A SIMPLIFIED SOLUTION FOR THE DEPTH OF CUT IN MULTI-PATH BALL END MILLING

Abstract

The axial depth of cut is an important factor in the dynamic cutting force analysis of milling. In multi-path ball end milling, it varies with the cutting edge position angle. General equations are derived from which the instant depth of cut in ball end milling can be calculated. Examples are given for four path increment modes. The cutting condition in each mode is discussed with respect to the depth of cut. The conditions needed to disengage the tip of the ball end mill from the cut are determined. The "step-up" increment mode has the most favorable cutting condition for cutter tip relief and high cutting velocity. In order to obtain an instant evaluation of the cutting stability, the equations of maximum depth of cut in ball end milling are derived. The exact solutions are obtained from the general equations for the instant depth of cut. More conservative estimates are obtained from the simplified solutions. The results in this paper can be used as a guide in NC part programming to select an optimal cutting strategy and to ensure a stable cutting process in ball end milling.     

球头铣刀高速铣削Cr12模具钢的振动特性分析

利用球头铣刀高速铣削Cr12模具钢,研究了切削速度、进给量和切削深度对主轴和刀具切削振动的影响变化规律,结果表明随着切削速度的增加,工件振动增加缓慢,而主轴的振动迅速增加,远超过工件的振动成为主振动,主轴进给方向的振动要小于非进给方向的振动。在小进给时,随着进给速度增加各向切削振动而迅速下降,在大进给速度时,各向振动随进给速度增加保持平稳;各通道的切削振动都随着切削深度的增大而增长,因此在高速铣削过程中,主轴振动为主振动,是影响加工表面质量的主要因素。     

Research of production times and cutting of the spur gears by end mill in CNC milling machine

In the current study, differently from the conventional manufacturing methods, cutting of spur gear by the end mill in the computer numerically controlled (CNC) vertical milling machine was purposed. For this aim, two different approaches, radial and axial cutting methods, were introduced. However, the cutting process is performed by use of only the radial cutting method. Parametric equations of tool paths for cutting the spur gear were derived. Regarding those equations, by using the macro-program of the Dyna 2009 Myte type CNC milling machine, a CAM program is developed. By varying the parameters in the tool paths such as module, number of teeth, face width of the spur gear, cutting depth, and cutting angle, spur gear was cut and the production time was obtained. Furthermore, the dimensions of new manufactured spur gear were measured by gear tooth vernies. The dimensions were also calculated by using mathematical expressions and it was concluded that the measured values are well agreeable with the calculated values. It was observed that the production time increases with increasing the module value or number of teeth and decreasing the cutting angle or the cutting depth.     

球头铣刀高速铣削淬硬Cr12模具钢的研究

通过球头铣刀高速铣削Cr12淬硬模具钢的实验,研究了切削用量对切削力和表面粗糙度的影响变化规律,并分析了产生这些变化的原因。研究结果表明：在球头铣刀高速铣削Cr12淬硬模具钢时,轴向力远远大于径向力,为主切削力;随着切削速度的增加,切削力和表面粗糙度值虽然呈现下降的趋势,但下降趋势不如普通切削时明显;切削力和表面粗糙度值随进给速度的增加而增加;当轴向切深在较小的范围内,切削力和表面粗糙度值随轴向切深增加而变化很小,只有当轴向切深超过一定值以后,切削力和表面粗糙度值才随轴向切深增加而迅速增加。     

Development of an automatic arc welding system using SMAW process

In end milling of pockets, variable radial depth of cut is generally encountered as the end mill enters and exits the corner, which has a significant influence on the cutting forces and further affects the contour accuracy of the milled pockets. This paper proposes an approach for predicting the cutting forces in end milling of pockets. A mathematical model is presented to describe the geometric relationship between an end mill and the corner profile. The milling process of corners is discretized into a series of steady-state cutting processes, each with different radial depth of cut determined by the instantaneous position of the end mill relative to the workpiece. For the cutting force prediction, an analytical model of cutting forces for the steady-state machining conditions is introduced for each segmented process with given radial depth of cut. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpiece material properties, as well as the relative position of the tool to workpiece. Experiments of pocket milling are conducted for the verification of the proposed method.     

A composite fitting model of discrete handbook data for peripheral end milling

Machining data handbooks are important reference books in the machining industry, as they provide recommended process parameter values for common machining operations. The machining data, although covering a wide range of relevant cutting conditions, are only listed under discrete cutting conditions. Rough interpolation-based calculations are often needed in order to estimate the process parameter values at the desired cutting condition. In this work, a composite fitting model is presented to fit a composite functional curve through the discrete handbook data of recommended cutting speeds and feeds with respect to the cutting condition of radial depth of cut for peripheral end milling. The objective is to establish a functional relationship from the handbook data such that recommended cutting speed and feed can be obtained for any given radial depth of cut. According to the tabulated layout of the machining data, the entire range of the radial depth of cut is divided into three segments having distinctive formulations and trends. Constraints are then imposed to preserve the trends and smoothly connect the adjacent segments. As a possible application of the presented model, a case study of machining a rectangular pocket is provided. Machining time of a potential process plan is readily evaluated based on the cutting speeds and feeds obtained from the composite model.     

Influence of milling strategy on the surface roughness in ball end milling of the aluminum alloy Al7075-T6

Surface roughness has an important role in the performance of finished components. End ball milling is used for achieving high surface quality, especially in complex geometries. Depending on the cutting conditions selected for ball end milling, different milling strategies can be applied. The produced surface quality is greatly affected from the selected milling strategy. The present paper examines the influence of the milling strategy selection on the surface roughness of an Al7075-T6 alloy. A number of cutting parameters are tested (axial and radial depth of cut, feed rate, inclination angles φ and ω) in order to perform 96 experiments and their results are processed using regression analysis and analysis of variance. All possible milling strategies are considered (vertical, push, pull, oblique, oblique push and oblique pull) and for each one of them, a mathematical model of the surface roughness is established, considering both the down and up milling. All models are statistically validated and experimentally verified, and can be used within the limits of the investigating cutting conditions. The polynomials produced are of the third order and the statistically most significant parameters are presented.     

Optimization of cutting conditions for minimum residual stress,cutting force and surface roughness in end milling of S50C medium carbon steel

Residual stresses are usually imposed on a machined component due to thermal and mechanical loading. Tensile residual stresses are detrimental as it could shorten the fatigue life of the component; meanwhile, compressive residual stresses are beneficial as it could prolong the fatigue life. Thermal and mechanical loading significantly affect the behavior of residual stress. Therefore, this research focused on the effects of lubricant and milling mode during end milling of S50C medium carbon steel. Numerical factors, namely, spindle speed, feed rate and depth of cut and categorical factors, namely, lubrication and milling mode is optimized using D-optimal experimentation. Mathematical model is developed for the prediction of residual stress, cutting force and surface roughness based on response surface methodology (RSM). Results show that minimum residual stress and cutting force can be achieved during up milling, by adopting the MQL-SiO₂ nanolubrication system. Meanwhile, during down milling minimum residual stress and cutting force can be achieved with flood cutting. Moreover, minimum surface roughness can be attained during flood cutting in both up and down milling. The response surface plots indicate that the effect of spindle speed and feed rate is less significant at low depth of cut but this effect significantly increases the residual stress, cutting force and surface roughness as the depth of cut increases.     

球头铣刀切削力计算机预报模型的数值仿真

借助建立的铣刀切削力、扭矩和切削功率的计算机预报模型 ,对平前刀面球头铣刀的切削性能进行了数值仿真研究 ;通过分析各种切削参数对切削性能的影响规律 ,获得了不同切削条件下球头铣刀切削力和扭矩的特征和变化趋势     

Geometry of chip formation in circular end milling

Machining along continuous circular tool-path trajectories avoids tool stoppage and even feed rate variation. This helps particularly in high-speed milling by reducing the effect of the machine tool mechanical structure and cutting process dynamics. With the increase in popularity of this machining concept, the need for detailed study of a valid chip formation in circular end milling is becoming necessary for accurate kinematic and dynamic modeling of the cutting process. In this paper, chip formation during circular end milling is studied with a major focus on feed per tooth and undeformed chip thickness along with their analytical derivations and numerical solutions. At first, the difference in the feed per tooth formulation for end milling along linear and circular tool-path trajectories is presented. In the next step, valid formulation of the undeformed chip thickness in circular end milling is derived by considering an epitrochoidal tooth trajectory with a wide range of the tool-path radius. The complex transcendental equations encountered in the derivation are dealt with, by a case-based approach to obtain closed-form analytical solutions. The analytical solutions of undeformed chip thickness are validated with results of numerical simulations of tool and tooth trajectories for circular end milling and also compared to the linear end milling. The close resemblance between analytical and numerical calculations of the undeformed chip thickness in circular end milling suggests validity of the proposed analytical formulations. As a case study, the cutting forces in circular end milling are calculated based on the derived chip thickness formulations and an existing mechanistic model. The calculation results reiterate the need of taking into account adjusted feed per tooth and valid chip thickness formulations in circular end milling, especially for small tool-path radii, for more realistic process modeling.     

The optimal cutting-parameter selection of heavy cutting process in side milling for SUS304 stainless steel

This paper presents an optimal cutting-parameter design of heavy cutting in side milling for SUS304 stainless steel. The orthogonal array with grey-fuzzy logics isapplied to optimize the side milling process with multiple performance characteristics. A grey-fuzzy reasoning grade obtained from the grey-fuzzylogics analysis is used as a performance index to determine the optimal cutting parameters. The selected cutting parameters are spindle speed, feed per tooth,axial depth of cut and radial depth of cut, while the considered performance characteristics are tool life and metal removal rate. The results ofconfirmation experiments reveal that grey-fuzzy logics can effectively acquire an optimal combination of the cutting parameters. Hence, performance in theside milling process for heavy cutting can be significantly improved through this approach.     

EFFECT OF PROCESS PARAMETERS AND TOOL SHAPE ON THE MACHINABILITY OF A PARTICULATE FILLED-POLYMER COMPOSITE MATERIAL FOR RAPID TOOLING

This paper presents the results of an experimental study on the effects of machining parameters (cutting speed, feed, depth of cut) and tool shape on chip formation, surface topography, resultant cutting force and surface roughness produced in flat and ball end milling of the Ren Shape-Express 2000™ aluminum particulate filled-polymer composite material. This material is shown to exhibit a brittle-to-ductile transition in chip formation with decreasing cutting speed. The transition is explained by the strain-rate sensitivity of the polymer matrix and is found to correlate well with a corresponding change in the surface roughness. The absence of clear feed marks on the milled surface explains why molds made from the composite material require less hand polishing than machined metal molds. The influence of cutting conditions and tool shape (flat end vs. ball-nose) on the cutting force, surface roughness, and workpiece breakout are discussed and relevant comparisons with conventional metal and polymer machining are made.     

模具钢Cr12MoV硬态铣削过程切削力的研究

切削力是铣削机理研究的重要对象,与刀具磨损和已加工表面质量等指标关系密切。本文通过软件ThirdWave建立了球头铣刀高速铣削模具钢Cr12MoV的仿真模型。该模型采用了网格自适应技术和删除技术。成功实现了切削力的高精度仿真,并对仿真模型进行了实验验证。模型分析了切入切出过程切削力的变化特性,同时也揭示了切削条件对切削力变化的影响规律。本研究成果可对切削工艺条件的合理选择提供借鉴。     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

Three-dimensional stability lobe and maximum material removal rate in end milling of thin-walled plate

Chatter phenomenon often occurs during end milling of thin-walled plate and becomes a common limitation to achieve high productivity and part quality. For the purpose of chatter avoidance, the optimal selection of the axial and radial depth of cut, which are decisive primary parameters in the maximum material removal rate, is required. This paper studies the machining stability in milling of the thin-walled plate and develops a three-dimensional lobe diagram of the spindle speed, axial, and radial depth of cut. Through the three-dimensional lobe, it is possible to choose the appropriate cutting parameters according to the dynamic behavior of the chatter system. Moreover, this paper studies the maximum material removal rate at the condition of optimal pairs of the axial and radial depth of cutting.     

An experimental investigation on micro machining of fine-grained graphite

Industrial applications of the micro milling process require sufficient experimental data from various micro tools. Research has been carried out on micro milling of various engineering materials in the past two decades. However, there is no report in the literature on micro milling of graphite. This paper presents an experimental investigation on micro machinability of micro milling of moulded fine-grained graphite. Full immersion slot milling was conducted using diamond-coated, TiAlN-coated and uncoated tungsten carbide micro end mills with a uniform tool diameter of 0.5 mm. The experiments were carried out on a standard industrial precision machining centre with a high-speed micro machining spindle. Design of experiments (DoE) techniques were applied to design and analysis of the machining process. Surface roughness, surface topography and burrs formation under varying machining conditions were characterized using white light interferometry, SEM and a precision surface profiler. Influence of variation of cutting parameters including cutting speeds, feedrate and axial depth of cut on surface roughness and surface damage was analysed using ANOVA method. The experimental results show that feedrate has the most significant influence on surface roughness for all types of tools, and diamond tools are not sensitive to cutting speed and depth of cut. Surface damage and burrs analysis show that the primary material removal mode is still brittle fracture or partial ductile in the experimental cutting conditions. 3D intricate micro EDM electrodes were fabricated with good dimensional accuracy and surface finishes using optimized machining conditions to demonstrate that micro milling is an ideal process for graphite machining.     

A 3D Predictive Cutting-Force Model for End Milling of Parts Having Sculptured Surfaces

A comprehensive, 3D mathematical model of desired/optimal cutting force for end milling of freeform surfaces is proposed in this paper. A closed-form predictive model is developed, based on a perceptive cutting approach, resulting in a cutting force model having a comprehensive set of essential cutting parameters. In particular, the normal rake angle, usually missing in most existing models of the same sort, is included in the developed model. The model also permits quantitative analyses of the effect of any parameters on the cutting performance of the tool, providing a guideline to improving the tool performance. Since the axial depth of cut varies with time when milling sculptured surface parts, an innovative axial depth of cut estimation scheme is proposed for the generation of 3D cutting forces. This estimation scheme improves on the practicality of most existing predictive cutting-force models for milling, in which the major attention has been focused on planar milling surface generation. In addition, the proposed model takes the rake surface on the flute of mills as an osculating plane to yield 3D cutting force expressions in only two steps. This approach greatly reduces the time-consuming mathematical work normally required for obtaining the cutting-force expressions. A series of milling simulations for machining freeform parts under specific cutting conditions have been performed to verify the effectiveness of the proposed cutting-force model. The simulation results demonstrate the accurate estimating capability of the proposed method for axial depth of cut estimation. The cutting force responses from the simulation exhibit the same trends as can be obtained using the empirical mechanic’s model referenced in the literature. Finally, from the simulation results it is also shown that designing a tool with a combination of different helix angles, having cutting force signatures similar to those of the single helix angle counterparts, is particularly advantageous.     

高速铣削时铣削力的研究

基于数控机床动力学测试分析和仿真系统,求得加工时的切削稳定域,确定加工参数的范围。在其它参数不变的情况下,通过对求得的切削力和功率的分析,得到转速高的铣削力相对较小,刀具螺旋角对铣削力的影响较小,切宽与铣削力不呈线性关系,切深与铣削力呈线性关系。文中对高速加工参数的选择有一定的指导意义。     

Off-line nominal path generation of 6-DoF robotic manipulator for edge finishing and inspection processes

Due to some special properties, alloy cast iron HTCuCrSn-250 is widely used to manufacture the cylinder block of the diesel engines. However, the additional alloying elements aggravated tool wear which is significantly affected by cutting parameters during machining process. In this paper, tool wear in face milling of alloy cast iron under constant material removal volume (MRV) condition was investigated. First, the relationship between tool flank wear (VB) and MRV was determined. Secondly, the wear morphology and mechanism were analyzed and a predicted model between cutting parameters and tool wear was proposed. Finally, the optimization was taken, and three groups of optimal parameters were obtained. This research illustrated that different combinations of cutting parameters result in different wear morphology and the main wear mechanisms are diffusion and oxidation. This research also indicated the two parameters, axial depth of cut and the radial depth of cut, which have significant impact on the tool wear. Meanwhile, a model between VB and the cutting parameters under the constant MRV condition during milling HTCuCrSn-250 was proposed.