Thin webs are the thin structures machined by the face of the end mill and they are widely used in the aerospace industry due to the advantages of compact structure, light weight and high strength-to-weight ratio [1] . However, significant deformation may occur during their milling process owing to their low rigidity, which seriously affects the machining efficiency and accuracy. Workpiece deformation and cutter deformation, which account for the majority of machining errors of thin-web parts, have been paid efforts to predict and reduce by many researchers in recent years.
Generally, the validated methodologies can be summarized into three subdivisions:
• Finite element method (FEM). Ibaraki et al. [2] developed an FEM-based model to simulate the deformation of a thinwalled workpiece during the milling process, which adopted an iterative algorithm to calculate the cutting force and deformation; Liu et al. [3] proposed a milling error prediction method based on FEM, which considered both the springback deformation of the workpiece and the material removal effect; Du et al. [4] proposed a deformation prediction model based on an analytical force model and ANSYS Parametric Design Language; Wang et al. [5] proposed a FEM-based cutter-workpiece engagement extraction method to predict the deformation errors caused by the milling force during the 5-axis flank milling process.
With the aid of matured commercial software, the FEM is convenient and prediction accuracy is acceptable. However, it usually takes hours or even days to get the simulation results due to the expensive computation costs. • Mechanism analysis and modeling method. Based on the calculation of tool/workpiece deflection, Kang et al. [6] proposed two efficient iterative algorithms to predict deformation errors and calculate the positions and magnitude of the maximum surface form errors, respectively; Tuysuz et al. [7] developed an efficient deformation error
Thin webs are the thin structures machined by the face of the end mill and they are widely used in the aerospace industry due to the advantages of compact structure, light weight and high strength-to-weight ratio [1] . However, significant deformation may occur during their milling process owing to their low rigidity, which seriously affects the machining efficiency and accuracy. Workpiece deformation and cutter deformation, which account for the majority of machining errors of thin-web parts, have been paid efforts to predict and reduce by many researchers in recent years.
Generally, the validated methodologies can be summarized into three subdivisions:
• Finite element method (FEM). Ibaraki et al. [2] developed an FEM-based model to simulate the deformation of a thinwalled workpiece during the milling process, which adopted an iterative algorithm to calculate the cutting force and deformation; Liu et al. [3] proposed a milling error prediction method based on FEM, which considered both the springback deformation of the workpiece and the material removal effect; Du et al. [4] proposed a deformation prediction model based on an analytical force model and ANSYS Parametric Design Language; Wang et al. [5] proposed a FEM-based cutter-workpiece engagement extraction method to predict the deformation errors caused by the milling force during the 5-axis flank milling process. With the aid of matured commercial software, the FEM is convenient and prediction accuracy is acceptable. However, it usually takes hours or even days to get the simulation results due to the expensive computation costs. • Mechanism analysis and modeling method. Based on the calculation of tool/workpiece deflection, Kang et al. [6] proposed two efficient iterative algorithms to predict deformation errors and calculate the positions and magnitude of the maximum surface form errors, respectively; Tuysuz et al. [7] developed an efficient deformation error
Thin webs are the thin structures machined by the face of the end mill and they are widely used in the aerospace industry due to the advantages of compact structure, light weight and high strength-to-weight ratio [1] . However, significant deformation may occur during their milling process owing to their low rigidity, which seriously affects the machining efficiency and accuracy. Workpiece deformation and cutter deformation, which account for the majority of machining errors of thin-web parts, have been paid efforts to predict and reduce by many researchers in recent years.
Generally, the validated methodologies can be summarized into three subdivisions:
• Finite element method (FEM). Ibaraki et al. [2] developed an FEM-based model to simulate the deformation of a thinwalled workpiece during the milling process, which adopted an iterative algorithm to calculate the cutting force and deformation; Liu et al. [3] proposed a milling error prediction method based on FEM, which considered both the springback deformation of the workpiece and the material removal effect; Du et al. [4] proposed a deformation prediction model based on an analytical force model and ANSYS Parametric Design Language; Wang et al. [5] proposed a FEM-based cutter-workpiece engagement extraction method to predict the deformation errors caused by the milling force during the 5-axis flank milling process.
With the aid of matured commercial software, the FEM is convenient and prediction accuracy is acceptable. However, it usually takes hours or even days to get the simulation results due to the expensive computation costs. • Mechanism analysis and modeling method. Based on the calculation of tool/workpiece deflection, Kang et al. [6] proposed two efficient iterative algorithms to predict deformation errors and calculate the positions and magnitude of the maximum surface form errors, respectively; Tuysuz et al. [7] developed an efficient deformation error prediction model based on model reduction technique, which greatly improved the computational efficiency; Wang et al. [8] developed a cutting sequence optimization algorithm to enhance the workpiece stiffness during the machining process; Li et al. [9] developed a calculation method of the deformation error in flank milling based on the differential increments between machined surface and design surface. They compensated the deformation error using tool path modification. Mechanism models usually have clear mathematical expression, which helps to build deep understanding of the cutting and deformation mechanism. However, to simplify the complex cutting process, many conditions are ignored or idealized, resulting in lower accuracy than FEM. For example, both elastic deformation and plastic deformation occur in the milling process while most of mechanism models focus on elastic deformation, which may cause poor prediction accuracy under the plastic deformation dominated condition. • Cutting parameters optimization method. Lee et al. [10] found an optimized tool position strategy through large amount of cutting experiment data; Gao et al. [11] optimized the cutting parameters and tool path to reduce the deformation error of the thin-walled parts. Cutting parameters optimization has been widely used in industry due to theoretical simplicity and high operability, however, it can be difficult and time consuming.
In addition to above methods, OMM system is growing fast in popularity in recent years, for the advantages of on-line measurement, high efficiency and high stability. Many researchers have developed machining error prediction system based on OMM. Huang et al. [12] applied the OMM inspection to the flank milling of an impeller and compensated the deformation error with modifying tool path; Liu et al. [13] proposed an isoplanar-based on-machine scanning method and a partitioned measuring and machining approach large thinwalled parts; Wang et al. [14] used OMM to measure the machining error of a thin-walled workpiece and calculated the machining error; Huang et al. [15] developed an OMM system to acquire the machining error of a tank bottom of the rocket. Most of the compensation ways of the above-mentioned methods are modifying the tool path, namely the G code. However, the G code modification could be very complex, especially in 5-aix machining, thousands of lines of code needing to be carefully modified. Another issue to be noticed is that modifying G code can hardly realize the compensation of high-density cutting points, especially when one line of code contains a long cutting distance. Aiming to achieve better OMM based compensation, a closed-loop machining error compensation method for thin web parts, which integrates automatic OMM inspection, machining error modeling and real time compensation, is proposed in this paper. The rest of this paper is organized as follows. The basic processes of the proposed method are presented in Section 2. The machining error analysis and modeling technique are shown in Section 3 and Section 4, respectively. In Section 5, a typical experiment on the pocket milling of a thin-web part is conducted to validate the effectiveness and accuracy improvement of the proposed method. Section 6 gives the summary of major contributions of this paper.
The machining status monitoring, on-machine measurement, error modeling and real time compensation are integrated into a highly automatic procedure, as shown in Fig.1 . The machining path is firstly generated using computer aided manufacturing software according to the workpiece geometry model. Then the G code is imported to the NC system and the rough/semi-finish machining is performed. After the semifinish machining is completed, the on-machine measurement is carried out to obtain the machined surface data, which is then compared with the designed geometry to calculate the machining errors. The error values are used to build error model utilizing Hampel filtering and machine learning technique. The real time compensation system communicates with the NC system and transfer the compensation values, which are computed in real time, to the NC system in real time and realize the compensation in the final finish machining process. Besides, there is a monitor and controller module to monitor the status of every step and automatically perform all the above-mentioned steps.
The real time compensation system is realized based on computer communication interface of the NC system, as shown in Fig. 2 . The software for the compensation system is developed in C# program language under the support of Author name / Procedia Manufacturing 00 (2019) 000-000 ML.NET, which is an open source and cross-platform machine learning framework. The software communicates with the NC system through Ethernet connection. Firstly, the compensation system reads real time coordinates of the cutting location, transfers to the trained deformation error model and computes the compensation values. The compensation values are then written back to the programmable machine controller of the CNC system and the zero point of the machining coordinate system is updated accordingly to achieve the machining error compensation. The above compensation loop can be completed within one scan cycle of programmable logic controller, which satisfies the requirement of real time compensation. Another advantage of the developed compensation system is that it is independent of the machine process, neither of G code or system parameters need to be modified.
The contact-type touch trigger probe is widely used as onmachine measurement measure due to its high accuracy and reliability. It can be installed on the spindle and perform rapid measurement of the machined workpiece without complex setup. Normally, it is supported by most of the mainstream NC systems in the market. Typically, a Renishaw RMP60 radio transmission probe is used as the main tool of OMM in this study. The measuring path generation function and the coordinate reading function are implemented based on its communication capability with the NC system.
The measuring path and the distribution of sampling points determine the measuring accuracy and reliability. Generally, higher probe point density results in higher inspection accuracy. In addition, the distribution of probe points also plays an important role as not all the points are equally important. Many researchers have paid efforts to this point. In our study, we referred to a well-established theory by Talón et al. [16] and also considered the probe efficiency to plan our probe strategy, which is to obtain sampling points by uniform equidistant distribution. The OMM measuring path is as shown in Fig. 3 , which is consistent with the cutting path. Because there will be no sudden changes in the measurement data in every square path in theory, the measuring data process, such as outliers filtering and error modeling, will be more convenient and the results will be more accurate. 
After the configuration of OMM system, the very important step in the proposed method is to build the machining error model, so the machining error description is first given. Figure  5 . shows a typical thin-web part, which is a pocket thin-web with the dimension of a b δ × × . Due to its low rigidity, serious deformation will occur under cutting forces. As shown in Fig.  6 , the solid black curves indicate the ideal cutting position of the cutter and ideal status of the workpiece while the red dashed curves indicate the actual position of the cutter and the actual shape of the workpiece. After the cutter passes, the workpiece will rebound, which results in less cutting volume, as shown in dashed blue curve. In addition, the material removal effect is also an important influence factor to the machining error because of the varying stiffness, especially when the workpiece is under high axial cutting depths. Combining with many other error sources like plastic deformation and cutter deformation, all above error sources interact with each other and the total deformation error can hardly be precisely predicted through theoretical analysis. However, all of above-mentioned errors can be measured through the OMM inspection, thus it is integrated and applied into the closed-loop machining error compensation system. 
The measured values are compared with the designed geometry to calculate the machining errors, the machining error vector is given by
(1) where m δ is the measured thickness value, i δ is the ideal thickness value of the thin-web part. The computed machining errors are as shown in the bar graph of Fig. 4 . Because there will be no sudden changes in the error values of every square path in theory, the Hampel filtering [17] based on L*MAD criterion is used to eliminate outliers and enhance the stability of the measured error values.
The boundary condition is also a vital factor to the modeling accuracy of the machining error. For the thin-web in this study, the machining error values in the edges of the pocket thin-web is theoretically 0 as the stiffness of the edges is theoretically infinite, so the machining error with boundary condition is , 0. x a or y b
where a is the length, b is the width of the thin-web part, as is shown in Fig. 5 . After the outliers filtering and boundary conditions setup, the pre-processed machining error data is used to build error compensation model. The Multiple Additive Regression Tree (MART) algorithm [18] , which has better accuracy and efficiency than traditional binary polynomial fitting, is used to build machining error compensation model. To achieve a satisfied accuracy, the MART algorithm requires a large amount of training data. However, more sampling points means more measuring time, thus, the triangulation-based cubic interpolation [19] is first used to expand the measuring error data. After the interpolation step, the MART algorithm is then used to train the compensation error model. The input to this algorithm is (x, y, z,e) , where x, y, z are the coordinate vectors of cutting locations and e is the label value vector of corresponding machining error. MART also takes a loss generating function as input, as for regression task, the loss function is defined as a square loss function: 
where , , x y z is the coordinate value, ê is the predicted label value and e is the true label value. This algorithm uses addictive training, it starts from constant prediction and adds a new function each time. 80% of the total data is used to train the model while the rest is used to evaluate the model. In order to validate the efficiency and accuracy improvement of the proposed method, a pocket milling example of a thin web part is given. The machining error compensation was achieved by moving the tool or workpiece in the opposite direction between the tool and workpiece to create a new error to offset the original machining errors. The compensation system was developed based on Fanuc Open CNC API Specifications (FOCAS) and the EMZPS function of Fanuc NC system. The principle diagram of the error compensation system is as shown in Fig. 7 . The compensation values are computed based on the machining error model established based on the method proposed in Section 3 and Section4, which is then imported to the main arithmetic unit. The coordinates values of the machine, which are the input of the compensation model, are obtained through the network interface in real time. The calculated compensation values are then transmitted to the NC system and the servo motors of the X, Y, Z axes are driven to realize the compensation.
A four-fluted flat carbide end mill with a diameter of 16 mm and a helix angle of 30° is used to cut the 6061-aluminum alloy thin web workpiece with a dimension of 250 250 mm mm × . The machine tool is a 3-axis vertical machining center with a Fanuc 0i mate CNC system. A Renishaw RMP60 radio transmission probe with a calibrated 6 mm φ ruby sphere is installed on the spindle to implement the OMM inspection. A laptop computer with an Intel i5-5300U quad-core processor and an 8G RAM was used to run the developed software system.
As shown in Fig. 8 , the left thin-web pocket was first machined without compensation, then the OMM inspection was automatically performed. The measuring data was automatically filtered, expanded and trained to build error compensation model. The real time compensation was then implemented during the milling of the right thin-web pocket. The thickness variations of 3 sets of machining experiment are list in Table 1 . The spindle speed was set to 6000 r/min, the feed rate was 0.02 mm/tooth and the radial cutting depth was 4.8 mm. During the 3sets of experiment, the cutting parameters remain same. The tool path consists of multiple squares from inside to outside, as shown in Fig. 3 . The OMM inspection path was consistent with the cutting path and consisted of 6 square paths and a total of 144 sampling points by uniform equidistant distribution. The spindle thermal expansion was strictly controlled by maintaining it in thermal equilibrium during the whole experiment process. 
After the initial setup of machining parameters and software configuration, no manual participation was required in the whole process of machining, OMM measuring and compensating. The on-machine measurement process of the thin-web pocket is as shown in Fig. 9 , the measuring of 144 sampling points was finished within 5 minutes. The pre-process of the measured data and the training of the compensation model were finished within 3 minutes. Multiple parameters including R-squared (R2), Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) are used for the model evaluation. The evaluation results of the trained model were: R2 is 0.9965; MSE is 1.374; RMSE is 1.1722. The computation time of each compensation value is within 3 milliseconds, which fulfill the requirement of the compensation cycle (~30 milliseconds).
The machining error comparisons of with and without compensation for experiment set 1, set 2 and set 3 are as shown in Fig. 10, Fig. 11 and Fig. 12 , respectively. Fig. 10 . (c), Fig.  11 . (c) and Fig. 12 . (c) are the error lines in the position of x=-160 mm of the workpiece. In terms of experiment set 1, since the initial workpiece thickness was 8 mm, the overall stiffness of the workpiece was good enough, which resulted in the fact that the main error source was elastic deformation and caused gentle positive machining error values. As shown in Fig. 10. (a) and Fig. 10. (b) , the machining error values were reduced from [0, 31] μm to [-8, 5] μm and the error surface was much flatter after compensation. The machining error range was decreased by 58.1%. In addition, the machining error in the middle of the workpiece is theoretically the largest, thus the error line in the middle is also shown in Fig. 10 . (c) to illustrate the compensation effect.
Similarly, Fig. 11 shows the error surfaces and error lines of experiment results of experiment set 2, in which the workpiece thickness is reduced from 4 mm to 2 mm. The stiffness of the machining point varied from good to low in the whole machining process, meaning both elastic and plastic deformation occurred in this process, so the machining error value also varied from positive to negative, as is shown in Fig.  11(a) . It can be difficult to consider both elastic and plastic deformation and establish theoretical machining error model. However, the proposed method can solve the problem of all stiffness conditions with the same procedure. After compensation, the machining error values were reduced from [-56, 23] μm to [-1, 24] μm and the error range was decreased by 68.4%. What to be noticed is that Fig. 10. (c) and Fig. 11 . (c) indicate the compensation can decrease more error values at 50 mm and -50 mm position comparing with 0 mm position. The reason may be that the middle of the workpiece is the axial feed area of the milling tool. The unstable milling force in the axial feed process results in sudden changes of the machining errors, which makes the modeling and fitting accuracy of this area lower than other areas.
For experiment set 3, the workpiece stiffness was low and the main error source was plastic deformation, which caused serious overcut of the whole surface. As shown in Fig. 12 , the machining error values were reduced from [-99, 0] μm to [-22, 15] μm and the error range was decreased by 62.6% after compensation. The smaller the thickness of the thin web workpiece, the smaller its rigidity, which results in higher stress under certain milling force. According to the stress-strain curve of 6061-aluminum alloy, when the stress reaches the yield point, the workpiece deformation changes from elastic stage to plastic stage. In the stage of elastic deformation, all the deformation of the workpiece rebounds after the milling tool passes. However, only part of the deformation rebounds in the stage of plastic deformation and the specific rebounded value is difficult to determine according to theoretical models. Thus, the OMM-based modeling method was applied to measure and compensate the comprehensive machining error.
The error ranges of all sets are reduced by more than 58.1% after above compensations, which indicates that the proposed method can be used for high precision machining of thin web parts. For the impact on the machine productivity, although the probing of 144 points in our study takes about 5 minutes, the proposed compensation method reduces the machining time by changing the machining strategy from two-layer milling (~31+31 mins) to one-layer milling (~31 mins). Taking the probing time into consideration, the machining productivity is improved by about ~41.9%. The machining error in this study refers to product quality, including the errors induced from machine tool, milling tool, fixture and the milling process. The proposed method obtains the errors through OMM, which is especially suitable to obtain all above-mentioned errors except for the error from the machine tool as the OMM system is installed on the machine tool. Compared with other modelbased approaches such as FEM-based method [3] [4] [5] and mechanism modeling method [6] [7] [8] [9] , the proposed method has the approximate prediction accuracy in terms of elastic deformation. However, none of other approaches considered the plastic deformation due to its complexity in simulation and mechanism analysis, which makes our proposed method more robust and more applicable.
In this paper, a highly automatic method that integrates machining status monitoring, OMM inspection, error modeling and real time compensation for improving machining efficiency and accuracy of thin-web parts is proposed. There are many error sources interacting with each other in the milling process, which makes comprehensive theoretical modeling very difficult or even impossible. Thus, the onmachine measurement is applied to measure the final comprehensive machining error. Also, the Hampel filtering and machine learning technique are used to train the compensation model to realize error prediction of high-density cutting points. The real time compensation is then performed based on FOCAS and EMZPS function of Fanuc NC system. The efficiency and accuracy of proposed method was validated through the compensation experiment of a thin-web pocket part. The experiment results revealed that the comprehensive machining error ranges were decreased by more than more than 58.1%. This method demonstrates immense potential for further applications in efficiency and accuracy improvement of thin-walled parts.
The proposed method will be applied to the efficiency and accuracy improvement of thin-walled freeform surface parts, such as compressor scroll, impeller blade and turbine blisk, in our future research. In addition, other possible influence factors of the machining accuracy, including repetitive positioning accuracy of the machine tool and tool wear, will also be taken into consideration.