Research and development of multi-axis CNC abrasive belt-grinding machine postprocessor

Multi-axis CNC abrasive belt-grinding machine is an essential piece of equipment for processing the turbofan engine fan blades. The quality of blades determines whether engine performance can be further improved. As one of the important means to ensure blade quality, the measurement of the blade is still in the stage of manually hand-held measurement, and it is urgent to introduce digital and intelligent means to improve this situation. In order to make the overall process of blade grinding and measurement digital and intelligent and make the CNC belt-grinding machine integrated into the intelligent manufacturing system, its core is to upgrade the grinding machine by installing intelligent devices for the grinding machine. The primary premise of the upgrade is to reconstruct the post-processing system of the machine tool. Therefore, this article established a multi-axis CNC abrasive belt-grinding machine’s precise geometry assembly model, developed the post-process module based on the machine kinematic chain, established and validated a virtual grinding machine virtual simulation environment, and completed the experimental verification with a specific type of wide string hollow fan blade. The experimental results show the correctness and effectiveness of the post-processing module and the virtual simulation environment. The work of this paper provides an essential platform for the subsequent upgrade of the grinder and the installation of an in-machine measurement system.


Introduction
The traditional machining methods of fan blades and large complex surfaces cannot guarantee accuracy and efficiency. The blades need to be manually polished after being roughly ground by milling machines [1,2]. The introduction of NC abrasive belt grinding can be an excellent solution to the disadvantages of the above situation because the abrasive belt grinding can grind the removal allowance and polish the profile. The NC belt-grinding machine produced by combining belt grinding with numerical control has the flexibility of belt grinding and the adaptability of CNC machine tools. Grinding with it will significantly improve the efficiency and surface quality of the complex surface machining [3,4]. In recent years, with the in-depth research on material removal allowance and grinding mechanism of belt grinding, belt grinding has become an important processing method for material removal manufacturing [5,6].
In blade mass production, grinding efficiency becomes particularly important. One of the best solutions is upgrading off-machine detection to on-machine measurement [7]. In this way, the blade only needs one clamping during the process of "detection-grind-detection-regrinding," which can significantly improve the machining efficiency and quality of the blade. The existing belt-grinding equipment has realized multi-axis CNC high-precision grinding. However, there are few CNC belt-grinding machines equipped with an in-machine measuring module, so it is necessary to install an on-machine measuring module on the existing grinding machine for upgrading. The primary premise of machine tool upgrading and transformation is to reconstruct its postprocessing system. Only after obtaining the open-source postprocessor can it provide an essential platform for the subsequent installation of an on-machine measurement system. In order to integrate the CNC belt-grinding machine into an intelligent manufacturing system, it is inevitable to establish the corresponding virtual simulation environment.
Converting tool position files into numerical control programs is usually called post-processing, and such transformation is necessary because the machine tool cannot recognize the tool position files. Tool contact coordinate and tool axis vector are the main parts of the tool position file, so the essence of post-processing is to convert the former into the motion of the machine tool's straight axis and rotation axis [8]. Regarding the kinematics solution of five-axis machine tools, Qiu [9] proposed forward and inverse solution formulas for double-swing head machine tools and a general solution for miscutting caused by singular problems regarding the kinematics solution of five-axis machine tools. My A et al. [10] established a new mathematical model which can obtain four important characteristics of machine tool kinematics and use them as quantitative parameters to analyze and compare the kinematic performance of five-axis machine tools. He et al. [11] proposed a general method for solving the kinematics of machine tools of arbitrary structure. Zuo et al. [12] proposed a post-processing algorithm for five-axis positioning milling based on analyzing the structural characteristics of a five-axis milling machine. So and Jung [13] proposed a general method to derive the direct kinematics equation by considering the orthogonal joint of a five-axis machine and deduced a practical algorithm for the inverse kinematics equation of a five-axis machine. Boz and Lazoglu [14] introduced a processor for a table tilt five-axis machine tool-based on generalized kinematics and variable feed rate. They proposed a method to eliminate motion singularity through spherical interpolation and NC data correction. Tutunea Fatan and Feng's study [15] focused on a general unified model for all five-axis machine tools with two rotating axes. They deduced the general coordinate transformation matrix of five-axis machine tools. Zhang [16] established a kinematic model of a double-tilted fiveaxis machine tool-based on uniform coordinate transformation and kinematic chain relationship and developed a post-processing processor. For others, SøRby [17] proposed an algorithm to calculate the inverse kinematics of a nearly singular five-axis machine for path errors during five-axis milling. Sun et al. [18] established the kinematic model of the machine tool and developed the post-processing module of a new 3-coordinate linkage 5-axis machine tool by using inverse kinematics. Yang et al. [19] proposed a generalized kinematic model that allowed the automatic configuration of all five-axis machine tools using screw theory. Zhou et al. [20] developed a postprocessor with optimized tool radius compensation for general machine tool configuration based on the generalized kinematic model.
With the updating of machine tools and new functions, there have been postprocessors for more moving axes. For six-axis belt-grinding machine tools, Cui et al. [21] propose a post-processing optimization algorithm for six-axis CNC polishing machining, which solves the fluctuation problem during six-axis CNC machining. Wang et al. [22] proposed a kinematic analysis and optimization method for generating NC codes of grinding blades. Tang et al. [23] establish the motion coordinate system of a multi-axis turning and milling CNC machine tool, derive the calculation formula for the turning angle of the machine tool and the coordinate transformation formula based on the motion chain analysis and coordinate transformation, and develop a special postprocessing software for CNC machine tools using JAVA language. Yuen and Altintas [24] proposed a new NC code generation algorithm based on kinematics analysis of nineaxis micro-machine tools.
In terms of NC simulation, VERICUT, developed by CGTECH in the USA, is a software specially oriented to numerical control machining simulation. It has the function of analyzing simulation results and can be nested with other mainstream CAD/CAM software. VERICUT is a mature numerical control simulation software with many applications [25]. Some very mature CAD/CAM software abroad, such as Cimatron, MasterCAM, Pro/E, UG, etc., can also achieve the simulation processing function. The research on numerical control simulation technology in China is a little later than in developed countries and regions abroad. The Nanjing University of Aeronautics and Astronautics also developed superman 2000CAD/CAM, which can realize the dynamic simulation of turning and milling [26]. Harbin Institute of Technology developed an NCMPS simulator, which can realize a 3D simulation of NC machining [27]. The SurfMill9.5 software developed by Beijing Fine Sculptural Group in 2021 integrates DT programming technology. By mapping actual production materials, process parameters and other information in the software, the virtual manufacturing platform, which is highly consistent with actual production, ensures that all production personnel can obtain accurate and consistent processing information in time. Based on this platform, this study will carry out a five-axis process analysis and optimization to eliminate the risk of five-axis processing in the software end, and facilitate safe and smooth five-axis processing.
This article aims to upgrade an existing CNC abrasive belt-grinding machine to provide open-source post-processing. Section 2 establishes the NC abrasive belt-grinding machine geometry assembly model, and Sect. 3 carries out the kinematics analysis of the machine tool. Section 4 verifies the effectiveness of the postprocessor by flat and hollow blade grinding and simulation experiment. At last, this paper ends with some conclusions.
2 Modeling and assembly of multi-axis CNC belt-grinding machine Figure 1 shows the MTS1600-500 CNC belt-grinding machine. It has the characteristics of high precision, high speed, and high rigidity. It can realize copying grinding, constant pressure grinding, and NC grinding and can meet the finishing and polishing of the appearance of a widestring hollow blade. Moreover, the blade shape precision is high, which ensures the blade's natural frequency and aerodynamic performance. However, the CNC belt-grinding machine does not configure the in-machine measurement device. The grinding process of the whole process still needs several clamping so that the grinding accuracy and efficiency cannot be further improved.

Structural analysis of CNC belt-grinding machines
Installing the machine measuring device on the highperformance CNC machine tool is an effective way to improve the machine tool processing efficiency and the qualified rate of finished products without spending vast sums of money at the same time. As the basis for installing the measuring device on the machine, it is necessary to establish the grinder's accurate geometric assembly model first. In this paper, combining real machine analysis and drawing analysis are used to analyze the structure of machine tools before modeling. The multi-axis CNC abrasive belt-grinding machine has a complex structure, many parts, and a large appearance. However, its core motion framework comprises several components or modules with different functions. By analyzing the structure of the multi-axis CNC belt grinder and excluding the parts that do not affect the virtual simulation, such as internal appliances, operation panel, and hydraulic system, as shown in Fig. 2, the CNC belt grinder can be divided into seven basic modules: machine tool base, X-axis, Y-axis, Z-axis, B-axis, C-axis, and tool components. The machine tool base includes the machine tool base body, longitudinal feed shaft, and transverse feed shaft; X-axis includes X-axis mobile components, worktable, and pneumatic tailstock; C-axis includes C-axis rotation components, sand-belt drive axle box, and box shell; the tool assembly includes tool shaft and the belt pulley; the Y-axis, Z-axis, and B-axis are all independent components.

Obtaining assembly dimensions of grinding machine key shafts
The dimensions of the above components are obtained through the attached drawings and actual measurements of the machine tool, and the geometric model of the machine tool is established based on the data. It is also necessary to obtain the assembly dimensions between the key axes of the machine tool to complete the assembly of each component. The process of obtaining this data is as follows.
According to the structural analysis of the machine tool, the X-axis moving part installs on the longitudinal feed shaft of the machine tool base, and the A-axis moving part is installed on the X-axis table flange. The X-axis movement path is consistent with the direction of the extension line of the rotation center of the A-axis, which determines the X direction of the machine tool coordinate system. The origin of the processing coordinate system locates at the center of the right end face of the fixture. When the fixture fastens to the workbench, the center of the right end face of the fixture coincides with the center of the left end face of the workbench flange. As shown in Fig. 3, the center of the left end face of the flange is O WT . Then at X = 0, that is, when the X-axis returns to zero; the origin of the machine tool coordinate system locates at the center of the left end face of the table flange in space. Table 1 shows the travel of each CNC abrasive belt grinder axis. It can be seen from the table that the Y-axis can return to zero, so move the Y-axis of the machine to Y = 0, then move the X-axis to the maximum stroke, and finally move the Z-axis to the minimum stroke. Under the current position, mark the position that is 126.   Figure 4 shows the specific location of the positioning hole center on the left end face of the tool holder.
Among them, the assembly between axis-B, axis-C, and the tool holder belt pulley directly affects the correctness of machine tool modeling. Exploring the relevant information of the machine tool to obtain a partly post-process program file, as shown in Fig. 5. On the plane perpendicular to the B-axis's rotational axis, there is a point with a horizontal distance of 42.672 mm and a vertical distance of  270.649 mm from the rotational axis of the B-axis. On the plane perpendicular to the C-axis of rotation, the horizontal distance between the same point and the C-axis of rotation is 43.054 mm, and the vertical distance is 78.051 mm. It is determined that this point is the reference point in the machine tool O S specified in the previous section. The document and the machine coordinate system position determination use the machine reference point as the key position point. Determining the machine tool reference point is necessary for establishing an accurate geometric assembly model for this multi-axis CNC belt grinder. Based on the above data, the positions of the B-axis coordinate system {B}, machine reference The position relationship between the coordinate system {B} and {S} is the key dimensional data for subsequent assembly. And the distance between B-axis and C-axis is 382mm , which shows that axes B and C do not intersect in space.
Let the machine reference point O S (as well as the positioning hole center on the left end face of the tool holder) be the assembly origin, and use the assembly dimensions of the key axes above for assembly. Figure 7 shows the geometric model of the CNC belt grinder that has been assembled.

Definition of the coordinate system
For post-processing derivation of the multi-axis CNC belt grinder, it is essential to establish the coordinate system of  each motion axis and the motion relationship between each axis first. In order to assist in deriving the motion relationships, the next step needs to establish a reference coordinate system {MF} (machine-based coordinate system), as shown in Fig. 8a. {MF} is a fixed spatial coordinate system, as shown in Fig. 8b. Within the coordinate system {MF}, let ⃗ i MF define the direction along with the X-axis guide of the machine tool, positive to the right. Let ⃗ j MF define the direction along with the Y-axis guide of the CNC grinding machine, positive away from the X-axis guide. Let � ⃗ k MF define the direction along with the Z-axis of the CNC grinding machine, positive upward, and the coordinate origin is the intersection of the A-axis and the B-axis common vertical line of the CNC grinding machine on the A-axis. The coordinate system {WT} is the table coordinate  Fig. 8b, and the origin of this coordinate system locates at the intersection of the left end face of the flange and its rotation center (A-axis).

Definition of the initial position of the machine motion axis
After defining the position of the reference coordinate system {MF}, it is also necessary to define the initial position of the multi-axis CNC belt grinder in this coordinate system (the position where the motion of the CNC grinder is zero). First, define the initial position of each rotary axis, as shown in Fig. 8b above, with the initial position of the A-axis set to be parallel to the flange notch plane p and plane ⃗ i MF − ⃗ j MF . The initial position of the B-axis is set to have the C-axis parallel to � ⃗ k MF ; the initial position of the C-axis is to have the central axis of the grinding wheel � ⃗ n T parallel to ⃗ i MF . Figure 9a shows the initial position of the linear axis of the multi-axis CNC belt grinder, and the initial position of the X-axis is defined as O MF , coinciding with O WT . As shown in Fig. 9c, the initial position of the Y-axis is defined as the

Machine table group kinematic chain
The derivation starts with the machine table group (workpiece motion chain). As shown in Fig. 10 below, the motion first moves X from the X-axis coordinate system along the ⃗ i-direction of {MF} and then passes to the A-axis coordinate system. That is, the X-axis coordinate system moves X distance relative to the {MF} coordinate system. From the schematic diagram of the motion transfer between the X coordinate system and the {MF} coordinate system, the transformation matrix MF T X expressed in the machine base coordinate system {MF} (reference coordinate system) for the points in the X coordinate system can be obtained.
As shown in Fig. 11, the A-axis coordinate system rotates by an angle A around the ⃗ i-direction of the X-axis coordinate system to transfer the motion to the workpiece. That is, the {WT} coordinate system rotates by an angle A for the X-axis coordinate system.
From the schematic diagram of motion transfer between the {WT} coordinate system and the X coordinate system, the transformation matrix X T WT expressed in the X coordinate system for the points in the table coordinate system {WT} is obtained as: The kinematic chain of the multi-axis CNC belt grinder table group can be obtained by combining the motion transfer of the X coordinate system with the {MF} coordinate system and the {WT} coordinate system, as shown in Fig. 12.

MF-Y-Z kinematic chain
The kinematic chain of the machine tool group is analyzed, and the motion is transferred from the {MF} coordinate system to the Y-axis coordinate system and then to the Z-axis coordinate system. Since both Y-axis and Z-axis are linear axes, the kinematic relationship is relatively simple. As shown in 10 Schematic diagram of motion transfer between X coordinate system and {MF} coordinate system Fig. 13, the motion is first moved Y by the Y-axis coordinate system along the ⃗ j-direction of {MF} and then passed to the Z-axis coordinate system. That is, the Y-axis coordinate system moves Y distance relative to the {MF} coordinate system, and the Z-axis coordinate system moves Z distance relative to the Y coordinate system. The transformation matrix MF T Y expresses the points of the {Y} coordinate system in the machine base coordinate system {MF} (reference coordinate system) obtained from the motion transfer of the {MF} coordinate system and the Y coordinate system as: The transformation matrix Y T Z expresses the points of the {Y} coordinate system in the {Z} coordinate system obtained from the motion transfer of the Y coordinate system and the Z coordinate system.
The multi-axis CNC belt grinder MF-Y-Z kinematic chain can be obtained from the {MF} coordinate system and the Y and Z coordinate system motion transfer, as shown in Fig. 14. Fig. 15, the B-axis of the abrasive belt grinder is mounted on the Z-axis. The B-axis is the axis of rotation. The B-axis coordinate system will make a rotational motion relative to the Z-axis coordinate system. The B-axis coordinate system rotates by an angle B in the ⃗ j-direction around the Z-axis coordinate system.

MF-Y-Z-B-C kinematic chain As shown in
The transformation matrix Z T B expresses the points of the {B} coordinate system in the {Z} coordinate system obtained from the motion transfer of the Z coordinate system and the B coordinate system. The previous structural analysis of the machine determines that the B-axis and C-axis of this multi-axis CNC belt grinder do not intersect in space, as shown in Fig. 16, and the common vertical distance between the two axes is d BC,i . Therefore, there is first a translation matrix T between the B-axis coordinate system and the C-axis coordinate system.
Furthermore, axis C is a rotary axis mounted on the B axis, which can make the rotary motion, as shown in Fig. 17.
Then, the transformation matrix B T C expresses the points of the {C} coordinate system in the {B} coordinate system obtained from the motion transfer of the{B} coordinate system and the {C} coordinate system: Figure 18 shows a multi-axis CNC belt grinder MF-Y-Z-B-C kinematic chain obtained.

MF-Y-Z-B-C-S-T kinematic chain
The above analysis derives the coordinate transformation matrix from the MF coordinate system to the C-axis coordinate system. 13 Schematic diagram of motion transfer between {MF} coordinate system and Y and Z coordinate system     According to the analysis of the machine structure and Fig. 18, let the center of the positioning hole on the left end face of the tool holder be the origin of the coordinate system {S}, and the center of the lower contact surface of the abrasive belt wheel be the origin of the coordinate system {T}. Figure 19 shows the established relationship between the position of the coordinate system The transformation matrix S T T of the points in the tool coordinate system {T} expressed in the {S} coordinate system can be obtained from the above figure. (3.8) A multi-axis CNC belt-grinding machine MF-Y-Z-B-C-S-T kinematic chain can be obtained, as shown in Fig. 20.

The kinematic chain of the whole machine tool
The overall kinematic chain of the machine consists of the table group kinematic chain and the tool group kinematic chain. That is, {WT}-X-{MF}-Y-Z-B-C-S-T, and the overall kinematic chain of the multi-axis CNC belt grinder is obtained as shown in Fig. 21.

Deriving the coordinate transformation matrix
According to the analysis of the kinematic chain of the machine table group, the transformation matrix MF T WT of the points in the

Fig. 21 CNC belt-grinding machine kinematic chain
According to the analysis of the kinematic chain of the machine tool group, the transformation matrix MF T WT of the points in the tool coordinate system {T} expressed in the machine base coordinate system {MF} (reference coordinate system) can be obtained by combining Eqs. (3.3) to (3.9).
After sorting, we can obtain MF T T : where the values of p,m,n are: From Eqs. (3.10) and (3.12), the transformation matrix WT T T of the points in the tool coordinate system {T} expressed in the table coordinate system {WT} is obtained.
A coordinate system is determined by the position of the origin and the direction of the three axes. So, the first (3.12) column of the transformation matrix WT T T of the points in the tool coordinate system {T} expressed in the table coordinate system {WT} represents the X direction of the tool coordinate system {T} under the {WT} coordinate system, the second column represents the Y direction, the third column represents the Z direction, and the fourth column represents the position of the origin. Let the knife contact be P c = (p c,x ,p c,y ,p c,z ), the tool axis vector be P c = (p n,x ,p n,y ,p n,z ). The table coordinate system {WT} of this multi-axis CNC belt grinder coincides with the programmed coordinate system, and the origin of the tool coordinate system {T} is expressed under the programmed coordinate system as follows: The expression of the unit vector in the Z direction in the tool coordinate system {T} under {WT} is the expression of the unit normal vector of the contact point on the surface in the coordinate system {WT}.

Determining the machine home position offset
In Sect. 2.3, it has been determined that when X = 0, the machine tool coordinate system origin is located in the center of the circle on the left end face of the table flange. When the machine tool moves to the X0Y0Z0A0B0C0 position, the machine tool is located in the center of the left end face of the flange point set as a reference point. This reference point is in practice for the center of the positioning hole on the left end face of the tool holder. The displacement (or rotation) of each machine tool axis under the machine tool coordinate system is zero. The initial position of the A-axis, B-axis, and C-axis is the same as in the machine tool-based coordinate system. The definition of the initial position of the linear axis of a multi-axis CNC belt-grinding machine differs from that under the machine base coordinate system. Figure 22a shows the current  Fig. 22d. When the machine tool axis moves to this position, the machine tool coordinate system origin is located at the center of the table flange left-end face circle in space. Figure 22 also shows why the X-axis, and Z-axis cannot return to zero because this position will produce serious interference. A comparison shows that the initial positions under the machine tool coordinate system {M} are offset from the initial positions under the reference coordinate system {MF} established in the derivation of the kinematic chain, as shown in Table 2.  As can be seen from Table 2, the reference coordinate system {MF} established by considering the kinematic chain derivation is offset from the machine tool coordinate system set up by the machine tool manufacturer, with where the subscripts with M are the values of the axes of motion in the machine's coordinate system.

sin B sin A cos B cos A cos
From the above equation, it follows that

Solving the coordinate transformation matrix
Substituting the bias-transformed machine coordinate values into the tool axis vector obtained from Eq. (3.15) gives: From the above equation, it follows that, and the following: In particular, Once the expression for the axis of rotation is obtained, this gives A post-processing algorithm for five-axis CNC belt grinders is obtained by solving the machine tool's coordinate transformation matrix. This algorithm converts the tool position file containing the tool axis vector p n , and the tool contact coordinates p c into NC code containing the motion of each axis. Based on this post-processing algorithm, five-axis post-processing can be implemented, providing an open post-processing platform for retrofitting on-machine measurement modules.

Multi-axis CNC belt-grinding machine post-processing simulation and experimental verification
The virtual simulation of the completed machine tool is used to simulate the machining of the CNC program obtained through the post-processor conversion, as shown in Fig. 23. This simulation environment verifies the correctness of the developed post-processor.
A typical sample part of this multi-axis CNC belt grinder is programmed with the process. The post-processor generates a tool position file and the CNC machining program. The verification of the post-processor is divided into three-axis machining verification and five-axis simultaneous machining verification. This study designs the flat parts as the three-axis machining verification object to match the existing tooling fixtures. For the five-axis simultaneous machining verification, this study uses the typical machining parts of this grinder-a certain type of wide chord hollow fan blade as the object.

Preparation of jigs and models for flat parts
The simulation is for better experimental verification. So, from the actual experiment perspective, the simulation designs the flat parts and builds its geometrical model based on the dimensions of the existing jigs and fixtures in the workshop. Figure 24 shows the existing tooling fixture for flat parts in the workshop. The key dimensions of its right side fixture are shown in Fig. 25, with fixture slot width W = 90 mm, slot depth D = 20 mm, and slot spacing H = 8 mm.
According to the dimensions of the fixture, to establish the size of 400 mm × 100 mm × 6 mm flat parts geometry model and in UG to complete the assembly, as shown in Fig. 26, the red arrow points to the top clamping and screw clamping. Create a blank model with dimensions of 400 mm × 100 mm × 7.5 mm and import the overall model into VERICUT.

Generation of grinding NC programs
In the UG machining module, plane milling is selected instead of grinding for the path planning of the grinding toolpath. As the width of the abrasive belt wheel is 25 mm, a flat-bottomed milling cutter with a diameter of 25 mm is   selected instead. The machining step is set to 10 mm. The cutting mode is selected as "reciprocating" according to the actual position of the grinding machine, and the part allowance is set to 0.5 mm. The tool center point is programmed to obtain the grinding toolpath, as shown in Fig. 27.
After confirming that the toolpath path for grinding flat parts is correct, the tool position file is output, and the NC program is generated from the tool position file by postprocessing using the post-processor developed in chapter 3, as shown in Fig. 28, and then the correctness of the program is verified by simulation and experimentation.

Reading the machining code to perform a grinding simulation
The design model of the flat part and the blank model are imported into VERICUT, and the converted NC program is read for virtual simulation machining; the simulation results are shown in Fig. 29. Figure 29a shows the completion of the virtual simulation environment for the flat part. Figure 29b shows the start of the virtual simulation for the flat part. In Fig. 29c, it can be seen that during the simulation process of the flat part, no interference or overcutting occurs between the grinding belt wheel and tool holder and the workpiece being machined. The grinding processing area is consistent with the setting, and the grinding toolpath trajectory is consistent with the setting; during the grinding simulation process, no problems such as machine overtravel, interference, and collision occur. In summary, the results of the virtual simulation show the correctness of the post-processor during the three-coordinate conversion and the correctness of the virtual simulation environment during the three-axis machining.

Experimental verification of flat pieces
The flat part is clamped onto the grinding machine, and the machining program is imported into the machine controller. As shown in Fig. 30, the preparation is complete, and the grinding process can begin. There was no interference with overcutting during the grinding process and no alarms on the travel of the motion axes. The machine completed the grinding process of the flat plate parts completely. During the grinding process, the flat plate made of Plexiglas was prone to bending due to its low rigidity. The grinding depth in the Z-direction could not be guaranteed. This error was due to the nature of the material and did not represent an error in the post-processor. The completed flat piece is shown in Fig. 31. The grinding process area is measured to be consistent with the set

Wide chord hollow fan blade CNC program simulation and experimental verification
Flat parts are machined in three axes, and the results of the flat part grinding simulation can partially verify the correctness of the derived post-processing and the virtual simulation environment built. In order to further validate the correctness of the post-processing and virtual simulation environment, this CNC belt-grinding machine will be used to validate the 5-axis machining of a wide chord hollow fan blade, a commonly machined part. The design model of a wide chord hollow fan blade was assembled with the blank model and its special fixture. A variable profile milling process was created in NX using the mill multi-axis type to program the blade back machining process. The grinding toolpath trajectory for the leaf back is shown in Fig. 32. After confirming and generating the tool position file, the post-processor generates the CNC machining program for the leaf back grinding.
Similar to the previous steps, this part of the work exports the completed fixture and blade design model and blank model in UG as stl format and selects the corresponding location in the component tree. Then, import the model into VERICUT and add the NC program obtained after the post-processor conversion to VERICUT to start the simulation. The virtual simulation of the grinding of a leaf back is shown in Fig. 33. During the simulation, there is no interference or overcutting between the grinding belt wheel and the machined workpiece, and the axes of motion do not exceed their travel. The results of the virtual simulation machining of the leaf backs are shown in Fig. 34, which shows that the CNC program can complete the grinding of the leaf backs correctly, proving the correctness of the developed post-processor and the virtual simulation environment of the machine tool.
To further verify the correctness of the post-processor, the wide chord hollow fan blade, a commonly machined part of this CNC belt grinder, will be used as an experimental verification object for 5-axis machining. The same machine and abrasives are used for the grinding of flat parts, namely, the MTS1600-500-6NC CNC belt grinder and 3 M™ Trizact™ 363FC abrasive belts in size 25 × 3500 (width (mm) × circumference (mm)) with a grit of A160.
In order to avoid damage to the machine or the blade due to unknown errors, this experimental verification will use a fan blade that was scrapped in the previous process to reduce the damage. The blade was scrapped due to a pitted dent in the upper left corner of the back of the blade caused by improper operation in the previous process, which had no effect on the overall strength of the blade during grinding and therefore had no impact on the experimental verification. The NC program is the post-processor-generated  machining program used in the simulation of the machining of the leaf back in chapter 4 above. The fan blade is clamped onto the grinding machine, and the corresponding machining program is imported into the machine controller. As shown in Fig. 35, the preparation is complete, and the grinding process can begin.   Figure 36 shows the overall appearance of the completed grinding of the fan blade backside, and Fig. 37 shows the partial details of the completed grinding of the fan blade backside. The experimental results show that the NC program generated by the post-processor can run correctly after being read by the machine tool, the grinding area is consistent with the setting, the machining path is consistent with the planning, and the obtained blade back grinding results are consistent with expectations. The results show that the postprocessor developed for this multi-axis CNC belt-grinding machine generates the CNC program accurately and without errors and demonstrates the grinding machine's correctness from geometric modeling to component assembly and then to the virtual simulation environment.

Conclusion
In order to improve the efficiency and accuracy of blade machining, this paper presents a method of deriving post-processing algorithms based on the structural analysis of the machine tool in the context of upgrading the MTS1600-500-6NC CNC belt-grinding machine, enabling the integration of the CNC belt-grinding machine into an intelligent manufacturing system.
On the basis of the geometrical assembly model of the CNC belt-grinding machine, the overall kinematic chain of the machine is constructed in order to derive the coordinate transformation matrix and to determine the machine's home position offset. A post-processing module based on the kinematic chain of the machine tool has been developed by deriving a coordinate transformation matrix, obtaining a post-processing algorithm for grinding machines, and constructing a post-processing coordinate transformation function. Finally, the correctness of the post-processor and machine geometry assembly model was verified by using a flat part and a certain type of wide chord hollow fan blade as the simulation object, the experimental verification was completed with this blade as the object, and the experimental results showed the correctness and effectiveness of the virtual simulation environment. The research results can also provide the basis for the subsequent upgrade of this grinding machine with an on-machine measurement system. Author contribution Hu Qiao and Ying Xiang proposed and developed the concepts related to the study. Hu Qiao contributed to the study of the post-processing algorithm for a multi-axis CNC belt grinder. Zhenxing Wei contributed to the modeling and assembly of a multi-axis CNC belt-grinding machine. Ruixiang Deng contributed to experimental verification and analysis. Tianhang Xu contributed to the analysis and manuscript preparation.

Funding
The research work of this paper is supported by Shaanxi Science and Technology Resources Open Sharing Platform (Project No.: 2021PT-006) and the common technology of "Intelligent manufacturing cell technology of engine hollow blades" (Project No.: 41423010701).

Declarations
Ethics approval The authors declare that this manuscript was not submitted to more than one journal for simultaneous consideration. Also, the submitted work is original and not has been published elsewhere in any form or language.
Consent to participate and publish The authors declare that they participated in this paper willingly and the authors declare to consent to the publication of this paper.

Conflict of interest
The authors declare no competing interests.