Xiozhong HAO, Yinggung LI,*, Chong HUANG, Mengqiu LI,Chngqing LIU, Ki TANG

a National Key Laboratory of Science and Technology on Helicopter Transmission, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China

b Hong Kong University of Science and Technology, Hong Kong, China

KEYWORDS ARIMA model;Deformation control;Deformation inspection data;Machining allowance allocation;Structural parts

Abstract Deformation resulting from residual stress has been a significant issue in machining. As allowance allocation can directly impact the residual stress on part deformation, it is essential for deformation control.However,it is difficult to adjust allowance allocation by traditional simulation methods based on residual stress,as the residual stress cannot be accurately measured or predicted,and many unexpected factors during machining process cannot be simulated accurately. Different from traditional methods, this paper proposes an allowance allocation method based on dynamic approximation via online inspection data for deformation control of structural parts. An Autoregressive Integrated Moving Average (ARIMA) model for dynamic allowance allocation is established so as to approach the minimum deformation, which is based on the in-process deformation inspection data during the alternative machining process of upside and downside.The effectiveness of the method is verified both by simulation cases and real machining experiments of aircraft structural parts,and the results show that part deformation can be significantly reduced.?2020 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Aircraft structural parts often have the characteristics of being large in size and requiring a high material removal rate (up to 95%1,2)in their production. In such cases the release of residual stress during machining can lead to serious deformation.3The machining deformation of aircraft structural parts has always been an important problem to be solved in aviation industry.Investigations showed that Boeing company had lost as much as 290 million Dollars in four projects due to part deformation,4and the European Union spent 10 million Euros every year in aerospace industry to avoid or correct machining deformation.5There are many factors affecting the machining deformation,6-11including the initial residual stress of the blank, the size and structure of the part, cutting tool parameters, process parameters et al, but it has been widely accepted that the most important factor is the redistribution of residual stress after material removal.12-14

Research on residual stress and machining deformation shows that machining deformation is determined by the residual stress of the material,the dimensions and shape of the part,and the position of the part in the blank.15Therefore, adjusting the relative position of the expected finished part in the blank by optimizing the allowance allocation is an effective way to control machining deformation. Different from traditional methods where the machining allowance is determined before machining process, an allowance allocation method based on dynamic approximation via online inspection data for deformation control of structural parts is proposed in this paper.

The dynamic allowance allocation of upside and downside is driven by in-process deformation inspection data, which is realized by taking advantages of a set of floating clamping fixtures. Part deformation is released and inspected during the machining process, and an ARIMA-based allowance allocation model is established based on deformation inspection data. According to the model, the allowance allocation of upside and downside of the part is dynamically adjusted for each necessary layer,and the residual stress is released by alternative machining of upside and downside of the part,therefore the machining deformation can be balanced to achieve the purpose of precise deformation control.

2. Related work

Machining deformation is one of the main reasons for part quality problems, so machining deformation control has become an important aspect to guarantee part quality. In order to control machining deformation, a lot of related researches have been developed by scholars, which will be introduced in two categories as follows.

(1) Deformation control by process adjustment.At present,machining process optimization based on deformation prediction is widely used for deformation control,which can be mainly be divided into three aspects: machining parameters optimization, machining sequence optimization and pre-stress imposition.

A) Deformation control by machining parameters optimization. The machining parameters include cutting speed, feed, cutting depth, tool geometry,tool fillet radius and wear,etc.Fuh and Wu16proposed a residual stress prediction model for milling aluminum alloy to control part deformation.Umbrello et al.17studied the effects of materials,tool geometry and machining parameters on residual stress, and proposed a deformation prediction model of cutting residual stress based on neural networks. Li et al.18proposed a novel model for finishing allowance optimization based on the simplex algorithm, which made 39-56%reduction of the overall machining deformation compared to that in conventional method.

B) Deformation control by machining sequence optimization.Sasahara et al.19studied the influence of various machining sequences on residual stress distribution during machining process by simulation, and an optimal machining sequence is obtained. Cerutti and Mocellin20established a model of stiffness and part deformation through simulation, and the influence of machining sequence on part deformation was studied. Outeiro et al.21studied the residual stress field distribution of a specific workpiece under different machining sequences based on simulation methods, and proposed a machining sequence optimization method. Chen et al.22proposed a method to optimize the machining sequence based on a genetic algorithm and part deformation was reduced.

C) Deformation control by pre-stress imposition. Ye et al.23adopted a new pre-stress method to actively control the residual stress state so as to improve the machining quality of bearing parts as well as fatigue life.He et al.24studied the influence of machining parameters and pre-stress on the residual stress of 40Cr steel through orthogonal tests, and the results showed that pre-stress can effectively improve the compressive residual stress.

(2) Deformation control by allowance adjustment. Compared with the above process adjustment for deformation control, the part allowance allocation strategy can directly and effectively change the bending moment of the residual stress on the part,thereby achieving the purpose of machining deformation control. Brinksmeier et al.15found that the machining of bearing rings at different positions in the blank would change the distribution of residual stress in the ring through experimental analysis,leading to different deformation.Nervi25established an ideal mathematical model for predicting machining deformation based on elasticity theory, and the research results showed that the position of the sample has a great influence on machining deformation.Zhang26analyzed the effect of the residual distribution on the machining deformation through numerical simulation and experiments, and the deformation analysis with T-section shrinkage samples was studied.

It can be found that the change of the part position in a blank for machining deformation control has been studied widely from the above analysis. However, current research on part allowance allocation strategies are mainly limited to static optimization, i.e., part allowance allocation has been determined before actual machining. Due to the limitations of the residual stress measurement methods which is still not high enough in accuracy, and it is always complicated and costly.27In addition to that, the uncertainty of the residual stress distribution of the blank during the machining process cannot be well estimated, so it is difficult to achieve accurate deformation control by numerical analysis.Therefore,the allocation strategy of the parts allowance for deformation control still needs to be studied in depth. This paper will focus on this issue by using the method of dynamic allowance allocation.

3. Mechanics principle of deformation related with allowance allocation

The bending moment caused by the residual stress can be changed by adjusting the relative position of the expected finished part in the blank, as shown in Fig.1.The part deformation is mainly attributed to the bending moment caused by the residual stress, as Eq. (1) shows, the bending moment M depends on the integral of the product of the internal residual stress of the part σ（z） and its corresponding distance to the middle layer of the part t（z）over the whole part area V.When the relative position of the expected finished part in the blank is changed, t（z）will be changed correspondingly, so the bending moment caused by the residual stress will also be changed,resulting in different part deformation after machining.

Therefore,part deformation can be controlled by adjusting the position of the expected finished part in the blank by optimizing the part allowance allocation. This paper will study how to optimize the part allowance allocation strategy so as to reduce part deformation.

4. Dynamic allowance allocation method via deformation inspection data

Aiming at the problem mentioned above, this paper proposed an allowance allocation method based on dynamic approximation via online inspection data for deformation control of structural parts.As shown in Fig.2,the blank is firstly divided into a fixed process layer and a dynamic adjustment layer.The dynamic allowance allocation of upside and downside is driven by the in-process deformation inspection data which is realized by taking advantage of a set of floating clamping fixtures.Part deformation is released and inspected during the machining process, and an ARIMA-based part allowance allocation model is established based on the deformation inspection data.According to the model, the allowance allocation of upside and downside of the part is dynamically adjusted, and the residual stress is released by alternative machining of upside and downside of the part,therefore the machining deformation can be balanced to achieve the purpose of deformation control.

4.1. Layering strategy of blank

In order to improve the machining efficiency by using the dynamic allowance allocation method, the part is divided into a fixed process layer and a dynamic adjustment layer according to the size and structure of the part and the corresponding blank. In the fixed process layer, constant machining parameters are used to remove the material of the fixed process layer,and the allowance is predefined,where the deformation inspection data can be used for deformation prediction model;in the dynamic adjustment layer, the upside and downside part allowance are allocated dynamically according to the dynamic allowance allocation method so as to achieve the purpose of deformation control.

The proportion of the fixed process layer and the dynamic adjustment layer in the blank is determined according to the size and structure of the part and the blank respectively. As the total allowance of the part in upside and downside is determined by the blank and part,the adjustment of allowance allocation of each side has a range. Essentially, the expected final part should be enveloped by the blank.When the top surfaces of upside or downside of the part are in the extreme positions of upside or downside of the blank,there are two extreme positions in upside and downside of blank formed by the bottoms of the upside and downside of the part.In order to ensure that the expected final part is enveloped by the blank, the bottoms of the upside and downside of the part should not overstep the two positions. Therefore, the layering strategy can be made based on the above principle.

Fig. 1 Mechanics principle of deformation related with allowance allocation.

Fig. 2 Dynamic allowance allocation method based on deformation inspection data.

The layering in the thickness direction of the blank is shown in Fig. 3, (a) when the part is at the upper limit of the blank,the machining layer between the upper surface of the blank and the upper surface of the bottom is divided into the upside fixed process layer;(b)when the part is at the lower limit of the blank, the machining layer between the lower surface of the blank and the lower surface of the bottom is divided into the downside fixed process layer, and the up and down fixed process layer are collectively referred as the fixed process layer;(c)the dynamic adjustment layer is defined between the upside fixed process layers and the downside fixed process layer. B and P represent the thickness of the blank and the part respectively, F and D represent the thickness of the fixed process layer and the dynamic adjustment layer respectively, Fuand Fdrepresent the thickness of the upside fixed process layer and the downside fixed process layer respectively, Wurepresents the distance from the web to the top of the upside rib and Wdrepresents the distance from the bottom to the top of the downside rib. Then the relationships among these variables are represented as follows:

4.2. ARIMA-based part allowance allocation model

In order to dynamically allocate the machining allowance of the upside and downside of the part during the machining process, the following scheme is adopted: in the dynamic adjustment layer, according to the part allowance allocation model,one sub-layer of one side will be firstly machined to balance the deformation of the completed fixed process layers;the next machining layer is selected according to the part allowance allocation model to balance the overall deformation of the part until the dynamic adjustment layer is finished.

First of all, the data sequence formed over time by the machining deformation of adjacent processes can be regarded as a random sequence, which can be approximately described by a time series mathematical model.Once this model is established, it can be used to predict the future deformation from the past and present deformation data. Therefore, an ARIMA28- based part allowance allocation model is established. The regression model is established for the dependent variable to its lag value, the present and lag values of the random error term during the process of transforming the nonstationary time series into a stationary time series,and the formula is represented as follows:

Fig. 3 Layering diagram of blank.

where ytis the current value, μ is a constant term, p and q are the order of the autoregressive model and the moving average model respectively, γiand θiare the correlation coefficients of the two models respectively,and εtis the error value.The steps to establish the model are described as follows:

(1) Obtain time series data of the observed system;

(2) Plot the data,observe whether it is a stationary time series; for the non-stationary time series, perform the dorder difference operation firstly and turn it into a stationary time series; if it is a stationary sequence, use the ARMA (p, q) model directly;

(3) After the second step, a smooth time series would be obtained. The autocorrelation function ACF and the partial autocorrelation function PACF are obtained for the stationary time series. The autocorrelation function ACF describes the linear correlation between time series observations and their past observations; the partial autocorrelation function PACF describes the linear correlation between time series observations and their past observations under the condition of given the intermediate observations. The best hierarchical p and the order q are obtained by analyzing the autocorrelation graph and the partial autocorrelation graph.

(4) From the d,q,and p obtained above,the ARIMA model is obtained. Then test the established model. Confirm whether the resulting model can match the observed data characteristics or not. If not, go back to step 2.

The deformation data in the machining process is regarded as time series data of the observed system, and the ARIMAbased part allowance distribution model is established. The machining side and machining depth of the next layer can be determined according to the model to balance the deformation that has happened, and finally approach the minimum deformation, so the final part deformation is expected to be controlled.

4.3. Dynamic allowance allocation method

The dynamic allocation method of parts allowance is based on the continuous alternative machining of upside and downside.The ARIMA-based allowance allocation model is established via the deformation inspection data of the part.The machining side and the corresponding machining depth of the next layer in the dynamic adjustment layer are determined according to the established ARIMA-based part allowance allocation model, and then to balance the deformation that has happened. By removing the machining allowance of the part through several iterations of the balance, a good deformation control effect is expected after the finishing process, as shown in Fig. 4.

The core of the above method for allowance allocation based on deformation inspection data is to approach the minimum deformation,which is realized by continuously adjusting the position of the part by alternatively removing the materials of the upside and downside.The detailed steps of the dynamic allowance allocation process are as follows:

(1) After the fixed process layer is completed, the deformation dfgenerated by the fixed process layer is inspected and the ARIMA-based part allowance allocation model is established according to the deformation inspection data of the part.

Fig. 4 Schematic diagram of dynamic allowance allocation method.

Table 1 Mechanical properties of the three materials.

(2) It is determined by the ARIMA-based part allowance allocation model that the machining side and machining depth to balance the previous deformation, then one sub-layer is machined to balance the deformation dfof the fixed process layer.

(3) Calculate the current allowance adof the dynamic adjustment layer after previous machining. If adis less than or equal to the finishing allowance FA, the last layer will be machined with cutting depth ad, and the machining is finished; if adis more than finishing allowance, the next step will be performed. The finishing allowance FA is a value set according to the specific machining condition so that the remaining allowance after the balance deformation can be removed and large deformation will not be caused.

(4) The maximum cutting depth and minimum cutting depth of each single layer on the upside of the part are determined according to the part allowance allocation model and process strategy. If the deformation of the single layer on the upside of the part is too small, the machining efficiency will be affected;and if the deformation is too large, it will result in an unbalanced result.For the detailed process, see Eq. (4) and Eq. (5), where PREmaxand PREminindicate the deformation determined by the part allowance allocation model as the corresponding maximum and minimum cutting depth respectively;TECmaxand TECminindicate the maximum and minimum cutting depth respectively according to the preset machining process; APmaxand APminrepresent the actual maximum cutting depth and the minimum cutting depth, so the upside cutting depth APuwill be properly selected within the range of APmaxand APmin.

(5) Machine the upside face of the part with the depth of APu, the part deformation inspection point is measured after the machining finished, and the deformation and the corresponding cutting depth are input into the ARIMA model to determine the cutting depth of the downside to balance the machining deformation.

Fig. 5 Establishment of simulation environment and the deformation data collection.

(6) Change the side to be machined,and prepare to machine the downside to balance the deformation.

(7) According to the ARIMA-based part allowance allocation model, the machining depth APdof the downside surface is determined to ensure that the deformation can be balanced. If the depth required for the downside exceeds APmax, the depth is divided into multiple layers on average for continuous machining.

(8) The deformation of the part is inspected, the deformation data and the corresponding cutting depth are input into the ARIMA model, which is convenient for calculating the maximum cutting depth and the minimum cutting depth of the single layer of the next layer.

(9) Repeat steps 3 to 9 until the machining allowance is machined, and it should be noted that the workpiece is fixed to the state before deformation release.

Fig. 6 Comparison of deformation between traditional method and proposed method of 6061 and 7075.

Fig. 7 Comparison of deformation between traditional method and proposed method of TC4.

The algorithm for the dynamic allocation method of the part allowance is described as follows:

Algorithm 1 The dynamic allowance allocation method Input:Machining deformation data set DEF=［DEF1，DEF2，...，DEFi，...，DEFn］Process:An ARIMA-based part allowance allocation model is established according to the deformation data DEF.Machine the dynamic adjustment layer according to the model to balance deformation df.Calculate the allowance ad of the dynamic adjustment layer after machining.for ad >FA do Determine the machining depth APu of the upside.Machine the upside with depth APu and inspect deformation.Determine the machining depth APd of the downside to balance the deformation.if APd >APmax APd is divided into multiple layers of continuous machining on average.else:Machine the downside with depth APd.Calculate the allowance ad of the dynamic adjustment layer.return ad.The last layer is cut with depth ad.end Output: The strategy of dynamic allocation of part allowance

5. Case study

In order to verify the deformation control effect of the proposed dynamic allowance allocation method, a set of comparison experiments are designed,where two blanks with the same batch and the same size are machined by using the proposed method and the traditional method respectively. In order to control the deformation and machining efficiency of the fixed process layers, the materials in the fixed process layer of the part are removed with alternative machining on the upside and downside for both of the methods. The overall idea of the experiments is as follows:

(1) For the traditional method, equal-allowance allocation for the upside and downside of the part was adopted,and continuous double-sided alternative machining is used to remove the remaining allowance of the upside and downside.

(2) For the proposed method, the remaining allowance is determined according to the dynamic allocation method of the part allowance in the dynamic adjustment layer.

Firstly,simulation verification is carried out.Finite element simulation of machining deformation was performed by using the commercial finite element software ABAQUS.The materials of aluminum alloy 6061,aluminum alloy 7050 and titanium alloy TC4 were simulated and calculated respectively. The mechanical characteristics of the three materials are shown in Table 1. Three blanks with different sizes and materials were established in the simulation environment, and initial residual stress of the blanks were introduced according to industrial experiences. The technique of deactivate and reactivate element was used to simulate the material remove process in the software, in which the stiffness matrix was set to zero to deactivate the element.The model was meshed with a unit area of 0.1 mm2to ensure the integrity of material removal.

The sizes of blanks with aluminum alloy 6061, 7050 and titanium alloy TC4 are 510 mm×30 mm, 600 mm×30 mm and 540 mm×24 mm respectively. The thickness of the aluminum alloy 6061 and 7050 blanks is 24 mm, while the thickness of the titanium alloy TC4 parts is 20 mm.The thickness of the bottom of the three blanks is 4 mm.Taking the middle area of the blank as the displacement constraint area,the deformation of the outermost two points of the part was recorded during the material removal process, as shown in Fig. 5.

(1) The simulation case study of the blank with aluminum alloy 6061. For the traditional method, the material was removed alternately at the fixed process layers with 2 mm depth on the upside and downside.In the dynamic layer, the upside of the part is firstly machined with2 mm depth, and then the downside is machined with 2 mm depth, and then the upside with 1 mm depth,finally the downside is machined with 1 mm depth.The deformation is shown in Fig. 6(a), where the maximum deformation is 0.256 mm during the whole process and the final deformation is 0.156 mm.For the proposed method,the same process as the traditional method was used in the fixed process layers. Dynamic allocation method of parts allowance is adopted in the dynamic adjustment layer. The deformation is shown in Fig. 6(b), where the maximum deformation during the whole process is 0.256 mm and the final deformation is 0.044 mm.

Table 2 Comparison results of final part deformation in simulation environment.

Fig. 8 Machining experimental environment and part information.

Table 3 Cutting parameters of experiments.

Fig. 9 Machining process and data collection.

Fig. 10 Part deformation in fixed process layer by traditional method.

(2) The simulation case study of the blank with aluminum alloy 7050. The same operations and cutting depth are adopted as the first simulation case study for the traditional method, and the deformation is shown in Fig. 6(c), where the maximum deformation is 0.221 mm during the whole process and the final deformation is 0.136 mm. For the proposed method, the same process as the traditional method is used for the fixed process layer. Dynamic allocation method of parts allowance is adopted in the dynamic adjustment layer. The deformation is shown in Fig.6(c),where the maximum deformation is 0.221 mm during the whole process and the final deformation is 0.036 mm.

(3) The simulation case study of the blank with titanium alloy TC4. The same operations and cutting depth are adopted as in the first simulation case study for the traditional method,and the deformation is shown in Fig.7(a), where the maximum deformation is 0.228 mm during the whole process, and the final deformation is 0.019 mm. For the proposed method, the same process as the traditional method is used as in the fixed process layer. The dynamic allocation method of parts allowance is adopted in the dynamic adjustment layer. The deformation is shown in Fig. 7(b), where the maximum deformation is 0.217 mm during the whole process, and the final deformation is 0.011 mm.

From the simulation analysis above, we find that the proposed method can achieve better results compared to traditional methods when applied to blanks with different sizes and different metal materials.For the titanium material,due to the small size and high Modulus of elasticity,the deformation magnitude is not so great,while the effect will be more obvious as the size is larger.All of the simulation results are shown in Table 2.

In this paper, aluminum alloy 6061 was used for real machining experimental verification, and the experimental blank size is 510 mm×140 mm×30 mm, as shown in Fig. 8(a). The thickness of the part is designed to be 24 mm, and the thickness of the bottom is 4 mm. The machining features of the upside and downside of the part are shown in Fig. 8(b).The layering result of the blank is shown in Fig.8(c),both of the fixed process layer of upside and downside are 10 mm,and the dynamic adjustment layer is 10 mm.

In order to balance the machining deformation by continuously machining the two sides of the part according to the allowance allocation model under one-time clamping, the authors’ team has developed a vertical-floating clamping device so as to facilitate the proposed method, as shown in Fig. 8(a). In addition to the functions of positioning and clamping, the most important of the vertical clamping device is to ensure the continuous alternative machining of the upside and downside of the part under one-time clamping. At the fixed clamping point,a combination of one plane and two pins is adopted to locate the workpiece,and 6 degrees of freedom of the workpiece are constrained so as to ensure the machining datum during the machining process; The floating clamps are unfixed during the machining intervals and the part deformation can be released and inspected, and then it is re-clamped for further machining. Combined with the rotating axis function of the five-axis machining center of DMU BLOCK 80P,the rotating C-axis can satisfy the requirement of quick switch of the machining sides of parts, which lays the foundation for continuous machining of aircraft structural parts on both sides to balance deformation.

The cutting parameters are shown in Table 3. The machining process and deformation inspection process are shown in Fig.9.The deformation data are collected for each machining layer,and different inspection points on the surface of the part are automatically measured by on-machine probe RenishawTM,and the spatial position measurement accuracy in a single direction is 0.001 mm,which can completely meet the precision requirement.

In the traditional method which has an equal-allowance allocation for the upside and downside of the part,the continuous double-sided alternative machining process is used to remove the fixed process layer. Inspection data are recorded after the 2 mm depth is machined in the upside, and this is the absolute value corresponding to the position before machining,C-axis is rotated 180 degrees to switch the machining sides of part, inspection data are recorded after the 2 mm depth is machined in the downside of part, and again this is the absolute value corresponding to the position before machining. The fixed process layer of the part is removed by repeated cycle machining,and the deformation surface of each layer can be fitted through the deformation data, as shown in Fig.10. When the first four layers of the upside and downside are machined,part deformation gradually increases.The maximum deformation is obtained when the fifth layer of the upside is machined, the maximum deformation of inspection points is 0.327 mm, and part deformation begins to decrease when the fifth layer of the downside is machined. The maximum deformation of inspection points is 0.263 mm after the fixed process layer is machined.

Fig. 11 Part deformation in dynamic adjustment layer by traditional method.

Fig. 12 Part deformation in fixed process layer by proposed method.

For the traditional method, the upside of the part is firstly machined with 2 mm depth, then the downside of the part is machined with 2 mm depth, and then the upside with 1 mm depth,finally the downside is machined with 1 mm depth.Part deformation of machining the dynamic adjustment layer is shown in Fig. 11. It can be found that the part deformation caused by the upside machining can be indeed reduced by the downside machining, and the final maximum part deformation of inspection points is 0.227 mm by the traditional method.

For the proposed method, the deformation surface of each layer can be fitted through the deformation data, as shown in Fig.12.When the first three layers of the upside and downside are machined,part deformation increases gradually.The maximum deformation is obtained when the fourth layer of the upside is machined, the maximum deformation of inspection points is 0.3 mm, and part deformation begins to decrease when the fourth layer of the downside is machined. The maximum deformation of inspection points is 0.223 mm after the fixed process layer is machined.

Fig. 13 Part deformation in dynamic adjustment layer by proposed method.

Table 4 Comparison of part deformation after finishing.

Dynamic allocation method of parts allowance is adopted in the dynamic adjustment layer. The deformation data obtained during the machining process are input into ARIMA model, and the ARIMA-based part allowance distribution model is established. Firstly the downside of the part is machined with a 4.1 mm depth to balance the deformation which has happened according to the model, the machining depth of 4.1 mm is divided into three layers with machining depth 1.5 mm, 1.3 mm, and 1.3 mm respectively. Then the upside is machined with 0.6 mm depth,and then the downside with 0.8 mm depth,finally the upside is machined with 1.5 mm depth according to the model. Part deformation of machining the dynamic adjustment layer is shown in Fig. 13. It has been found that the final maximum part deformation of inspection points is 0.032 mm by the proposed method.

The feasibility of this method was verified by the comparison experiments with the traditional method which is an equal-allowance allocation of the upside and downside of the part,and a smaller deformation is achieved,the real machining experiment results are shown in Table 4.

It should be noted that the method proposed in this paper is applicable to various sizes of structural parts with double sides machining.If it is to be used for other sizes of structural parts,a special set of clamping device is required. And a general clamping device can also be made so as to adapt to structural parts with the sizes of a certain range.

6. Conclusions and future work

The machining deformation of structural parts has been a serious issue for part quality control, and this paper proposes an allowance allocation method based on dynamic approximation via online inspection data for deformation control of structural parts by taking advantage of a vertical floating clamping system. The machining allowance on both sides of the part is dynamically adjusted according to the ARIMA-based part allowance allocation model during the machining process,and the part deformation is controlled by approaching the minimum deformation with continuously adjusting the position of the part and alternatively removing the materials of the upside and downside. The proposed approach is verified both by simulation and real machining experiments. In contrast to the existing methods which only use simulation based on inaccurate residual stress to determine allowance before machining process, this paper proposed a new idea to dynamically determine the allowance based on in-process deformation data, and this can provide a reference for intelligent machining for the purpose of deformation control, as well as other machining quality control.

Although promising results have been achieved in this paper, there is still much work deserved to do in the future:(1)Allocation adjustment of machining allowance by considering stiffness change of each layer for more precise control of part deformation; (2) Allocation adjustment of machining allowance for different kinds of structural parts.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The research work presented in this paper was primarily cosupported by the National Natural Science Foundation of China(No.51775278)and National Science Fund of China for Distinguished Young Scholars (No. 51925505).