Wall thickness error prediction and compensation in end milling of thin-plate parts

Highlights

• A novel method for FE modeling of thin-plate part is developed to improve the computational efficiency.

• It is revealed for the first time that the surface topography of the finished thin-walled part is formed by the repeated cutting with the bottom edge of the cutter (BEC) in end milling.

• An effective the wall thickness errors prediction method is developed to calculate the time- and position-dependent deformations of the part.

• An iterative adjustment method is proposed to determine the modified ACDs for compensation of the wall thickness errors.

Abstract

End milling has been widely adopted to machine the thin-plate parts that play increasingly important role in the aerospace industry, due to the advantages of high machining accuracy and fine machined surface quality. In this paper, a systematic method is proposed to predict and compensate the wall thickness errors in end milling of thin-plate parts. The errors are caused by the static deflections induced by the varying cutting force imposed on the weakly rigid part. To improve the efficiency of computing the part deformation, a novel FE model is firstly developed by combing the methods of substructure analysis, special mesh generation and structural static stiffness modification. Then, the time- and position-dependent deformations of the part are calculated based on the proposed FE model to predict the wall thickness errors left on the finished part. It reveals for the first time that the surface topography of the finished thin-plate part is formed by the repeated cutting with the bottom edge of the cutter (BEC) in end milling. Owing to the coupling between the axial cutting depth (ACD) and the force-induced deflection, the modified ACDs for compensation of the static wall thickness errors are finally determined by an iterative adjustment method. The proposed method is verified by three-axis end milling experiments. The experiment results show that the predicted wall thickness errors match well with the really measured ones, and the errors are reduced by 77.18% with the help of the proposed compensation method. Moreover, the proposed FE model reduces the computational time elapsed for error prediction by 67.44% as compared with the benchmark FE model.

Introduction

End milling is widely employed for machining thin-plate parts, such as the fuel tank barrel of a rocket. However, due to the weak rigidity of thin-plate parts and large cutting force in machining process, undesirable static and dynamic deflections may occur along the wall thickness direction and result in wall thickness tolerance violation.

Dynamic deformations or chatter in thin-plate parts machining have been extensively studied in the past few decades. Chatter can be avoided by selecting the chatter-free machining parameters, such as the cutting depth and the spindle speed, based on the stability lobe diagram [[1], [2], [3]], or by adding extra mass and damper to the processing region [4]. More effective chatter suppression strategies are referred to Ref. [5]. Under the chatter-free conditions, the force-induced static deformation is the dominant factor which leads to tolerance violation of thin-plate parts. To alleviate the harmful effect of static deformation, lots of efforts have been made in terms of the prediction and compensation of the machining errors cause by the static deformations, reviewed as follows.

The on-machine measurement (OMM) is generally adopted to compensate the static deformation in the thin-plate parts machining. The main ideas of the OMM are on-machine inspection of the machining errors and offline adjustment of the NC programs, which avoids the extra error caused by repetitively clamping. Myeong-WooCho et al. [6] obtained the topography of the machined surface by using a touch-trigger probe installed on the spindle and then corrected the surface errors for the same workpiece in three-axis machining. Bi and Huang [7] applied the OMM to compensate the machining errors in five-axis flank milling. Chen et al. [8] extracted the systematic errors from the machining errors obtained from the OMM system and then compensated them by modifying the toolpath. Recently, Ge et al. [9] established an integrated error compensation model for thin web parts by applying the OMM inspection and a machine learning algorithm. However, due to the coupling of the cutting force and the machining parameters, an alternate process of OMM and toolpath adjustment has to be carried out to guarantee the machining tolerance, which pays the price of decreasing the machining efficiency. Hence, the method of machining error measurement and compensation via the OMM is extremely time-consuming, especially for large thin-plate parts end milling.

Recently, the real-time measurement and compensation methods have been employed in the machining of thin-plate parts. They are able to modify the toolpath or the processing parameters in real time. Yang et al. [10] developed a real-time tool deformation compensation system to reduce the machining surface errors by measuring the cutting force and adjusting the position of the tool. Liu et al. [11] established a dynamic feature model to realize the real-time compensation of the elastic deformations. Wang and Bi [12] developed a forecasting compensation method to reduce the impact of the time-delay from the perspective of the frequency response characteristics. Wang et al. [13] presented a method for real-time compensation of the thickness errors of large thin-plate parts caused by the deformations in a mirror milling machine tool by iterative adjustment of the ACD. However, the deformation errors cannot be measured directly in most cases and it is difficult to incorporate the customized software package into the mainstream commercial CNC system. These drawbacks restrict the extensive application of the real-time compensation methods to end milling of thin-plate parts.

The offline simulation methods are also widely employed to predict and compensate the static deflections of thin-plate parts. With this method, the static deflections are firstly predicted based on the accurate cutting force model and the FE model of the workpiece, and then compensated through the offline mirror modification of the toolpath. Kline et al. [14] predicted the static deflection errors in the machining process using a Finite Element Method (FEM). Wang et al. [15] proposed a FEA-based cutting process optimization algorithm to reduce the flexible workpiece deformation. However, the coupling effect between the process parameters and the static deformations has been neglected in their works. To solve this problem, Budak and Altintas [16], Tsai and Liao [17] adopted the iterative strategy to predict both the cutting force and its induced deformations whilst considering the material removal. Ratchev et al. [[18], [19], [20]] developed an error prediction and compensation approach for machining flexible thin-plate parts based on an advanced Finite Element Analysis (FEA). By using an irregular FE mesh of the workpiece, Wan et al. [21,22] realized error prediction and control in peripheral milling of thin-plate parts. Recently, Li, Zhu and Altintas et al. [23] predicted the dimensional surface form errors in five-axis flank milling of thin-plate parts by incorporating a structural stiffness modification procedure into the FE model of the part, and then the surface form errors are compensated via tool path optimization based on the prediction results [24]. Altintas et al. [25] improved the computational efficiency of predicting deflection errors in ball end milling of flexible blades by using the sub-structuring technique. On this basis, Habibi et al. [26] compensated the tool and part deflections by simultaneously modifying the tool orientation and position. However, the above offline simulation methods are mainly implemented for flank milling machining of small thin-plate parts. With respect to larger thin-plate parts, these prediction methods have poor computational efficiency because of the oversize FE models. More importantly, since the direction of weak rigidity of thin-plate parts is along the axis of the milling tool, end milling of thin-plate parts is different from peripheral or flank milling of the parts, as shown in Fig. 1. It should be noted that the peripherally milled thin-plate parts are usually called thin-walled parts in the machining literature. At present, there is a lack of effective simulation methods for predicting the force-induced deformation errors in end milling of thin-plate parts. Therefore, an efficient prediction model needs to be constructed for the following compensation of the static deflections in end milling of large thin-plate parts.

This paper proposes an effective method to predict and compensate the wall thickness errors caused by the static deformation in end milling of thin-plate parts. A novel FE model is proposed to improve the efficiency of calculating the static deflection based on the substructure analysis while the computational accuracy could be guaranteed. To our knowledge, it is the first time to reveal the surface form errors caused by the bottom edge of the cutter (BEC) in end milling of flexible thin-plate parts. Due to the coupling between the ACDs and the deformations, a method of iterative adjustment of ACD is conducted to modify the programmed ACDs for compensating the wall thickness errors.

The remainder of this paper is organized as follows. In Section 2, the static deformation of the thin-plate part is calculated through a novel FE model. The prediction of the wall thickness errors is introduced in Section 3. The compensation of the wall thickness errors is presented in Section 4, followed by experimental verification in Section 5. Finally, conclusions are drawn in Section 6.