Performance of Five-Axis Machine Tool and Intelligent Machining Process

In this study, the processing performance of a five-axis machine tool was analyzed to identify processing weaknesses as the basis for subsequent structural improvements. Data were then integrated through the Abductory Induction Mechanism (AIM) polynomial neural network to predict intelligent processing quality, and an in-depth investigation was conducted by importing processing parameters to predict the surface quality of the finished product. The finite element analysis method was used to analyze the static and dynamic characteristics of the whole machine and to test the structural modal frequency and vibration shape. For modal testing, the experiment used various equipment, including impact hammers, accelerometers, and signal extractors. Subsequent planning of modal frequency band processing experiments was conducted to verify the influence of natural frequencies on the processing level. Finally, according to the machine processing characteristics, a processing experiment was planned. The measurement record was used as the training data of the AIM polynomial neural network to establish the processing quality prediction model. After analysis and an actual machine test comparison, the three-axis static rigidity values of the machine were X: 1.63 Kg/μm, Y: 1.93 Kg/μm, and Z: 3.95 Kg/μm. The modal vibration shape maximum error of the machine was within 6.2%. The processing quality prediction model established by the AIM polynomial neural network could input processing parameters to achieve the surface roughness prediction value, and the actual relative error of the Ra value was within 0.1 μm. Based on the results of cutting experiments, the influence of the dynamic characteristics of the machine on the processing quality was obtained, especially in the modal vibration environment, which had an adverse effect on the surface roughness. Hence, the surface roughness of the workpiece processed by the machine could be predicted.

method using finite amplitude. The results showed that the size distribution of the critical depth of the cut is affected by the process damping, and the percentage increase in the cut depth is closely related to the tool direction and the frequency response function (FRF). Liu et al. [3] considered the effect of elastic interaction to analyze the influence of the anchor bolt pretightening sequence on the pre-tightening state. The results showed that the pre-tightening sequence from the middle to the side can ensure uniform deformation of the machine bed.
Muñoz-Escalona et al. [4] studied a geometric model for predicting the surface roughness of square inserts in face milling. The Taguchi method was used as an experimental design, and the surface roughness of the milled surface was measured using a non-contact profiler. Zhao et al. [5] proposed a surface-roughness prediction model and showed that the tool posture has a significant influence on the surface roughness, which means that the angle of the tool can be controlled to improve the surface roughness of the processing. Wang et al. [6] proposed a fiveaxis tooth surface milling surface roughness control method using feed rate optimization based on surface topography analysis. According to this model, the influence of tool runout and workpiece curvature on the surface profile was analyzed.
Wang et al. [7] proposed a model by which the predicted surface morphology was determined, and the factors affecting the development trend of roughness were analyzed.
Tomov et al. [8] suggested the relationship between the parameter prediction model and thesurface roughness formation process. Das et al. [9] explored artificial neural networks and predicted the cutting force and surface roughness generated during CNC milling. García-Plaza et al. [10] optimized surface roughness monitoring by focusing on vibration signal analysis.
Accordingly, the signal statistical measurements and frequency bands were correlated with surface roughness. Rasagopal et al. [11] studied the influence of processing parameters on the surface roughness and cutting force of mixed aluminum metal matrix composites. The results were optimized and analyzed using the Taguchi method. Mansour et al. [12] developed a mathematical model of surface roughness based on the cutting speed, feed rate, and cutting axial depth. Abouelatta [13] identified a correlation between surface roughness and cutting vibration during turning, and they derived a mathematical model of the predicted roughness parameters based on cutting parameters and machine tool vibration. Lin et al. [14] constructed a prediction model for surface roughness and cutting force. Once the machining parameters are given, the surface roughness and cutting force can be predicted through the network.
Ostasevicius et al. [15] proposed a method to improve the surface roughness. The method is based on the excitation of a specific higher vibration mode of the turning tool and it reduces the harmful vibration in the machine tool and workpiece system by increasing the energy dissipation inside the tool material. Sahin et al. [16] found that the feed rate is the main factor affecting the surface roughness, and good agreement between the predicted and experimental surface roughness was observed within a reasonable range. Öktem et al. [17] studied the best cutting conditions to achieve the smallest surface roughness in mold surface milling. Lalwani et al. [18] studied the influence of cutting parameters on the cutting force and surface roughness in finishing hard turning. PauloDavim et al. [19] established a surface roughness prediction model using neural networks using cutting conditions, such as cutting speed, feed rate, and cutting depth, as influencing factors. Their analysis showed that the cutting speed and feed rate have a significant effect on reducing the surface roughness, while the depth of cut has the smallest effect. Liu et al. [20] proposed a model that can provide valuable information about the effects of cutting parameters on surface roughness. Diniz et al. [21] studied the effect of changing the cutting speed, feed, and nose radius on the surface roughness of a workpiece with and without cutting fluid. Muthukrishnan et al. [22] used the input parameters of the cutting depth, cutting speed, and feed, and the output parameter was the surface finish of the machined part. The surface finish of machining can be predicted under cutting conditions within the operating range. Rawangwong et al. [23] used tungsten carbide tools for the face milling of semi-solid metal AA7075. They used Taguchi's experimental method to determine the three control factors-the cutting speed, feed rate, and depth of cut-to obtain more satisfactory surface roughness. Wang et al. [24] used an abductive network to construct a network model, and one output was surface roughness. Chen et al. [25] proposed an AIM polynomial network with the material properties provided as input to generate a model that predicts the tool geometry.
The machine tool industry is gradually advancing in terms of intelligent machine tool manufacturing. Accordingly, this study recorded the measurement results of the cutting experiment under different dynamic characteristics and parameters of the machine in the cases of the respective processing parameters, construction methods, and cutting materials. It employed a similar neural network construction to be effective. It is expected that the model for predicting the surface quality of the finished product can reduce processing costs and can thus be used as a basis for follow-up control experiments. When the processing parameters are imported, the surface roughness can be predicted using the network.

Materials and Methods
The experimental hardware equipment used in this research included a five-axis machine tool, LM load cell, German Mahr sensor probe, Millimar C1200 displacement display meter (LVDT), impact hammer (Kistler 9726A20000), accelerometer (Endevco Model 65-100), spectrum analyzer, SE-4000 non-contact surface roughness meter, and Olympus STM 6 highprecision tool microscope. The software included the finite element analysis software ANSYS Workbench, spectrum analysis software Novian, modal post-processing software MEscope, Static Stiffness acquisition and analysis software, and the AIM polynomial neural network. The experimental process is illustrated in Fig. 1.

Analysis and Test
When the machine is processing, the relative movement of the spindle end to the work platform will affect the surface quality and accuracy of the workpiece. Therefore, static rigidity simulation analysis was conducted for the spindle relative to the work platform. According to the analysis results, the X-axis relative displacement was 182.7 μm, and the static rigidity value was 1.64 (Kg/μm). The Y-axis relative displacement was 145.5 μm, and the static rigidity value  software, curve fitting is performed, and the sum of the imaginary part of the FRF is determined to calculate the frequency and damping value of each mode and to view the trend of each mode.
After comparing the finite element analysis (FEM) with the experimental mode (EMA), the maximum error ratio was 6.2%, the minimum error ratio was 2%, and the average error ratio was 4.7%. This finding verifies that the geometric model and the parameter settings, such as the material properties and boundary conditions, are aligned with the characteristics of the actual machine.

Cutting experiment
In the cutting experiment, we used ultra-fine tungsten steel and aluminum end mills; the cutting material was Al-6061, and the processing method was down-milling. The different axial and radial depths of the cut conditions were used to explore the surface roughness results.

Fig. 5 Cutting diagram and milling cutter specifications
Based on the modal analysis and experimental results, a cutting experiment was planned to assess the vibration shape trend of the entire machine, and the relative movement of the spindle end and the working platform was divided. First, the spindle speed was set to 4066 rpm (67.7 Hz) by down-milling. The main mode was the spindle vibration relative to the worktable.
The surface roughness obtained by processing was Ra 0.54 µm, as shown in Fig. 6(b). The rotation speed was 5226 rpm (87.1 Hz) using the down-milling method. The main mode was the spindle vibrating up and down relative to the worktable. The surface roughness obtained by machining was Ra 16.96 µm. The surface after cutting using the tool is shown in Fig. 6(b).

Number of blades 2
Helix angle (degrees)

Prediction model and cutting testing
A polynomial network was employed to construct the predictive model, decompose the complex system into relatively simple subsystems through polynomial function nodes, and then combine the subsystems into many different levels. The input data were subdivided simultaneously and transmitted to each functional node. The function node used a polynomial function to calculate a limited amount of input data and obtain an output as the input of the next layer. Thus, the training structure of the entire polynomial network was established in sequence.
Then, the optimal network construction, hierarchical features, and functional node were automatically generated according to the predicted square error rule.

Multi-function node type
The polynomial function reorganizes all polynomial node patterns as follows: where , , are the input values, 1 is the output value, and , and are the coefficients of the polynomial function node. Commonly used polynomial nodes are the normalizer, single node, double node, triple node, white node, and unitizer. The definitions are as follows: 1. Normalizer: Converts the original variable into a normalized input variable; the average is 0, the variance is 1, and its polynomial function is expressed as 1 = 0 + , where is the original input variable; 1 is the normalized output variable; and 0 and are the coefficients. 3. Double node: The two input variables, the output variable, and the input variable have a third-order polynomial relationship. The polynomial function is expressed as 1 = 0 + 1 1 + 2 2 + 3 1 2 + 4 2 2 + 5 1 2 + 6 1 3 + 7 2 3 , where 1 , 2 are input variables; 1 is the output variable, and 0 , 1 , 2 ,…. 7 are coefficients.

6.
Unitizer: Converts the output variable of the network into an actual output variable, and its polynomial function is expressed as 1 = 0 + 1 1 , where 1 is the input variable, 1 is the output variable, and 0 and 1 are coefficients.
The polynomial function node is used to construct the prediction model of the processing parameters and surface roughness Ra values. The polynomial network filters variables that have no contribution. The output of any node can be used as the input of the next layer and is combined with the original input for subsequent comparison. The network is synthesized layer by layer until the network mode converges and satisfies the prediction square error (PSE) rule.
Before constructing a polynomial network, it is necessary to import training data, learn the synthesis algorithm through the polynomial network, and determine the best network structure according to the minimum prediction square error method. PSE is a heuristic measurement of the expected square error of a network of independent data. PSE is defined as The fitting square error (FSE) occurs when constructing a network model with the training data. FSE can be expressed as where n is the number of training data, ̅ is the expected value of the training combination, and is the predicted value obtained from the network, Addionally, KP is the complexity penalty, and the KP value can be obtained from equation (8): where K is the number of coefficients in the network, N is the number of training data, and 2 is the number of error variances between the prediction model and the actual model from the training database of the synthetic network. The complexity penalty factor (CPM) is an adjustable parameter that is used when synthesizing a polynomial network model. When N increases or 2 decreases, a polynomial network is used to construct the training data, which has higher credibility, and the network structure becomes more complex.
In equation (10), the matching accuracy increases as the PSE decreases. Under normal circumstances, the more complex the network model, the smaller the FSE value, and the higher the matching accuracy. In other words, the more complex the network is, the greater is the KP value. Therefore, PSE produces a trade-off between network model complexity and accuracy.
In the network synthesis and calculation, the best network refers to the network with the smallest PSE value. Moreover, the CPM can be used to adjust the balance between the model complexity and accuracy. When the CPM value in the PSE increases, a more complex network is avoided. Conversely, when the CPM value decreases, a more complex network is adopted.

Fig. 8 Convergent prediction square error
In this study, the processing parameters of the UX300 machine were experimentally planned. The tool and cutting material were initially fixed, and then the processing parameters were used as the software input variables. The input data were as follows: rpm was the spindle speed, F was the feed rate, ap was the axial direction, and ae was the radial depth of cut. The measurement result of the SE-4000 non-contact surface roughness measuring instrument was set as the output data, which were the surface roughness Ra value of the workpiece. The input and output factors were placed into the polynomial network model for modeling. The reliability of the model was verified by predicting the parameters that had not been tested through the AIM polynomial network model. The results were then compared with those of the machine processing. The AIM software parameters were adjusted to a suitable fit and could then be converted into program codes and added to the machine controller.

Prediction model and verification
By importing into the AIM polynomial network model the machining parameter data that have not yet undergone cutting experiments, the predicted surface roughness Ra value can be obtained, and the actual machining and predicted results can be compared. The surface roughness error range is approximately within the Ra value of 0.1 µm. The experimental findings show that the parameter processing results are within the predictable range, that is, this polynomial network model has a certain degree of reference value, and the quality of the processed surface can be predicted from the polynomial model.

Conclusion
The starting point of this study was machine model analysis. A virtual machine model of the five-axis machine tool UX300 was constructed using ANSYS for static rigidity and dynamic analysis. The boundary conditions and material properties were improved by comparing the actual machine characteristics to simulate the real scenario. Static rigidity and modal experiments were performed to prove this finding of improvement. The static rigidity values of the two-axis of the five-axis machine tool spindle against the bed were X: 1.63 Kg/µm and Y: 1.93 Kg/µm; the maximum modal error ratio was 6.2%, the minimum error ratio was 2%, the average error ratio was 4.7%.
After studying and understanding the dynamic characteristics of the machine in depth, we planned the modal frequency band processing parameters and conducted modal cutting experiments to prove that the machine processing frequency had a substantial impact on the

Conflicts of Interest:
The authors declare no conflict of interest.