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.     

On cutter deflection surface errors in peripheral milling

Cutter deflections induce significant amount of surface error on machined components and it is one of the major obstacles towards achieving higher productivity in peripheral milling operation. These surface errors do not take one particular form and their shape and profile measured along axial direction, varies significantly with cutting conditions. The understanding and characterization of all possible surface error types is of immense value to process planners as it forms a basis for controlling and compensating them. This paper presents a methodology to classify surface error profiles and to relate the same with cutting conditions in terms of axial and radial engagement between cutter and workpiece. The proposed characterization scheme has been validated using computational studies and machining experiments. The importance of proposed characterization is further demonstrated in understanding peripheral milling of curved geometries where workpiece curvature influences radial engagement of the cutter that often changes surface error shape both qualitatively and quantitatively. Computational and experimental studies undertaken to study machining of curved geometries underline the importance of proposed characterization scheme in identifying correct cutting conditions for a given machining situation.     

Active integration of tool deflection effects in end milling. Part 2. Compensation of tool deflection

This study presents a compensation method in milling machining in order to take into account tool deflection during tool-path generation. Tool deflection that occurs during machining, and especially when flexible tools such as end mills are used, can result in dimensional errors on workpieces. The study presented here is part two of a two-part paper. In part one the cutting force models and the surface prediction method have been presented.Here the focus is on tool deflection effects' integration during the generation of the tool path. A strategy is proposed that modifies the nominal tool trajectory, compensates for the machining errors due to tool deflection, without degrading the production performance and the machined accuracy. The methodology allows optimization of the tool path trajectory in order to achieved a specified tolerance. Some experimental results are presented.     

Modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces

The paper presents modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces. The paper differs from previous work in this area, in two respects. Firstly it deals with milling of variable curvature geometries unlike zero and constant curvature geometries dealt in the past. Secondly true tooth trajectories are considered for modelling process geometry in milling of curved surfaces instead of simpler circular tooth trajectories. Mathematical expressions for, feed per tooth along cutter contact path, entry and exits angles of tooth, undeformed chip thickness and surface error are derived and effect of workpiece curvature on these variables is studied. As cutting forces depend on these process variables, physical experiments were also performed to study the effect of workpiece curvature on cutting forces. Process simulation experiments carried out show the need for modelling true tooth trajectories instead of circular tooth trajectories particularly for curved geometries. Results also show that using simpler constant curvature models to variable curvature geometries for the purpose of estimation of process geometry variables could be erroneous.     

Tool deflection and geometrical error compensation by tool path modification

Accuracy of CNC machined components is affected by a combination of error sources such as tool deflection, geometrical deviations of moving axis and thermal distortions of machine tool structures. Some of these errors can be decreased by controlling the machining process and environmental parameters. However other errors like tool deflection and geometrical errors that have a big portion of total error need more sophisticated solutions. Conventional error reduction methods are considered as low efficiency and human dependent methods. Most of recently developed solutions cannot fulfill workshop needs and are limited to research papers. In the present study, machining code modification strategy has been considered as an applicable and effective solution to enhance precise machined components. Appropriate tool deflection estimation model as well as geometrical error analyzing methods have been selected and complementary algorithms for compensation of these errors have been developed. Metal cutting process has been modeled in a 3D simulation environment and implemented in force/deflection calculations. A software has been developed to generate compensated tool path NC program by tracing the initial tool path and compensating deflection/geometry deviations. The new procedure developed in the present work has been validated by machining Spline contours. The results show that using the new method, accuracy of machined features can be improved by about 8-10 times in a single pass.     

A novel spindle inclination error identification and compensation method in ultra-precision raster milling

In the ultra-precision raster milling (UPRM) process, the existence of spindle inclination error can directly affect the dimensional accuracy of machined components. This study developed a novel spindle inclination error identification and compensation method based on the groove cutting in UPRM. In this method, the tilt angle of the intersection curve of two toruses (ICTT) generated from two neighboring rotary cuts in UPRM was measured to identify the spindle inclination error. A mathematical model was developed to simulate the ICTT profile and present the relationship between the tilt angle of ICTTs and the spindle inclination error by solving the differential of the ICTT function, by which the spindle inclination error can be solved under the given cutting parameters and the tilt angle of ICTTs. The effects of cutting parameters on the tilt angle of ICTTs were explored. An error compensation procedure was designed and a group of groove cutting experiments was conducted to identify and compensate the spindle inclination error. The theoretical and experimental results show that the proposed method can compensate for the spindle inclination error effectively and accurately.     

Process geometry modeling with cutter runout for milling of curved surfaces

Prediction of cutting forces and machined surface error in peripheral milling of curved geometries is non-trivial due to varying workpiece curvature along tool path. The complexity in this case, arises due to continuously changing process geometry as workpiece curvature varies along tool path. In the presence of cutter runout, the situation is further complicated owing to changing radii of cutting points. The present work attempts to model process geometry in machining of curved geometries and in the presence of cutter runout. A mathematical model computing process geometry parameters which include cutter/workpiece engagements and instantaneous uncut chip thickness in the presence of cutter runout is presented. The developed model is more realistic as it accounts for interaction of cutting tooth trajectory with that of preceding teeth trajectories in computing process geometry. Computer simulation studies carried for this purpose has shown that it is essential to account for teeth trajectory interactions for accurate prediction of process geometry parameters. This aspect is further confirmed with machining experiments, which were conducted to validate this aspect. From the outcomes of present work, it is clearly seen that the computation of process geometry during machining of curved geometries and in presence of cutter runout is not straightforward and requires a systematic approach as presented in this paper.     

Effect of cutter runout on process geometry and forces in peripheral milling of curved surfaces with variable curvature

This paper presents a novel method for cutting force modeling related to peripheral milling of curved surfaces including the effect of cutter runout, which often changes the rotation radii of cutting points. Emphasis is put on how to efficiently incorporate the continuously changing workpiece geometry along the tool path into the calculation procedure of tool position, feed direction, instantaneous uncut chip thickness (IUCT) and entry/exit angles, which are required in the calculation of cutting force. Mathematical models are derived in detail to calculate these process parameters in occurrence of cutter runout. On the basis of developed models, some key techniques related to the prediction of the instantaneous cutting forces in peripheral milling of curved surfaces are suggested together with a whole simulation procedure. Experiments are performed to verify the predicted cutting forces; meanwhile, the efficiency of the proposed method is highlighted by a comparative study of the existing method taken from the literature.     

Active integration of tool deflection effects in end milling. Part 1. Prediction of milled surfaces

Tools deflection that occurs during machining, and especially when flexible tools such as end mills are used, can result in dimensional errors on workpieces. The study presented here is part one of a two-part paper: it deals with the estimation of cutting forces and the prediction of milled surface. The second part will focus on a methodology that allows to optimize the production rate by compensating the deflection and meeting the part tolerance.Cutting force models have been and are still the subject of a lot of research. The model used is based on Kline and Devor's [5]: a polynomial approximation whose coefficients are obtained by least square methodology is used for the calculation of cutting forces. The machined surface (two axis machining) is determined using the contact point methodology and some experimental tests are done to validate the models.     

Modelling the machining dynamics of peripheral milling

The machining dynamics involves the dynamic cutting forces, the structural modal analysis of a cutting system, the vibrations of the cutter and workpiece, and their correlation. This paper presents a new approach modelling and predicting the machining dynamics for peripheral milling. First, a machining dynamics model is developed based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces, which are mathematically modelled and experimentally verified by the authors [Liu, X., Cheng, K., Webb, D., Luo, X.-C. Improved dynamic cutting force model in peripheral milling—Part 1: Theoretical model and simulation. Int. J. Adv Manufact Tech, 2002, 20, 631–638; Liu, X., Cheng, K., Webb, D., Longstaff, A. P., Widiyarto, H. M., Jiang, X.-Q., Blunt, L., Ford, D. Improved dynamic cutting force model in peripheral milling—Part 2: Experimental verification and prediction. Int. J. Adv Manufact Tech, 2004, 24, 794–805]. Then, the mechanism of surface generation is analysed and formulated based on the geometry and kinematics of the cutter. Thereafter a simulation model of the machining dynamics is implemented using Simulink. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machine centre were measured in both normal and feed directions by an instrumented hammer and accelerometers. Then a set of well-designed cutting trials was carried out to record and analyse the dynamic cutting forces, the vibrations of the spindle head and workpiece, and the surface roughness and waviness. Corresponding simulations of the machining processes of these cutting trials based on the machining dynamics model are investigated and the simulation results are analysed and compared to the measurements. It is shown that the proposed machining dynamics model can well predict the dynamic cutting forces, the vibrations of the cutter and workpiece. There is a reasonable agreement between the measured and predicted roughness/waviness of the machined surface. Therefore the proposed approach is proven to be a feasible and practical approach analysing machining dynamics and surface roughness/waviness for shop floor applications.     

Geometric and force errors compensation in a 3-axis CNC milling machine

This paper proposes a new off line error compensation model by taking into accounting of geometric and cutting force induced errors in a 3-axis CNC milling machine. Geometric error of a 3-axis milling machine composes of 21 components, which can be measured by laser interferometer within the working volume. Geometric error estimation determined by back-propagation neural network is proposed and used separately in the geometric error compensation model. Likewise, cutting force induced error estimation by back-propagation neural network determined based on a flat end mill behavior observation is proposed and used separately in the cutting force induced error compensation model. Various experiments over a wide range of cutting conditions are carried out to investigate cutting force and machine error relation. Finally, the combination of geometric and cutting force induced errors is modeled by the combined back-propagation neural network. This unique model is used to compensate both geometric and cutting force induced errors simultaneously by a single model. Experimental tests have been carried out in order to validate the performance of geometric and cutting force induced errors compensation model.     

Effect of direction of parameterization on cutting forces and surface error in machining curved geometries

The present paper investigates the effect of two variables, namely direction of parameterization and cutter diameter on process geometry, cutting forces, and surface error in peripheral milling of curved geometries. In machining of curved geometries where the curvature varies continuously along tool path, the process geometry variables, namely feed per tooth, engagement angle, and maximum undeformed chip thickness too vary along tool path. These variations will be different when a given geometry is machined from different parametric directions and with different cutter diameters. This difference in process geometry variations result in changed cutting forces and surface error along machined path. This aspect has been studied for variable curvature geometries by machining from both parametric directions and using cutters of different diameter. The computer simulation studies carried out show considerable amount of shift in the location of peak cutting forces with the change in cutting direction and cutter diameter, particularly in concave regions of workpiece geometry. A new parameter γ that relates the instantaneous curvature of workpiece with cutter radius is defined. The larger value of γ is an indicator of greater shift in the location of peak forces from the point of maximum curvature on the workpiece. The simulation results are validated by carrying out machining experiments with curved workpiece geometry and are found to be in good agreement.     

The application of tool deflection knowledge in process planning to meet geometric tolerances

Machine tool deflections due to cutting forces can result in dimensional errors on workpieces. The problem is most severe when flexible tools such as end mills are used. When dimensioned features are specified with tolerances, process planning should examine the compromise between achieving high productivity rates and meeting dimensions within the specified tolerances. The use of geometric dimensioning and tolerancing permits interaction between size and position and makes bonus tolerances available. The errors occurring in end milling are first examined and modelled using regression methods. A procedure is proposed for selecting optimal feed rates that ensure that tolerances can be met. The process is demonstrated in machining a slot using the down milling mode. The use of a tolerance analysis chart clarifies the results of the test in relation to the tolerance standards. The need to consider the transient errors at the exit of the cut is demonstrated.     

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.     

Model for surface topography prediction in peripheral milling considering tool vibration

This paper presents a model for the prediction of surface topography in peripheral milling operations taking into account that the tool vibrates during the cutting process. The model includes the effect of tool vibrations in the equations of the cutting edge paths, which are transformed into equivalent polynomial equations and solved for discrete positions along the feed direction by applying a standard root finder. Through this procedure, surface topography generation is simplified with respect to other models in literature. The model allows the topography, the roughness values and the form errors of the milled surface to be predicted. Cutting test results show good agreement with model predictions.     

伺服刀架系统的反复反馈误差补偿控制

对于具有滞后特性的伺服刀架系统,采用自校正ＰＩＤ控制。在此基础上,为进一步提高伺服刀架系统的跟踪精度,提出了反复反馈误差补偿控制方法。理论分析和实验结果都表明,该控制方法以有效地提高伺服刀架的跟踪精度。     

An experimental and numerical study on the face milling of Ti-6Al-4V alloy: Tool performance and surface integrity

This paper is concerned with the experimental and numerical study of face milling of Ti-6Al-4 V titanium alloy. Machining is carried out by uncoated carbide cutters in the presence of an abundant supply of coolant. Experimental analysis is conducted by focusing on the measurement of specific cutting energy, surface integrity and tool performance. The experimental analysis is supplemented by simulations from a 3D finite element model (FEM) of face milling simulation where needed. A tool wear model parameterized from FEM predictions of the tool-chip interface temperature, contact stress and chip velocity is presented. Tool wear patterns are described in terms of various cutting conditions and the influence of tool wear on surface integrity is investigated. Tool wear predictions based on the 3D FEM simulation show good agreement with experimental tool wear measurements. The highest cutting speed realized for the cutting tool material is 182.9 m/min (600 sfpm). Good surface integrity in terms of favorable residual stress and surface finish is achieved under the machining conditions used with limited tool wear. Residual stresses imparted to the machined surface are shown to be compressive.     

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.     

Improvement of surface flatness in face milling based on 3-D holographic laser metrology

This paper presents two approaches to improve the flatness of face milled surface based on 3-D holographic laser measurement. The first approach, cutting depth compensation method, generates a compensation cutting profile that is ideally a mirror image of the surface profile from a straight cutting path. The surface profile describes the machined surface along the feed direction and is extracted using surface decomposition technique developed in this study. Issues of back-cutting and gouging, which limit the applicability of this approach, are also addressed. The second prescribed approach is the feed rate optimization method. In this technique, the tool feed rate is altered to match the axial force on the cutter with the local compliance of the workpiece. This is performed with the aim of reducing force-induced distortion. Experiments using aluminum workpieces and 50.8 mm diameter face mill demonstrate that the surface flatness can be reduced from 32 to 7 μm with the cutting depth compensation method. With the optimized feed rate, the flatness can be reduced by 19 μm with the same cycle time as that of the original constant feed rate.     

An advanced FEA based force induced error compensation strategy in milling

The study introduces a multi-level machining error compensation approach focused on force-induced errors in machining of thin-wall structures. The prediction algorithm takes into account the deflection of the part in different points of the tool path. The machining conditions are modified at each step when the cutting force and deflection achieve a local equilibrium. The machining errors are predicted using a theoretical flexible force-deflection model. The error compensation is based on optimising the tool path taking into account the predicted milling error. The error compensation scheme is simulated using NC simulation package and is experimentally verified.