Surface Location Error Research Articles

Closed-Form Time-Domain Solutions of Arbitrary-DOF Forced Vibrations and of Surface Location Error for General-Helix Cylindrical Milling Tools

Closed-Form Time-Domain Solutions of Arbitrary-DOF Forced Vibrations and of Surface Location Error for General-Helix Cylindrical Milling Tools

Pose Optimization in Robotic Milling Based on Surface Location Error

AbstractIndustrial robots have become a suitable alternative to machine tools due to their flexibility, low cost, and large working space. However, the compliance of the robot system makes it prone to produce large deformations and vibrations during machining, resulting in poor machining accuracy and surface quality. In order to improve the machining performance of the robot, a posture optimization method for robotic milling with the redundant degree of freedom is introduced. First, modal tests are conducted at sampled points to obtain the configuration-dependent parameters of the structural dynamics of the robotic milling system. These experimental data are combined with the inverse distance weighted (IDW) model to further predict the modal parameters at the unsampled points. Then, considering the dynamics model of the system, the optimization model based on surface location error (SLE) is proposed to obtain the optimal robotic posture. Finally, a series of experiments illustrate that pose optimization based on SLE can improve the machining accuracy and surface machining quality.

Prediction of Surface Location Error Considering the Varying Dynamics of Thin-Walled Parts during Five-Axis Flank Milling

Surface location error (SLE) caused by forced vibration is a key factor to determine the quality of the finished part. When machining thin-walled structures with sculptured surfaces, the complicated milling process is significantly influenced by the vibration due to the flexibility of the part. The dynamics of the part are dominant and vary with the material removal during machining. This paper presents a prediction method of SLE considering the varying dynamics of thin-walled parts in five-axis flank milling. The in-process part is decomposed into unmachined and machined portions, which are both modelled based on the thin-plate theory. The dynamics models of the two portions are coupled using the substructure method. Coordinate transformation based on the screw theory and the general cutting dynamics model for five-axis flank milling is employed to transform the cutting force vectors and frequency response function (FRF) to the same coordinate system for the prediction of SLE. The proposed method is validated with five-axis flank milling tests and SLE measurements on a thin-walled twisted part. It is shown that the average error of the proposed method for SLE prediction is less than 5 μm, and the calculation is almost 8 times faster than the typical finite element method.

A Novel Gegenbauer Wavelet-Based Approach for Stability and Surface Location Error Analyses of Milling Process

Abstract This paper proposes a novel wavelet-based method for the computation of the milling stability and surface location error (SLE). The governing equation of milling processes considering the self-vibration and forced-vibration is formulated as a delayed differential equation with state space form. The total time period is considered as a whole, sampled by the Chebyshev nodes. Then, the vibration displacement corresponding to each sampling grid point is fitted by a weighted linear sum of Gegenbauer orthogonal polynomials. A new method named direct differentiation based algorithm (DDBA) is proposed to determine these weight coefficients, which gets rid of dependence on the classic differential operator. On the one hand, the Floquet matrix is constructed to calculate the milling stability. On the other hand, the coefficient matrix independent of time is established to predict the SLE. The benchmark and experimentally verified examples are employed to validate the effectiveness of the proposed approach. The optimal combination of orthogonal polynomials is fixed by exploring the effect of the control parameter on the predictive accuracy. At last, the calculation vulnerability that can cause the prediction accuracy to be dropped obviously in some step lengths is revealed and repaired.

Bifurcations analysis in implicit maps through the dynamics of cumulated surface errors in milling

In this contribution, we examine the evolution of surface errors during consecutive milling operations. Its description is based on a nonlinear implicit map, which is suitable to investigate the surface quality. It describes the series of consecutive Surface Location Errors (SLE) in roughing operations. As one of the principal results of the paper, bifurcations related to the fixed point of the implicit map are analyzed via normal form theorem. We determined a formula for the criticality of the bifurcation, which allows the approximate computation of the arising period-two solution. The method is demonstrated for the surface error model of milling, and the results are verified by numerical computations. Although the amplitude of the SLE would be negligible, its derivatives has a great influence in the model, which can cause stability problems.

Surface location error prediction in 2.5-axis peripheral milling considering tool dynamic stiffness variation

In peripheral milling, surface accuracy is crucial for the quality of the machined components, and it is one of the reasons why milling is still essential in the manufacturing field. Nonetheless, both static phenomena, like tool deflections, and dynamic issues such as forced vibrations, impact on the accuracy of the components causing surface errors. In this context, the prediction of surface error is an important tool to guarantee surface accuracy and increase productivity at the same time. This paper presents a novel approach to predict surface location error in 2.5-axis peripheral milling operations considering the stiffness variation along the axial depth of cut. The proposed approach discretizes the endmill in small discs, and it evaluates analytically the cutting force along the cross-feed direction for each disc in the frequency domain. Then, tool dynamic stiffness, which is expressed in terms of frequency response function (FRF), is computed considering the stiffness variation along the tool axis. Finally, the presented approach couples the cutting forces with the tool stiffness, and it evaluates surface error along the tool axis. The method was experimentally tested in different conditions to verify its effectiveness and its limits. The results obtained show how static and dynamic aspects and stiffness variation contribute to surface errors in peripheral milling operations.

Generalized modeling of milling dynamics for the 4DOF machining system with asymmetric flexibility

Asymmetric flexibility of the machining system exists widely in the practical milling process. In this paper, a generalized milling dynamics modeling method for an asymmetric flexible 4DOF cutter-workpiece system is proposed, which is further used to reveal how the asymmetric flexibility affects the milling dynamics characteristics. The regenerative milling force model is firstly established through the coupling coefficient matrix, in which the milling condition with non-parallel direction between the axis directions of coordinate system, the vibration directions of system DOF and the acting directions of milling force are well handled. Then, a generalized 4DOF milling dynamics model considering a new dimension, namely the cutter and workpiece feed direction angle combination ψ (ψc, ψw), is presented. The studies point out that the milling dynamics characteristics of the asymmetric flexible machining system, including the milling stability and surface location error (SLE), have a significant feed direction-dependent feature. Moreover, the generation mechanism of this kind of asymmetric milling dynamics has been successfully clarified. The proposed method has been experimentally validated by a series of milling tests in an asymmetric flexible machining system. Lastly, the influences of the asymmetry degree of the system flexibility, milling type and radial depth of cut on the milling dynamics are both analyzed by numerical simulation.

Feed Direction-Dependent Milling Dynamics of an Asymmetric Flexible Machining System

Abstract Asymmetric flexible machining system has been widely used in numerical control machining. In traditional milling dynamics model, the cutter feed direction is usually defined as parallel to its vibration DOF, while the nonparallel condition and its induced milling dynamics response are not deeply considered. This paper presents a general dynamics modeling method for asymmetric flexible machining systems. First, to the best of the author’s knowledge, a new dimension named feed direction is proposed, which is used to establish the generalized coupling relationship between the vibration displacement and the regenerative milling force, thus improve the applicability of the milling dynamics model and reduce the experimental workload compared with the traditional modeling. Second, through the theoretical and experimental research, it is shown that the asymmetric flexible machining system has a significant feed direction-dependent characteristics, and implied the existence of high performance machining region with higher stability and lower surface location error (SLE) by contrast with the symmetric milling system and the traditional models. Finally, by controlling the feed direction angle, the milling parameters in roughing and finishing operations are optimized, and the machining efficiency has been greatly improved on the premise of stable cutting and machining accuracy.

A novel scheme with high accuracy and high efficiency for surface location error prediction

A novel scheme with high accuracy and high efficiency for surface location error prediction

State dependent regenerative stability and surface location error in peripheral milling of thin-walled parts

Chatter avoidance and error control are the core issues accompanying milling processes of thin-walled parts. Owing to the high flexibility of workpiece, the cutting vibrations can easily reach dozens of micrometers and become comparable to the nominal chip thickness. However, the classic dynamic models usually neglect the influence of system state on regenerative stability and surface location error (SLE), which consequently reduces the prediction accuracy. In this paper, the coupling relationships between cutter-workpiece engagement, time delay and system state are modeled by means of analyzing the true teeth trajectories that are composed of tool rotation, feed movement and cutting vibrations. The resultant dynamic model is a state dependent delay differential equation, which is capable of accounting for the fly-over and multi-regeneration nonlinear phenomena too. Afterwards, an efficient numerical algorithm is proposed to accurately compute the dynamic responses. By contrast to classic time domain simulation techniques, the proposed algorithm uses discrete root finding scheme to determine the state dependent time delay and the state dependent cutter-workpiece engagement, which ensures its high computational efficiency. Based on the proposed dynamic model and numerical algorithm, the stability limits and SLE are finally obtained, and experimentally validated on two thin-walled plates using two variable pitch tools. Theoretical comparison and experimental results reveal that the proposed state dependent dynamic model successfully predicts the milling stability and SLE while the classic model fails. The state dependency of regenerative stability and SLE is further investigated and explained in detail.

Increasing Part Geometric Accuracy in High Speed Machining using Cascade Iterative Learning Control

High speed machining provides high productivity and low machining cycle times. Post machining, there can exist differences between desired and measured part geometry due to tool deflection induced from higher feedrates. Reducing the feedrate leads to an increase in machining time. Using predicted drive responses on a virtual CNC with an integrated surface location error model, this research is the first time Iterative Learning Control (ILC) has been applied to reduce part geometry errors from tool deflection. Validation machining trials demonstrated that the ILC scheme improved machining performance whilst maintaining machining times when compared to a baseline part program.

Generation Mechanism and Quality of Milling Surface Profile for Variable Pitch Tools Considering Runout

Abstract Surface profile is one of the foremost aspects to evaluate milling performance. Its generation mechanism is affected by a variety of factors such as tool geometry, runout values, and process parameters and thus still deserves further investigation. This paper aims to propose a unified method to study the surface generation mechanism and to predict the machining quality for variable pitch tools considering runout. First, a Floquet theory based algorithm is extended to analyze the machining stability and output the dynamic responses of the machining system. The resultant trajectories of cutting edges are obtained by kinematic synthesis of system vibrations, tool rotations, and machining feed. Next, both the surface location error (SLE) and the surface roughness are simultaneously extracted from the edge trajectories. A series of cutting tests are performed to validate the prediction results. Some new characteristics of the machined surface profile in terms of form errors and teeth marks are discovered and theoretically explained. Finally, the joint influences of tool geometry, runout values, and process parameters on the surface generation mechanism and quality are analyzed in detail with the proposed method.

Model-based phase shift optimization of serrated end mills: Minimizing forces and surface location error

Serrated cutting tools emerged for higher chip removal in rough milling operations. In this paper, attention is simultaneously paid to cutting forces and surface quality. The mechanics of the milling system with serrated end-mills was studied using force and surface topography models. A stationary milling force model was developed including the main geometric parameters of the serrated profile. For a complete understanding, a surface topography model was developed to predict the resulting machined surfaces. To ensure reliability and generality, the characterizations of three different tools and respective experimental validations were done. Then, the effect of the phase shift parameter ψ among cutters was set on the target. A search algorithm, combining the results from both models, was proposed to find the best tools that minimize simultaneously forces and roughness. These results are useful for toolmakers in tool design step, as for machinists and process engineers, when it comes choosing the optimum tool parameters.

Prediction of cumulative surface location error at the contact zone of in-process workpiece and milling tool

The surface location error (SLE) is used to evaluate the machining error caused by forced vibration at the contact zone during the stable machining. When the workpiece was machined continuously, the convergent SLE would change with the dynamic response of the workpiece as well. In this paper, we first established the conservative stability lobe diagram (SLD) caused by regenerative effect, and excluded the instability induced by cumulative effect with continuous radial immersion. An assumption was made that multiple immersion-by-immersion was equivalent to one immersion with the same material removal, and then the in-process workpiece (IPW) dynamics was obtained by means of structural dynamic modification. Finally, we used the improved third-order full discretization method to obtain the predicted cumulative surface location error (CSLE) with considering the dynamics of milling tool and workpiece simultaneously. Based on the stable machining parameters, the cutting tests and measurement were performed. The experimental results showed that the proposed model could effectively predict the distribution of CSLE. Under the same spindle speed, the CSLE at different cutter locations were not the same and the difference was obvious, which indicated that the dynamics from the workpiece played an important role in the formation of CSLE during the continuous machining process and should be included in the predicted model.

Assessment of Friction Behavior with Surface Location Error Analysis in Milling Process

Accurate roundness or circularity measurement is essential to obtain correct functioning of assemblies, making roundness an important quality control parameter in manufacturing industry. Since circular motion while milling a circular work piece leads to quadrant glitches, a phenomenon familiar with existence of highly nonlinear friction behavior, roundness measurement was conducted to investigate this surface location error due to feed rate of the moving work table. This paper presents friction behavior on a milling process circular work piece in line resulted from identified surface error location (SLE).

Research on the Effects of Machining Parameters on the Surface Location Error for a Milling Process

The surface location error is an inevitable phenomenon which is caused by the forced vibration under a stable machining process. The surface location error (SLE) is dependent on the machining parameters. Therefore, this paper proposes a method to study the effect of each machining parameter on the surface location error. An algorithm based on the cutting force dynamic model is proposed to predict the SLE in frequency domain. And then a case study is performed on the milling process of a real vertical machining center. The variation ranges of the spindle speed, axial cutting depth, radial cutting depth and feed rate per tooth are first determined. Eight specific values of each machining parameter is selected, and an orthogonal experiment table is established to arrange the schemes to predict the corresponding SLEs. Then the range analysis is used to analyse the values of the machining parameters and the obtained SLEs. Results show that the spindle speed is the most dominant factor affecting the SLE and an optimal machining parameters combination related to a minimum SLE is determined based on the optimal level of each machining parameter.

Radial Throw in Micromilling: A Simulation-Based Study to Analyze the Effects on Surface Quality and Uncut Chip Thickness

This paper presents a simulation study toward analyzing the effect of radial throw in micromilling on quality metrics and on the deviation in tool-tip trajectory from its prescribed pattern. Both the surface location error (SLE) and the sidewall (peripheral) surface roughness are analyzed. The deviation in tool-tip trajectory is evaluated considering the flute-to-flute variations in the uncut chip thickness and changes in the tooth spacing angle. Radial throw indicates the instantaneous radial location of the tool axis, thereby capturing all salient features of tool-tip trajectory deviations, such as the general elliptical form of the radial motions. This is in contrast to the concept of run-out, which is a scalar quantity (total indicator reading) indicating the total displacement or change in the radial throw measured from a perfect cylindrical surface for one complete rotation of the axis. As such, measurement and analysis of radial throw is essential to understanding micromachining processes. In our previous work, we described an experimental approach for accurate determination of radial throw when using ultra-high-speed micromachining spindles. In this work, we present a simulation-based study to relate radial throw parameters and form to SLE, sidewall surface roughness, flute-to-flute variations of uncut chip thickness, and changes in tooth spacing angle for a two fluted micro-endmill. As expected, our study concludes that the magnitude, orientation, and form of radial throw all significantly affect the studied quality metrics, tooth spacing angle, and the flute-to-flute chip thickness variations. Specifically, the presence of radial throw with an elliptical form induces up to 50% variation in SLE, up to 20% variation in sidewall surface roughness, up to 60% variation in tooth spacing angle deviations, and up to 50% variation in flute-to-flute chip thickness. As such, the presented simulation approach can be used to assess the direct (kinematic) effects of the radial throw parameters on the quality metrics and chip thickness variations.

Analysis on milling stability of fuel tank's bottom combined with surface location error prediction

The bottom of fuel tank is a lightweight thin-walled part with large size and complex surfaces. Its processing quality directly determines the reliability of the whole rocket. This paper conducts the predictions of both milling stability and surface location error (SLE) based on the theory of regenerative chatter vibration. We proposed a new type of stability lobe diagram (SLD) combined with the contour map of SLE. Then, we studied the changes of the bottom's dynamic parameters through FEA method, which would be influenced by the removal of material during machining. By using the dynamic parameters as inputs, we obtained a series of SLDs and the processing parameters which will lead to no-chatter and low SLE under different processing periods. The efficient and high-precision milling of the fuel tank's bottom can also be guaranteed.

Multi-Objective Machining Parameters Optimization for Chatter-Free Milling Process Considering Material Removal Rate and Surface Location Error

In machining parameters optimization of a chatter-free milling process, the inevitable surface location error (SLE) reflecting the machined workpiece dimension accuracy has been barely considered as one objective representing the machining quality, lowering the optimization accuracy. Therefore, this paper provides an approach to establish a multi-objective optimization model, where the material removal rate (MRR) represents the machining efficiency and the SLE predicted in time-domain represents the machining quality. The non-dominated sorting genetic algorithm (NSGA-II) method is used to solve the multi-objective model and provide pareto optimal solutions to first determine some ideal optimal solutions. Then the analytic hierarchy process (AHP) and grey target decision (GTD) methods are combined to select one most satisfactory optimal solution which has a well balance between the MRR and SLE. A multi-objective model was established and taken as a case study to maximize the MRR and minimize the SLE. Comparison study was performed on this multi-objective model and two other mono-objective models for obtaining the optimal MRR and SLE respectively, which was combined with the influences of machining parameters on SLE to show the necessity of conducting a multi-objective optimization. Milling tests were conducted based on the solved optimal machining parameters, and the well consistence between the measured and predicted SLEs shows that the proposed multi-objective optimization method can provide an effective approach to balance the machining efficiency and quality when there are conflicts between different objectives.

A novel approach with time-invariant transition matrix for surface location error prediction in low radial immersion milling

This paper proposes a novel approach with time-invariant transition matrix to predict surface location error (SLE) for low radial immersion milling. In considerations of regenerative and steady cutting thicknesses, the milling process is first concluded as a delay differential equation (DDE). Subsequently, ordinary differential theory is adopted to formulate the response of the machine tool system using the indirect integral scheme. According to Taylor series, the self- and forced-excited term is expanded by linear approximation in turn to deduce a discrete closed map. Taking advantage of this map, a novel transition matrix without any relation to the change of time is established in total tooth passing period to predict the SLE. To verify the effectiveness of the proposed approach, two experimentally validated examples are conducted. The results demonstrate that the method is of higher computational accuracy and efficiency.