A manufacturing model of an end mill using a five-axis CNC grinding machine

This paper presents a manufacturing model of a flat-end mill using a five-axis computer numerical control (CNC) grinding machine. The profile of the helical groove can be precisely calculated using a given wheel profile and the relative movements between the workpiece and the grinding wheel. The results of the calculation of the numerical control (NC) data for all the grinding processes of the end mill are fully presented in the paper. The NC data for the machining end mill were generated from the developed program by using the given design parameters of tool geometry, wheel geometry, wheel setting, and machine setting. The effects of the design and manufacturing of the end mill were analyzed based on the computer simulation and experiment results. This study provides a practical and efficient model for the manufacturing of an end mill using a CNC grinding machine with simple programming techniques. The prediction of the end mill geometry for the designing of the proper configuration of the end mill before manufacturing and generating the NC code for machining in a CNC machine is necessary to save time and to reduce the manufacturing cost.     

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...     

A novel CNC grinding method for the rake face of a taper ball-end mill with a CBN spherical grinding wheel

A novel method using a CBN spherical grinding wheel to grind the rake face of a taper ball-end mill and the configuration of corresponding CNC tool grinder are presented. This method utilizes the self-adaptation characteristics of a sphere to decrease the number of simultaneous cooperative axes of a CNC tool grinder and to smooth the rake face on the transition area between the taper and the ball-end of the mill. In order to obtain an accurate normal rake angle, which is one of the key factors affecting tool cutting performance, a moving coordinate system based on the required normal rake angle and the cutting edge was established. Then, by the proposed moving coordinate system, an algorithm to determine the position and orientation of a spherical grinding wheel, the basis of CNC code generation, is proposed and the relevant formulations are deduced. The 3D simulation of rake face grinding for a taper ball-end mill with constant helical angle indicates that the number of simultaneous cooperative axes of the CNC tool grinder is decreased from five to four and the smooth transition of the rake face is realized by the proposed method herein.     

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.     

Kinematic simulation of the uncut chip thickness and surface finish using a reduced set of 3D grinding wheel measurements

This paper combined experimentally-measured grinding wheel topography data taken around the entire circumference of the grinding wheel with a kinematic simulation of the grinding process. Several new methods were developed in order to create the resulting high-fidelity and computationally-efficient simulation. First a novel peak-removal technique was developed and applied to effectively remove erroneous peaks in the raw wheel topography data. Next a method was found to determine only the active cutting points on the wheel model by considering the kinematics of the grinding process. This new approach was able to reduce the simulation time from over twelve hours to about four seconds without losing any information about the cutting edge–workpiece interaction. The resulting predicted workpiece surface was then experimentally validated by carrying out a grinding experiment using the same grinding wheel used to develop the grinding wheel computer model and then measuring the resulting workpiece surface profile. Good agreement between simulated and experimental workpiece profiles was observed. Finally, the validated simulator was used to develop a kinematically-exact method to calculate the maximum uncut chip thickness and the simulation results were investigated for different depths of cut, wheel speeds and workpiece feeds.     

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.     

<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.     

Characteristics of Inclined Planes According to the Variations of Cutting Direction in High-Speed Ball-End Milling

The recent developments of the manufacturing industry require the machining of freeform surfaces using a ball-end mill. The ball-end mill is geometrically complex. For this reason, there are frequent changes of the contact point between a workpiece and a tool, which changes the machining characteristics when machining a freeform surface. In this study, a comparative evaluation of cutting characteristics will be made for a workpiece with inclined planes at angles of 15°,30°, and 45° each using four possible tool paths in down cutting. Then, tool life will be evaluated for heat-treatment materials of high hardness before obtaining the optimal tool path, which makes machining stable and improves tool life.     

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.     

Simulation and assessment of diamond mill grinding wheel topography

The topography of grinding wheel has a remarkable effect on grinding process. In this paper, the topographies of two mill grinding wheels with different grain sizes were measured by using an Olympus confocal scanning laser microscope. Kolmogorov–Smirnov normality tests were carried out to obtain distribution characteristics of abrasive grains. The test results indicate that the surface of grind wheel is of non-Gaussian nature. Consequently, a non-Gaussian statistical model was proposed to simulate the mill grinding wheel topography. Simultaneously, some parameters of “Birmingham 14” were introduced to assess the grinding wheel surface quantitatively. Simulated profile of the grinding wheel is found to correspond well in appearance with that of the actual grinding wheel.     

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.     

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。     

Some observations on profile wear in creep-feed grinding

Tests were performed to investigate the effect of various parameters on the wear of a profiled grinding wheel when creep-feed grinding a nickel-base alloy. The wear of a number of different radii, angles and profile heights was monitored. It was found that this wear was strongly influenced by the total distance travelled by an individual grit while in contact with the workpiece and by the workpiece feed rate. In addition, using a neat oil grinding fluid resulted in less wear than a water-based fluid and a 120 grit wheel wore less than a 60–80 grit wheel. A simple theoretical model was developed for predicting the effect of stock removal rate on profile wear in the creep-feed grinding of a “difficult-to-grind” material and this gave good correlation with the experimental trends.     

Workpiece roundness profile in the frequency domain: an application in cylindrical plunge grinding

In grinding, most control strategies are based on the spindle power measurement, but recently, acoustic emission has been widely used for wheel wear and gap elimination. This paper explores a potential use of acoustic emission (AE) to detect workpiece lobes. This was achieved by sectioning and analysing the AE signal in the frequency domain. For the first time, the profile of the ground workpiece was predicted mathematically using key frequencies extracted from the AE signals. The results were validated against actual workpiece profile measurements. The relative shift of the wave formed on the surface of the part was expressed using the wheel-workpiece frequency ratio. A comparative study showed that the workpiece roundness profile could be monitored in the frequency domain using the AE signal during grinding.     

Reduced models of grinding wheel topography and material removal to simulate dynamical aspects in grinding

Increasing competition and short product life cycles make it necessary to optimize and evaluate the outcome of manufacturing processes. In tool grinding, models for the final workpiece geometry and cutting forces are of particular interest. To establish a valid general grinding model, we investigated the cutting process and the influence of local grinding wheel engagements on the material removal. We consequently developed models of material removal and grinding wheel topography, which capture the main correlations in grinding. In combination, temporal cutting forces and final workpiece geometry are predictable and are in excellent agreement with experimental data. The introduced models are valid for grinding in general, since they are solely based on the geometry and process parameters, and hence are applicable for manufacturing process optimization.     

Study of grinding tool profiling for robotic processes

In the fabrication and maintenance of hydroelectric turbines, the reconstruction by grinding of certain high-curvature surfaces such as junctions has not yet been robotized and must now be done manually. The problem is related to the very fast grinding wheel wear and the difficulty in controlling the position and orientation of the robot's grinder to adjust to changes in wheel shape. If the grinding wheel orientation is kept constant with respect to the workpiece, wheel-workpiece conformity increases, specific energy increases, the material removal rate drops and glazing of the wheel may occur. This article presents a method for controlling simultaneously the profile of both the workpiece and the grinding wheel. The orientation of the wheel is oscillated to maintain a constant wheel profile throughout its life and thus achieve better control in material removal. Research results provide the basis for robotic grinding tool profiling.     

CBN球面砂轮数控磨削复杂形状刀具

提出一种新的磨削加工工艺,即采用CBN球面砂轮数控磨削复杂形状刀具,利用球面的自适应性,以减少所需CNC磨床联动轴数,并实现球头铣刀不同形状刀体接合处前刀面的光滑过渡。同时,新工艺为新型的复杂曲面CNC磨削工艺系统的开发提供理论参考。在以AutoCAD2006为基础构建的磨削仿真加工平台上,以典型的圆锥球头立铣刀前刀面的磨削加工为例,验证了该方法在减少机床联动轴数以及实现前刀面光滑过渡问题中的可行性和有效性。     

基于传热反算建立磨削三维热模型的新方法

首先使用热电偶测量平面磨削时CBN砂轮与工件接触区下方处不同位置点温度;然后基于传热反问题理论,优化实际测量温度值与理论仿真温度值间的目标函数,反算出进入工件的热量,从而得出进入工件的能量比例;最后建立磨削三维热模型,计算出不同磨削时刻工件表面温度。实验结果表明,CBN砂轮进入工件的能量比例与实际值相吻合,基于传热反算方法建立磨削三维热模型具有可行性。     

Fabrication of small aspheric moulds using single point inclined axis grinding

Single point inclined axis grinding techniques, including the wheel setting, wheel–workpiece interference, error source determination and compensation approaches, were studied to fabricate small aspheric moulds of high profile accuracy. The interference of a cylindrical grinding wheel with the workpiece was analysed and the criteria for selection of wheel geometry for avoiding the interference was proposed. The grinding process was performed with compensation focused on two major error sources, wheel setting error and wheel wear. The grinding results showed that the compensation approach was efficient and the developed grinding process was capable to generate small aspheric concave surfaces on tungsten carbide material with a profile error of smaller than 200 nm in PV value after two to three compensation cycles.     

Form-truing error compensation of diamond grinding wheel in CNC envelope grinding of free-form surface

In computer numerical control (CNC) grinding of free-form surface, an ideal arc profile of trued diamond grinding wheel is generally employed to plan 3D tool paths, whereas its form-truing errors greatly influence the ground form accuracy. A form-truing error compensation approach is proposed by using an approached wheel arc profile to replace the previously designed ideal one. The objective is to directly compensate the trued wheel arc-profile errors. It may avoid the time consumption of traditional approach that compensates the measured coordinate point errors of workpiece to an iterative grinding operation. First, the 3D tool path surface was constructed to plan the 3D tool paths. Second, the CNC arc truing of grinding wheel was conducted to analyze the form-truing error distribution relative to the applied wheel arc profile. Then, the form-truing error compensation was carried out in CNC envelope grinding. Finally, the iterative closest point (ICP) algorithm was used to match the measured coordinate points of workpiece to ideal free-form surface. It is shown that the 3D tool path surface constructed is practicable to plan arbitrary 3D tool paths for the form-truing error compensation. The ICP matching may be used to investigate 3D ground form error distribution. It is confirmed that the form-truing error compensation can directly improve the 3D ground form accuracy. It may decrease the 3D ground form error by about 20% when the 2D form-truing error is reduced by about 58% using the same truing conditions for CNC grinding.