Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

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.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.     

复杂形状工件的端铣切削力模型

以传统的端铣切削力模型为基础，提出了一种新的端铣加工中静态切削力的预报模型。该模型考虑了复杂的工件形状和不同的铣刀进给轨迹。给出了一种新的工件和铣刀接触算法。     

Effects of cutting edge geometry, workpiece hardness, feed rate and cutting speed on surface roughness and forces in finish turning of hardened AISI H13 steel

In this study, the effects of cutting edge geometry, workpiece hardness, feed rate and cutting speed on surface roughness and resultant forces in the finish hard turning of AISI H13 steel were experimentally investigated. Cubic boron nitrite inserts with two distinct edge preparations and through-hardened AISI H13 steel bars were used. Four-factor (hardness, edge geometry, feed rate and cutting speed) two-level fractional experiments were conducted and statistical analysis of variance was performed. During hard turning experiments, three components of tool forces and roughness of the machined surface were measured. This study shows that the effects of workpiece hardness, cutting edge geometry, feed rate and cutting speed on surface roughness are statistically significant. The effects of two-factor interactions of the edge geometry and the workpiece hardness, the edge geometry and the feed rate, and the cutting speed and feed rate also appeared to be important. Especially honed edge geometry and lower workpiece surface hardness resulted in better surface roughness. Cutting-edge geometry, workpiece hardness and cutting speed are found to be affecting force components. The lower workpiece surface hardness and honed edge geometry resulted in lower tangential and radial forces.     

Tool paths and cutting technology in computer-aided process planning

This paper reports on the development of a module to calculate automatically tool paths and cutting conditions for metal cutting operations. Process planning must select correct cutting conditions to minimise disturbances on the shop floor owing to tooling problems. Tool path and cutting condition algorithms to generate reliable NC programs have been designed. The algorithms have been implemented in the framework of a generative computer-aided process planning system, called PART. Geometrical requirements to avoid chipping of cutting teeth are considered in tool-path calculation. The cutting conditions are calculated using metal cutting process models. A method has been developed to calculate cutting forces for milling operations based on experimental data of cutting forces in turning. In the process models, various constraints of the machine tool, cutting tool, and the workpiece are considered.     

Mill-cut: a neural network system for the prediction of thermo-mechanical loads induced in end-milling operations

This paper presents the design and implementation issues of a generalized system called mill-cut, developed for the prediction of cutting forces and temperature in end-milling operations. Based on an ANN approach, mill-cut predicts all the three components of cutting forces and average shear plane temperature for a given set of machining parameters broadly categorized into three groups viz. (i) cutting tool geometrical parameters (ii) cutting parameters and (iii) workpiece material properties. In the present work, for representing overall machining condition, 15 machining parameters having major impact on the cutting forces and cutting temperature were chosen. The feed-forward back-propagated ANN architecture has been incorporated, which was initially trained with analytical data before incorporating it as part of an integrated system. Results obtained from the proposed model show good agreement with the experimental/numerical (FEM based) results available in the literature.     

CALCULATION OF THE SPECIFIC CUTTING COEFFICIENTS AND GEOMETRICAL ASPECTS IN SCULPTURED SURFACE MACHINING

This article presents a method for obtaining the shear and ploughing specific cutting coefficients for a ball-end milling cutting force model. Thus, by using the proposed calculation method, the need for introducing variable shear cutting coefficients has been identified. This fact is due to the dependency among the specific cutting coefficients and the cutting edge inclination angle, which is variable in ball-end mills. Linear, quadratic and cubic polynomial shear cutting coefficients have been calculated, and the degree of adjustment obtained in each approach has been analyzed. At the same time, the expressions of the ploughing specific coefficients have been analyzed. The proposed calculation method has been applied to the following materials: a 7075-T6 aluminum alloy and a 52HRC AISI H13 tool steel. The results obtained from the validation demonstrate how the obtained coefficients are capable of predicting cutting forces over a wide range of cutting conditions. Finally, the results from applying the coefficients calculated in horizontal slot milling tests have been introduced in a model capable of calculating cutting forces in slope milling cases, which validates the calculation method proposed as a generic method for estimation of cutting coefficients.     

Mechanistic modeling of cutting forces in micro-end-milling considering tool run out,minimum chip thickness and tooth overlapping effects

This work proposed an improved mechanistic model for prediction of cutting forces in micro-milling process. The combined influences of tool run out, trochoidal trajectory of the tool center, overlapping of tooth, edge radius and minimum chip thickness are incorporated in this model to realize the exact cutting phenomenon. Moreover, an improved undeformed chip thickness algorithm has been presented by considering tool run out, minimum chip thickness and trajectory of all passing teeth for one complete revolution of the tool instead of only the current tooth trajectory. For estimation of tool run out, a model based on the geometry of the two fluted end mill cutter has been developed. Effects of trochoidal trajectory of the tool center and tool run out are found to be significant as each tooth has a different chip load. Further, the effect of minimum chip thickness is found to be significant at lower feed value. The proposed model has been validated by micro-milling experiments on Ti6Al4V-titanium alloys using uncoated flat end mill cutter. The predicted cutting forces were found to be in good agreement with the experimental cutting forces in both feed and cross feed directions.     

Cutting force formulation of taper end-mills using differential geometry

In this paper, a mechanistic model to formulate the nonlinear three-dimensional (3-D) cutting forces of taper end-mills by means of differential geometry is presented. The relationship between the tool geometry and the cutting force directions is analyzed. A cutting coefficient estimation procedure is developed. The model is verified by milling carbon steel specimens. For a set of given cutting conditions, the results show close agreement between the measured cutting forces and the model predictions.     

高速切削30CrNi3MoV淬硬钢切屑形成机理的试验研究

通过30CrNi3MoV淬硬钢的高速切削试验,观察和测量不同切削条件下切屑形态的演变过程、锯齿状切屑形成的临界切削条件、切削力.结果表明,切削速度和刀具前角是影响切屑形态和切削力的主要因素,随着切削速度的提高,在某一临界切削速度下,切屑形态由带状屑转变为锯齿状切屑,随着刀具前角由正前角逐渐变为负前角,临界切削速度明显减小,当锯齿状切屑形成时,切削力大幅度降低.使用金属切削过程中绝热剪切临界切削条件判据对锯齿状切屑形成临界切削速度预测的结果表明,锯齿状切屑形成的根本原因是主剪切区内发生周期性的绝热剪切断裂.     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.     

An Enhanced Force Model for Sculptured Surface Machining

The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.     

An Enhanced Force Model for Sculptured Surface Machining

Abstract

The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.     

On modeling of cutting forces in micro-end milling operation

Micro-end milling is used for manufacturing of complex miniaturized components precisely in wide range of materials. It is important to predict cutting forces accurately as it plays vital role in controlling tool and workpiece deflections as well as tool wear and breakage. The present study attempts to incorporate process characteristics such as edge radius of cutting tool, effective rake and clearance angles, minimum chip thickness, and elastic recovery of work material collectively while predicting cutting forces using mechanistic model. To incorporate these process characteristics effectively, it is proposed to divide cutting zone into two regions: shearing- and ploughing-dominant regions. The methodology estimates cutting forces in each partitioned zone separately and then combines the same to obtain total cutting force at a given cutter rotation angle. The results of proposed model are validated by performing machining experiments over a wide range of cutting conditions. The paper also highlights the importance of incorporating elastic recovery of work material and effective rake and clearance angle while predicting cutting forces. It has been observed that the proposed methodology predicts the magnitude and profile of cutting forces accurately for micro-end milling operation.     

Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

考虑刃口半径作用时切削力的预报

切削力的理论计算及其准确预报是金属切削领域和刀具设计的重要课题之一。本文给出了考虑刃口半径作用的切削模型 ,分析了临界切削厚度对切削力的影响 ,预报结果表明切削力的理论预测与实验数据相吻合     

A Cutting Force Model for a Waved-Edge End Milling Cutter

This paper presents a model for predicting the cutting forces for waved-edge milling cutters that are widely used in rough machining. The development of the model is based on the analysis of the complicated cutting edge of waved-edge cutter. According to the existing local cutting force model and from the relationship of local cutting force and chip load, local cutting force can be derived. Then the model is obtained by dividing the cutter into a number of differential elements in the axial direction and summarising the resultant cutting force produced by each differential cutter disc engaged in the cut. A numerical algorithm is introduced for the calculation of total force and the calibration of the relevant parameters in the model. A series of experiments under different cutting conditions are conducted to confirm the validity of the developed model. The agreement between the experimental and simulative results is satisfactory, which shows that the model is effective for cutting force prediction in end milling with waved-edge cutters. ID="A1"Correspondance and offprint requests to: Prof. L. Zheng, Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, 100084, P. R. China. E-mail: lzheng@tsinghua.edu.cn     

超精密切削机理的流体力学分析模型

随着加工硬件性能的提高 ,有色金属的超精密加工技术已相对成熟。但是对微小切削深度时的加工过程还没有建立起比较满意的模型 ,因为还没有深刻了解超精密加工机理。本文提出了基于流体力学的超精密切削模型 ,考虑了切削刀具几何形状 (包括切削刃半径 )、后刀面工件材料弹性回复的影响。使用该模型可以预测超精密加工过程中刀具刃口的影响、尺寸效应、切削力以及切屑的卷曲半径和刀 -屑的接触长度等。     

MACHINING OF CORTICAL BONE: SURFACE TEXTURE,SURFACE INTEGRITY AND CUTTING FORCES

Cutting, drilling and reaming of human bone are conducted in total joint replacement procedures and the placement of dental implants. In the current study orthogonal machining of cortical bone was performed and the cutting and thrust forces, as well as the machined surface quality, were evaluated over a range of osteon orientations and cutting conditions. Results showed that cutting perpendicular to the osteons resulted in the highest machining forces, largest surface roughness and extensive sub-surface damage for some parametric conditions. The average surface roughness of the machined bone ranged from 1 μm to over 70 μm, was largest for positive rake angle tools and increased with the depth of cut. There was no correlation between the cutting forces and machined surface quality. While negative rake angle tools resulted in the largest cutting forces, they provided the lowest surface roughness and highest apparent surface quality. Overall, the results show that orthogonal cutting of bone can result in near-surface damage that reduces the degree of contact between bone and implanted devices and is potentially detrimental to the post-surgical recovery rate.