钻头螺旋槽的优化设计及其计算机仿真

分析加工钻头时螺旋槽与砂轮的几何运动关系,运用微分几何和运动学原理建立螺旋槽和砂轮的数学模型。在此基础上开发螺旋槽的CAD/CAM系统。利用该系统可以根据已知的螺旋槽或砂轮的形状分别求出砂轮或螺旋槽的截面形状,为实现螺旋槽优化设计和砂轮修整的数控化奠定基础。     

Computer-Aided Geometrical Analysis of the Fluting Operation for Twist Drill Design and Production. II. Backward Analysis, Wheel Profile, and Simulation Studies

A computer-aided 'backward' analysis based on the contact curve method has been developed to determine the required grinding wheel profile for generating a given drill flute profile design and fluting machine settings. The required grinding wheel profile was expressed in digitised form as well as in terms of two curve-fitted circular arcs whose radii and centre coordinates represented the required wheel dresser settings on the typical flute grinder modelled. The 'backward' analysis was integrated with the 'forward' analysis from the first paper to form a CAD/CAM package with graphics modules. Simulation studies have shown that only a portion of the required digitised wheel profile was physically feasible so that only the portion of the flute profile generated by an enveloping process precisely matched the design flute profile while the flute profile in the web region, generated by the locus of point of discontinuity on the wheel profile, approximated the design flute profile. Furthermore, the typical drill flute design geometry can never be precisely generated by this flute grinding method. When the required wheel profile is represented by two circular arcs the entire generated flute profile is an approximation of the design flute profile, albeit a very good approximation. It has also been shown that wheel setting angle greater than the drill helix angle has to be used to avoid undercutting the heel and lip corners when the required wheel profile is represented by two circular arcs, unlike for the digitised wheel profile when the wheel setting angle can be equal to the helix angle. The use of the CAD/CAM package to determine six wheel dresser settings and machine settings for drill flute production has been illustrated.     

微钻头螺旋槽的数学模型及其CAD方法

应用微分几何及运动学,在建立起刀具和螺旋面之间的基本啮合条件的基础上,得出了刀具和螺旋面之间的关系,建立了刀具及微钻头螺旋槽的数学模型。通过对螺旋槽加工问题的分析求解,得出了微钻头螺旋槽加工的ＣＡＤ方法。开发了螺旋槽ＣＡＤ系统,利用该系统,可方便地求得在给定刀具条件下微钻头螺旋槽的廓形。     

非共轴螺旋后刀面微钻的五轴联动刃磨方法及其钻削性能研究

微细钻头的几何结构是影响刀具钻削性能和微孔加工质量的关键因素。非共轴螺旋面钻尖由连续的螺旋后刀面组成,相比平面钻尖能有效的提高刀具的刃磨效率及其钻削性能。针对非共轴螺旋面钻尖,推导后刀面形成过程中螺旋运动发生线的位置方程,建立了基于砂轮和钻头接触线的后刀面数学模型。根据六轴数控工具磨床的运动原理,提出非共轴螺旋后刀面五轴联动刃磨方法。分析砂轮与螺旋槽之间的相对运动关系,提出微细钻头螺旋槽的数控加工方法。进行非共轴螺旋后刀面微钻的刃磨试验,验证了该刃磨方法的可行性。进而采用制备出的具有相同几何结构参数的平面、锥面和非共轴螺旋面微细钻头进行不锈钢钻削试验,结果表明非共轴螺旋面和锥面微钻的钻削力、后刀面磨损明显小于平面微钻,并且非共轴螺旋后刀面微钻的横刃磨损程度小于平面和锥面微钻。研究证实了所提出的五轴联动刃磨方法可以有效地制备出较高钻削性能的非共轴螺旋后刀面微细钻头。     

加工螺旋槽的铲齿成形铣刀的铲磨

介绍了加工螺旋槽的成形铣刀的制造工艺,并对铲磨齿形用的成形砂轮截形设计方法进行了分析,介绍了在ＡｕｔｏＣＡＤＲ１４环境下,利用内嵌的ＡｕｔｏＬＩＳＰ语言,二次开发的成形铣刀铲磨砂轮截形ＣＡＤ系统。     

重磨螺旋槽滚刀时砂轮修形自动编程系统的开发

磨削螺旋槽滚刀前刃面时,为获得砂轮母线需要通过调整靠模圆柱的角度,反复试切,影响了生产效率。针对该问题本文以VC++为开发工具,根据开刃磨过程中刀具前刃面的成形原理,建立了计算砂轮理论廓形的数学模型,精准地计算出砂轮的廓形,实现了数控开刃磨砂轮廓形数控加工NC代码的自动编程。     

A Mathematical Model for Manufacturing Ball-End Cutters Using a Two-Axis NC Machine

The paper presents a mathematical model for producing a ball-end cutter by first defining the helical angle as the angle between the cutting edge and the centre-line axis. The velocities of the cutter in the radial and axial directions are then derived based on a given rotating speed. The radial feed speed of the grinding wheel is calculated according to the groove cross-section passing through the centre of the ball-end cutter. A ball-end cutter of constant helical angle is designed and produced by using a two-axis NC machine. To enhance the dimensional accuracy of the mathematical model, a compensatory grinding operation is also proposed and applied to the ball-end cutter. A ball-end milling cutter is selected for design and manufacture to illustrate the effectiveness of the proposed design and numerically controlled (NC) manufacturing procedure. The result of data verification indicates that the proposed procedure is systematic, straightforward and reliable. The ball-end cutter that is designed, refined and produced by using a simple two-axis NC machine is accurate enough to meet the specified tolerance.     

Modeling,simulation and manufacturing of drill flutes

The designing of twist drill flutes (as well as that of end mills and of some combined tools) cannot be separated from the way they are manufactured. The aim of this paper is to present an intuitive direct method for modelling, simulation and manufacturing of the drill flutes with different shapes using conical grinding wheels with standardized shapes. The mathematical approach is described, which enables us to determine the flute profile in a section perpendicular to its axis as well as the manufacturing parameters. The grinding wheel has an initial position with respect to the cylindrical work piece, which is described using four parameters (Denavit Hartenberg parameters). We have presented algorithms in pseudocode that produce the flute shape and that compute the optimum parameters of the wheel position in the manufacturing process. Subsequently, a software application based on the aforementioned model is able to create visualizations of the flute shape. The analysis of the flute shape has enabled us to understand the influence of the geometrical parameters and the position of the grinding wheel on the resulting product in the grinding process. The order in which these parameters are to be set is also specified. We have built atlases of maps presenting the influence of the geometrical parameters and the position of the grinding wheel in the grinding process upon the shape of the flute. The validity of the method is proven by the agreement of the computed values with the input and output data produced by experiment. The proposed method allows helical flutes to be generated solely by using cylindrical and conical grinding wheels of standard shapes.     

成形铣刀铲磨后角时砂轮的选择

推导出盘形成形铣刀在铲磨后角时,根据铣刀的参数快速选择砂轮最大半径的方法,以及砂轮选择时应注意的问题,为盘形成形铣刀的设计、铲磨工艺参数的选择以及铲磨机床的设计,提供一定的参考.     

NC data generation for 6-axis machine tools to produce a helical drill

This study presents a design methodology for grinding a specific helical drill on a CNC 6-axis grinding machine. The proposed methodology comprises three steps: (1) deriving a mathematical model of the helical drill, (2) establishing the ability matrix of the multi-axis grinding machine according to Denavit-Hartenberg (D-H) notation, and (3) constructing configuration matrices to express the required grinding wheel positions and orientations while machining the flute and flank surfaces of the drill. The NC data for the motion values of each axis are obtained by equating the corresponding elements of the CNC ability matrix and the configuration matrices of the grinding wheel. To verify the proposed methodology, a designed helical drill is machined on a 6-axis CNC tool-grinding machine. The methodology presented in this study integrates the drill design and manufacturing activities, thereby making possible the implementation of a more flexible, automatic, cost efficient and controllable design and production process.     

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。     

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...     

加工螺旋槽成形铣刀的计算机辅助设计

讨论了加工螺旋槽的成形铣刀的计算机辅助设计问题。通过采用Pro／E技术,利用Pro／Toolkit开发工具开发了一个基于VC＋＋环境下的计算机辅助设计系统。设计者只需输入所加工螺旋槽工件的法端截形和成形铣刀的结构参数,系统就会自动生成成形铣刀的三维模型。     

A Precision Tool Model for Concave Cone-End Milling Cutters

The paper presents a comprehensive manufacturing model that can be used to produce a concave cone-end milling (CCEM) cutter on a two-axis NC machine. A CCEM cutter possesses many distinct features that are superior in many cases to the traditional flat-end milling cutter for producing parts with multiple sculptured surfaces. Based upon the given design parameters and criteria, the equation of the helical flute groove and the curve of the cutting edge at the end of the helical flute are derived and presented. By using an inverse problem-solving technique, the sectional profile of the grinding wheel, the tool compensation for machining, and the feedrate of both NC axes are consequently obtained. The design results are compared with the measured data obtained from the NC produced CCEM cutter. The satisfactory comparative verification indicates that the tool design and manufacturing model presented in this paper is theoretically sound and it can be automated easily. The proposed method is widely applicable for the mass production of various high-efficiency milling cutters.     

Study on Rotating Cutters with Different Definitions of Helical Angle

This paper presents the similarities and differences of the design models of the cutting edge and flute section corresponding to the different definitions of the helical angle. The correlative models and simulation results for the cutting edge are presented. The section profile and relative feeding velocities of the grinding wheel in the NC machining of the cutter are deduced. The effects of design and manufacture of the cutter are analysed according to a computer simulation of the flute surface enveloped by the grinding wheel. In addition, the deviation of cutting edge, residual material and lack of land caused by the modified radial feeding velocity are taken into consideration. In order to finish the residual material and rebuild the land of the cutter, a post-process method has been developed in this work. Based on the differences of the results, a rotating cutter that has a constant angle between the cutting edge and generatrix curve has many advantages in its design and for NC grinding. Therefore, it is suggested that the helical angle defined as the angle between the cutting edge and the generatrix curve is a better choice when designing a rotating cutter.     

Computer-Aided Geometrical Analysis of the Fluting Operation for Twist Drill Design and Production. I. Forward Analysis and Generated Flute Profile

A computer-aided 'forward' analysis, based on a typical automated flute grinder used in drill production, has been developed to study the flute generation process and the intended or design flute profile of twist drills. It has been shown that the flute grinder involved three machine setting variables and seven wheel profile variables for generating the flute for each drill specification. Based on the recommended wheel profile and machine settings, the forward analysis has shown that the flute profile was partly generated by the 'envelope' of the wheel profiles and partly by the locus of the point of discontinuity on the wheel profile. Furthermore, these numerical simulation studies have shown that the intended or design lip flute profile closely approximated the ideal profile for straight lip production while the heel profile closely approximated a parabolic curve tangential to the core or web diameter and passing through the heel corner. Numerical simulation of the effect of the machine settings has shown that the wheel setting angle has to be set greater than the specified helix angle in order to avoid undercutting and generate the intended flute profile for straight lip production while the other setting variables had no major influence on the generated flute profile in practice. Apart from clarifying longstanding ambiguities in the geometry and specification of flute profile of twist drills, this investigation has provided essential information for the development of the 'backward' analysis considered in the next paper.     

点磨削快速成形与非直线刃钻头的成形刃磨研究

提出了点磨削成形的快速成形磨削新原理和新方法。这是一种紧密依靠CAD／CAM技术的新的成形磨削方法，其原理与快速原型制造类似。作为应用特例，对双曲后刀面等不能用普通形状砂轮刃磨的非直线刃麻花钻进行了快速成形刃磨。     

ZK蜗杆磨削中砂轮廓形的智能化修整

提出了包含多个砂轮修整参数的锥面砂轮数学模型，推导出了基于该砂轮模型的ZK蜗杆齿面方程。在此基础上，讨论了数学模型中修整参数对砂轮廓形的影响规律，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进行高精度、实时地自动修整。     

A practical optimization design of helical geometry drill point and its grinding process

Drill with helical geometry drill point was developed to avoid the disadvantages of planar drill. For the visualization design and optimization of helical drill, a numerical modeling and simulation CAD system has been developed based on the mathematical models of helical drill. The characteristics of helical drill, such as lip clearance angle along cutting lip, heel clearance angle along flank surface, cutting edge inclination angle, rake angle, and so on, are described. Therefore, drill geometric parameters are modified reasonably according to different drilling requirements by the aid of the developed CAD simulation system. Besides, grinding parameters are obtained to guide the flank grinding process of helical drill. A case has been given to demonstrate the function of the system. And the calculated grinding parameters in the above case have been applied on a five-axis CNC grinding machine RollomΛtic 620XS with an assistant fixture to accomplish the flank grinding process. Drill geometry of ground drill shows good agreement with the simulative one, which validates the accuracy of proposed model method and relative CAD system.     

Analyses of Drill Flute and Cutting Angles

The analysis of drill cutting angles is important for the design of high-performance drill geometry. The cutting angles along the cutting edge of a drill are determined by the combination of its flute and flank surfaces. This paper examines the analysis of both flute and flank surface models and the evaluation of drill cutting angles. A new mathematical model for an arbitrary drill flute face is developed by sweeping the polynomial representation of the flute cross-sectional curve along the drill axis, with a helical movement. On the basis of the quadratic flank face, a relationship between the grinding and the geometrical design parameters of the flank face is also established. The vector analysis method is employed for the analysis of the cutting angles for various drill geometries. A comparison of the analytical results with the actual measured cutting angles of an example drill has shown that the average error is less than 5%.