Generalized dynamic model of metal cutting operations

This paper presents a unified mathematical model which allows the prediction of chatter stability for multiple machining operations with defined cutting edges. The normal and friction forces on the rake face are transformed to edge coordinates of the tool. The dynamic forces that contain vibrations between the tool and workpiece are transformed to machine tool coordinates with parameters that are set differently for each cutting operation and tool geometry. It is shown that the chatter stability can be predicted simultaneously for multiple cutting operations. The application of the model to single-point turning and multi-point milling is demonstrated with experimental results.     

Error compensation in machine tools — a review: Part I: geometric,cutting-force induced and fixture-dependent errors

Accuracy of machined components is one of the most critical considerations for any manufacturer. Many key factors like cutting tools and machining conditions, resolution of the machine tool, the type of workpiece etc., play an important role. However, once these are decided upon, the consistent performance of the machine tool depends upon its ability to accurately position the tool tip vis-à-vis the required workpiece dimension. This task is greatly constrained by errors either built into the machine or occurring on a periodic basis on account of temperature changes or variation in cutting forces. The three major types of error are geometric, thermal and cutting-force induced errors. Geometric errors make up the major part of the inaccuracy of a machine tool, the error caused by cutting forces depending on the type of tool and workpiece and the cutting conditions adopted. This part of the paper attempts to review the work done in analysing the various sources of geometric errors that are usually encountered on machine tools and the methods of elimination or compensation employed in these machines. A brief study of cutting-force induced errors and other errors is also made towards the end of this paper.     

The feasibility of eigenstructure assignment for machining chatter control

The eigenstructure assignment algorithm is proposed for controlling machining chatter by changing the response of the machine tool structure to dynamic cutting forces through the change of its modal properties so that the interaction between the tool and workpiece can be altered. The determination of the desired modal shapes is derived from a concept similar to gain scheduling in adaptive control system theory. By using computer simulations, the desired eigenstructure of the machine tool structure for different cutting conditions is determined and used to form the scheduling table. The gain matrix is adjusted according to the scheduling table and cutting conditions. It was found from experimental results that by changing the principal direction of the machine tool structure, the machining system could be stabilized and that the use of the proper eigenstructure to suppress machine tool chatter could significantly increase the material removal rate. Simulations have shown that the responses of the controlled machining system have been altered from unstable to stable, proving the feasibility of the proposed chatter control concept.     

Error compensation in machine tools — a review: Part II: thermal errors

Accuracy of machined components is one of the most critical considerations for any manufacturer. Many key factors like cutting tools and machining conditions, resolution of the machine tool, the type of workpiece etc., play an important role. However, once these are decided upon, the consistent performance of the machine tool depends upon its ability to accurately position the tool tip vis-à-vis the required workpiece dimension. This task is greatly constrained by errors either built into the machine or occurring on a periodic basis on account of temperature changes or variation in cutting forces. The three major types of error are geometric, thermal and cutting-force induced errors. Geometric errors make up the major part of the inaccuracy of a machine tool, the error caused by cutting forces depending on the type of tool and workpiece and the cutting conditions adopted. This part of the paper attempts to review the work done in analysing the various sources of geometric errors that are usually encountered on machine tools and the methods of elimination or compensation employed in these machines. A brief study of cutting-force induced errors and other errors is also made towards the end of this paper.     

Investigation of the effect of rake angle on main cutting force

This paper presents a study of comparison of empirical and experimental results for main cutting force during machining rotational parts by unworn cutting tools. A dynamometer was designed and produced for measuring the forces. Two strain gauges were placed at the correct position on the machine tool and cutting tool at the design stage. Correct gauge positioning sensed displacements of the tool caused by cutting forces. AISI 1040 was used as the workpiece material. Main cutting force (F_c) was measured for eight different rake angles changing from negative to positive values at five different cutting speeds. The depth of cut and feed rate were kept throughout the experiments. Empirical results according to Kienzle approach were compared with experimental results. Main cutting force was observed to have a decreasing trend as the rake angle increased from negative to positive values. The deviation between empirical approach and experiments was in the order of 10–15%.     

Cutting forces modeling considering the effect of tool thermal property—application to CBN hard turning

Force modeling in metal cutting is important for a multitude of purposes, including thermal analysis, tool life estimation, chatter prediction, and tool condition monitoring. Numerous approaches have been proposed to model metal cutting forces with various degrees of success. In addition to the effect of workpiece materials, cutting parameters, and process configurations, cutting tool thermal properties can also contribute to the level of cutting forces. For example, a difference has been observed for cutting forces between the use of high and low CBN content tools under identical cutting conditions. Unfortunately, among documented approaches, the effect of tool thermal property on cutting forces has not been addressed systemically and analytically. To model the effect of tool thermal property on cutting forces, this study modifies Oxley’s predictive machining theory by analytically modeling the thermal behaviors of the primary and the secondary heat sources. Furthermore, to generalize the modeling approach, a modified Johnson–Cook equation is applied in the modified Oxley’s approach to represent the workpiece material property as a function of strain, strain rate, and temperature. The model prediction is compared to the published experimental process data of hard turning AISI H13 steel (52 HRc) using either low CBN content or high CBN content tools. The proposed model and finite element method (FEM) both predict lower thrust and tangential cutting forces and higher tool–chip interface temperature when the lower CBN content tool is used, but the model predicts a temperature higher than that of the FEM.     

Feasibility study of in-process compensation of deformations in flexible milling

During the machining of thin-walled parts, deformation can occur resulting in dimensional errors. These dimensional errors cause a variation on cutting forces. From the actual measured cutting forces and the estimated forces resultant from rigid machining, it is possible to determine the value of this deformation. Based on this, an on-line system for compensating workpiece errors, has been developed. The system is based on correcting the relative position of the tool-workpiece during machining by means of a piezoelectric actuator. The objective is achieved in real time to compensate for the part deformations from the measurement of the cutting forces, without the programming of the tool path trajectories in the machine tool being affected.     

Theoretical-experimental modeling of milling machines for the prediction of chatter vibration

Productivity of high speed milling operations can be seriously limited by chatter occurrence. Chatter vibrations can imprint a poor surface finish on the workpiece and can damage the cutting tool and the machine. Chatter occurrence is strongly affected by the dynamic response of the whole system, i.e. the milling machine, the tool holder, the tool, the workpiece and the workpiece clamping fixture. Tool changes must be taken into account in order to properly predict chatter occurrence. In this study, a model of the milling machine-tool is proposed: the machine frame and the spindle were modeled by an experimentally evaluated modal model, while the tool was modeled by a discrete modal approach, based on the continuous beam shape analytical eigenfunctions. A chatter identification technique, based on this analytical-experimental model, was implemented. Tool changes can be easily taken into account without requiring any experimental tests. A 4 axis numerically controlled (NC) milling machine was instrumented in order to identify and validate the proposed model. The milling machine model was excited by regenerative, time-varying cutting forces, leading to a set of Delay Differential Equations (DDEs) with periodic coefficients. The stability lobe charts were evaluated using the semi-discretization method that was extended to n>2 degrees of freedom (dof) models. The stability predictions obtained by the analytical model are compared to the results of several cutting tests accomplished on the instrumented NC milling machine.     

Modelling and simulation of chatter in milling using a predictive force model

A predictive time domain chatter model is presented for the simulation and analysis of chatter in milling processes. The model is developed using a predictive milling force model, which represents the action of milling cutter by the simultaneous operations of a number of single-point cutting tools and predicts the milling forces from the fundamental workpiece material properties, tool geometry and cutting conditions. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. Runge–Kutta method is employed to solve the differential equations governing the dynamics of the milling system for accurate solutions. A Windows-based simulation system for chatter in milling is developed using the predictive model, which predicts chatter vibrations represented by the tool-work displacements and cutting force variations against cutter revolution in both numerical and graphic formats, from input of tool and workpiece material properties, cutter parameters, machine tool characteristics and cutting conditions. The system is verified with experimental results and good agreement is shown.     

Tool wear effect on cutting forces: In routing process of Aleppo pine wood

This paper uses the cutting forces in a routing process of Aleppo pine wood to estimate the tool wear effect. The aim is to obtain further information about the tool wear effect by monitoring the variation in the cutting forces. A Kistler 9257A 3 axes Dynamometer was positioned under the workpiece to measure the cutting forces at frequencies up to 10,000 Hz. The experiments were carried out on a CNC routing machine RECORD1 of SCM. A carbide tool was used and the cutting parameters were fixed. The cutting speed was approximately 25 m/s. Dasylab software was used to capture the data. The results show a correlation between the tool wear and the computed angle (θ), between the tangential and cutting forces. In fact, the variation of (θ) is unstable in the running period and stable in the linear wear zone, included in the interval [?1.11°; ?1.10°]. This study was performed as part of a development program for the Algerian wood industry, hence the selection Aleppo pine wood as the working material.     

A new dynamic model for drilling and reaming processes

This paper presents a new computer simulation model for drilling and reaming processes. The model is made of four parts: the force model for the cutting lips, the force model for the chisel edge, the dynamic model for the machine tool (including the cutter) and the regenerative correlation between the force and machine tool vibration. The models for the forces and the machine tool are similar to the existing models. The key to the model is the regeneration correlation between the cutting forces and the machine tool vibration. It uses a new 3D chip formation model to describe the interaction between the cutter and the workpiece. The model can predict the dynamic forces and chatter limit. It also reveals several interesting phenomena, such as how the feed and the point angle of the drill affect the chatter limit. The model is implemented using C++ language with an interface to I-DEAS™ CAE software system. The simulation results are validated experimentally by both drilling and reaming under various cutting conditions. The experiment results show that the simulation is accurate with average error about 10%. A number of research issues are also proposed for the future work.     

Real-time cutting force induced error compensation on a turning center

A real-time error compensation system has been developed to reduce the cutting force induced planar error of a two-axis turning center by using sensing, metrology, modeling, and computer control techniques. Ten error components are formulated as a two-dimensional error field. A piezoelectric force sensor mounted in the pocket under the tool turret is used to characterize the cutting forces. A compensation controller based on an IBM/PC has been linked with the existing computer numerical controller (CNC) to correct machine errors in real time. Three different types of cutting tests were performed and the results showed that the maximum diameter error in the workpiece was reduced by 67–85% using this compensation system.     

Dimensional errors in longitudinal turning based on the unified generalized mechanics of cutting approach.: Part I: Three-dimensional theory

During the machining of a part, a new surface is generated together with its dimensional deviations. These deviations are due to the presence of several phenomena (workpiece deflection under strong cutting forces, vibration of the machine tool, material spring-back, and so on) that occur during machining. Each elementary phenomenon results in an elementary machining error. Consequently, the accuracy of the manufactured workpiece depends on the precision of the manufacturing process, which it may be controlled or predicted.The first part of this work presents a new model to evaluate machining accuracy and part dimensional errors in bar turning. A model to simulate workpiece dimensional errors in longitudinal turning due to deflection of the tool, workpiece holder and workpiece is shown. The proposed model calculates the real cutting force according to the Unified Generalized Mechanics of Cutting approach proposed by Armarego, which allows one to take into account the three-dimensional nature (3D) of the cutting mechanism. Therefore, the model developed takes advantage of the real workpiece deflection, which does not lie in a plane parallel to the tool reference plane, and of the real 3D cutting force, which varies along the tool path due to change in the real depth of cut. In the first part of the work the general theory of the proposed approach is presented and discussed for 3D features. In the second part the proposed approach is applied to real cases that are mostly used in practice. Moreover, some experimental tests are carried out in order to validate the developed model: good agreement between numerical and experimental results is found.     

Prediction of cutting forces in milling of circular corner profiles

This paper proposes an approach to predict the cutting forces in peripheral milling of circular corner profiles in which varying radial depth of cut is encountered. The geometric relationship between an end mill and the corner profile is investigated and a mathematical model is presented to describe the different phases of the cutter/workpiece contact. The milling process for circular corner 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. A time domain analytical model of cutting forces for the steady-state machining conditions is introduced to each segmented process for the cutting force prediction. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpirece material property, as well as the relative position of the tool to workpiece. Experiments are conducted and the measured forces are compared to the predictions for the verification of the proposed method.     

Mechanistic force modeling of single point cutting tool in terms of grinding angles

The cutting tool angles have conventionally been presented using projective geometry in terms of the projections of cutting edges on respective planes, which makes the visualization of geometry difficult, particularly for complex tools. Modeling a cutting tool using the actual grinding angles can simplify the geometric definition of the tools and provide a comprehensive and simple definition of tools for downstream applications. The paper presents the 3D definition of the faces of a single point cutting tool (SPCT) in terms of 3D rotational grinding angles and maps the new tool nomenclature with the ASA, ORS and NRS nomenclatures. A mechanistic model is subsequently proposed to predict the forces in terms of the grinding angles, chip thickness and velocity using second degree polynomial function, unlike the conventionally used logarithmic ones. The model has been calibrated for HSS tool and Mild Steel workpiece combination for end turning of a tubular workpiece based on the regression analysis of a central composite design of the experiments. The results have been discussed and the model has been validated for a new set of experimental data. The model shows a good correlation to the observed results.     

Experimental and numerical investigations of single abrasive-grain cutting

The present work will provide an in-depth analysis of the abrasive-grain cutting process using a combination of experimental observations and finite element simulations. The workpiece material was AISI 4340. The cutting tool was spherical in shape with a 0.508 mm radius and was fabricated from diamond. The experiments were conducted at cutting speeds of 5−30 m/s in 5 m/s increments and depths of cut from 0.3 to 7.5 μm. The analysis provided a comprehensive understanding of the abrasive-grain cutting process related to the friction between the cutting tool and the workpiece, the material mechanics of the workpiece, and the cutting mechanics of the operation. It was found that the normal forces increased as cutting speed increased due to strain-rate hardening of the workpiece and that the tangential forces decreased as cutting speed was increased due to a reduction in tool-workpiece friction and due to a change in cutting mechanics. The scratch profiles showed that the cutting mechanics changed as cutting speed was increased due to a reduction in material pile-up height. The approximate uncut chip thicknesses for the transitions from elastic, elastoplastic, and fully plastic cutting were identified and were found to increase as cutting speed was increased.     

Correction of dynamic effects on force measurements made with piezoelectric dynamometers

An original method for measuring dynamic forces using a commercial piezoelectric dynamometer is presented. This approach is based on the construction of a correction function taking into account the dynamic behavior of the mechanical environment: milling machine, measuring device and workpiece assembly. It allows measurement of the cutting forces for a large frequency domain exceeding the bandwidth of the piezoelectric dynamometer used. Through the located excitations, the complex equation of Transmissibility between the cutting forces and the dynamometer measurements is obtained. The methodology has been applied for a three-component commercial dynamometer fixed on a milling machine. It has been validated by means of the addition of controlled sinusoidal excitations. This method has applications in high-speed machining and in cutting processes involving instabilities.     

Workpiece and Tool Handling in Metal Cutting Machines

Recently many researchers have focused substantial efforts on understanding the cutting process in mechanics, capability and design. Advances in machine performance with research towards high performance cutting (HPC) and high speed cutting (HSC) have led to improved tool properties and application of advanced materials. Because of that, primary processing time has been successfully reduced, which leads to the need for re-focusing on reduction of secondary processing time. Minimizing the time for workpiece and tool changing, re-positioning, workpiece handling, and tool handling systems shift attention towards improvement of these systems which are currently installed in various metal cutting machine tools. This paper presents an approach for the assessment of the technological effectiveness of workpiece and tool handling systems for metal cutting machine tools, gives an overview of the state of the art of these systems, surveys recent developments and elaborates requirements for future systems.     

Three-dimensional cutting process analysis with different cutting velocities

This paper uses the large deformation large strain finite-element theory, the updated Lagrangian formulation and the incremental theory approach to develop a 3D elastic-plastic analytical model that examines metal cutting on the tool tip and twin nodes on the machined face. The geometric position and the critical value of strain energy density, combined with twin node treatment, are also introduced to serve as the continuous chip separation criterion.

Finally, the 3D low-velocity cutting condition of mild steel was explored to analyze changes in the appearances of the workpiece and the chip, the distribution of stress and strain, and the progress of changes in the cutting force. The impact of different cutting velocities and the initial conditions of the residual stress were studied to understand the impact of various cutting conditions on the machined workpiece. The numerical average cutting forces are compared with the experimental cutting forces with the different low-cutting velocities to verify that the 3D cutting model that has been developed is reasonable.     

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.