Estimation of cutter deflection and form error in ball-end milling processes

This paper presents a method to analyze the 3-dimensional form error of a ball-end milled surface due to the elastic compliance of the cutting tool. In order to estimate the form error in various cutting modes, the cutting force and the cutter deflection models including the effect of the surface inclination were established. The cutting forces were calculated by using the cutter contact area determined from the Z-map of the surface geometry and the current cutter location. The tool deflection responding to the cutting force was then calculated by considering the cutter and the holder stiffness. The cutter was modeled as a cantilever beam consisting of the shank and the flute. The stiffness of the holder was measured experimentally. Various experimental works have been performed to verify the validity of the proposed model. It is shown that the proposed method is capable of accurate prediction of cutting forces and the surface form error.     

The form error prediction in side wall machining considering tool deflection

In this research, an effective method for the form error prediction in side wall machining with a flat end mill is suggested. The form error is predicted directly from the tool deflection without surface generation by cutting edge locus with time simulation. The developed model can predict the surface form error accurately about 300 times faster than the previous method. Cutting forces and tool deflection are calculated considering tool geometry, tool setting error and machine tool stiffness. The characteristics and the difference of generated surface shape in up milling and down milling are discussed. The usefulness of the presented method is verified from a set of experiments under various cutting conditions generally used in die and mold manufacturing. This study contributes to real time surface shape estimation and cutting process planning for the improvement of form accuracy.     

Controlling toolholder fretting through simple design modifications

During machining, cutting forces exerted on a toolholder may cause its shank to deflect and impact on the spindle pocket surface. This repetitive impact between the spindle and toolholder may result in a fretting condition. Over time, this fretting condition leads to wear and corrosion damage that is costly to repair and can potentially affect machining performance. Since fretting conditions are caused by vibrations and different toolholder designs will have different dynamic characteristics, it is possible to find those designs that would minimise shank deflections, and thus minimise the fretting condition. In this paper, through finite element simulations and experimental testing, two types of toolholders were studied: straight shank and tapered shank. It was found that within typical operating frequencies, shank deflections were less in tapered designs than in straight designs. Also, the deflections decreased as the length of the toolholder decreased. However, increasing the body diameter of the toolholder had no significant effect. Accordingly, a number of simple design modifications (changing the diameter and length of the toolholders) are suggested to minimise the fretting condition.     

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.     

Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations

This paper presents a general, integrated model of the spindle bearing and machine tool system, consisting of a rotating shaft, tool holder, angular contact ball bearings, housing, and the machine tool mounting. The model allows virtual cutting of a work material with the numerical model of the spindle during the design stage. The proposed model predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, as well as contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The proposed models are verified experimentally by conducting comprehensive tests on an instrumented-industrial spindle. The study shows that the accuracy of predicting the performance of the spindles require integrated modeling of all spindle elements and mounting on the machine tool. The operating conditions of the spindle, such as bearing preload, spindle speeds, cutting conditions and work material properties affect the frequency and amplitude of vibrations during machining.     

Real-time estimation of cutting forces via physics-inspired data-driven model

A method is presented to estimate the cutting forces in real time within machine tools for any spindle speed, force profile, tool type, and cutting conditions. Before cutting, a metrology suite and instrumented tool holder are used to induce magnetic forces during spindle rotation, while on-machine vibrations, magnetic forces, and error motions are measured for various combinations of speeds and forces. A physics-inspired data-driven model then relates the measured accelerations to the magnetic forces, such that during cutting, on-machine measured vibrations are used in the model to estimate the cutting forces in real time.     

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.     

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.     

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.     

High frequency bandwidth cutting force measurement in milling using capacitance displacement sensors

This article presents a method of measuring cutting forces from the displacements of rotating spindle shafts. A capacitance displacement sensor is integrated into the spindle and measures static and dynamic variations of the gap between the sensor head and the rotating spindle shaft under cutting load. To calibrate the sensing system, the tool is loaded statically while the deflection of the tool is measured with the capacitance probe. With this calibration, the displacement sensor can be used as an indirect force sensor. However, the measurement bandwidth is limited by the natural modes of the spindle structure. If cutting force frequency contents are within the range of the natural modes of the spindle structure or higher, the measurements are distorted due to the dynamic characteristics of the spindle system. In order to increase the bandwidth of the indirect force sensor by compensating for the spindle dynamics, the design of a Kalman filter scheme, which is based on the frequency response function (FRF) of the displacement sensor system to the cutting force, is presented in this paper. With the suggested sensing and signal processing method, the frequency bandwidth of the sensor system is increased significantly, from 350 to approximately 1000 Hz. The proposed indirect force sensor system is tested experimentally by conducting cutting tests up to 12,000 rpm with a five-fluted end mill. Besides cutting forces, the measured displacements can also be affected by factors such as roundness errors, unbalance at different speeds, or dilatation of the spindle shaft due to temperature variations. Methods to compensate for these disturbing effects are also described in the paper.     

The form error reduction in side wall machining using successive down and up milling

In this paper, the form error reduction method is presented in side wall machining. Cutting forces and tool deflection are calculated considering surface profile generated by the previous cutting such as roughing and semi-finishing. Using the form error prediction from tool deflection curve, the effects of tool teeth numbers, tool geometry and cutting conditions on the form error are analyzed. The characteristics and the differences of generated surface shape in up and down milling are also discussed and over-cut free condition in up milling is presented. The form error reduction method through successive down and up milling has been suggested. The effectiveness and usefulness of the suggested method are verified from a series of cutting experiments under various cutting conditions. It is confirmed that the form error prediction from tool deflection in side wall machining can be used in proper cutting condition selection and real time surface error simulation for CAD/CAM systems. This research also contributes to cutting process optimization for the improvement of form accuracy in die and mold manufacture.     

Characteristics of stiffness and contact stress distribution of a spindle–holder taper joint under clamping and centrifugal forces

An understanding of the contact characteristics of a spindle–holder joint in machine tools calls for an in-depth analysis of its performance under machining conditions. This study specifically aims to model a spindle–holder taper joint to predict the stiffness and stress distribution under different clamping and centrifugal forces. A spindle–holder taper joint subjected to clamping and centrifugal forces was modeled using the finite element method. The stress distribution of the interface was revealed and it was found that the von-Mises stress had a non-linear distribution because of the clamping force of the holder. The centrifugal forces were included in the model to analyze the deformation of the joint. At high speed the centrifugal force caused a stress concentration at the large end of the holder. A typical 7/24 taper joint of a BT50 holder was investigated to identify the stiffness using a special experimental platform. The axial and radial stiffnesses, as well as the hysteresis cycles were obtained to predict the contact characteristics with different clamping forces. The experimental results showed that the model presented in this study was efficient in predicting the characteristics of the spindle–holder joint. The method presented is useful in identifying the dynamics of a spindle–holder and can thus be used to optimize the spindle system.     

Virtual Design and Optimization of Machine Tool Spindles

An integrated digital model of spindle, tool holder, tool and cutting process is presented. The spindle is modeled using an in-house developed Finite Element system. The preload on the bearings and the influence of gyroscopic and centrifugal forces from all rotating parts due to speed are considered. The bearing stiffness, mode shapes, Frequency Response Function at any point on the spindle can be predicted. The static and dynamic deflections along the spindle shaft as well as contact forces on the bearings can be predicted with simulated cutting forces before physically building and testing the spindles. The spacing of the bearings are optimized to achieve either maximum dynamics stiffness or maximum chatter free depth of cut at the desired speed region for a given cutter geometry and work-piece material. It is possible to add constraints to model mounting of the spindle on the machine tool, as well as defining local springs and damping elements at any nodal point on the spindle. The model is verified experimentally.     

Tool positioning error (TPE) characterisation in milling

Where the geometrical features so permit, the {workpiece–work-holding fixture} assembly is generally considered to be infinitely rigid. The {tool–tool-holder–spindle} assembly and the machine axes are then deformed under the action of the cutting forces. This deformation leads to a positioning error of the tool in relation to the theoretical position. With the aim of taking this positioning error into account, the inaccuracies obtained during end milling and side milling were experimentally modelled from the cutting conditions used for a given machine/mill/material triplet (TriM). Our “Virtual Worker” then used these models to predict machining errors according to the type of machining and to compensate for them.     

5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement

Deformation of the part and cutter caused by cutting forces immediately affects the dimensional accuracy of manufactured parts. This paper presents an integrated machining deviation compensation strategy based on on-machine measurement (OMM) inspection system. Previous research attempts on this topic deal with deformation compensation in machining of geometries in 3-axis machine tools only. This paper is the first time that concerned with 5-axis flank milling of flexible thin-walled parts. To capture the machined surface precision dimensions, OMM with a touch-trigger probe installed on machine׳s spindle is utilized. Probe path is planned to obtain the coordinate of the sampling points on machined surface. The machined surface can then be reconstructed. Meanwhile, the cutter׳s envelope surface is calculated based on nominal cutter location source file (CLSF). Subsequently, the machining error caused by part and cutter deflection is calibrated by comparing the deviation between the machined surface and the envelope surface. An iteration toolpath compensation algorithm is designed to decrease machining errors and avoid unwanted interference by modifying the toolpath. Experiment of machining the impeller blade is carried out to validate the methodology developed in this paper. The results demonstrate the effectiveness of the proposed method in machining error compensation.     

Assessment of Force-Induced Errors in CNC Turning

This paper describes a procedure to evaluate the force-induced errors occurring in cylindrical turned components. This procedure is based on a model which represents the real-time stiffness of the spindle-bearing system and the rotational clamping stiffness of the component held in a chuck. The stiffness values are determined from a single cutting test in which the deflection of a test bar is measured. The model also takes into account the stiffness of the component and toolpost. The model is validated by comparing the predicted error in the cylindricity of a machined bar with the measured value.     

A shape memory alloy based tool clamping device

The traditional collet-chuck mechanism for tool clamping is a significant source of errors in spindles due to stack-up tolerances. This, in turn, adversely affects the tool's error motions particularly in demanding micro-cutting operations performed with ultra-high-speed miniaturized spindles. Hence, novel thought for miniature tool clamping is needed to minimize tool run-out and error motions in order to meet the necessary cutting speeds and accuracy requirements. In this paper a couple of Shape Memory Alloy (SMA) based solutions for the clamping of miniature tools will be explored. For clamp actuation the so-called Two-Way Shape Memory Effect (TWSME) property of NiTi SMAs will be exploited. The basic principles, design requirements, analysis and physical realization of these devices will be discussed. It will be shown through experimental verification tests that clamping forces in excess of tens of Newtons are possible, confirming thus the feasibility of the proposed solutions.     

基于CAE和神经网络的切削参数优化

提出了一种以变形加工误差为约束的基于有限元分析和神经网络的切削参数优化方法.针对复杂工件夹具系统在切削过程中的变形问题进行有限元刚度计算,然后通过神经网络的方法拟合切削参数和工件夹具系统变形误差之间的关系.并以加工生产效率最大化为目标,在保证加工精度的前提下优化切削参数.从而实现以工艺成本最小化来提高零件的加工精度.     

Error compensation in flexible end milling of tubular geometries

There are many machining situations where slender tools are used to machine thin walled tubular workpieces. Such instances are more common in machining of aircraft structural parts. In these cases, cutting force induced tool as well as workpiece deflections are quite common which result into surface error on machined components. This paper presents a methodology to compensate such tool and workpiece induced surface errors in machining of thin walled geometries by modifying tool paths. The accuracy with which deflections can be predicted strongly depends on correctness of the cutting force model used. Traditionally employed mechanistic cutting force models overestimate tool and workpiece deflections in this case as the change of process geometry due to deflections is not accounted in modeling. Therefore, a cutting force model accounting for change in process geometry due to static deflections of tool and workpiece is adopted in this work. Such a force model is used in predicting tool and workpiece deflection induced surface errors on machined components and then compensating the same by modifying tool path. The paper also studies effectiveness of error compensation scheme for both synclastic and anti-clastic configurations of tubular geometries.     

A new method to quantify radial error of a motorized end-milling cutter/spindle system at very high speed rotations

The radial error motion of a machine tool cutter/spindle system is critical to the dimensional accuracy of the parts to be machined. The spindle's radial error motions can be measured by mounting a sphere target onto the spindle as a reference. A set of sensors is used to measure displacements of the reference sphere in various directions to determine spindle error motions. This measurement technique can be reliably carried out when the spindle is at rest or at low rotational speeds. However, at very high speeds, the reference sphere must be carefully centered and balanced to avoid introducing additional error motions. In addition, the sensors must be held with very rigid mounts in order to avoid measurement errors caused by vibrations. For high-speed end milling spindles, the spindle is operated with a cutter. The cutter must be removed when mounting a reference sphere. Because the cutter itself can introduce errors due to centering and unbalancing effects, the error motions measured by the reference sphere method do not include the error caused by the cutter. This paper introduces a new and practical method to provide an indicator of the radial error of a motorized end-milling cutter/spindle system at very high speed rotations without the need of a reference sphere. This indicator of the radial error is based on the size of the cutting marks produced by the end mill, which is attached to the spindle. The cutting marks are circular, and their diameters are related to the radial error of the cutter/spindle system. Quantitative precision analysis was carried out to confirm the accuracy and repeatability of this new measurement technique. This technique has been implemented in order to determine the effects of the spindle speed, the level of unbalanced mass, and the spindle stiffness on the cutter/spindle's radial error. The results reveal that the centrifugal force generated by the unbalanced mass is the main factor causing the increase in radial error. One way to compensate for the effect of unbalanced mass is to increase the spindle stiffness. Experimental results confirm that a higher front bearing preload can render the spindle stiffer, thus reducing the radial error of the cutter/spindle system. Finally, it should be pointed out that the proposed cutting mark measurement cannot replace the sphere method because it cannot provide time-resolved or angle-resolved information as those obtained from polar charts. However, the proposed cutting mark measurement can provide the characterization of the spindle with the cutter attached. As a result, both methods can complement each other to provide a more complete picture of the behavior of the cutter/spindle system at high speeds.