿面模型,以剃齿刀齿面修形量误差平方和最小为优化目标,确定优化砂轮锥底角及安装压力角参数,磨削后的齿面修形两误差达到精度要求,为设计制造径向剃齿刀提供了依据。     

A manufacturing model of helical groove on rotary burr and a universal post processing method

A systematic machining theory and precision method to determine cutter location in a grinding system is presented for rotary burr. First, the helical cutting edge on various kinds of revolving surfaces is built. Then, based on the geometry model of the helical cutting edge, the smooth spiral rake surface with constant normal rake angle and flank surface can been formed during the one-pass grinding process by this method. No interference between the grinding wheel and workpiece happens by the wheel special rotation. The method has the characteristic of detaching the grinding wheel path solution from specified machining conditions. The grinding wheel path is suitable for different NC machine tools through post processing. Meanwhile, a mechanism kinematic model of the NC machine tool is built, and a generalized algorithm for post-processing of multi-axis NC machine tools is presented. This model is applied to arbitrary configuration of NC machine tool, and the motion value for each axis will be generated by the inputting structure and motion parameters of the machine tool. The model, together with the machining method mentioned in this paper, make the calculation and generation of the grinding wheel path simpler and universal. At last, the validity of the method given in the paper is identified by an example of grinding.     

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     

基于Pro/E的渐开线圆柱蜗杆的参数化建模研究

主要阐述了通过曲线、曲面、实体的流程进行蜗杆参数化建模的方法。首先进行了柱面坐标系下两个端面齿形的渐开线、齿根圆弧、齿顶圆弧以及螺旋母线的方程推导,讨论了齿根圆大于和小于基圆两种情况的处理方法,完成了单头蜗杆齿槽的线框模型。然后,通过造型工具生成曲面模型,通过旋转绘制蜗杆齿坯,使用曲面实体化切除方法生成实体模型、齿槽阵列、添加参数关系,生成通用圆柱蜗杆的参数化实体模型。     

渐开线圆柱齿轮参数的测量与计算

针对单个渐开线斜齿圆柱齿轮的测绘问题，提出一种借助渐开线齿形，齿向检测仪来精确确定齿轮参数的方法，以实现原样测绘制造。     

Mathematical model of a helical gear with asymmetric involute teeth and its analysis

This paper describes a simple approach based on the gear theory for deriving a helical gear with asymmetric involute teeth. A helical gear with asymmetric involute teeth can be easily obtained through the envelope theory for the one-parameter family of surfaces. The mathematical models for asymmetric helical gears can be provided by the application of two imaginary rack cutters. The investigation on the undercutting analysis of the asymmetric helical gear is studied based on the developed mathematical model and the method of tooth-profile shifting. Here we provide geometric modeling of the designed asymmetric helical gear meshing when assembly errors are present. Stress analysis for the helical and the cylindrical forms are constructed. To illustrate the effectiveness of the approach, an analytical expression of helical gear with asymmetric involute teeth is given.     

Mathematical model of a helical gear with asymmetric involute teeth and its analysis

This paper describes a simple approach based on the gear theory for deriving a helical gear with asymmetric involute teeth. A helical gear with asymmetric involute teeth can be easily obtained through the envelope theory for the one-parameter family of surfaces. The mathematical models for asymmetric helical gears can be provided by the application of two imaginary rack cutters. The investigation on the undercutting analysis of the asymmetric helical gear is studied based on the developed mathematical model and the method of tooth-profile shifting. Here we provide geometric modeling of the designed asymmetric helical gear meshing when assembly errors are present. Stress analysis for the helical and the cylindrical forms are constructed. To illustrate the effectiveness of the approach, an analytical expression of helical gear with asymmetric involute teeth is given.