Workpiece Deflection Research Articles

On modeling of cutting forces in micro-end milling operation

ABSTRACTMicro-end milling is used for manufacturing of complex miniaturized components precisely in wide range of materials. It is important to predict cutting forces accurately as it plays vital role in controlling tool and workpiece deflections as well as tool wear and breakage. The present study attempts to incorporate process characteristics such as edge radius of cutting tool, effective rake and clearance angles, minimum chip thickness, and elastic recovery of work material collectively while predicting cutting forces using mechanistic model. To incorporate these process characteristics effectively, it is proposed to divide cutting zone into two regions: shearing- and ploughing-dominant regions. The methodology estimates cutting forces in each partitioned zone separately and then combines the same to obtain total cutting force at a given cutter rotation angle. The results of proposed model are validated by performing machining experiments over a wide range of cutting conditions. The paper also highlights the importance of incorporating elastic recovery of work material and effective rake and clearance angle while predicting cutting forces. It has been observed that the proposed methodology predicts the magnitude and profile of cutting forces accurately for micro-end milling operation.

Precision measurement of Z-slide vertical error motion of an ultra-precision lathe by using three-probe method

This paper presents a precision measurement of the Z-slide vertical error motion of an ultra-precision lathe based on a three-probe measurement method. The vertical error motion of the Z-slide, which is composed of the vertical parallelism error motion and the vertical straightness error motion, is measured by utilizing three displacement measuring probes to scan a self-cut roll workpiece and an accurate straightedge, respectively. A series of factors which could influence the measurement of the vertical error motion, including the error motion of the spindle, the surface form error of the reference object and the horizontal error motion of the Z-slide, are all successfully removed by using the proposed three-probe measurement system with an error separation method. The influence of the gravity induced deflection of the roll workpiece on the measurement of the Z-slide vertical parallelism error motion is also discussed. Experiments were carried out to verify the feasibility of the proposed methods on a three-axis ultra-precision lathe. The vertical straightness error motion was evaluated to be 133 nm with a measurement repeatability of 21 nm and the vertical parallelism error motion was evaluated to be 12.1 μm with a measurement repeatability of 38 nm.

Study in dimension precision of micro straight thin wall with Ti-6Al-4V titanium alloy under mesoscale

Deflection problems are important causes of deterioration to the dimensional precision of machining micro thin-walled components. Under mesoscale, the deflection of the cutting tool and micro thin-walled workpiece model is established based on the Euler-Bernoulli cantilever beam theory. Then a novel average thickness prediction model of micro straight thin wall is set up considering the runout, cutting tool, and workpiece deflection. Afterwards, based on experimental data, the model is modified by introducing a scale factor K. This modified model has been calibrated and validated with Ti-6Al-4V titanium alloy, and it can provide very accurate prediction results for the micro straight thin wall at average thickness. In addition, the law of micro thin wall milling forces is also studied. In the end, the effect of different micro straight thin-walled stiffness on micro thin-walled dimensional accuracy is analyzed. The study found that for the thickness of micro straight thin walls, 100 μm is an inflection point to distinguish dimension precision between macroscale and mesoscale.

Real-Time Deflection Monitoring for Milling of a Thin-Walled Workpiece by Using PVDF Thin-Film Sensors with a Cantilevered Beam as a Case Study.

Thin-walled workpieces, such as aero-engine blisks and casings, are usually made of hard-to-cut materials. The wall thickness is very small and it is easy to deflect during milling process under dynamic cutting forces, leading to inaccurate workpiece dimensions and poor surface integrity. To understand the workpiece deflection behavior in a machining process, a new real-time nonintrusive method for deflection monitoring is presented, and a detailed analysis of workpiece deflection for different machining stages of the whole machining process is discussed. The thin-film polyvinylidene fluoride (PVDF) sensor is attached to the non-machining surface of the workpiece to copy the deflection excited by the dynamic cutting force. The relationship between the input deflection and the output voltage of the monitoring system is calibrated by testing. Monitored workpiece deflection results show that the workpiece experiences obvious vibration during the cutter entering the workpiece stage, and vibration during the machining process can be easily tracked by monitoring the deflection of the workpiece. During the cutter exiting the workpiece stage, the workpiece experiences forced vibration firstly, and free vibration exists until the amplitude reduces to zero after the cutter exits the workpiece. Machining results confirmed the suitability of the deflection monitoring system for machining thin-walled workpieces with the application of PVDF sensors.

Surface quality analysis in ball end milling of Inconel 718 cantilevers by response surface methodology

The ball end milling process is commonly used for generating complex three-dimensional sculptured surfaces with definite curvature. In such cases, variation of surface properties along with the machined surface is not well understood. Therefore, this article investigates the effect of machining parameters on the quality of surface in ball end milling of thin-shaped cantilever of Inconel 718. A distinct variation is also observed in the measured values of deflection of workpiece: surface roughness and surface damage in different regions, that is, fixed end, mid portion and free end of machined surface. The experiments were conducted according to the central composite design with four factors, namely, cutting speed, feed, workpiece thickness and workpiece inclination with tool path orientation. It is observed that the process parameters have statistically significant effect on machined surface of Inconel 718. Horizontal tool path condition during milling is most favourable in all aspects of surface quality with high speed and lower feed. The surface roughness values at the fixed end of plate are less as compared with that of mid portion and free end sides. Scanning electron microscope images show various defects such as side flow, smeared layer, microparticle, grooves and feed marks.

Methodology for aluminium part machining quality improvement considering mechanical properties and process conditions

The manufacturing of structural aluminium alloy parts requires several steps of both forming processes and heat treatments. Before machining, which is usually the last step of the manufacturing, the workpiece has thus undergone multiple manufacturing steps involving unequal plastic deformations which are source of residual stresses. During machining, where up to 90% of the initial workpiece volume can be removed, the mechanical equilibrium of the part evolves constantly with the redistribution of the initial residual stresses. For thick, large and complex parts in highly alloyed aluminium, this redistribution of the residual stresses can leads to an unexpected behaviour of the workpiece and is the main reason for both workpiece deflections (during machining) and post-machining distortions (after unclamping). These two phenomena can lead to the nonconformity of the part with the geometrical and dimensional tolerance specifications and therefore to the rejection of the part or to additional conforming steps. As a consequence, the mechanical behaviour of the workpiece has to be considered during the definition of the machining process plan to improve the machining accuracy and the robustness of the process and thus to ensure the conformity of the machined part with the dimensional and geometrical specifications, i.e. to ensure the desired machining quality. In this paper, the numerical tool developed in [1] is used to conduct an analysis on the influence of the initial workpiece residual stress state, of the fixture layout as well as of the machining sequence on the machining quality. This analysis is performed on a part which has been specially designed and which can be considered as being representative of real aerospace parts. Several comparisons with experimental results are performed, one of them using digital image correlation (DIC) measurements. Results obtained show a good agreement, validating both the prediction of the behaviour of the workpiece during machining and the prediction of the machined part geometry. Based on the results of this analysis, a classification of the parameters has been performed depending on their influence on the machining quality. A first methodology allowing to define machining process plans adapted to the initial workpiece stress state has then been created based on the previous classification. This methodology is composed of a procedure and basic guidelines which are both presented in detail. An example of an application of this methodology is then introduced, demonstrating the benefits of the approach developed in this work.

Prediction of Dynamic Milling Stability considering Time Variation of Deflection and Dynamic Characteristics in Thin-Walled Component Milling Process

The milling stability of thin-walled component is an important problem in the aviation manufacturing industry. The milling stability is influenced by both deflection characteristic and dynamic characteristic of workpiece. Moreover, in the material removal, the deflection and dynamic characteristics of workpiece are time-variant on the change of machining positions. Thus, the milling stability is also time-variant. In order to investigate the time variation of deflection and dynamic characteristics of workpiece, a new computational model was established in this paper. Based on the influences of the deflection and the dynamic characteristics of workpiece, a new stability lobes diagram which can show different stability domains and chatter domains in different process positions was obtained. Experimental testing has been conducted to validate the established new model.

On milling of thin-wall conical and tubular workpieces

Thin-wall tubular-geometry workpieces have been widely applied in aircraft and medical industries. However, due to the special geometry of this kind of workpieces and induced poor machinability, the desired accuracy of machining tends to be greatly degraded, no matter what type of metal-cutting task such as milling, drilling or turning is undertaken. Though numerous research reports are available that the tool path can be planned on the basis of preset surface profile before actual milling operation is performed, it is still difficult to predict the real-time surface profile errors for peripheral milling of thin-wall tubular workpieces. Instead of relying on tool path planning, this research is focused on how to real-time formulate the appropriate applied cutting torque via feedback of spindle motor current. On the other hand, a few suitable cutting conditions which are able to prevent potential break/crack of thin-wall workpieces and enhance productivity but almost retain the same cutting quality is proposed in this research. To achieve this goal, estimated surface profile error on machined parts due to deflections caused by both tool and workpiece is studied at first. Traditionally, by adjusting cutting parameters such as feed rate or cut depth, the deflection of tool or workpiece can be expected not to exceed the specified limit. Instead, an effective feedback control loop is proposed by this work for applying real-time appropriate applied cutting torque to prevent potential break/crack of the thin-wall conical workpieces. The torque estimation approach by spindle motor current feedback and the corresponding fuzzy logic controller are employed. Compared with constant cutting torque during milling operation in tradition manner, it is observed that the time consumption of milling cycle by aid of the aforesaid fuzzy logic controller is greatly shortened while the resulted cutting accuracy upon finish of workpiece can be almost retained.

Modeling Methodology of Flexible Milling Force for Thin-Walled Component on High Speed Peripheral Milling Processing System

This study has developed a model in order to show the relationship between deflection of the low-rigidity processing system such like thin-walled component and the flexible milling force. The new model takes the deflection of cutter-workpiece system into account. The cutting force is analyzed simulatively by utilizing modified Newton–Raphson iterative algorithm. The simulative results show that the total normal deflection of workpiece–cutter system is the main factor affecting the change of cutting force.

Influence of the machining sequence on the residual stress redistribution and machining quality: analysis and improvement using numerical simulations

The manufacturing of aluminium alloy structural aerospace parts involves multiple steps, the principal ones being the forming (rolling, forging etc.), the heat treatments and the machining. During this last step, the final geometry of the part is obtained. Before machining, the workpiece has therefore undergone several manufacturing steps resulting in unequal plastic deformation and metallurgical changes which are both sources of residual stresses. On large and complex aluminium alloy aeronautical parts, up to 90 % of the initial workpiece volume can be removed by machining. During machining, the mechanical equilibrium of the part is in constant evolution due to the redistribution of the initial residual stresses.The residual stress redistribution is the main cause of workpiece deflections during machining as well as of post-machining distortion (after unclamping). Both can lead to the non-conformity of the part with the geometrical and dimensional tolerance specifications and therefore to a rejection of the part or to additional conforming steps. In order to improve the machining accuracy and the robustness of the process, the effect of the residual stresses has to be considered for the definition of the machining process plan. In this paper, a specific numerical tool [2] allowing to predict workpiece deflections during machining and post-machining distortion is used to study the influence of the machining sequence on the machining quality in taking into consideration the initial residual stresses. A first machining process plan defined as the reference case is simulated. Simulation results are then compared with experimental ones showing the feasibility to use the developed tool to predict the machining quality depending on the initial residual stresses, the fixture layout and the machining sequence. Using the computational tool, a method to optimise the machining quality depending on the initial workpiece and on the machining sequence is presented. A machining process plan allowing to respect the tolerance specifications is then defined. This demonstrates the feasibility to adapt and to optimise the machining process plan to ensure conformity of the part with the tolerance specifications.

Effect of workpiece stiffness on thrust force and delamination in drilling thin composite laminates

During drilling thin composite laminates, workpiece stiffness affects drilling process through bending and release movement. A new mechanical model for thrust force prediction was developed to quantitatively describe influence of workpiece stiffness. Its effect on delamination was also investigated. Derivative of workpiece deflection caused by thrust force was calculated to obtain dynamic feed rate. Then, thrust force was predicted as a function of drill geometry, specific energy and dynamic feed rate. Experiments of drilling woven CFRP plates had been performed with different feed rate and unsupported length. Results showed that the presented model could fit measurement thrust force nicely except exit stage, in which local deformation and crack of uncut material brought forward the force drop point. Delamination damage was observed at low stiffness even though thrust force did not exceed the critical value. Analysis results indicated that dynamic feed rate was a more suitable critical parameter for delamination-free drilling.

Modeling of machined surface quality in high-speed ball-end milling of Inconel-718 thin cantilevers

Machining of thin flexible parts in the aerospace and power industries often involves workpiece deflection majorly influencing the machined surface quality. Very few attempts have been done so far to address issues in the ball-end milling of thin cantilever-shaped parts made of “difficult-to-machine” materials. The objective of this paper is to optimize the machining parameters under the design constraints such as workpiece thickness, workpiece inclination, and cutter orientation to get the best possible machined surface quality. Accordingly, correlations between surface quality and the workpiece deflection have been developed. Independent variables were optimized using a central composite design (CCD) with each variable taken at five levels. All the results were compared with the results obtained by the ball-end milling on flat and horizontal cantilever without an inclination. Analytical models have been developed to predict the instantaneous workpiece deflection, undeformed chip thickness, and width of cut and correlated them with the machined surface quality. The lowest surface roughness of ~1 μm Ra was obtained at a higher cutting speed of 120 m/min and a lower feed rate of 400 mm/min, on thicker workpiece (>5 mm) inclined at an angle of 45° along with the horizontal outward cutter orientation. The dimensional accuracy (width of cut) and the workpiece deflection can be predicted more accurately during ball-end milling of thicker Inconel-718 workpiece inclined at higher angles.

Modeling, simulation, and optimization of five-axis milling processes

The five-axis milling is widely applied to complex surface machining. When cutting forces of milling processes increase, the consequent workpiece and tool deflections may result in poor machining quality and high processing cost. There are a lot of researches on three-axis milling processes simulation, but very few about five-axis milling. To solve these disadvantages, this paper presents an integrated system containing modeling, simulation, and optimization of five-axis milling processes. The system has three major applications: (1) simulation verification of milling processes, (2) cutting forces prediction, and (3) cutting parameters (feedrate) optimization. The material removal process simulation used for verifying the five-axis milling is based on the three-dexel (depth element) model, and the cutter-workpiece engagement regions are extracted from the geometric model. According to the extracted cutter-workpiece engagement regions, the instantaneous cutting forces could be predicted. The feedrate is off-line modified for balancing the given maximum or the reference cutting forces with the predicted cutting forces on different machining steps. The developed system is validated experimentally to show that the modeling, simulation, and optimization methods could improve the accuracy and efficiency of five-axis milling processes.

Study on Virtual Machining Process of Peripheral Milling of Thin-Walled Workpiece

Thin-walled workpiece is easy to deform in machining. In order to predict the dimensional error of machined surface of thin-walled workpiece, computer simulation technology is studied, which is called virtual machining process. For the simulation of workpiece deformation, much numerical analysis should be done. Research indicates using FEA (Finite Element Analysis) in each step of simulation process needs too much time to meet the requirements of industrial application. Therefore it is important to decrease the simulation time. In this paper, a new method is proposed to realize rapid analysis of workpiece deflection in virtual machining process, which combines rapid analytical solution method with a few times of accurate FEA, thus greatly decreases the time required for whole simulation. For the simulation, several peripheral milling process models are presented with increasing order of sophistication and accuracy, which can be applied to simulate cutting process with the effect of workpiece deformation caused by cutting force. In the final section, the comparison between simulation results and experiments shows the proposed methods and models can closely predict dimensional error and texture of machined surface of flexible workpiece.

Systematic Simulation Method for the Calculation of Maximum Deflections in Peripheral Milling of Thin-Walled Workpieces with Flexible Iterative Algorithms

Due to the deflection of tool and workpiece induced by cutting force, there is a high complexity associated with the prediction of surface form errors in the peripheral milling process of thin-walled workpieces. And the prediction of surface form errors induced by cutting deflection is the precondition for process optimization and error compensation. This paper proposes a systematic simulation procedure suitable for surface form errors prediction in peripheral milling of low rigid thin-walled workpiece. Some key algorithms with the judgment of contacts between the cutter and the workpiece, the flexible iterative algorithm as well as the tool/workpieces deflection prediction using FE model are developed and presented in detail. Comparisons of the form errors and cutting forces obtained numerically and experimentally confirm the validity of the proposed algorithms and simulation procedure.

Modeling techniques for simulating workpiece deflections in NC milling

Due to the time- and position-dependent dynamic behavior of the workpiece, the prediction of process dynamics during the five-axis milling of thin-walled free-formed surfaces is a challenge from the modeling point of view. In this paper, three different techniques for modeling workpiece deflections and their integration into a system for simulating the NC milling process will be discussed by means of analyzing the machining of a turbine blade.

Analysis of the machining accuracy when dry turning via experiments and finite element simulations

Workpiece and tool are subjected to severe mechanical and thermal loads when turning. These loads cause thermal expansions and mechanically induced deflections of the tool and the workpiece. Such deformations induce deviations from the nominal workpiece geometry. In order to decrease these deviations, the cutting condition needs to be optimized prior to actual machining. In this paper, the accuracy of machining when dry turning aluminum is analyzed via experiments and finite element simulations. For this purpose, seven characteristic values were used: the forces, the deflection of the workpiece, the quantity of heat in the workpiece, the temperature distribution in the workpiece, the temperature of the tool, the temperature of the tool holder, and the actual dimension of the workpiece after turning. These experimentally determined results serve in addition as boundary conditions for a 3D finite element model of the workpiece, which calculates the deformations of the workpiece. The continuous removal of material affecting the temperature distribution in the workpiece is considered. The actual dimensions of the workpiece after turning revealed a remarkable influence of the cutting condition used on the accuracy of machining. Differences of up to 116 μm regarding the deviation from the nominal workpiece diameter of 30 mm were observed. The analysis of the machining accuracy reveals that particularly the use of both high cutting speeds and feeds enhances the accuracy of machining when dry turning aluminum.

Two efficient iterative algorithms for error prediction in peripheral milling of thin-walled workpieces considering the in-cutting chip

Due to the deflection of tool and workpiece induced by cutting force, there is a high complexity associated with the prediction of surface form errors in peripheral milling of thin-walled workpieces. Based on the systematic study of in-cutting chip, this paper proposes a new efficient iterative algorithm named flexible iterative algorithm (FIAL)， which is suitable for surface form errors prediction in peripheral milling of low rigid thin-walled workpiece. In FIAL, an iterative scheme for calculations of tool/workpiece (TW) deflections are developed by considering the former convergence cutting position, and in the scheme a new important variable Δ is proposed for the calculation of radial cutting depth which never been considered before. Based on FIAL and the analytical study of in-cutting chip, a double iterative algorithm (DIAL) is brought forwarded to calculate the positions and magnitude of the maximum surface form errors, which always take the peak point include in each iterative step. Comparisons of the form errors and cutting forces obtained numerically and experimentally confirm the validity of the proposed algorithms and simulation procedure. The experimental and analytical results have shown that FIAL is faster in the iteration convergent speed and more accurate than the rigid iterative algorithm in surface form errors prediction, and DIAL is proved to be valid in the maximum errors prediction.

長尺な軸のフライス加工における工作物挙動の解析と加工条件最適化 (第1報)

The productivity of circular shafts with a straight groove and/or a plane surface on outside surface of workpiece was much improved by the development of CNC lathe having a milling spindle. However, for milling of shafts with a large length and a small diameter, workpiece deflection induced by cutting forces causes deterioration of surface quality and chatter vibration. This investigation deals with an analysis of workpiece behavior and optimization of the machining conditions for ball-end milling a shaft with a small flexural rigidity in the direction of perpendicular to the shaft axis. In this paper, to apply a previously developed cutting model to milling of shafts, geometric quantities such as contact region between the cutting edge and the workpiece surface, and distribution of undeformed chip thickness along the cutting edge are analyzed. Cutting forces are calculated by using the cutting model and an energy method. Then, the workpiece deflection is analyzed on the basis of calculated results of cutting forces, and the variation of the above quantities with tool rotational angle are compared with experimental results at various tool locations on the workpiece. It is found that both of the cutting forces and the workpiece deflection take each maximum value at a location where the tool axis reaches close to the perpendicular plane passed the axis of the workpiece. Through the comparison of the results obtained by analysis of resonance frequency of the workpiece and that obtained by impact test using impulse hammer it is shown that the possibility of avoiding the occurrence of chatter vibration.

Machining forces prediction for peripheral milling of low-rigidity component with curved geometry

This study has developed a model in order to predict machining forces for milling low-rigidity component with curved profile. Differing from conventional models used for straight geometries, the new model takes both the deflection of work piece-cutter system and the continuous change of curvature of machined part into account. In the model, a profile with variable curvature is defined and the feed rate per tooth on the profile is derived subsequently. The cutting force is analyzed simulatively by utilizing modified Newton–Raphson iterative algorithm. The simulative results show that the total radial deflection of workpiece–cutter system is the main factor affecting the change of cutting force. Moreover, the feed rate per tooth and its corresponding cutting force changes according to the curvature of the profile. Finally, experiments were carried out to verify the accuracy of the models.