Machining Error Prediction Research Articles

Predicting error for machining thin-walled blades considering initial error

A multistage machining process is employed to machine the blades with low stiffness. Nonetheless, machining errors can be transferred and accumulate throughout the multistage machining process, complicating the precise prediction of the final accuracy of thin-walled blades. Consequently, this paper introduces a machining accuracy prediction model for thin-walled blades that takes into account initial error. The machining error prediction model of thin-walled blades is developed using Gaussian process regression optimized by the sparrow search algorithm (SSA-GPR) with the initial contour error, depth of cut, feed per tooth, and spindle speed as inputs, and the machining error as the output. And the results show that the prediction accuracy of the SSA-GPR is 6.73 % higher than that of the Gaussian process regression (GPR), 13.73 % higher than that of the back propagation neural network (BPNN), and 32.32 % higher than that of the support vector machine regression (SVR). The influence of the initial error and milling parameters on the machining error is analyzed through the length-scales of the Gaussian kernel function. The findings indicate that the depth of cut, feed per tooth and initial error significantly affect the machining error, whereas the spindle speed has a minor impact on the machining error. Furthermore, the 3D graph based on the SSA-GPR shows that the increase of the initial error will increase the machining error of thin-walled blades. This research provides a theoretical foundation for the process optimization of thin-walled blades.

Prediction of machining errors for free-form surfaces based on an improved grey model (1,N)

An improved grey model (GM) for predicting free-form surface machining errors was established to address the low measuring efficiencies of coordinate measuring machines (CMMs) and the low prediction accuracy of the GM(1,1) model. A number of points on a free-form surface are measured with a CMM, and machining errors are obtained. Ideas from metabolic methods and the GM(1,N) prediction model were combined. To reduce the impact of random fluctuations of the machining errors, a Markov prediction model was then used to correct the fitted results for the residuals and obtain the predicted results of the machining errors for free-form surfaces, thus improving the prediction accuracy of the model. The predicted results of the metabolic GM(1,1) and metabolic GM(1,N) models were then compared. The experimental results showed that the combination of metabolic theory, a grey model, and Markov theory effectively improved the prediction accuracy.

Research into Dynamic Error Optimization Method of Impeller Blade Machining Based on Digital–Twin Technology

A TC4 impeller blade is a typical weak, rigid, thin–walled part. The contact area between a cutting tool and a workpiece has strong time–varying characteristics. This leads to a strong non–linear variation in cutting load. So, in this kind of part, the processing error is difficult to control. To solve this problem, a method of processing error prediction and intelligent controlling which considers the effect of tool wear time variation is proposed by combining digital–twinning technology. Firstly, an iterative model for digital–twin process optimization is constructed. Secondly, an iterative prediction model of the machining position following the milling force and considering the effect of tool wear is proposed. Based on these models, the machining error of the TC4 impeller blade under dynamic load is predicted. Dynamic machining error prediction and intelligent control are realized by combining the digital–twin model and the multi–objective process algorithm. Finally, the machining error optimization effect of the proposed digital–twin model is verified via a comparison experiment of impeller blade milling. In terms of the precision of milling force mapping, the average error after optimization is less than 8%. The maximum error is no more than 14%. In terms of the optimization effect, the average error of the optimized workpiece contour is reduced by about 20%. The peak contour error is reduced by approximately 35%.

Efficient prediction of machining errors caused by tool deflection in down milling

Efficient prediction of machining errors caused by tool deflection in down milling

In-situ prediction of machining errors of thin-walled parts: an engineering knowledge based sparse Bayesian learning approach

In-situ prediction of machining errors of thin-walled parts: an engineering knowledge based sparse Bayesian learning approach

Machining error prediction scheme aided smart fixture development in machining of a Ti6Al4V slender part

Machining of slender (low rigidity) parts is associated with tool/workpiece deflections due to induced cutting forces resulting in machining error (dimensional inaccuracy of the machined surface). The development of smart fixtures is seen as an enabler for reduction of machining error. To reduce lead times, the smart fixtures need to be designed in an efficient way by using more virtual simulations and less physical iterations. This paper presents the development of a novel methodology for machining error prediction in milling of a fixture-workpiece system. The methodology integrates a cutting force model, a finite element based fixture-workpiece system and a multi-step error predictive approach. The methodology was first validated on a flexible thin-wall Ti6Al4V slender part where less than 6% difference was achieved between predicted and measured machining error. The difference between predicted and measured cutting forces was approximately 6%. After the gained confidence, the methodology was applied to the flexible thin-wall Ti6Al4V slender part encompassed by a fixture with three actuators acting as supports. The predicted machining error was reduced from the range of 0.2–0.33 mm (no actuators) to the range of 0.12–0.14 mm (with three actuators). This demonstrated the capability of the developed methodology to aid the design of future smart fixtures with the potential to reduce lead times during their development.

A two-step machining and active learning approach for right-first-time robotic countersinking through in-process error compensation and prediction of depth of cuts

• Two-step process method for online compensation and prediction of machining errors • Data-driven models require large training datasets for accurate predictions • Training data is very expensive to obtain for high-value manufacturing processes • Active learning is used to identify the most informative data for model training • Right-first-time robotic machining and reduced inspection costs are achieved Robotic machining processes are characterised by errors arising from the limitations of the industrial robots. These robot-related errors can compromise the overall manufacturing process performance, resulting in final products with dimensions different from the nominal specifications. To avoid accumulation of errors through several manufacturing stages, a quality inspection step is usually performed after the cutting operation. This work presents an innovative two-step manufacturing method for achieving right-first-time characteristics in robotic machining operations through in-process inspection and compensation of the systematic errors, whilst collecting suitable training data for building predictive models. The key idea behind the proposed method is based on the observation that under certain conditions, the robotic machining errors remain largely consistent, and therefore by splitting the process into two similar steps and having an inspection step in between, a prediction and then compensation of the systematic errors would be possible. A Gaussian Process Regression (GPR) framework is applied for the creation of robust process models that predict the post-process inspection result from in-process signal features, with the associated confidence intervals. An active learning algorithm that makes online decisions on the inspection task based on the current confidence of the models, is also proposed. The two-step machining method and the active learning approach were both tested on a robotic countersinking process experiment. The results showed that the in-process inspection and error compensation of the proposed two-step machining method was able to achieve final countersink depths very close to the desired target, confirming the potential for right-first-time robotic machining. In addition, the active learning results highlighted the ability of the algorithm to reduce the number of required post-process inspections, thus saving both time and costs, whilst also identifying novel data relevant for the model training.

Experimental study on cutting factors of multi-layer machining for large aerospace thin-walled structural parts

Large aerospace thin-walled structures will produce deformation and vibration in the machining process, which will cause machining error. In this paper, a cutting experimental method based on multi-layer machining is proposed to analyze the influence of cutting tool, cutting path, and cutting parameters on machining error in order to obtain the optimal cutting variables. Firstly, aiming at the situation that the inner surface of the workpiece deviates from the design basis, the laser scanning method is used to obtain the actual shape of the inner surface, and the method of feature alignment is designed to realize the unification of the measurement coordinate system and machining coordinate system. Secondly, a series of cutting experiments are used to obtain the machining errors of wall thickness under different cutting tools, cutting paths, and cutting parameters, and the variation of machining errors is analyzed. Thirdly, a machining error prediction model is established to realize the prediction of machining error, and the multi-objective optimization method is used to optimize the cutting parameters. Finally, a machining test was carried out to validate the proposed cutting experimental method and the optimal cutting parameters.

A gear machining error prediction method based on adaptive Gaussian mixture regression considering stochastic disturbance

A gear machining error prediction method based on adaptive Gaussian mixture regression considering stochastic disturbance

Research on machining error prediction and compensation technology for a stone-carving robotic manipulator

Stone-carving robotic manipulators (SCRMs) have a broad range of applications due to their high efficiency, diverse processing capabilities, and strong flexibility. However, due to its weak rigidity, the milling accuracy of an SCRM is lower than that of a computer numerical control (CNC) machine for working stone into special shapes, making it difficult to meet the requirements of stone milling processing. To improve the milling accuracy of SCRMs, multi-iteration error compensation technology considering the coupling relationship between compensation and deformation is proposed in this paper. First, a global stiffness model of an SCRM in which the robot arm bars are regarded as flexible links is established, and the relationship between the milling force and milling depth is fitted based on a milling force prediction model. Then, the machining error and milling depth when processing a marble workpiece are predicted. Finally, a multi-iteration method is applied for calculation using an interval correction strategy to construct a discrete control system for error compensation in the SCRM. The feasibility and effectiveness of the proposed compensation technology are verified by an experiment using the KUKA-240-2900 SCRM system.

A hybrid driven approach to integrate surrogate model and Bayesian framework for the prediction of machining errors of thin-walled parts

Thin-walled structural parts are widely used in aerospace industry, the prediction of machining errors of these parts has attracted more and more attention over the past decades. Due to the complicated time-varying nonlinear characteristics and the lack of experimental data, it is difficult to use the mechanism model or data-driven model to predict the machining errors directly. To solve those problems, a hybrid driven approach to integrate surrogate model and Bayesian framework is proposed to predict the machining errors of thin-walled parts. The Gaussian process regression algorithm is embedded in the mechanism model to predict the cutting forces and flexibility, so as to establish the surrogate model for the prediction of machining errors. Besides, the surrogate model is calibrated by considering the uncertainties of cutting forces and tool wear. Five unknown calibration coefficients are analyzed through the Bayesian framework and determined by the Markov Chain Monte Carlo algorithm. A hybrid driven approach is introduced to train the prediction model. Both simulation data through mechanism analysis and experimental data through technological test are extracted. Compared with the mechanism model or data-driven model, the testing results have indicated that the proposed prediction model has higher efficiency and accuracy. The prediction time of a single point is reduced to 5.46ms and the root mean square error of the proposed prediction model is 4.5137μm.

Iterative from error prediction for side-milling of thin-walled parts

Deformation is an unavoidable phenomenon in a thin-walled milling operation, which causes the radial cutting depth to deviate from the initial position and change the tool-workpiece meshing boundary. Milling force is an important factor in the deformation; thus, the phenomenon of machining deformation mechanism is revealed and a machining error prediction model based on the force-deformation coupling relationship is developed in this paper. Discrete micro-cutting disks of the thin-walled parts take into account the deformations and milling cutting force of different contact relationships in the cutting area. The tool-workpiece contact relationship (single-flute cutting and double-flute cutting) is determined by different cutting parameters and the deflection of thin-walled parts is introduced. A detail iterative strategy is developed to calculate the milling force after deformation and the tool-workpiece meshing boundary. By modifying the instantaneous chip thickness of each micro-cutting disk, a new force-deformation coupling relationship and a time-based deformation matrix of different contact relationships are obtained. The machining error is calculated by considering the part deformation and the surface generation mechanism. After finishing systematic experiments, a comprehensive comparison between the model in mechanical prediction and experiments proves that the model captures the material removal mechanism that produces machining error. The results show that the proposed method can effectively predict the machining error.

A New Error Prediction Method for Machining Process Based on a Combined Model

Machining process is characterized by randomness, nonlinearity, and uncertainty, leading to the dynamic changes of machine tool machining errors. In this paper, a novel model combining the data processing merits of metabolic grey model (MGM) with that of nonlinear autoregressive (NAR) neural network is proposed for machining error prediction. The advantages and disadvantages of MGM and NAR neural network are introduced in detail, respectively. The combined model first utilizes MGM to predict the original error data and then uses NAR neural network to forecast the residual series of MGM. An experiment on the spindle machining is carried out, and a series of experimental data is used to validate the prediction performance of the combined model. The comparison of the experiment results indicates that combined model performs better than the individual model. The two-stage prediction of the combined model is characterized by high accuracy, fast speed, and robustness and can be applied to other complex machining error predictions.

Ultra-Precision Machining of a Compound Sinusoidal Grid Surface Based on Slow Tool Servo.

Compound sinusoidal grid surface with nanometric finish plays a significant role in modern systems and precision calibrator, which can make the systems smaller, the system structure more simple, reduce the cost, and promote the performance of the systems, but it is difficult to design and fabricate by traditional methods. In this paper, a compound freeform surface constructed by a paraboloidal base surface and sinusoidal grid feature surface is designed and machined by slow tool servo (STS) assisted with single point diamond turning (SPDT). A novel combination of the constant angle and constant arc-length method is presented to optimize the cutting tool path. The machining error prediction model is analyzed for fabricating the compound sinusoidal grid surface. A compound sinusoidal grid surface with 0.03 mm amplitude and period of 4 is designed and cutting process is simulated by use of MATLAB software, machining experiment is done on ultra-precision machine tool, the surface profile and topography are measured by Taylor Hobson and Keyence VR-3200, respectively. After dealing with the measurement data of compound freeform surface, form accuracy 4.25 μm in Peak Village value (PV), and surface roughness 89 nm in Ra are obtained for the machined surface. From the theoretical analysis and experimental results, it can be seen that the proposed method is a reasonable choice for fabricating the compound sinusoidal grid surface.

Nonlinear dynamic characteristic of the spindle-cutter system

A nonlinear dynamic model of spindle-cutter coupling system under cutting force, which takes into account the cutter stiffness and the nonlinearity of bearing clearance, is established. Analysis of the cross-section of a two-flute end mill is conducted to determine cutter stiffness. Then, the calculated cutter stiffness is introduced into the nonlinear dynamic model of coupling system. In the modeling of cutting force, the cutting width takes into account the cutter tip displacement. Moreover, nonlinear dynamic characteristics of spindle-cutter coupling system are studied and the effects of bearing clearance on the response of cutter tip are discussed as well, considering unbalanced force. The numerical results show that the bearing clearance strongly affects the equilibrium position. With different values of bearing clearance and rotation speed, the responses of cutter tip exhibit periodic, quasi-periodic and chaotic characteristics. Dynamic characteristics of spindle-cutter system depends on the bearing clearance and rotation speed. The proper bearing clearance and rotation speed should be chosen to ensure a stable cutting and high cutting rate according to the bifurcation diagram. The response of the cutter tip is a quasi-periodic motion when the cutting force is considered. The time-domain response of cutter tip predicted by nonlinear dynamic analysis can provide the basis for machining error prediction.

Error compensation of thin plate-shape part with prebending method in face milling

Low weight and good toughness thin plate parts are widely used in modern industry, but its flexibility seriously impacts the machinability. Plenty of studies focus on the influence of machine tool and cutting tool on the machining errors. However, few researches focus on compensating machining errors through the fixture. In order to improve the machining accuracy of thin plate-shape part in face milling, this paper presents a novel method for compensating the surface errors by prebending the workpiece during the milling process. First, a machining error prediction model using finite element method is formulated, which simplifies the contacts between the workpiece and fixture with spring constraints. Milling forces calculated by the micro-unit cutting force model are loaded on the error prediction model to predict the machining error. The error prediction results are substituted into the given formulas to obtain the prebending clamping forces and clamping positions. Consequently, the workpiece is prebent in terms of the calculated clamping forces and positions during the face milling operation to reduce the machining error. Finally, simulation and experimental tests are carried out to validate the correctness and efficiency of the proposed error compensation method. The experimental measured flatness results show that the flatness improves by approximately 30 percent through this error compensation method. The proposed method not only predicts the machining errors in face milling thin plate-shape parts but also reduces the machining errors by taking full advantage of the workpiece prebending caused by fixture, meanwhile, it provides a novel idea and theoretical basis for reducing milling errors and improving the milling accuracy.

Effect of Machining Precision Caused by NC Gear Hobbing Deformation

Research on the effect of main spindle deformation which is caused by hobbing force of gear hobbing machine is an important way to diminish or control the machining tolerance of gear. This paper bases on the structure and technique parameter of some typical large-scale NC gear hobbing machine, and the theory of bend and deformation of beam, a novel equation was proposed in this paper to calculate the hobbing force and deformation by practical hobbing parameter. By calculating and analyzing gear hobbing force and deformation data, we can conclude a change rule between hobbing force and deformation with spindle rotative velocity and hobbing depth. And we can reach a conclusion that we should increase hob rotative velocity and feed in a small hobbing depth in several times, it will diminish cutting force, deformation of hob and workpiece spindle, which will improve the machining precision, efficiency and diminish product scrap ratio. It also prove this research approach has reference value for optimizing gear hobbingmachine structure design, choice of processing technique parameter and machining error prediction and compensation.

Study on the response surface model of machining error in internal lathe boring

To achieve high quality and precision of machining products, the machining error must be examined. The machining error, defined as the difference between designed surface and the actual tool, is generally caused by tool deflection and wear, thermal effects and machine tool errors. Among these error sources, tool deflection is usually known as the most significant factor. The tool deflection problem is analyzed using the instantaneous cutting forces on the cutting edge. This study presents a model of the machining error caused by tool deflection in the internal boring process. The machining error prediction model was described by the surface response method using overhang, feed per revolution and depth of cut as the factors for the analysis. The least square method revealed that overhang and depth of cut were significant factors within 90% confidence intervals. Analysis of variance (ANOVA) and residual analysis show that the second-order model is adequate.

The Research on Milling Temperature and Heat Deformation of Tool in Virtual Numerical Control Simulation

Joint modeling of exponentially fitting and least square method was proposed for key technical problems on milling temperature and heat deformation of tool in virtual numerical control (NC) simulation. Mathematic model of surface temperature and its influencing factors based on ball-end mill was established. Correlation coefficients of model are over 0.8, and the errors comparing with the experimental ones are within 10%, which shows that the model meets precision requirement, and fitting effect is good. By this model a mathematical model of the ball-milling cutter’s thermal deformation was established, and the relative error is small by comparing with test values, which proves that this model has high calculation precision and practical meaning. A simulation prediction system of milling temperature and ball-end mill’s heat deformation in virtual NC was developed based on above mentioned models, which can provide theoretical basis for machining error prediction, optimizing milling parameters and improving machining quality.

Prediction of machining errors, taking account of technological inheritance

Prediction of machining errors, taking account of technological inheritance