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 .     

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 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.     

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.     

A novel mathematical model for grinding ball-end milling cutter with equal rake and clearance angle

In this paper, new mathematical models and grinding methods of ball-end milling cutter were proposed based on the orthogonal spiral cutting edge curve. In order to avoid interference, a conical wheel was also designed and employed to grind the rake and rear faces of ball-end milling cutter on a five-axis grinder. Mathematical models of both rake face with equal rake angle and rear face with equal clearance angle were established to improve the machining characteristics of ball-end milling cutter. The design and simulation software of ball-end milling cutter was developed to design and optimize different shapes of both rake face and rear face. Furthermore, grinding experiment of the new ball-end milling cutter was carried out to confirm the validation of the mathematical models.     

整体硬质合金球头铣刀螺旋槽建模技术研究

球头铣刀外形复杂,工序繁多,在曲面加工中应用广泛。对整体硬质合金球头铣刀刃线和螺旋槽进行数学建模,采用等导程刃线模型生成S型球头刃线,解决球面刃线与柱面刃线过渡不光滑问题。采用蝶形砂轮刃磨螺旋槽,求解砂轮刃磨位姿。利用MATLAB对球头铣刀刃线模型进行仿真验证,计算砂轮位姿变换过程,并基于MATLAB软件中GUI模块设计砂轮磨削工艺系统。     

A Study of Manufacturing Models for Ball-End Type Rotating Cutters with Constant Pitch Helical Grooves

Most of the published work on developing design and manufacturing models of rotating cutters lacks generality and integrity. In this paper, a systematic method that integrates design, manufacture, simulation, and remedy has been developed for a ball-end type rotating cutter. The principles of differential geometry and kinematics facilitate the development of correlative models of the cutting-edge and helical groove. Based on the envelope condition, approaches for solving the direct and inverse problems related to the manufacturing models are also presented. The influences of relative feed speeds of the grinding wheel in machining the groove are discussed, and following this the proposed feed speeds are designed. The effects of design and virtual manufacture of the cutter are analysed according to the computer simulation results of the groove surfaces enveloped by the grinding wheel. In addition, the post-process methods are introduced to finish the residual material and the land of the cutter.     

Manufacturing models for design and NC grinding of truncated-cone ball-end cutters

This paper presents a set of mathematical models for the design and manufacture of the helical flute and cutting-edge curve of a pair of truncated-cone ball-end cutters. The section profile and relative feeding velocities of the grinding wheel in NC machining of the cutter are deduced. In addition, the deviation of the cutting-edge curve, residual material and the land lack 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, the technique for compensation has been developed in this research. 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.     

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.     

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.     

<Emphasis Type="Bold">CNC Rake Grinding for a Taper Ball-End Mill with a Torus-Shaped Grinding Wheel</Emphasis>

A new grinding method using a torus-shaped grinding wheel and a machining path generation method with a novel moving coordinate system are proposed. With this new grinding method, the smooth spiral rake surface of a taper ball-end mill with constant helical angle and constant normal rake angle can be formed during one grinding process and the normal rake angle can be obtained accurately. The novel moving coordinate system is established based on taking account of both the cutting edge curve and the cutter body surface. By means of the novel moving coordinate system, the machining path generation becomes very simple. The proposed grinding method and the machining path generation method are verified by 3D simulation results.     

球头铣刀刃口曲线的求解及螺旋沟槽的二轴联动数控加工

给出了球头螺旋铣刀三种不同螺旋刃口曲线的求解公式和二轴联动数控加工时砂轮的截形和相对运动求解模型,根据实得沟槽的模型和计算机模拟结果分析了存在的不足,并给出了相应的后处理方法。     

球头铣刀的设计与仿真

提出了一种应用计算机绘图软件和OpenGL设计球头铣刀的方法,建立了一种球头铣刀的前刀面与后刀面的数学模型.通过OpenGL建模,建立了仿真处理系统和球头铣刀的螺旋柱面、球头(包括前刀面、排屑槽、主后刀面和副后刀面)和砂轮的三维仿真模型.应用数学模型和VC++软件平台,并利用OpenGL控制界面实现了设计结果的可视化及...     

Design and fabrication of a new micro ball-end mill with conical flank face

Micro ball-end milling is an efficient method for the fabrication of micro lens array molds. However, it is difficult to meet the machining quality of micro dimple molds due to the wear and breakage of the milling cutter, which presents large challenges for designing geometric structure and edge strength of micro ball-end mills. In this study, a new configuration of a micro ball-end mill for micro dimple milling is designed and named the micro conical surface ball-end mill. The cutting edge is formed by intersecting the conical surface and the inclined plane. A practical grinding method is proposed based on the kinematic principle of the six-axis computer numerical control (CNC) grinding machine for micro conical surface ball-end mills and is validated by grinding simulations and experiments. Micro dimple milling experiments are conducted on the hardened die steel H13 to investigate the cutting performance of the mill. The milling force, the micro dimple roundness error, and the tool wear morphology are observed and analyzed. The results show that the radial milling force is more stable and the wear resistance is improved for the micro conical surface ball-end mill compared to the traditional micro spiral blade ball-end mill. Therefore, a more stable roundness at the entrance hole of the micro dimple can be obtained by using this design after a number of micro dimples have been milled.     

Practical and reliable carbide drill grinding methods based on a five-axis CNC grinder

The carbide drill is an important hole-machining tool. Modern processing solutions set higher requirements for the accuracy and efficiency of carbide drill manufacturing. This paper presents a detailed study of mathematical models of the spiral groove, conical flank, and cutter clearance and proposes three practical and reliable grinding methods using only one standard straight wheel. The spiral groove is ground by controlling three crucial structure parameters: the spiral angle, core diameter, and rake angle. The conical flank is ground by controlling the relief angle, chisel edge angle, and apex angle. The cutter clearance is ground by controlling the ridge width and clearance depth. With these schemes, the wheel position parameters can be computed conveniently and quickly using computer programming, overcoming the low calculation accuracy of empirical formulae and thereby enhancing the efficiency. Using the wheel position parameters, the NC codes applicable to five-axis CNC grinders can be obtained. Furthermore, the reliability of the proposed grinding methods can be verified through CAD simulation and practical manufacture on a five-axis CNC grinder.     

A High-Precision Surface Grinding Model for General Ball-End Milling Cutters

The paper presents a high-precision manufacturing model for grinding the surface profiles of general ball-end milling (GBEM) cutters. The geometric shape of the grinding wheel is derived with a positive cone angle specifically for grinding the GBEM cutters. The concepts of radial equidistant lines and oblique equidistant surfaces are employed to model the front ball-end profile, the front cutting surface, the rear cutting surface, and the cutting-edge curve of the GBEM cutter. The front cutting surface model is obtained by computing the intersection of the rotating tool surface and the motion enve-ope of the grinder. The cutting-edge curve model is estimated by computing the intersection curve of the front cutting surface and the ball head of the GBEM cutter. A special model of the grinding mechanism is also derived and used to produce the rear surface of the cutter. Both the cutting-edge curve and the surface model are solved simultaneously in order to ensure that the cutting-edge curve leans physically against the rear-cutting surface. The geometry of the full front-end cutter shape and the parameters of the associated manufacturing processes are numerically optimised to ensure best grinding quality is achieved on the surfaces of the GBEM cutter. The concept of oblique equidistant surfaces is applied to produce a family of cutters of similar shapes with an accuracy corresponding to a user-specified allowable tolerance. One numerical example is presented to illustrate the usefulness and effectiveness of the proposed modelling methodology. Numerical results indicate that the proposed manufacturing model and grinding procedure are capable of producing a family of GBEM cutters accurate to a specified tolerance.     

THE GEOMETRY, SPECIFICATION AND PREDICTIVE FORCE MODELS FOR PLANE FACED BALL-END MILLING CUTTERS AND OPERATIONS

In this paper the geometry and specification of ball-end milling cutters are studied and discussed followed by an outline of the development of computer-aided predictive models for the three force components, torque and power in plane faced ball-end milling operations, based on the 'Unified-Generalised Mechanics of Cutting Approach'. The models allow for six milling modes, namely; slotting, 'on-centre' end-milling and 'off-centre' end-milling, each machining at the cutter ball-end cutting edge only or at the cutter ball-end and cylindrical periphery cutting edges for two or more flute cutters. The models include all the tool and cut geometrical variables and the cutting speed as well as the tool-workpiece material combination (via the database of basic cutting quantities). The models are verified through extensive numerical simulation studies and a comprehensive experimental testing programme. Good qualitative and quantitative correlation has been found between predicted and measured fluctuating and average force components and torque.     

Cutter workpiece engagement region and surface topography prediction in five-axis ball-end milling

Based on the machining tool path and the true trajectory equation of the cutting edge relative to the workpiece, the engagement region between the cutter and workpiece is analyzed and a new model is developed for the numerical simulation of the machined surface topography in a multiaxis ball-end milling process. The influence of machining parameters such as the feed per tooth, the radial depth of cut, the angle orientation tool, the cutter runout, and the tool deflection upon the topography are taken into account in the model. Based on the cutter workpiece engagement, the cutting force model is established. The tool deflections are extracted and used in the surface topography model for simulation. The predicted force profiles were compared to the measured ones. A reasonable agreement between the experimental and the predicted results was found.     

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.     

Research on grinding staggered teeth on ball-end rotary burr

Staggered teeth type rotary burr is a new cutter with a special rotary surface. Since branch cutting edges are interlaced with main cutting edges on the sphere of the rotary burr and only main cutting edges pass by the zenith of the ball, it greatly widens the chip flutes and improves machining properties of cutter teeth nearby the zenith. The machining properties of staggered teeth type rotary burr are better than general ball-end rotary burr’s. Although it is widely used, the research of rotary burr with staggered teeth is not great. In this paper, firstly the helical cutting edge equations on sphere are built. Then, based on the geometry model of helical cutting edge, a helical stagger teeth design is presented and theory of grinding helical grooves of staggered teeth is studied in detail. The smooth spiral rake surface and flank surface can be formed during one-pass grinding process by this method. At last, the validity of the theory given in the paper is identified by example of grinding.