Deflection Error Prediction and Minimization in 5-Axis Milling Operations of Thin-Walled Impeller Blades

: To enhance accuracy as well as efficiency in process of machining operations, the virtual machining systems are developed. Free from surfaces of sophisticated parts such as turbine blades, airfoils, impellers, and aircraft components are produced by using the 5-axis CNC machine tools which can be analyzed and developed by using virtual machining systems. The machining operations of thin walled structures such as impeller blades are with deflection errors due to cutting forces and cutting temperatures. The flexibility of thin walled impeller blades can cause machining defects such as overcut or undercut. So, the desired accuracy in the machined impeller blades can be achieved by decreasing the deflection error in the machining operations. To minimize the deflection of machined impeller blades, optimized machining parameters can be obtained. An application of virtual machining system in predicting and minimizing the deflection errors of 5-Axis CNC machining operations of impeller blades is presented in the study to increase accuracy and efficiency in process of part production. The finite element analysis is applied to obtain the deflection error in machined impeller blades. In order to minimize the deflection error of impeller blades in the machining operations, the optimization methodology based on the Genetic algorithm is applied. The impeller is machined by using the 5-axis CNC machine tool in order to validate the developed virtual machining system in the study. Then, the machined impeller is measured by using the CMM machines to obtain the deflection error. As a result, the deflection error of in machining operations of impeller by using 5-Axis CNC machine tools can be decreased in order to enhance accuracy and efficiency of part manufacturing.


Introduction
In order to increase accuracy in machining operations, virtual machining systems are recently applied to the process of part production using CNC machine tools. The systems can analyze the process of machining operations to be developed. To enhance efficiency in process of machining operations, applications of the virtual machining systems in optimizations of the machining process can be developed. Optimized parameters of machining operations can be obtained using optimization methodologies in order to decrease the deflection error in machining operations of thin walled components. So, developed methods of part production using machining operations can be presented using virtual machining systems in order to increase added values in produced parts.
The integral impeller and bladed disk are extensively used in different aircraft engines. The jet engine parts are produced with high level of accuracy and reliability regarding the safety concerns of aviation parts in order to present a good performances in working conditions. The application of the impeller in the HF-120 turbofan engine (GE-Honda) is shown in the figure 1 [1].
The sophisticated parts with free form surfaces such as impeller blades are machined by using the -axis CNC machine tools. The machining operations using the 5-axis CNC machine tools are always with complexities and challenges which are studied in many research works. In machining operations of thin walled structures such as impeller blades, the deflection error is created due to the cutting forces and cutting temperature. The flexibility of thin walled impeller blades can cause machining defects such as overcut or undercut. So, the deflection error can create inaccuracy in machined parts which should be analyzed and decreased. The high accuracy requirement in machining operations of complex parts such as jet engine impeller blades is with complexities and challenges. As a result, the virtual machining system which can analyze and decrease the deflection error in machining operations of thin walled impellers can provide a key tool in terms of accuracy enhancement of machined impellers using 5-Axis CNC machine tools.

2-Review of research works in the deflection errors of thin walled machined parts
A framework for accuracy enhancement in milling operations of thin-walled narrow-vane turbine impeller of NiAlbased superalloy is presented by Zhao et al. [2] to increase accuracy and reliability of machined turbine impeller. In order to decrease the vibration and deformation in ball-end milling of thin-walled impeller blades, an optimization methodology for the cutting tool orientation is developed by Huang et al [3]. To increase accuracy in 5-axis machining operations of impeller blades, optimized strategy for finishing operations in the final step of the machining process is presented by Chaves-Jacob et al. [4]. The machining operations errors in 5-Axis adaptive flank milling of thin walled impeller blades is analyzed and decreased by Huang et al. [5] to develop the process of machining operations of flexible parts. To analyze an decrease the deflection error in milling thin-walled impeller blade, an advanced method to predict the deflection error is investigated by Liu et al. [6].
To reduce the deflection error in milling operation of flexible parts due to the cutting forces, the mathematical modelling of the thin-walled workpiece is investigated by Khandagale et al. [7]. An advanced method of deflection error prediction in peripheral milling of thin-walled workpieces is presented by Kang and Wang [8] in order to increase accuracy in machined parts. To decrease the deflection errors due to instability and deformation in the machined parts, the milling operations of light alloys with thin walled structures is studied by Del Sol et al. [9]. The effects of the cutting tool parameters such as tool helix angle to the accuracy and quality of machined parts is studied by Bolar and Joshi [10] in order to increase accuracy of machined parts by using the milling operations. Effects of machining parameters to the surface roughness and form errors in 4-axis milling of thin-walled free-form parts is studied by de Oliveira et al. [11]to reduce the deflection errors in the machined parts.
To simulate and analyze the cutting tool and workpiece deflection error in the machining operations of low rigidity thin walled parts, an advanced numerical modelling system is presented by Bolar and Joshi [12]. To compensate and decrease the deflection error in the flank milling operations of thin walled parts, an advanced cutting tool path optimization method is developed by Li and Zhu [13]. To increase surface quality and accuracy of machined impellers by using 5-Axis CNC machine tools, an advanced machining parameters optimization system is presented by Wang et al. [14]. An advanced machining parameter optimization system is investigated by Ratchev et al. [15] to enhance surface quality of machined thin walled parts by reducing the workpiece deflection errors. To compensate the strength loss due to the presence of the cut-out under bending operation, experimental investigation of buckling of wind turbine tower cylindrical shells with opening and stiffening is investigated by Dimopoulos and Gantes [16]. Structural efficiency of a wind turbine blade is studied by Buckney et al. [17] in order to improve designing process, minimizing weight and reducing the cost of wind energy.
To analyze and modify the machining operations in virtual environments, virtual machining systems and applications is presented by Soori et al. [18][19][20][21]. Virtual machining system and application is also presented by Altintas and Merdol [22] in order to obtain optimized condition of milling operations. In order to predict and minimize the deflection errors in five-axis milling operations of thin-walled parts such as impeller blades, an advanced methodology is proposed in the study. A virtual machining system is developed in the study to predict and minimize the deflection error of thin walled impeller blades by calculating the cutting forces as well as cutting temperatures at each position of cutting tool along machining paths. The Finite Element Analysis (FEM) is used to calculate the deflection error in the machined impeller. To minimize the deflection error, optimization technique based on the genetic algorithm is developed in order to obtain the optimized machining parameters. Experiment of machining operations of the impeller blade is carried out by using the 5-axis CNC machine tool in order to validate the effectiveness of the developed virtual machining system in the study. Then, to obtain the deflection error, the machined part is measured by using the CMM machines. As a result, accuracy as well as efficiency in process of impeller machining operations can be increased by applying the developed algorithm in the study. The method to calculate cutting forces in milling operations of thin walled parts and cutting temperatures are presented in the section 3 and 4 respectively. The deflection error of thin-wall workpiece in machining operations is analyzed in the section 5. The developed virtual machining system to predict and minimize the defection error is presented in the section 6. Finally, to validate the developed virtual machining system to minimize the deflection error of thin walled machined impeller blades, the section 7 is presented.

3-Cutting force model in milling operations of thin walled parts
To calculate the cutting forces in 5-axis machining operation of thin walled parts, the cutting force model developed by Li et al. [23] is implemented. The figure 2 [23] shows the basic structural movement of the end-mill operation which is described by two guiding curves during five-axis milling operations.
The two guided curves of ( ) and ( ) are defined in order to simulate the cutting tool paths in the machining operations. As a result, cutter location of the (CL) can be described by using a moving feed coordinate as: Where ( ) is the feed vector at the cutting tool tip which is due to the guiding curve ( ). Moreover, is described in the plane defined by the feed direction and axis vectors of cutting tool along machining paths and is normal to this obtained plane. Also, ( ) presents the unit vector along the cutting tool axis, The cutting tool in 5-Axis milling operations of thin walled parts is within cutting entry angle for ℎ cutting element of cutting tool as is shown in the figure 3 [23].  3. The entry angle for the ℎ cutting element of cutting tool during the five axis milling of thin walled workpiece [23].
The cutting entering angle can be presented as, Where , is the entry angle of the cutting tool along machining paths, , , are the deflection errors of the cutting tool and workpiece for the normal direction of the ℎ cutter element surface on the ℎ flute of the cutting tool, respectively. Moreover, is the rotation radius of the ℎ cutter element on the ℎ flute of the cutting tool. In five axis milling operations of the thin walled parts, the cutting tool orientation is changing continuously due to cutting tool paths on the free form surfaces and new angles and positions of flexible parts during machining operations. As a result, the cutter runout should be considered in terms of cutting forces calculation [23]. The figure  4 shows the instantaneous uncut chip thickness calculation by considering the cutter runout during the five axis milling operations of thin walled parts [23].  4. The instantaneous uncut chip thickness calculation by considering the cutter runout during the five axis milling operations of thin walled parts [23].
As a result, the uncut chip thickness for the ith cutter element of the jth flute by considering the kth previous flute at angular position and cutter location u can be obtained as, Where, Where is the rotation radius of the ℎ cutter element on the ℎ flute and is the feed per tooth along machining paths. As a result, the applied cutting forces in the radial, tangential and axial directions of the ith axial disk element of the jth flute can be calculated in the differential format as follows, Where the shear and edge force coefficients are presented as ( = , , ) and ( = , , ) respectively. The differential chip width and flute length of the ℎ cutter element is presented by and respectively. Also, in order to obtain the ℎ cutter element of the ℎ flute which is engaged in the cutting process, the ( ) window function is determinate as, As a result, the calculated cutting forces in the radial, tangential and axial directions for each cutting element can be transformed into the feed or workpiece coordinate system as,

Cutting temperature model
The process of chip formation in the machining operations generates heat in the cutting zone which increases the temperature of cutting tool and workpiece.
The equation of the cutting temperature regarding the cutting parameters is presented by Shaw [24] as, Where θ is temperature of cutting process (degree Celsius), is temperature coefficient obtained by material of workpiece, machine tool, and cutting tool geometry parameter. The b1, b2, b3, and b4 are exponents influencing the machining parameters V, , and , as cutting speed (m/minutes), feed rate (mm/z), radial feed and axial feed (mm) respectively.
Where θ is temperature (degree Celsius), is cutting speed (m/minutes), is feed rate (mm/z), and are radial feed and axial feed (mm) respectively.

4-Deflection error analysis of thin-wall workpiece in machining operations
The dimensional error of machined surfaces is the amount of deviation in actual machined surface from the nominal surface of workpiece CAD model. The machining operations of thin walled parts are with deflection error as a result of cutting forces as well as cutting temperature. The workpiece deflects to a new position due to cutting forces and cutting temperatures which creates dimensional error and inaccuracy in process of machining operations. The surface dimensional error due to the cutting forces and cutting temperature is shown in the figure 5 [26].

Fig. 5.
The surface dimensional error due to the cutting forces and cutting temperature [26].
The corresponding surface dimensional error can be presented as Eq. (14) [26], Where, , and , are the normal projections of the cutting force and cutting temperature induced deflection error for the Point P, respectively. Also, and are the nominal and specified radial depth of cut, respectively.

5-Virtual machining system to predict and minimize the deflection error
In order to develop applications of the virtual machining systems in the deflection error prediction and minimization of thin walled machined parts, the Visual Basic programming language is used in the study. Nominal machining path, the geometry and material properties of cutting tool as well as the CAD model of workpiece are input to the system. The developed virtual machining system can obtain the cutting forces regarding the cutting tool details and parameters of machining operations. So, cutting forces at each position of cutting tool along machining paths can be calculated. The cutting force calculator dialogue box is shown in figure 6. In order to obtain the deflection error in the machining operation, the cutting temperature at each position of cutting tool along machining paths is calculated by the developed software. Then, obtained data from the cutting forces as well as cutting temperature are transferred to the Abaqus R2016X FEM analysis software [27] to calculate the deformation error of machined part. The mesh is applied to the CAD model of thin walled impeller blades in order to calculate the temperature and cutting force-induced deflection error in milling operations. The predicted cutting forces and cutting temperature at the each position of cutting tool along machining paths are applied to each node of the meshed model of the workpiece in order to measure node displacement. As a result, the deflection error due to cutting forces and cutting temperatures at each position of cutting tool can be calculated and presented. Flowchart and strategy of the virtual machining system in cutting force calculation and deflection error prediction is shown in the figure 7. Fig. 7. Flowchart of the virtual machining system in calculation of cutting force, cutting temperature and deflection error prediction.
The appendix A is the developed algorithm of the virtual machining system in the study.
To obtain the optimized machining parameters in terms of deflection error minimizations, the genetic algorithm is applied. The natural process of evolution and set of chromosomes is introduced in terms of optimization process. The initial population for the optimization process is created using the binary encoding process. To provide evaluation criteria in the optimization process and rank the chromosomes in population, the fitness function is calculated as is presented in the Eq. (15) [28].
Where ( ) and ( ) are fitness function and objective function respectively. The reproduction, crossover and mutation are main operators of the algorithms. In order to create a faster convergence to the optimized parameters, The operators as reproduction, crossover and mutation are applied to the initial population of the optimization process. To simulate the surface roughness of machined parts by using the mathematical concepts, the Eq. (16) [29] is presented.

= (17)
Where is the distance of cutting tool to reach to the operational zone and is feed rate.
Also, cutting tool life should be maximized in the optimization process in order to decrease the cost of machining operation. The cutting tool life can be shown as the Eq. (18) [29].
Where is the contact proportion of cutting edge with workpiece per revolution, is 33.98 for the HSS tools and 100.05 for the carbide tools, = 0.14, is cutting speed (mm/minutes) , = 0.28, is 0.15 for HSS tools while it reaches a maximum of 0.30 for carbide tools, and are slenderness ratio and chip cross-section which can be shown as Eq. (19) and Eq. (20) respectively [29].
Where depth of cut and is feed rate in machining operations. According to the Eq. (12) and Eq. (13), the cutting temperature can be reduced by decreasing the feed rate and spindle speed. Also, according to the Eq. (16), the surface roughness can be decreased by reducing the feed rate. But, the machining time will be increased by reducing the feed rate according to the Eq. (17). Moreover, increasing the spindle speed can decrease the cutting forces according to the Eq. (8) and cutting tool life according to the Eq. (18). It is clear that the presented mathematical models of the cutting forces, cutting temperature, time of machining operations, surface roughness, feed rate and cutting tool life are related together which should be considered as an optimization problem. As a result, an optimization process of machining parameters as is shown in the figure 8 should be implemented to calculate the optimized feed rate and spindle speed in machining operations. In the appendix B, the optimization method algorithm is described. The Matlab programming language is used to obtain the optimized machining parameters in order to minimize the deflection error. As a result, optimized feed rate and spindle speed are obtained in order to minimize the deflection errors in milling operations of thin walled impellers.

Validation
The impeller is machined by using the A 5-axis CNC milling machine tool Kondia HM 1060 In order to validate the presented virtual machining system in the study. The impeller material is AL 7075. The dimensions of Al impeller in millimeter unit is shown in the Figures 9.  To simulate machining operations of impeller by using a 5-Axis CNC milling machine tool, the Masterccam software [30] is used. The cutting tool paths and machining strategies is shown in the figure 10.     The cutting force model of 5-axis CNC machine tools in machining operations of thin walled parts presented by Zhang et al. [32] is used in this study to calculate the cutting forces in virtual environments. The average of cutting forces for milling operations of thin walled blades by using 5-axis CNC milling machine tool Kondia HM 1060 are measured by Kistler dynamometer in order to calculate the coefficients of specific cutting force. The spindle rotating speed is 3000 rpm and the feed per tooth and feed rate are 0.5 mm 100 mm/min respectively. As result, the specific cutting force coefficients are obtained as Table 2. Table 2. The specific cutting force coefficients.
The Abaqus software [27] is used to measure the deflection errors of impeller blade due to the cutting forces and cutting temperature. So, the calculated deflection error of the machined thin-walled impeller by using the FEM method is shown in the figure 15.  A good compatibility is obtained in comparison of the results of the experimental test and predicted deflection error of the machined thin-walled impeller. Optimized machining parameters are calculated using the developed optimization techniques in the study based on the genetic algorithm. To measure the cutting forces in the machining operation, the Kistler dynamometer is used. Then, the measured cutting forces are applied in the optimization algorithm of the figure 8 and appendix B in order to provide input data for the optimization process. In the optimization process, the population size of 39 is selected with the iterated for 306 generations. Also, the probability of crossover of 0.68 and mutation of 0.001 are selected. As a result, the feed rate 170 mm/min and the spindle speed 260 m/min are obtained. Measured and predicted surfaces roughness of machined turbine blade by using optimized machining parameters is shown in the figure 17. Fig. 17. Measured and predicted deflection error of machined thin-walled impeller blade by using optimized machining parameters.

Conclusion
An application of virtual machining system is developed in the study in order to predict and minimize the deflection errors in 5-Axis milling operations of thin walled impellers. So, the cutting forces and cutting temperature at each position of cutting tool along machining paths is calculated by by considering the CAD model of workpiece, cutting conditions and cutting tool geometries. The Finite Element Method is used to obtain the deflection error in the thin wall workpiece. To validate the developed method in the study, a real impeller is machiied by using the 5-Axis CNC machine tool. To obatin the deflection error, the machind blade is measured by using the CMM machine. To calculate the compatibility rate in the developed system, the obtained results from the virtual machining system and experimental tests are compared. A 91.6% compatibility in comparison to the experimental and virtual machining system results is obtained. To minimize the residual stress in machining operation, optimized machining parameters using the Genetic algorithm is obtained. As a result, 24.4% reduction in defelction error of machined impeller blade is obtained using the optimized machining parameters. So, the developed method in the study can decrease the defelction error in the machining operations of the thin walled impeller baldes to increase accuracy and efficiency in part menaufacturing process. Furthermore, it is concluded that applications of the optimizations techniques in the virtual machining systems can increase accuracy and reliability of machined parts by using machining oerations. The method can be applied to the more soghistacted parts with free form surfaces such as turbine baldes in order to increase accuracy of machined thin walled surfaces due to deflection error redcution. To enhance the qulaity of machined parts, the deflection errors in the cutting tool and workpiece due to cutting forces can be predcited and compenstaed. Morover, the developed system in the study can be applied to the surfaces quality of macined parts in order to be improved. These are future reaserch works of the authours.

Availability of data and materials
All data and materilas of the research work were availabile for the authors.