Cutting force model for multi-toothed cutting processes and force measuring equipment for face milling

This article presents a mechanical cutting force model for multi-tooth cutting processes, where initial position errors in radial and axial direction, eccentricity and edge wear are taken into account. The cutting forces are presented for each individual cutting edge, and in a system of coordinates where one axis is parallel to the cutting speed vector at any instant. The process parameter cutting resistance, C_r is derived from the measured main cutting force F_M. C_r should be regarded as a parameter since it is always increasing with decreasing values of theoretical chip thickness h₁. A new way of measuring cutting forces in multi-tooth cutting processes is also presented. Eight cutting force components are measured on the tool close to each of the four cutting edges. The aroused signals are filtered, amplified, A/D-converted and put together in a serial stream for transmission through a hollow spindle via a fibre optic cable. The signals are sent from the rotating spindle to the frame of the machine over an air gap with Light Emitting Diodes. They are then demultiplexed, D/A-converted, and stored in a PC-based eight channel oscilloscope. With this measurement equipment it is possible to directly measure the cutting forces acting on each individual cutting edge.     

A study on instantaneous cutting force coefficients in face milling

In this paper, the characteristics of instantaneous cutting force coefficients in face milling are studied. In order to estimate instantaneous cutting force coefficients in face milling, the relationships between instantaneous cutting force coefficients and measured cutting force signals are derived. A series of experiments are then conducted to study the natures of instantaneous cutting force coefficients. The relationships between instantaneous cutting force coefficients and other cutting parameters are also established. It is found that the normal force coefficient is mainly affected by chip thickness and cutting speed; the vertical force coefficient is mainly affected by chip thickness, cutting edge length and cutting speed; and that the horizontal force coefficient is not only affected by chip thickness, cutting speed and length of cut, but also the variation rate of chip thickness.     

A worn tool force model for three-dimensional cutting operations

Previous studies have shown that there is a region on the flank of a worn cutting tool where plastic flow of the workpiece material occurs. This paper presents experimental data which shows that in three-dimensional cutting operations in which the nose of the tool is engaged, the region of plastic flow grows linearly with increases in total wearland width. A piecewise linear model is developed for modeling the growth of the plastic flow region, and the model is shown to be independent of cutting conditions. A worn tool force model for three-dimensional cutting operations that uses this concept is presented. The model requires a minimal number of sharp tool tests and only one worn tool test. An integral part of the worn tool force model is a contact model that is used to obtain the magnitude of the stresses on the flank of the tool. The force model is validated through comparison to data obtained from wear tests conducted over a range of cutting conditions and workpiece materials. It is also shown that for a given tool and workpiece material combination, the incremental increases in the cutting forces due to tool flank wear are solely a function of the amount and nature of the wear and are independent of the cutting condition in which the tool wear was produced.     

Experimental studies of cutting force variation in face milling

The purpose of this paper is to present a developed cutting force model for multi-toothed cutting processes, including a complete set of parameters influencing the cutting force variation that has been shown to occur in face milling, and to analyse to what extent these parameters influence the total cutting force variation for a selected tool geometry. The scope is to model and analyse the cutting forces for each individual tooth on the tool, to be able to draw conclusions about how the cutting action for an individual tooth is affected by its neighbours.A previously developed cutting force model for multi-toothed cutting processes is supplemented with three new parameters; eccentricity of the spindle, continuous cutting edge deterioration and load inflicted tool deflection influencing the cutting force variation. A previously developed milling force sensor is used to experimentally analyse the cutting force variation, and to give input to the cutting force simulation performed with the developed cutting force model.The experimental results from the case studied in this paper show that there are mainly three factors influencing the cutting force variation for a tool with new inserts. Radial and axial cutting edge position causes approximately 50% of the force variation for the case studied in this paper. Approximately 40% arises from eccentricity and the remaining 10% is the result of spindle deflection during machining. The experimental results presented in this paper show a new type of cutting force diagrams where the force variation for each individual tooth when two cutting edges are engaged in the workpiece at the same time. The wear studies performed shows a redistribution of the individual main cutting forces dependent on the wear propagation for each tooth.     

A three-dimensional analytical cutting force model for micro end milling operation

In the present day manufacturing arena one of the most important fields of interest lies in the manufacturing of miniaturized components. End milling with fine-grained carbide micro end mills could be an efficient and economical means for medium and small lot production of micro components. Analysis of the cutting force in micro end milling plays a vital role in characterizing the cutting process, in estimating the tool life and in optimizing the process. A new approach to analytical three-dimensional cutting force modeling has been introduced in this paper. The model determines the theoretical chip area at any specific angular position of the tool cutting edge by considering the geometry of the path of the cutting edge and relates this with tangential cutting force. A greater proportion of the helix face of the cutter participating in the cutting process differs the cutting force profile in micro end milling operations a bit from that in conventional end milling operations. This is because of the reason that the depth-of-cut to tool diameter ratio is much higher in micro end milling than the conventional one. The analytical cutting force expressions developed in this model have been simulated for a set of cutting conditions and are found to be well in harmony with experimental results.     

Radial immersion angle estimation using cutting force and predetermined cutting force ratio in face milling

Radial immersion ratio is an important factor to determine the threshold for tool conditioning monitoring and automatic force regulation in face milling. In this paper, a method of on-line estimation of the radial immersion angle using cutting force is presented. When a tooth finishes sweeping, a sudden drop of cutting force occurs. This force drop is equal to the cutting force that acts on a single tooth at the swept angle of cut and can be obtained from the cutting force signal in feed and cross-feed directions. The ratio of cutting forces in feed and cross-feed directions acting on the single tooth at the immersion angle is a function of the immersion angle and the ratio of radial-to-tangential cutting force. In this study, it is found that the ratio of radial-to-tangential cutting force is not affected by cutting conditions and axial rake angle. Therefore, the ratio of radial-to-tangential cutting force determined by just one preliminary experiment can be used regardless of the cutting conditions for a given tool and workpiece material. Using the measured cutting force during machining and a predetermined ratio, the radial immersion ratio is estimated in the process. Various experiments show that the radial immersion ratio and instantaneous ratio of the radial to tangential direction cutting force can be estimated very well by the proposed method.     

A voxel-based kinematic simulation model for force analyses of complex milling operations such as wobble milling

Mechanical machining of fiber reinforced plastics poses special challenges due to the heterogeneous and anisotropic material composition. Process strategies for the generation of drill holes, which aim at directing the resultant process forces toward the center of the workpiece, have been shown to obtain good machining results with less process induced damage. However, these strategies (e.g. wobble milling) might involve complex multiaxial tool movements and are thus very difficult to analyze and optimize. A voxel-based kinematic simulation program has been set up, which allows analyses of process forces for arbitrary milling operations based on the time-resolved determination of the cutting thickness and multivariate process force regression models. A basic analysis of the process of wobble milling is presented as well. It confirms that the resultant process forces are directed toward the center of the workpiece when the outer material layers are machined. The resultant force is directed in a favorable direction throughout the complete cut during the actual process step of wobble milling.     

A model for thread milling cutting forces

This paper presents a mechanistic model for prediction of the thread milling forces. The mechanics of cutting for thread milling is analyzed similar to the end milling process but with modified cutting edge geometry. The chip thickness and cutting force models are developed considering the unique geometry of the tool. The model has been calibrated for 6061 Aluminum and validated. The effects of tool and thread geometry have been studied using the model.     

Development of micro milling force model and cutting parameter optimization

Taking the minimum chip thickness effect,cutter deflection,and spindle run-out into account,a micro milling force model and a method to determine the optimal micro milling parameters were developed.The micro milling force model was derived as a function of the cutting coefficients and the instantaneous projected cutting area that was determined based on the machining parameters and the rotation trajectory of the cutter edges.When an allowable micro cutter deflection is defined,the maximum allowable cutting force can be determined.The optimal machining parameters can then be computed based on the cutting force model for better machining efficiency and accuracy.To verify the proposed cutting force model and the method to determine the optimal cutting parameters,micro-milling experiments were conducted,and the results show the feasibility and effectiveness of the model and method.     

Predictive cutting force model in complex-shaped end milling based on minimum cutting energy

A force model is presented to predict the cutting forces and the chip flow directions in cuttings with complex-shaped end mills such as ball end mills and roughing end mills. Three-dimensional chip flow in milling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. Because the cutting thickness changes with the rotation angle of the edge in the milling process, the surface profile machined by the previous edge inclines with respect to the cutting direction. The chip flow model is made using the orthogonal cutting data with taking into account the inclination of the pre-machined surface. The chip flow direction is determined so as to minimize the cutting energy, which is the sum of the shear energy on the shear plane and the friction energy on the rake face. Then, the cutting force is predicted for the chip flow model at the minimum cutting energy. The predicted chip flow direction changes not only with the local edge inclination but also with the cutting energy consumed in the shear plane cutting model. The cutting processes with a ball end mill and a roughing end mill are simulated to verify the predicted cutting forces in comparison with the measured cutting forces.     

Predicting cutting forces in face milling

It is shown how orthogonal machining theory can be applied to predict the cutting forces in face milling from a knowledge of the work material properties and cutting conditions. Predicted and experimental results are compared.     

A closed form mechanistic cutting force model for helical peripheral milling of ductile metallic alloys

A closed form mechanistic model is developed for cutting forces in helical peripheral milling (endmilling) of ductile metallic alloys. This paper presents an alternative derivation, using the frontal chip area, to describe two series of cutting force expressions—one using a Heaviside unit step function and the other using a Fourier series expansion. A specific advantage of the present work is highlighted by deriving analytical expressions for sensitivity coefficients required to analytically propagate the uncertainty in the cutting-force model parameters. Another advantage is that even very small radial immersions can be used to derive cutting coefficients reliably, along with their variances. The aforementioned analytical investigations are applied to a series of experimental cutting tests to estimate the force-model cutting coefficients. Experimental investigations include the study of a tool having radial runout. Finally, confidence intervals are placed on predicted forces which experimentally verify the validity of the proposed force model.     

A predicted milling force model for high-speed end milling operation

In this study, a predicted milling force model for the end milling operation is proposed. The speed of spindle rotation, feed per tooth, and axial and radial depth of cut are considered as the affecting factors. An orthogonal rotatable central composite design and the response surface methodology are used to construct this model. The milling force per spindle revolution period obtained from each treatment is equally divided into suitable sections. The extreme value of the milling force in each section is selected to build the predicted model so as to predict the extreme force in each section for any cutting conditions within the specified range of the design database, including the speed of spindle rotation, feed per tooth, and axial and radial depth of cut. Moreover, the predicted extreme force in each section is applied to reconstruct the milling force waveform by means of the expansion of the Fourier series. The predicted model presented in this paper is adequate for a 95% confidence interval, and shows good correlation between experimental and predicted results.     

Simplified and efficient calibration of a mechanistic cutting force model for ball-end milling

Accurate evaluation of the empirical coefficients of a mechanistic cutting force model is critical to the reliability of the predicted cutting forces. This paper presents a simplified and efficient method to determine the cutting force coefficients of a ball-end milling model. The unique feature of this new method is that only a single half-slot cut is to be performed to calibrate the empirical force coefficients that are valid over a wide range of cutting conditions. The instantaneous cutting forces are used with the established helical cutting edge profile on the ball-end mill. The half-slot calibration cut enables successive determination of the lumped discrete values of the varying cutting mechanics parameters along the cutter axis whereas the size effect parameters are determined from the known variation of undeformed chip thickness with cutter rotation. The effectiveness of the present method in determining the cutting force coefficients has been demonstrated experimentally with a series of verification test cuts.     

Simulation of cutting process in peripheral milling by predictive cutting force model based on minimum cutting energy

The cutting force and the chip flow direction in peripheral milling are predicted by a predictive force model based on the minimum cutting energy. The chip flow model in milling is made by piling up the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. The cutting edges are divided into discrete segments and the shear plane cutting models are made on the segments in the chip flow model. In the peripheral milling, the shear plane in the cutting model cannot be completely made when the cutting point is near the workpiece surface. When the shear plane is restricted by the workpiece surface, the cutting energy is estimated taking into account the restricted length of the shear plane. The chip flow angle is determined so as to minimize the cutting energy. Then, the cutting force is predicted in the determined chip flow model corresponding to the workpiece shape. The cutting processes in the traverse and the contour millings are simulated as practical operations and the predicted cutting forces verified in comparison with the measured ones. Because the presented model determines the chip flow angle based on the cutting energy, the change in the chip flow angle can be predicted with the cutting model.     

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.     

Modeling micro-end-milling operations. Part I: analytical cutting force model

A new analytical cutting force model is proposed for micro-end-milling operations. The model calculates the chip thickness by considering the trajectory of the tool tip while the tool rotates and moves ahead continuously. The proposed approach allows the calculation of the cutting forces to be done accurately in typical micro-end-milling operations with very aggressively selected feed per tooth to tool radius (f_t/r) ratio. The difference of the simulated cutting forces between the proposed and conventional models can be experienced when f_t/r is larger than 0.1. The estimated cutting force profile of the proposed model had good agreement with the experimental data.     

An improved cutting force and surface topography prediction model in end milling

During the milling operation, the cutting forces will induce vibration on the cutting tool, the workpiece, and the fixtures, which will affect the surface integrity of the final part and consequently the product's quality. In this paper, a generic and improved model is introduced to simultaneously predict the conventional cutting forces along with 3D surface topography during side milling operation. The model incorporates the effects of tool runout, tool deflection, system dynamics, flank face wear, and the tool tilting on the surface roughness. An improved technique to calculate the instantaneous chip thickness is also presented. The model predictions on cutting forces and surface roughness and topography agreed well with experimental results.     

Determination of process parameters through a mechanistic force model of milling operations

Mechanistic process parameters for the end milling operation are determined for 11L17 free machining steel, 2024 aluminum and 62-35-3 free machining brass by analyzing the measured cutting force data and using a mechanistic force model. It has been found that pressure and friction acting on the cutter-chip interface decrease with the increase of feed rate, while the cutting speed has a negligible effect on some of the material-dependent parameters. Process parameters are summarized into empirical equations as functions of feed rate and tool rotation angle for each workpiece material. The use of sampled force data in the computation of the process parameters reduces the amount of testing greatly compared to those methods that utilize only average force data.     

A cutting power model for tool wear monitoring in milling

This paper describes a cutting power model in face milling operation, where cutting conditions and average tool flank wear are taken into account. The cutting power model is verified with experiments. It is shown with the simulations and experiments that the simulated power signals predict the mean cutting power better than the instantaneous cutting power. Finally, the cutting power model is used in a cutting power threshold updating strategy for tool wear monitoring which has been carried out successfully in milling operations under variable cutting conditions.