Statics and Modal Analysis of Main Frame of Composite Board Detaching Sleeve Equipment

. A new type of special machine tool for stripper sleeve was developed according to the stripper sleeve process of composite board. In order to ensure the reliability of the mainframe structure and the performance of the linear guide mechanism, the static structural analysis and modal analysis of the mainframe are carried out. The results show that the maximum stress of the supporting beam under the main frame is about 48.18 MPa, the maximum strain is 0.00023, and the maximum stress of the four-legged column is about 5.35 MPa, which is full of strength and stiffness design requirements. The end-cutting mechanism is installed on the beam through the installation plate. The deformation of the beam has a great influence on the operation accuracy of the linear guide mechanism and the cutting accuracy of the end-cutting mechanism. The maximum displacement in the X and Y directions of the installation plate is 0.014 mm, 0.030 mm and 0.197 mm, respectively, which meets the normal use requirements and cutting accuracy requirements of the linear guide mechanism. The first six natural frequencies of the mainframe are 2.963 – 47.137 Hz. In order to make the mainframe have good dynamic characteristics, avoid resonance and meet the end-cutting requirements of the composite board, the motor speed should be controlled between 300 – 493 r / min.


Introduction
A kind of core board material is closely combined with the metal frame and two layers of steel sheet to form a metal composite board [1]. Before use, it is necessary to remove the outer steel sleeve composed of the steel sheet and the metal frame. The composite board stripper equipment is a new type of equipment to remove the outer steel sleeve of the metal composite board. The designed mainframe, as the support structure of the stripper equipment, has a large size, total length of 3.57 m, width of 2.5 m, and height of 2.4 m. It is mainly used to withstand the gravity load generated by the end-cutting mechanism, the reaction force generated by the leveling mechanism, and the influence of motor excitation. Under the influence of these complex loads, the mainframe will deform, resulting in changes in the cutting accuracy of the end-cutting mechanism and the motion accuracy of the linear guide mechanism, affecting the performance of the entire mechanical equipment. Therefore, the mainframe should not only have sufficient strength and stiffness, but also have good dynamic characteristics. Many domestic and foreign scholars have done a lot of research on the static and dynamic performance of mechanical structure. P. Thejasree [2] carried out the finite element analysis on the of crankshaft under alternating load, and studied the influence of crankshaft stress on the reliability and life of engine, which provided theoretical support for the lightweight design of crankshaft . Hou Yangguo [3] proposed a conforming band method based on spline FSM, which is suitable for the static analysis of thin-walled structures with transverse stiffeners. The finite element method was used to carry out the static analysis and buckling analysis of thin-walled structures with transverse stiffeners, and the accuracy of the composite band method was verified. Khondaker Sakil Ahmed [4] used the finite element analysis method to study and analyze the strength, stiffness and fatigue life of a drilling active lifting structure in practical application, and obtained the influence of environmental factors on its structural performance, which provided guidance for the design of offshore jack-up drilling platform in the future. Leonardo B. Saint Martin [5] used the operational modal analysis technology to extract the modal parameters of a rotating machinery structure. Compared with the experimental modal analysis technology, the accuracy of the operational modal analysis technology was verified, which provided a theoretical basis for the prediction and analysis of structural modal parameters by the operational modal analysis. Han Fei [6] proposed a modal analysis method of double-beam system based on dynamic stiffness, and used a method based on dynamic stiffness to study the influence of elastic support on the dynamic characteristics of mechanical system and the change law of dynamic stiffness in frequency domain, which can quickly obtain the information of frequency and modal shape of the system.
Most of the above studies used the finite element analysis method to carry out the finite element analysis of the mechanical structure, and explored whether the static and dynamic performance of the frame structure met the requirements, so as to verify the rationality of the structural design. However, the relevant standards of nonstandard machine tools were not studied. In this paper, the finite element analysis of the mainframe of the composite board stripper sleeve equipment is carried out to explore the strength and stiffness characteristics of the overall structure of the main frame under static load and whether the displacement of the guide slider mechanism caused by the deformation of the mainframe meets the relevant standards of the non-standard machine tool, and whether the deformation of the beam leads to the cutting accuracy of the equipment can meet the requirements. In addition to meeting the static strength requirements of the mainframe structure, the dynamic characteristics of the structure should be further studied to avoid the resonance of the mainframe by avoiding the natural frequency of the mainframe, which provides an important theoretical basis for the reliability of the overall structural performance of the stripper equipment.

Working Principle and Structure Design of Mainframe
During the working process, the composite board is sent to the workbench, the positioning mechanism makes the composite board move to the middle of the workbench, the leveling mechanism starts, and the bending composite board is flattened. The positioning mechanism and the leveling mechanism are installed on the lower support beam of the mainframe, and the end-cutting mechanism of the beams on both sides of the mainframe is installed to complete the cutting work at both ends of the composite board.
The mainframe of the composite board stripper equipment can effectively absorb the static load generated by the leveling device when it works, and also has good dynamic characteristics under the normal working state of the end-cutting mechanism. Therefore, it is determined that the mainframe of the composite stripper equipment is mainly composed of leg columns, lower beams, beams, lower support beams and upper bending beams. The endcutting mechanism is installed on the crossbeams on both sides of the mainframe through the linear guide and the mounting plate. The leveling mechanism is mainly composed of multiple cylinders and installed on the crossbeams under the mainframe to bear the reaction force generated in the flattening process of the composite plate. The mainframe structure design is shown in Fig. 1. Installation plate of end-cutting mechanism 5. Positioning mechanism 6. Levelling mechanism 7.
Composite board According to the actual size of the composite board stripper equipment, SolidWorks software was used to establish the overall three-dimensional model, and then the mainframe part was extracted. The chamfer, hole forming, thread hole and bolt structure included in the mainframe model were simplified, which was convenient for subsequent grid division and analysis and calculation. The simplified model is shown in Fig. 2. The mainframe material is Q235 and its material properties [7] are shown in Table 1.  The mainframe is a welded part. In order to reduce the error of calculation results, the welded joints of the mainframe structure should be connected by solder joints. The local amplification diagram of the solder joint connection is shown in Fig. 3. The contact surface type of the welded joint is set as friction contact, and the friction coefficient is 0.2. The mainframe is mainly divided by hexahedral mesh, and a small number of irregular or complex contact parts are segmented to divide tetrahedral mesh, which is conducive to reducing calculation time and improving calculation accuracy [8]. The mesh size of the finite element model of the mainframe is controlled to 40 mm. The total number of mesh divided is 85068, and the number of nodes is 27454. The meshing effect is shown in Fig. 4.  The bottom foot of one column of the mainframe is fixed on the ground, and the remaining three feet can produce translational displacement in the horizontal direction ; due to the large quality of the mainframe itself, the influence of its own gravity factor should be considered. End-cutting mechanisms with mass of about 704.3 kg were installed on both sides, and leveling and positioning devices with mass of about 26.9 kg, 14.7 kg, 21.6 kg, 21.6 kg, 21.6 kg, 14.7 kg and 21.6 kg were installed on the middle beam; the pressure is 0.7MPa and the cylinder diameter is 100mm. After calculation, the cylinder generates about 0.23 MPa reverse pressure on the lower support beam when it works. According to the above constraint and load distribution law, the corresponding boundary conditions are added to the mainframe, as shown in Fig. 5.

Analysis of Result
After the solution, the equivalent stress, strain and deformation distribution cloud diagrams of the overall structure of the mainframe are extracted, as shown in Fig.  6, Fig. 7 and Fig. 8.    [9], the strength and stiffness of the main frame are checked, which meet the design requirements. The specific results are shown in Table 2. The cutting mechanism is installed on the installation plate of the beams at both ends of the mainframe, and the installation schematic diagram is shown in Fig. 9. 1. End-cutting mechanism 2. beam 3. Installation plate When the mainframe is loaded, the deformation of the beams at both ends will lead to the displacement of the installation plate. Due to the linear guide mechanism is installed in the end-cutting mechanism, without considering the error between the linear guide and the end-cutting mechanism itself, the displacement of the installation plate directly affects the service life of the linear guide and the cutting accuracy of the whole equipment. The X and Y direction displacement cloud images of the installation plate are extracted as shown in Figures 10 and 11. The analysis shows that the displacement of the installation plate in the X direction is about 0.014 mm, and the displacement in the Y direction is about 0.030 mm. According to Modern Mechanical Design Manual [9], the displacement of the bottom surface of the linear guide can not exceed 0.15 mm, and the displacement of the side of the guide can not exceed 0.10 mm, which meets the motion requirements of the linear guide. At the same time, the installation plate displacement also affects the cutting accuracy of the equipment. According to the milling accuracy range of the milling machine, it is 0.54 mm, which meets the cutting accuracy requirements.

Modal Analysis of Mainframe
Modal analysis is mainly used to study the dynamic characteristics of the structure. Modal is the inherent vibration characteristics of the mechanical structure, and each mode has a specific natural frequency and modal shape [10,11]. In order to avoid the resonance of the mainframe under the excitation of the motor and affect the reliability of the structure of the stripper equipment, it is necessary to carry out the modal analysis of the mainframe, study the dynamic characteristics of the mainframe, and understand the change law of the natural frequency and vibration mode of each order of the mainframe.
The excitation source of the mainframe is mainly generated by the motor of the end-cutting mechanism. When the motor works steadily, it can be regarded as the rotor moving in a uniform circular velocity. The relationship [12] between the generated excitation frequency ( ) f Hz and its own rotational speed ( / min) n r is : The speed range of the motor is 0 ~ 2000r / min, and the excitation frequency range is 0 ~ 33.3Hz calculated by (1) formula. According to Mechanical Vibration and Noise [13], the natural frequency of the mainframe has the following relationship with the excitation frequency : Formula :  frequency ratio ; n  the natural frequency of the frame ;  for excitation frequency.    is taken as the resonance interval [14]. In order to ensure that some natural frequencies and vibration modes are not omitted in the study of the mainframe mode, the extraction of the modal frequency interval of the mainframe should be appropriately broadened to 0 -50 Hz. The results of the first six modal natural frequencies and the corresponding modal characteristics are shown in Table 3. Outward deformation of two columns in front of mainframe It can be seen from Table 4 that the first six natural frequencies of the mainframe are in the range of 2.963 -47.137, which is the same as the range of external excitation frequency, indicating that the mainframe will resonate under the external excitation frequency, and the low-order frequency has a great influence on the dynamic performance of the mainframe structure. In order to avoid the resonance phenomenon of the main frame, the excitation frequency should be controlled to avoid the natural frequency of the main frame, and the speed of the motor should be controlled between 222 and 493 r / min to avoid the natural frequency of the main frame. According to the experimental test of the cutting process of the composite board, when the motor speed reaches 300 r / min, it can meet the cutting requirements of the composite board. In order to avoid the natural frequency of the mainframe structure, avoid the resonance phenomenon of the mainframe and meet the cutting quality of the composite board, the motor speed range should be selected between 300 and 493 r / min.

Conclusion
In this paper, the mechanical device of composite stripper sleeve is developed. The finite element method is used to analyze the structural performance of the mainframe. The mainframe meets the requirements of static structural design. In order to avoid the resonance of the mainframe, the motor speed range of the end-cutting mechanism is determined to be 300 ~ 493 r / min, which provides a theoretical basis for the reliability of the overall structural performance of the composite board stripper sleeve equipment. The specific conclusions are as follows : (1) Through the static analysis of the mainframe, it can be seen that there is stress concentration in the middle part of the lower support beam, the maximum stress value is about 48.18 MPa, the maximum deformation is about 0.43 mm, the maximum strain is about 0.00023, and the maximum stress on the four-legged column is about 5.35 MPa, which meets the strength and stiffness requirements of the mainframe. The maximum displacement of the mounting plate in X and Y directions is about 0.014 mm, and 0.030 mm, which meets the requirements of linear guide and equipment cutting accuracy.
(2) The excitation frequency range of the end-cutting mechanism installed on the mainframe is about 5 -33. 3 Hz. In order to study the dynamic performance of the mainframe structure, the modal analysis is carried out. The first six natural frequencies of the mainframe are extracted to be 2.963 -47.137 Hz. In order to avoid the natural frequency of the mainframe structure, prevent the over-resonance of the mainframe, and meet the cutting requirements of the composite board, the motor speed should be controlled between 300 -493 r / min.