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.     

Tool deflection compensation in peripheral milling of curved geometries

This paper presents compensation of surface error due to cutting force-induced tool deflections in a peripheral milling process. Previous research attempts on this topic deal with error compensation in machining of straight geometries only. This paper is concerned with peripheral milling of variable curvature geometries where the workpiece curvature changes continuously along the path of cut. In the case of curved geometries, both process geometry and the cutting forces have shown to have strong dependence on workpiece curvature and hence variation of surface error along the path of cut. This calls for a different error compensation strategy than the one which is normally used for machining straight geometries. The present work is an attempt to improve accuracy in machining of curved geometries by use of CNC tool path compensation. Mechanistic model for cutting force estimation and cantilever beam model for cutter deflection estimation are used. The results based on machining experiments performed on a variety of geometries show that the dimensional accuracy can be improved significantly in peripheral milling of curved geometries.     

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.     

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.     

Sculpture surface machining: a generalized model of ball-end milling force system

A new mechanistic model is presented for the prediction of a cutting force system in ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter location (CL) file, cutter and workpiece geometries. Furthermore, an analytical approach is used to determine the instantaneous chip load (with and without runout) and cutting forces. In addition to predicting the cutting forces, the model also employs a Boolean approach for a given cutter, workpiece geometries, and CL file to determine the surface topography and scallop height variations along the workpiece surface which can be visualized in 3-D. The results of model validation experiments on machining Ti-6A1-4V are also reported. Comparisons of the predicted and measured forces as well as surface topography show good agreement.     

Mechanics and dynamics of general milling cutters.: Part I: helical end mills

A variety of helical end mill geometry is used in the industry. Helical cylindrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining industry. While the geometry of each cutter may be different, the mechanics and dynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills used in the industry. The end mill geometry is modeled by helical flutes wrapped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip thickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. The predicted and measured cutting forces, surface roughness and stability lobes for ball, helical tapered ball, and bull nosed end mills are provided to illustrate the viability of the proposed generalized end mill analysis.     

Dynamics of boring processes: Part III-time domain modeling

This article presents a mathematical model and a computational algorithm for the time domain solution of boring process dynamics. The model is developed in a modular form; it includes a workpiece geometry and surface topography module, a kinamatics and tool position module, a dynamic chip load module, a dynamic cutting force prediction module and a structural dynamics module. The time domain model takes cutting process parameters, tool and workpiece geometries and modal parameters of the structure as inputs. It predicts instantanous cutting forces and vibrations along the machining time, and machined workpiece topography as outputs. Some of the simulated and experimental results for various cutting conditions are presented and compared for validation purposes.     

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.     

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.     

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.     

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.     

Simulation of flank milling processes

The paper presents prediction of cutting forces when flank milling ruled surfaces with tapered, helical, ball end mills. The geometric model of the workpiece is imported from standard CAD systems, and the tapered helical ball end mill is modeled as the combination of sphere and cone primitives in ACIS^© solid modeling environment. The intersection of cutter and part with a ruled surface is evaluated, and the cutter entry into and exit angles from the work material are modeled, and stored as a function of tool center coordinates along the path. The cutter entry and exit angles, the immersion angles, are used as boundary conditions in predicting the cutting forces along the path. The methodology allows prediction of cutting load distribution on the tool and part, as well optimization of machining cycle times by scheduling the feedrate in such a way that torque, power and static deflections can be maintained at safe levels.     

球头铣刀铣削斜面的三维有限元仿真研究

在能源动力、汽车、航空航天、模具制造等关键零部件的加工过程中,球头铣刀因其特有的刀具几何结构,常作为零件加工的最终成型刀具。考虑到在球头铣刀立铣加工中不同的刀具与工件相对姿态会对切削过程产生不同的影响,本文研究切屑形成和不同走刀方式下切削过程中各物理量(切削力、切削温度等)的变化情况,结合有限元仿真技术在切削加工中的应用,建立硬质合金球头铣刀铣削斜面的有限元模型,模拟相同切削参数下,八种不同走刀方式的球头铣削过程,分析刀具切入切出工件时切屑的形成过程,探究切削力和切削温度的变化规律。仿真结果表明:不同的走刀方式,平均切削合力各不相同,同时切屑和工件的最大切削温度也出现较大差异,而斜坡上坡逆铣的走刀方式所对应的平均切削合力和最大切削温度均最优。     

The application of an inclined end mill machining strategy on 3-axis machining centres

An inclined end mill machining strategy offers an effective machining method for manufacturing low curvature free-form surfaces. The machined surface profile is a close match to the required surface geometry, and standard end mills are available at competitive prices. The amount of surface finishing work is therefore reduced, and the inclined cutting action prolongs the tool life. Although this machining strategy has these advantages, it is not commonly used in manufacturing industry, because it needs the facilities of costly 5-axis machining centres and appropriate post processors are required to generate the NC codes for these advanced machine tools. This paper proposes a simple method which extends the machining capability of the conventional 3-axis machining centre to give the same specifications as a 5-axis machine, and therefore allow the inclined end mill machining strategy to be used on 3-axis machines. The method involves tilting the workpiece instead of tilting the end mill during the machining process. The tool paths are determined by the workpiece rotation and cutter contact point offset equations. The amount of excess material on the machined surface is minimized by choosing optimum pitching and rolling angles at the work set-up stage. The experimental results indicate that the quality of the machined surfaces is improved in comparison with the surfaces machined by ball-nosed cutters, e.g. the resulting cusp volume is reduced by 64%. The research suggests that the need for advanced and expensive 5-axis machining could be satisfied in a more economical machining environment. As a result, the machining cost of the products may be significantly reduced.     

Milling force prediction using a dynamic shear length model

Modelling of cutting forces in milling is often needed in machining automation. In this paper, a new method for the determination of the cutting forces in face milling is presented, which applies a predictive machining theory originally developed for orthogonal cutting to milling operations, with a dynamic shear length model developed and incorporated. The proposed dynamic shear length model is developed based on the analysis for the true tooth trajectories of a milling cutter, taking into account of the characteristic wavy surface effects in milling. The prediction for the cutting forces is carried out at each step of the angular increment of cutter rotation from input data of fundamental workpiece material properties, tool geometry and cutting conditions. Cutting forces at a cutter tooth can be predicted once the shear angle, shear length, shear plane area, and the shear flow stress along the shear length have been determined. The milling force prediction using the dynamic shear length model is verified through milling experimental tests. The sensitivity of the difference between the static and dynamic shear length models with respect to the feed per tooth and the cutter diameter is discussed.     

An improved process simulation system for ball-end milling of sculptured surfaces

A simulation system is developed in this paper, which deals with the geometry and mechanics of machining with ball-end milling cutters. The geometry of the workpiece, the cutter, and the cutter/workpiece engagement is modeled using a geometric simulation system. This module uses a commercial solid modeler (ACIS) as a geometric engine and automatically extracts the critical geometric information required for the physical simulation system. To calculate the instantaneous cutting forces, a new mechanistic force model is developed. This force model takes into account the variations of the cutting coefficients along the cutting edge, and considers the variations of the rake angle and the chip flow direction on the rake face. The calibration of the developed model is performed for half-immersion ball-end milling operation. The applicability of the developed system is verified experimentally for various up-hill angles. It is shown that as the up-hill angle increases, the ball-nose tip engagement decreases which in turn significantly affects the magnitude of the resultant forces. Also, lower cutting forces and powers are experienced if cutting with the vicinity of the tool tip is avoided.     

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.     

Theoretical modelling and simulation of cutting forces in face milling with cutter runout

A new approach to theoretical modelling and simulation of cutting forces in face milling is presented. Based on a predictive machining theory, the action of a milling cutter is modeled as the simultaneous actions of a number of single-point cutting tools. The milling forces are predicted from the workpiece material properties, cutter parameters, tooth geometry, cutting conditions and types of milling. The properties of the workpiece material are considered as functions of strain, strain-rate and temperature in the cutting region. It takes into account the effect of the intermittent contact between each milling tooth and the workpiece on the temperature in the cutting region. It also takes into account the effect of cutter runout on the undeformed chip thickness. Milling experiments have been conducted to verify the proposed model. Good agreements between the experimental and simulated results are presented.     

Off-line modelling and planning of optimal clamping forces for an intelligent fixturing system

An intelligent fixturing system (IFS) for machining aims to adaptively adjust the clamping forces to achieve minimum deformation of the workpiece according to the cutter position and the cutting forces. This paper presents the concept, architecture, control scheme, models and methodologies for an IFS. Using off-line simulations and on-line experimental verifications, the performance of the proposed IFS is evaluated and verified. As adaptive clamping forces appropriate to the dynamic machining environment are employed, the IFS offers higher quality of machined parts and greater robustness to disturbances. This system is suitable for application in high-precision machining environment as well as flexible manufacturing systems (FMS).     

Generation of a regularly aligned surface pattern and control of cutter marks array by patch division milling

In this paper, a patch division milling technique that can generate a geometric surface pattern by means of a ball-end mill on a surface is proposed. The finished surface is divided into many same-size small patch segments such as triangles, quadrilaterals, or hexagons. The whole inside area of each patch is machined along a helical tool path with a high feed rate. A geometric surface pattern is generated by the cutting edges of the ball-end mill within the patch area, and after the machining of a series of patches, the machined surface is covered with many patches. It is shown that the aligned state of the cutter marks array on the patch can be controlled by the cross-feed, the feed speed per tooth, the number of teeth and the side length of the patch. A simulator was also developed to predict the aligned state of the cutter marks array in the patch. Comparing the machining on the patch division milling between an inclined flat surface and a cylindrical surface, the regularly aligned surface pattern and cutter marks array were found to agree well with the simulation results. The objective of this research is to establish the cutting method of generating regularly aligned surface pattern on the complex-shaped workpiece efficiently. If the surface pattern on the complex-shaped workpiece could be formed only by the ball-end milling with a machining center, it will be a very effective tool for the machinery industry.