Mechanics and dynamics of general milling cutters.: Part I: helical end mills

A variety of helical end mill geometry is used in the industry. Helical cylindrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining industry. While the geometry of each cutter may be different, the mechanics and dynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills used in the industry. The end mill geometry is modeled by helical flutes wrapped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip thickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. The predicted and measured cutting forces, surface roughness and stability lobes for ball, helical tapered ball, and bull nosed end mills are provided to illustrate the viability of the proposed generalized end mill analysis.     

Design of hob cutters for generating helical cutting tools with multi-cutting angles

This paper studies the design of hob cutters for generating the multi-cutting angles (radial rake angle, relief angle, and clearance angle) of helical cutting tools in one hobbing process. The current manufacturing process can be greatly improved if the cutting edges in the normal section profile, the rack profile, of a hob cutter are designed with several cutting edges with different pressure angles, so that the helical cutting tools with multi-cutting angles can be formed in one generating process. This paper, therefore, designs a rack profile of a hob cutter consisting of three straight cutting edges with different pressure angles and a curved cutting edge. By applying the equations of designed rack profiles of hob cutters, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing, the mathematical models of the helical cutting tool can be derived. In addition, the formulas for the radial cutting angle, relief angle, and clearance angle can be derived. Meanwhile, solid modelling of the helical cutting tool can be carried out with computer graphics programming. The results of this paper will contribute to the improvement of the design technology of hob cutters, to enhance the manufacturing processes of helical cutting tools, and to assist tool-related industries in upgrading their technology and competitive abilities.     

Estimation of the rotational speed limit of milling cutters with screwed indexable inserts

During the process of high speed cutting (HSC), fast rotating milling cutters are subject to much higher centrifugal forces than cutting forces. This fundamental factor requires to take into account more stringent safety considerations when working on the concept and design of HSC tools. This paper focuses on the operational safety and speed limit of commonly used HSC milling head cutters with indexable inserts being clamped by high-strength countersunk head screws. The spin burst test results of those tools with radial and tangential insert connections are summarized. The analytical formulas to estimate the failure speeds of both insert connections are developed and discussed based on theoretical analysis on insert connection mechanism. Calculation results show a good correlation with the experimental results from spin burst tests. Finally, a new analytical-empirical approach to determine the speed limits and maximum permissible rotational speeds of both types of tools based on a high confidence level is presented. The approach proposed is suggested for a reliable estimate of the speed limits and maximum permissible rotational speeds for fast rotating tools with screwed radial or tangential indexable inserts.     

Feedrate scheduling for indexable end milling process based on an improved cutting force model

In CNC machining, an optimal process plan is needed for higher productivity and machining performance. This paper proposes a mechanistic cutting force model to perform feedrate scheduling that is useful in process planning for indexable end milling. Indexable end mills, which consist of inserts and a cutter body, have been widely used in the roughing of parts in the mold industry. The geometry and distribution of inserts compose a discontinuous cutting edge on the cutter body, and tool geometry of indexable end mill varies with axial position due to the geometry and distribution of inserts. Thus, an algorithm that calculates tool geometry data at an arbitrary axial position was developed. The developed cutting force model uses cutting-condition-independent cutting force coefficients and considers run out, cutter deflection, geometry variation and size effect for accurate cutting force prediction. Through feedrate scheduling, NC code is optimized to regulate cutting forces at given reference force. Experiments with general NC codes show the effectiveness of feedrate scheduling in process planning.     

A novel hob cutter design for the manufacture of spur-typed cutters

Spur-typed cutters with multiple cutting angles are important tools frequently used in the manufacture of many machine elements. Due to their complex geometry, the production of these cutters involves milling and several grinding processes. Such a complex manufacturing process, coupled with the need for expensive manufacturing tools, makes the cutters costly.Undercutting is a phenomenon that causes weakness at the root of a gear. Engineers use shifted gears, modified tooth profiles, or changes in the pressure angle to overcome undercutting in gears. However, in this paper, by utilizing the undercutting phenomenon, a novel design of straight-sided hob cutter with multiple pressure angles is proposed for the manufacture of spur-typed cutters. With the simultaneous application of multiple pressure angles, this tool design concept significantly simplifies the manufacturing process. The effects of cutting angles, the degree of undercutting, and the width of the top land of the cutter are studied. The concepts and results proposed in this paper are beneficial as design guidance for tool designers and manufacturers.     

Neural image processing of the wear of cutting tools coated with thin films

Small milling cutters are susceptible to very small changes in geometry on the surface of the cutting edge that are substantial when machining at the microscale. The purpose of this paper is to show how to design a neural image processing program to accurately determine the amount of wear accumulated on small milling cutters after successive machining operations. After determining the amount of wear on a small milling cutter, the program creates the appropriate amount of compensation to be used for a computer numerical control (CNC) machining program that will account for in-process tool wear. This paper was presented at the fourth International Surface Engineering Congress and Exposition held August 1–3, 2005 in St. Paul, MN.     

Ultimate capability of variable pitch milling cutters

Variable pitch milling cutters intend to increase performance, but off-the-shelf cutters do not ensure this generally. Depending on the milling process they are selected for, they can perform better or even worse than uniform pitch cutters do. Improved performance can be guaranteed by considering the reflected dynamic behaviour of the machine/tool/workpiece system. This work presents the achievable upper and lower capability bounds by introducing so-called stabilizability diagrams of a hypothetical variable pitch milling cutter that is tuned continuously along the stability boundaries. Robustly tuned milling cutters are designed for selected spindle speed ranges, which are experimentally tested both under laboratory and industrial conditions.     

Time domain model of plunge milling operation

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of spindle axis which has the highest structural rigidity. This paper presents time domain modeling of mechanics and dynamics of plunge milling process. The cutter is assumed to be flexible in lateral, axial, and torsional directions. The rigid body feed motion of the cutter and structural vibrations of the tool are combined to evaluate time varying dynamic chip load distribution along the cutting edge. The cutting forces in lateral and axial directions and torque are predicted by considering the feed, radial engagement, tool geometry, spindle speed, and the regeneration of the chip load due to vibrations. The mathematical model is experimentally validated by comparing simulated forces and vibrations against measurements collected from plunge milling tests. The study shows that the lateral forces and vibrations exist only if the inserts are not symmetric, and the primary source of chatter is the torsional–axial vibrations of the plunge mill. The chatter vibrations can be reduced by increasing the torsional stiffness with strengthened flute cavities.     

磨削印刷线路板铣刀时的锯齿现象及其消除

本文针对金刚石砂轮磨削印刷线路板(PCB)铣刀过程中铣刀切削刃产生的锯齿现象进行了分析,研究了砂轮粒度、砂轮转速以及切沟速度对铣刀切削刃锯齿的影响.研究结果表明,随着砂轮粒度的减小,切削刃质量得到提高,砂轮转速和切沟速度对切削刃质量都有影响,其中砂轮粒度对切削刃质量的影响最为重要.     

新型Ta-C涂层铣刀切削性能研究

目的研究Ta-C涂层刀具与普通类金刚石涂层刀具切削2A50铝合金时的性能对比。方法通过实验比较两刃、四刃Ta-C涂层铣刀和两刃、四刃普通类金刚石涂层铣刀,在干式切削条件下切削2A50铝合金的性能。通过相同切削条件下刀具切削距离的长短,比较刀具的使用寿命,并在显微镜下观察切屑的表面形貌,用表面粗糙度仪检测铝合金表面的粗糙度。结果两刃Ta-C涂层铣刀干式切削铝合金时的使用寿命最长,切削距离为116 m。Ta-C涂层铣刀与普通类金刚石涂层铣刀加工工件的表面粗糙度总体呈上升趋势,两刃Ta-C涂层铣刀加工出来的工件表面质量较好,工件表面粗糙度均值为0.692μm。结论相同刀刃数量且结合力良好的涂层铣刀相比较,Ta-C涂层铣刀较普通类金刚石涂层铣刀加工出来的工件表面粗糙度平均值低,同种涂层加工得到的切屑表面微观形貌无明显差别。Ta-C涂层铣刀与普通类金刚石涂层铣刀切削铝合金时,抑制粘刀效果都十分明显,但Ta-C涂层铣刀效果更优。     

An improved process simulation system for ball-end milling of sculptured surfaces

A simulation system is developed in this paper, which deals with the geometry and mechanics of machining with ball-end milling cutters. The geometry of the workpiece, the cutter, and the cutter/workpiece engagement is modeled using a geometric simulation system. This module uses a commercial solid modeler (ACIS) as a geometric engine and automatically extracts the critical geometric information required for the physical simulation system. To calculate the instantaneous cutting forces, a new mechanistic force model is developed. This force model takes into account the variations of the cutting coefficients along the cutting edge, and considers the variations of the rake angle and the chip flow direction on the rake face. The calibration of the developed model is performed for half-immersion ball-end milling operation. The applicability of the developed system is verified experimentally for various up-hill angles. It is shown that as the up-hill angle increases, the ball-nose tip engagement decreases which in turn significantly affects the magnitude of the resultant forces. Also, lower cutting forces and powers are experienced if cutting with the vicinity of the tool tip is avoided.     

Optimum orientation of a torus milling cutter: Method to balance the transversal cutting force

In this paper, a new method for tool positioning in milling on torus cutters with round inserts is presented. A new criterion associated with balancing of the transversal cutting force is used to compute a tool orientation. The considered tool inclination is towards the back of the tool. In this case, all inserts work simultaneously and generate a continuous cutting phenomenon. Each of the inserts produces a transversal cutting force; some being positive while others are negative. A small tool axis inclination angle leads to balancing the transversal cutting force exerted on the tool and then reducing deflection and vibrations in milling operations. Firstly, this approach to the dynamic aspects relating to cutting forces in the milling process is significant for mould and die manufacturing since it allows polishing time to be reduced. In addition, as vibrations are reduced, enhanced surface quality can be obtained directly on free-form surfaces such as aeronautic fittings.     

Cutting force prediction of sculptured surface ball-end milling using Z-map

The cutting force in ball-end milling of sculptured surfaces is calculated. In sculptured surface machining, a simple method to determine the cutter contact area is necessary since cutting geometry is complicated and cutter contact area changes continuously. In this study, the cutter contact area is determined from the Z-map of the surface geometry and current cutter location. To determine cutting edge element engagement, the cutting edge elements are projected onto the cutter plane normal to the Z-axis and compared with the cutter contact area obtained from the Z-map. Cutting forces acting on the engaged cutting edge elements are calculated using an empirical method. Empirical cutting mechanism parameters are set as functions of cutting edge element position angle in order to consider the cutting action variation along the cutting edge. The relationship between undeformed chip geometry and the cutter feed inclination angle is also analyzed. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged cutting edge elements. A series of experiments were performed to verify the proposed cutting force estimation model. It is shown that the proposed method predicts cutting force effectively for any geometry including sculptured surfaces with cusp marks and a hole.     

机夹式型线铣刀刀片槽检测技术研究

机夹式型线铣刀主要用于核电轮槽加工。为了降本增效,研制该铣刀,刀体可重复利用。刀片槽决定各刀片的位置关系,对铣刀型线起决定性作用,但刀片槽的检测复杂,检测效率低下。在保证检测效率的同时,必需保证检测精度。基于Leitz Reference 600软件在三坐标测量仪上检测刀体刀片槽,研究出高效率测量该刀体刀片槽的方法;针对检测难点进行详细分析,解决了检测瓶颈,大大提高了工作效率。     

Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out

Radial cutter runout is a common issue in milling processes and has a direct effect on milling stability due to variations of resulting chip load and forces. This paper presents a new method to effectively model and predict the instantaneous cutting forces in 5-axis milling processes with radial cutter runout based on tool motion analysis. First, the undeformed chip thickness model taking runout effect into account is established under continuous change of cutter axis orientation by means of the sweep traces of cutter edges. Second, the engaged cutting edge is determined and cutting coefficients are subsequently calibrated. Finally, the method of identifying runout parameters from the measured cutting forces is proposed, and mechanistic method is then applied to predict the cutting force. Since this method is completely based on the relative motion analysis of tool-part, it can reduce the prediction errors of cutting forces effectively and is suitable for generic rotation cutters. Several validation examples are given under different cutting conditions to prove its effectiveness and accuracy. The results reveal that the developed method can predict the cutter forces with a high accuracy and has the ability to be used in simulations and optimizations of five-axis machining.     

Failure modes of PDC cutters under different loads

The capability of several types of flat PDC cutters to withstand combined loads were tested and evaluated by the impact and cutting of single PDC cutter on granite in a linear impact-cutting table.The primary failure modes of PDC cutters withstanding different combined loads were investigated and analyzed.The suggestions of enhancing PDC cutters to be suitable for drilling very hard rock have been made.     

球头铣刀动力学模型及其铣削加工稳定性的研究

根据螺旋刃球头铣刀的几何模型,考虑切削加工时刀齿的有交切削区及再生效应,建立球头铣刀的单刃切削力模型;进行模态实验和参数识别,建立螺旋刃球头铣刀的动力学模型;在Matlab环境下,基于龙格-库塔法对球头铣刀铣削加工过程稳定性进行仿真,结果表明:该模型能很好地描述切削过程中的稳定性及振动等动学特性,对于实际铣削加工过程及实验机的优化设计具有指导意义。     

Process simulation using finite element method — prediction of cutting forces, tool stresses and temperatures in high-speed flat end milling

End milling of die/mold steels is a highly demanding operation because of the temperatures and stresses generated on the cutting tool due to high workpiece hardness. Modeling and simulation of cutting processes have the potential for improving cutting tool designs and selecting optimum conditions, especially in advanced applications such as high-speed milling. The main objective of this study was to develop a methodology for simulating the cutting process in flat end milling operation and predicting chip flow, cutting forces, tool stresses and temperatures using finite element analysis (FEA). As an application, machining of P-20 mold steel at 30 HRC hardness using uncoated carbide tooling was investigated. Using the commercially available software DEFORM-2D™, previously developed flow stress data of the workpiece material and friction at the chip–tool contact at high deformation rates and temperatures were used. A modular representation of undeformed chip geometry was used by utilizing plane strain and axisymmetric workpiece deformation models in order to predict chip formation at the primary and secondary cutting edges of the flat end milling insert. Dry machining experiments for slot milling were conducted using single insert flat end mills with a straight cutting edge (i.e. null helix angle). Comparisons of predicted cutting forces with the measured forces showed reasonable agreement and indicate that the tool stresses and temperatures are also predicted with acceptable accuracy. The highest tool temperatures were predicted at the primary cutting edge of the flat end mill insert regardless of cutting conditions. These temperatures increase wear development at the primary cutting edge. However, the highest tool stresses were predicted at the secondary (around corner radius) cutting edge.     

行星复合铣削及其刀具研究

行星复合铣削方法是复合加工方法的一种实现形式,该加工方法所产生的切削力较普通端铣加工的切削力有大幅度的降低,从而能有效地降低切削热、减少工件变形、提高刀具寿命。行星复合铣削方法切削力大幅度地降低的主要原因是该方法的切削轨迹使其能将厚切削层分解为细小的切削层,而该方法中的立铣刀的螺旋角和半径对实际切削力的影响很小。行星复合铣削方法在刀盘低速旋转时就能实现高速切削,有效地避开了高速旋转刀盘的动平衡问题,结合其切削力小的优势,通过增大刀盘直径并增加立铣刀数量来提高加工效率。行星铣刀采用行星轮系结构,能够达到行星复合铣削方法切削轨迹要求,具有扭矩大、运转可靠等优势。     

Novel methods for rapid assessment of tool performance in milling

The paper examines the effectiveness of two innovative techniques designed to rapidly optimize a milling application. One of them relates to quantifying the relative wear of different insert grades concurrently in a single cutting test, by mounting the inserts in the same cutter, for a quick comparative performance evaluation. Experimental results that illustrate the validity and limitation of this concept, and a scheme for enhancing the reliability of the test method are presented. The other technique refers to rapid identification of the optimum feed/tooth that corresponds to maximum tool life. This entails a test wherein individual inserts in the cutter are subject to feed/tooth that are multiples of a base value, by selectively leaving appropriate number of consecutive insert pockets unoccupied. These novel techniques complement known accelerated tool life tests, and are expedient for industries that engage short production runs, in terms of selecting a suitable insert grade for an application, and determining optimal cutting conditions for the selected grade.