Specific cutting force coefficients modeling of end milling by neural network

In a high precision vertical machining center, the estimation of cutting forces is important for many reasons such as prediction of chatter vibration, surface roughness and so on. The cutting forces are difficult to predict because they are very complex and time variant. In order to predict the cutting forces of end-milling processes for various cutting conditions, their mathematical model is important and the model is based on chip load, cutting geometry, and the relationship between cutting forces and chip loads. Specific cutting force coefficients of the model have been obtained as interpolation function types by averaging forces of cutting tests. In this paper the coefficients are obtained by neural network and the results of the conventional method and those of the proposed method are compared. The results show that the neural network method gives more correct values than the function type and that in the learning stage as the omitted number of experimental data increase the average errors increase as well.     

Feedrate optimization for variant milling process based on cutting force prediction

Machining process modeling, simulation and optimization is one of the kernel technologies for virtual manufacturing (VM). Optimization based on physical simulation (in contrast to geometrical simulation) will bring better control of a machining process, especially to a variant cutting process – a cutting process so complex that cutting parameters, such as cutting depth and width, change with cutter positions. In this paper, feedrate optimization based on cutting force prediction for milling process is studied. It is assumed that cutting path segments are divided into micro-segments according to a given computing step. Heuristic methods are developed for feedrate optimization. Various practical constraints of a milling system are considered. Feedrates at several segments or micro-segments are determined together but not individually to make milling force satisfy constraints and approach an optimization objective. After optimization, an optimized cutting location data file is outputted. Some computation examples are given to show the optimization effectiveness. This revised version was published online in October 2004 with a correction to the issue number.     

Improved calculation of the cutting force in end milling

Determination of the cutting force in end milling on the basis of the Johnson–Cook phenomenological model is described. The numerical results obtained by this method are compared with experimental data.     

Identification of instantaneous cutting force coefficients using surface error

Cutting force coefficients are the key factors for efficient and accurate prediction of instantaneous milling force. To calibrate the coefficients, this paper presents an instantaneous milling force model including runout and cutter deformation. Also, forming of surface error is analyzed, and a surface error model considering runout is proposed. Using surface errors of two experiments completed with the same cutting conditions but different axial depth only, cutter deformation is obtained. Then, a new approach for the determination of instantaneous cutting force coefficients is provided. The method can eliminate influences of the other factors except cutter deformation and runout. A series of experiments are designed, and the results are used to identify the parameters. With the evaluated coefficients and runout parameters, the instantaneous milling force and surface error are predicted. A good agreement between predicted results and experimental results is achieved, which shows that the method is efficient, and effect of runout on surface error is not negligible.     

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.     

A study on calibration of coefficients in end milling forces model

This paper presents an improved approach to calibrate the cutting coefficients in an end-milling model. In order to predict end-milling forces, lots of simulative models are established. In order to use them, coefficients in the models, for example, cutting pressure constants etc., must firstly be calibrated experimentally, and simulative precision and applicability of the models are influenced by them. For simplicity, using average forces to calibrate cutting parameters are widely adopted by lots of researchers. However, the existence of an instruments zero-drift, noise, etc., will have effect on the precision of experimental data, so, it is difficult to directly obtain exact average-cutting forces through experimental data. Aiming at the above problem, the paper investigates milling forces in the frequency domain, discusses the impact of experimental data at different frequencies on cutting force coefficients and the influence of sensitivity of error on experimental data at different frequencies on coefficients is studied. Based on the research, an improved method to calibrate the cutting coefficients is provided. Based on a series of experiments and numerical simulations, the validity of the method is confirmed. At the end of the paper, some useful conclusions are drawn.     

Analysis on nonlinear dynamics of a thin-plate workpiece in milling process with cutting force nonlinearities

This paper aims to investigate the nonlinear dynamics of a thin-plate workpiece during milling process with cutting force nonlinearities. By modeling the thin-plate workpiece as a cantilevered thin plate and applying the Hamilton’s principle, the equations of motion of the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations. Using the Galerkin’s approach, the equations of motion are reduced to a two-degree-freedom nonlinear system. The method of Asymptotic Perturbation is utilized to obtain the averaged equations in the case of 1:1 internal resonance and foundational resonance. Numerical methods are used to find the periodic and chaotic oscillations of the cantilevered thin-plate workpiece. The results show that the cantilevered thin-plate workpiece demonstrate complex dynamic behaviors under time-delay effects, the external and parametric excitations.     

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.     

Investigation of the milling stability based on modified variable cutting force coefficients

The cutting force signal distortion is caused by the dynamic characteristics of cutting force testing system. In order to handle this issue, we propose two improvements in the traditional inverse filtering technology. Firstly, we use three-spline interpolation method instead of the curve fitting method to fit the frequency response function of the test system which basically improves the accuracy of fitting. Secondly, the low-pass filter is added before the inverse filter to eliminate the influence of the high-frequency noise signal on the cutting force signal. We choose the cavity-free surface of outer covering parts of mold of automobile as research objects. The inverse filter dynamic compensation technology has been used to remove the influence of the dynamic characteristics of the test system and the high-frequency noise on the cutting force signal. The effectiveness of the proposed method is verified by relative milling experiments. Based on the experimentally measured forces after dynamic compensation, the modified cutting force coefficients are obtained using the average milling force method. The variation law of the cutting force coefficients with the axial depth, the radial width, and the feed rate is examined. Based on the modified variable cutting force coefficients, the 3D stability of the ball end milling cutter surface has been obtained using full-discretization approach. Combining the results from the cutting experiment and the nonlinear method, the stability prediction based on the modified variable cutting force coefficient can improve the prediction accuracy. The results provide theoretical support for the optimization of the machining process of the cavity-free surface of outer covering parts of mold of automobile.     

Tool wear monitoring system for CNC end milling using a hybrid approach to cutting force regulation

A tool wear monitoring system is indispensable for better machining productivity, with the guarantee of machining safety by informing of the time due for changing a tool in automated and unmanned CNC machining. Different from monitoring methods using other signals, the monitoring of the spindle current has been used without requiring additional sensors on the machine tools. For reliable tool wear monitoring, only the current signal from tool wear should be extracted from the other parameters to avoid exhaustive analyses on signals in which all of the parameters are fused together. In this paper, the influences of force components from different parameters on the measured spindle current are investigated, and a hybrid approach to cutting force regulation is employed for tool wear signal extraction from the spindle current. Finally, wear levels are verified with experimental results by means of real-time feedrate aspects, varied to regulate the force component from tool wear.     

Fast evaluation of cutting forces in milling, applying no approximate models

A new method for fast evaluation of cutting forces in milling is introduced and tested experimentally. Unlike all existing procedures, which include the use of cutting models and approximate assumptions, in this method, the elementary functions of the cutting force are obtained from measured values only.The basic force functions for the whole feed range are acquired from one experiment using a single-tooth full-diameter (slot) milling, applying a specially developed procedure. The milling experiment is conducted under low-impact conditions, enabling accurate measurement and convenient signal processing. The basic force functions are then integrated and superimposed, using known procedures, to combine the total force in any multitooth milling combination. In this work the method is explained and tested experimentally.The suggested method enables a reliable evaluation of the cutting forces, while demanding minimal experimental work, the method applies to cutters having complicated edge geometry, and to high speed milling.Nomenclature a radial depth of cut 0<a<D - feed per tooth ratio 0<1 - d axial depth of cut - D cutter diameter - a/D radial depth ratio - cutter rotation angle - cutter rotation angle [6] - F _x,y,z() instantaneous edge cutting forces in fixture coordinates - F _t,r,z() instantaneous edge cutting forces in tool coordinates - F _x,y,z ^* F_t,r,z tool cutting force components on a multitooth cutter - h instantaneous chip thickness [6] - h* equivalent edge coefficient [6] - r ₁,r ₂ tangential radial ratio coefficient [6] - K _T tangential specific cutting force [4] - K _R radial specific cutting force [4] - N number of teeth - R _r resolution reduction factor - t instantaneous chip thickness - S ₁,S feed per tooth     

Computer-aided measurement of cutting forces applied to the wear of an end milling cutter

Information about cutting forces and wear and their dependence on cutting conditions, time etc. is necessary in all machining operations. This paper deals with the fundamental determination of cutting forces and wear in face milling and describes the computer-aided measurement equipment used for different tests. Some results including the variation of cutting force with feed, speed, time, cutting length and wear are presented.     

Empirical models and optimal cutting parameters for cutting forces and surface roughness in hard milling of AISI H13 steel

In the present research, an attempt has been made to experimentally investigate the effects of cutting parameters on cutting forces and surface roughness in hard milling of AISI H13 steel with coated carbide tools. Based on Taguchi’s method, four-factor (cutting speed, feed, radial depth of cut, and axial depth of cut) four-level orthogonal experiments were employed. Three cutting force components and roughness of machined surface were measured, and then range analysis and analysis of variance (ANOVA) are performed. It is found that the axial depth of cut and the feed are the two dominant factors affecting the cutting forces. The optimal cutting parameters for minimal cutting forces and surface roughness in the range of this experiment under these experimental conditions are searched. Two empirical models for cutting forces and surface roughness are established, and ANOVA indicates that a linear model best fits the variation of cutting forces while a quadratic model best describes the variation of surface roughness. Surface roughness under some cutting parameters is less than 0.25 μm, which shows that finish hard milling is an alternative to grinding process in die and mold industry.     

Machining strategy in five-axis milling using balance of the transversal cutting force

Several solutions can be considered to resolve the problem of positioning a cutting tool on a free-form surface when five-axis milling. To choose a unique solution, in addition to the cutter–workpiece contact, an additional criterion can be taken into account. This may concern the local geometry of the surface or yet again the width milled to maximise the metal removal rate, but technological criteria relating to the cutting phenomenon and the quality of the surface produced are not considered. The present article introduces a strategy applying positioning combined with balancing of the transversal cutting force. This method involves using the ploughing effect of the milling cutters by simultaneously engaging the teeth located to the front of the cutter in relation to the feed movement and also those to the rear. The positioning obtained stabilises the cutter and contributes to making a net improvement in its dynamic behaviour. This leads in turn to significantly higher quality of the milled surface. The article presents a method to apply balancing of the transversal cutting force to two types of machining passes and elaborates an associated strategy to plan cutter paths enabling an improvement in surface quality to be achieved.     

An analytical expression for end milling forces and tool deflection using Fourier series

In this research, a novel and generalized analytical expression of cutting force and tool deflection in end milling is presented as a function of tool rotational angle and other cutting parameters. The discontinuous cutting force function caused by periodic tool entry and exit is changed to an integrable continuous function using Fourier series expansion. Tool deflection is also formulated explicitly by the direct integration of the distributed loads along the helical cutting edges. Cutting conditions, tool geometry, runout components, and the stiffness of tool clamping part are considered in estimating the cutting force and tool deflection. Cumbersome computational procedures needed to check whether segmented cutting edges are engaged in cutting or not are eliminated by this proposed method. The presented analytical approach has advantages in flexibility, prediction time, and accuracy as compared with other numerical techniques. In addition, the effects of cutting conditions and run-outs, such as eccentricity and tilting on the cutting force and tool deflection, can be analyzed quantitatively in the time domain or frequency domain. The validity and effectiveness of the suggested method are verified through a series of cutting tests. The model presented in this research can be used in real-time machining error estimation and cutting condition selection for error minimization since the form accuracy is easily estimated from the acquired tool deflection curve.     

Three-dimensional chatter stability prediction of milling based on the linear and exponential cutting force model

Stability lobes are widely used to avoid chatter which restricts the machining quality and productivity. A lot of work has been done to predict the stability lobes fast and accurately. However, most of them are based on the linear force model, and the chatter stability limit is formulated as independent on the feed rate, which is inconsistent with the machining practice. By referencing with the zero-order solution, this paper investigates the chatter stability prediction based on the exponential force model. Focusing on the cutters with a lead angle (i.e., inserted face mill, the ball-end mill, and bull-nose end mill) where chatter is likely to be brought up in Z direction, the stability model is extended to three-dimensional. Taylor equation is utilized to linearize the exponential expressions when computing the directional coefficients in order to solve the stability limit analytically as the linear force model. Simulation results show that the exponential force model agrees with the measurements as well as the linear force model in the cutting force prediction, and it is able to demonstrate the feed rate effect on the stability limit. The stability limit is found to be increased as the feed rate increases, which is evidenced by the time domain simulation. Cutting tests are performed in the end to verify the stability model. The proposed model could be reduced to either X/Y dimensional or linear force model-based stability model by further simplifications.