Modeling and experimental verification of cutting forces in gear tooth cutting

Due to complex cutting edge profile of an involute cutter, calculations of chip width and consequently cutting force are quite problematical. This article presents a mechanistic approach in the prediction of cutting force components arising in the course of gear tooth cutting by an involute form cutter. To permit calculation of chip width (and so cutting forces), a discrete model is utilized and cutting force components are then derived using Kienzle approach. Moreover, several experiments are performed under different cutting conditions to prove the effectiveness and accuracy of the used method. The results have revealed that cutting force components can be predicted in form gear tooth cutting with a significant accuracy.     

基于真实刀刃轨迹的立铣刀切削厚度模型

瞬时切削厚度是铣削加工建模研究的重要参数之一。通过分析刀刃切削轨迹,可以得到准确的瞬时切削厚度,但需要求解复杂的超越方程。通常对切削刀刃轨迹进行不同程度的简化来求解近似的瞬时切削厚度。为得到准确的瞬时切削厚度,提出一种新的切削厚度计算模型。基于立铣刀真实切削刀刃轨迹,对近似的切削厚度模型进行补偿,得到较传统计算方法更为准确的结果,计算过程也更为简单。通过切削力试验验证,该模型可以得到更好的动态切削力预测结果。     

Thermoviscoplastic modelling of oblique cutting: forces and chip flow predictions

A modelling of oblique cutting for viscoplastic materials is presented. The thermomechanical properties and the inertia effects are accounted for to describe the material flow in the primary shear zone. At the tool–chip interface, a temperature-dependent friction law is introduced to take account of the extreme conditions of pressure, velocities and temperature encountered during machining. The chip flow angle is calculated by assuming that the friction force is collinear to the chip flow direction on the tool rake face. Due to the temperature dependence of the friction law at the tool–chip interface, the chip flow angle predicted by the model, is affected by the cutting speed, the undeformed chip thickness, the normal rake angle, the edge inclination angle and the thermomechanical behavior of the work material. This dependence and the trends predicted by the present approach are confirmed by experimental observations. Effects of cutting conditions on the cutting forces are also presented and compared to experiments.     

基于黏结-滑移摩擦模型的304不锈钢切削力仿真研究*

通过预测加工304不锈钢时产生的切削力,从而对切削参数和刀具几何参数进行优化,是提高304不锈钢的加工精度、切屑控制及保障刀具寿命的基础。建立304不锈钢切削仿真模型,为提高模型的精确性,选择Johnson-Cook本构方程和黏结-滑移摩擦模型。结果表明：采用黏结-滑移摩擦模型的切削力预测结果更为准确,表明相对于纯剪切摩擦与库仑摩擦模型,黏结-滑移摩擦模型能更准确地描述刀-屑摩擦特性。展开不同参数下的切削力研究,研究发现：切削力随着刀具前角、后角和切削速度的增大而减小,随切削刃钝圆半径和切削厚度、宽度的增大而增大,其中切削宽度、厚度及前角对切削力大小影响较大。研究结果为304不锈钢切削效率的提高和切削机制的研究提供了理论依据。     

Application of a variable flow stress machining theory to helical end milling

A methodology of modeling chip geometry of flat helical end milling based on a variable flow stress machining theory is presented in this article. The proposed model is concerned with the variation of the width of cut thickness. The nonuniform chip thickness geometry is discretized into several segments based on the radial depth of cut. The chip geometry for each segment is considered to be constant by taking the average value of the maximum and minimum chip thickness. The maximum chip thickness for each chip segment is computed based on the current width of cut, feed per tooth and the cutter diameter. The subsequent radial depth of cut is subtracted from the discretized size of the width of cut to obtain the minimum chip thicknesses. The forces for each segment are summed to obtain the total forces acting on the system of the workpiece and the tool. The cutting forces can be predicted from input data of work material properties, cutter configuration and the cutting conditions used. The validation of the proposed model is achieved by correlating experimental results with the predicted results obtained.     

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.     

Cutting force prediction for ball-end mills with non-horizontal and rotational cutting motions

Accurate cutting force prediction is essential to precision machining operations as cutting force is a process variable that directly relates to machining quality and efficiency. This paper presents an improved mechanistic cutting force model for multi-axis ball-end milling. Multi-axis ball-end milling is mainly used for sculptured surface machining where non-horizontal (upward and downward) and rotational cutting tool motions are common. Unlike the existing research studies, the present work attempts to explicitly consider the effect of the 3D cutting motions of the ball-end mill on the cutting forces. The main feature of the present work is thus the proposed generalized concept of characterizing the undeformed chip thickness for 3D cutter movements. The proposed concept evaluates the undeformed chip thickness of an engaged cutting element in the principal normal direction of its 3D trochoidal trajectory. This concept is unique and it leads to the first cutting force model that specifically applies to non-horizontal and rotational cutting tool motions. The resulting cutting force model has been validated experimentally with extensive verification test cuts consisting of horizontal, non-horizontal, and rotational cutting motions of a ball-end mill.     

Thermomechanical approach for the modeling of oblique machining with a single cutting edge

This article aims to predict performances of oblique machining with a single cutting edge. A thermomechanical approach for the modeling of oblique cutting with a single cutting edge is proposed. A good agreement was found between predicted and experimental data. New rules were established to determine experimentally the average friction coefficient and chip flow angle at the rake face. The computation algorithm permits to predict all thermomechanical parameters such as cutting forces, cutting temperatures, and chip geometry. Besides, all predicted oblique machining parameters are mainly controlled by the Po-criterion, which is defined as the ratio of tool–chip contact length to uncut chip thickness.     

Suppression of forced vibration due to chip segmentation in ultrasonic elliptical vibration cutting of titanium alloy Ti–6Al–4V

Ultrasonic elliptical vibration cutting of titanium alloy Ti–6Al–4V is investigated in this research. Because products made of Ti–6Al–4V alloy are usually designed for possessing low-rigidity structures or good-quality cut surfaces, machining requirements such as low cutting forces and slow rate of tool wear need to be fulfilled for realization of their precision machining. Therefore, the ultrasonic elliptical vibration cutting is applied as a novel machining method for those products. Machinability of Ti–6Al–4V alloy by the ultrasonic elliptical vibration cutting with cemented carbide tools is examined to figure out suitable cutting conditions for precision machining of Ti–6Al–4V alloy. As experimental results, generated chips, cutting forces, and profiles of cut surfaces are indicated. A forced vibration problem occurred due to the segmented chip formation, which is also well-known in the ordinary non-vibration cutting. Therefore, characteristics of the forced vibration due to the chip segmentation are investigated in this research. Through the experiments, it is found that the frequency and magnitude of the forced vibration have relation with the average uncut chip thickness and cutting width. Especially, it is found that the averaging effect can suppress the forced vibration, i.e. the chip segmentation tends to occur randomly over the large cutting width, and hence the force fluctuations with random phases tend to cancel each other as the cutting width increases relatively against the average uncut chip thickness. Based on the investigations, a new practical strategy to suppress the forced vibration due to chip segmentation is proposed and verified. Using the proposed method significantly decreased cutting forces and good quality of surfaces are obtained when the forced vibration is suppressed compared to the ordinary non-vibration cutting results. Therefore, the results suggest that the precision machining can be realized without sacrificing the machining efficiency by increasing the width of cut and decreasing the average uncut chip thickness.     

NANOSCALE CUTTING OF MONOCRYSTALLINE SILICON USING MOLECULAR DYNAMICS SIMULATION

It has been found that the brittle material, monocrystalline silicon, can be machined in ductile mode in nanoscale cutting when the tool cutting edge radius is reduced to nanoscale and the undeformed chip thickness is smaller than the tool edge radius. In order to better understand the mechanism of ductile mode cutting of silicon, the molecular dynamics (MD) method is employed to simulate the nanoscale cutting of monocrystalline silicon. The simulated variation of the cutting forces with the tool cutting edge radius is compared with the cutting force results from experimental cutting tests and they show a good agreement. The results also indicate that there is silicon phase transformation from monocrystalline to amorphous in the chip formation zone that can be used to explain the cause of ductile mode cutting. Moreover, from the simulated stress results, the two necessary conditions of ductile mode cutting, the tool cutting edge radius are reduced to nanoscale and the undeformed chip thickness should be smaller than the tool cutting edge radius, have been explained.     

EFFECT OF CRYSTALLOGRAPHIC ORIENTATION ON CUTTING FORCES AND SURFACE FINISH IN DUCTILE CUTTING OF KDP CRYSTALS

In order to investigate the influence of material anisotropy in ductile cutting of Potassium Dihydrogen Phosphate (KDP) crystals, experiments of face cutting of (001) plane of KDP crystals are carried out by using an ultra-precision lathe with a single point diamond tool. The cutting forces, surface finish, and surface roughness in all crystallographic orientations of the machined surface are measured, and a power spectrum analysis method is used to reveal the cutting force patterns. The experimental results show that the cutting forces and surface roughness vary greatly with different crystallographic orientations of KDP crystal, and that amplitude variation of cutting forces and surface finish is closely related with the cutting parameter of the maximum undeformed chip thickness. With the maximum undeformed chip thickness below 30 nm, the amplitude variation of cutting force and surface finish is minimized, and a super-smooth surface with consistent surface finish in all the crystallographic orientations can be achieved. The surface roughness is 2.698 nm (Ra) measured by Atomic Force Microscope (AFM). These findings provide criteria for achieving a large-scale KDP crystal with consistent super-smooth surface using ductile cutting technology.     

EFFECT OF CUTTING CONDITIONS ON THE SERRATED CHIP FORMATION IN HIGH-SPEED CUTTING

Titanium alloy Ti6A14V has been widely used in many engineering fields due to its attractive specific strength and corrosion resistance. A deep understanding of the material's machinability is of primary importance. This article investigates the serrated chip formation mechanism of Ti6Al4V alloy under high-speed cutting by finite element analysis. The effect of the cutting conditions on the serrated chip formation is analyzed comprehensively. The study found that when the initial chip thickness becomes small or when the rake angle becomes large, the size of sawtooth decreases and the number of sawtooth increases. The serrated chip morphology is more sensitive to the initial chip thickness. The severe fluctuation of cutting forces is caused by the formation of sawtooth in chipping. To minimize the serrated chipping in high-speed machining, the initial chip thickness is the most important factor to consider.     

A study of the effect of tool cutting edge radius on ductile cutting of silicon wafers

Ductile mode cutting of silicon wafers can be achieved under certain cutting conditions and tool geometry. An experimental investigation of the critical undeformed chip thickness in relation to the tool cutting edge radius for the brittle-ductile transition of chip formation in cutting of silicon wafers is presented in this paper. Experimental tests for cutting of silicon wafers using diamond tools of different cutting edge radii for a range of undeformed chip thickness are conducted on an ultra-precision lathe. Both ductile and brittle mode of chip formation processes are observed in the cutting tests. The results indicate that ductile cutting of silicon can be achieved at certain values of the undeformed chip thickness, which depends on the tool cutting edge radius. It is found that in cutting of silicon wafers with a certain tool cutting edge radius there is a critical value of undeformed chip thickness beyond which the chip formation changes from ductile mode to brittle mode. The ductile-brittle transition of chip formation varies with the tool cutting edge radius. Within the range of cutting conditions in the present study, it has also been found that the larger the cutting edge radius, the larger the critical undeformed chip thickness for the ductile-brittle transition in the chip formation.     

The upper bound of tool edge radius for nanoscale ductile mode cutting of silicon wafer

For ductile mode cutting of brittle materials, such as silicon wafers, the undeformed chip thickness has to be smaller than the tool edge radius. In practical application, for high production rate, the undeformed chip thickness is expected to be as large as possible. Therefore, the tool edge radius is expected to be as large as possible. In this study, the upper bound of the tool edge radius is investigated through cutting experiments.     

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.     

AN ANALYTICAL MODEL OF OBLIQUE CUTTING WITH APPLICATION TO END MILLING

A new analytical cutting force model is presented for oblique cutting. Orthogonal cutting theory based on unequal division shear zone is extended to oblique cutting using equivalent plane approach. The equivalent plane angle is defined to determine the orientation of the equivalent plane. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of shear strain rate. The flow stress is calculated from Johnson-cook material constitutive equation. The predictions were compared with test data from the available literature and showed good correlation. The proposed model of oblique cutting was applied to predict the cutting forces in end milling. The helical flutes are decomposed into a set of differential oblique cutting edges. To every engaged tooth element, the differential cutting forces are obtained from oblique cutting process. Experiments on machining AISI 1045 steel under different cutting conditions were conducted to validate the proposed model. It shows that the predicted cutting forces agree with the measurements both in trends and values.     

An experimental study of edge radius effect on cutting single crystal silicon

According to the hypothesis of ductile machining, brittle materials undergo a transition from brittle to ductile mode once a critical undeformed chip thickness is reached. Below this threshold, the energy required to propagate cracks is believed to be larger than the energy required for plastic deformation, so that plastic deformation is the predominant mechanism of material removal in machining these materials in this mode. An experimental study is conducted using diamond cutting for machining single crystal silicon. Analysis of the machined surfaces under a scanning electron microscope (SEM) and an atomic force microscope (AFM) identifies the brittle region and the ductile region. The study shows that the effect of the cutting edge radius possesses a critical importance in the cutting operation. Experimental results of taper cutting show a substantial difference in surface topography with diamond cutting tools of 0° rake angle and an extreme negative rake angle. Cutting with a diamond cutting tool of 0° rake angle could be in a ductile mode if the undeformed chip thickness is less than a critical value, while a ductile mode cutting using the latter tool could not be found in various undeformed chip thicknesses.     

曲面铣削过程加工路径对切削力和磨损的影响研究

针对不同走刀路径下的复杂曲面加工过程进行球头铣刀铣削Cr12MoV加工复杂曲面研究,分析不同走刀路径下铣削力和刀具磨损的变化趋势。试验结果表明:通过对比分析直线铣削和曲面铣削过程中的最大未变形切屑厚度,可以得出单周期内曲面铣削的力大于直线铣削过程的力,铣削相同铣削层时环形走刀测得的切削力普遍大于往复走刀测得的切削力;以最小刀具磨损为优化目标,运用方差分析法分析得出不同走刀路径的影响刀具磨损的主次因素,同时利用残差分析方法建立球头铣刀加工复杂曲面刀具磨损预测模型,并通过试验进行验证。     

Prediction of cutting forces in helical milling process

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.     

Characteristics of ultrasonic vibration-assisted ductile mode cutting of tungsten carbide

In this study, investigations were carried out to evaluate the characteristics of ultrasonic vibration-assisted cutting of tungsten carbide material using a CNC lathe with CBN tool inserts. The cutting forces were measured using a three-component dynamometer, and the machined workpiece surfaces and chip formation were examined using a SEM. The experimental results showed that the radial force F _x was much larger than the tangential force F _z and axial force F _y . The SEM observations on the machined workpiece surfaces and chip formation indicated that the critical condition for ductile mode cutting of tungsten carbide was mainly the maximum undeformed chip thickness when the tool cutting edge radius was fixed, that is, the ductile mode cutting can be achieved when the maximum undeformed chip thickness was smaller than a critical value. Corresponding to the chip formation mode (ductile or brittle), three types of the machined workpiece surfaces were obtained: fracture free surface, semi-fractured surface and fractured surface. It was also found that the cutting speed has no significant effect on the ductile chip formation mode.