CNC laser cutting machine is a machine tool that uses laser as a cutting tool to process workpieces. The main hardware includes machine bed, crossbeam, worktable, laser, cutting head, stabilizer, chiller, electrical control cabinet, gas source (oxygen, nitrogen, air), etc.

The system includes electrical system, mechanical system, air path system, optical system, hydraulic system, lubrication system, cooling system, etc.

In this article, finite element static and modal analysis were conducted on the important component of CNC laser cutting machine – the Y-axis beam. Three-dimensional finite element method was used to analyze the deformation of Y-axis beam under various typical working conditions, extract the deformation law, establish a three-dimensional model based on SolidWorks software, and conduct finite element analysis of the beam using the Simulation module.

Based on this, modal analysis was carried out on the Y-axis beam to solve the natural frequencies of the first five orders and the corresponding vibration modes, to verify the feasibility of the design structure, and to provide a theoretical basis for the size structure and optimization design of mechanical equipment.

CNC laser cutting machine is an ideal equipment for sheet metal processing, widely used in industries such as switch cabinets, computers, textile machinery, instruments and meters, automobiles, elevators, and grain machinery, both domestically and internationally.

Laser belongs to non-die processing, with strong processing flexibility, which can shorten the development cycle of new products in the sheet metal industry, improve product accuracy and interchangeability, and is particularly suitable for multi-variety small-batch processing.

The deformation and vibration of the Y-axis beam in actual work will directly affect the processing accuracy of the laser cutting head.

In order to ensure the practicality and processing accuracy of the equipment, the actual structure is discretized into element grids using the finite element method. Each element has a simple shape and is connected through nodes. The unknown quantity on each element is the displacement of the node. The stiffness matrix of each individual element is combined to form the overall stiffness matrix of the entire model. The stress of each element is calculated by the change of displacement on the node.

## Working principle and beam structure of CNC laser cutting machine

The laser cutting industry has gone through more than 60 years of development since its inception in 1960. It has undergone several major changes from YAG (crystal laser) to CO2 (carbon dioxide laser), and now to fiber laser.

The working principle of a laser cutting machine is that the laser beam generated by the laser emits through the lens to focus on a tiny spot at the focal point. The spot heats up the material and the laser beam moves along the material to complete the cutting process.

CNC laser cutting machines use a gantry structure. The sliding saddle moves along the X-directional guide rail on the bed, while the crossbeam is equipped with a horizontal linear guide rail (Y-directional). The Z-axis component is connected to the Y-directional guide rail through a slider, and the laser cutting head is installed on the Z-axis slide plate. The bed is fixed on the foundation and can be seen as a rigid body.

Due to the large length-to-diameter ratio and flexibility of the Y-axis crossbeam, it is prone to deformation, and therefore becomes one of the core components affecting the accuracy of laser cutting machines.

The Y-axis structure is shown in Figure 1, where the crossbeam serves a supporting function, requiring the material to have good stiffness and toughness, as shown in Table 1.

Material type | Q235-A weldment |

Density | 7860kg/m^{3} |

Elastic modulus | 212GPa |

Poisson’s ratio | 0.288 |

## Establishing a finite element calculation model for the Y-axis crossbeam

Before analyzing the model, the Y-axis crossbeam is simplified based on the characteristics of the main structure and working load of the laser cutting machine. After simplification, a finite element analysis simplified solid model of the Y-axis crossbeam is established, as shown in Figure 2.

(1) The overall structure of the CNC laser cutting machine is symmetric, and the supporting forces are basically balanced. The Y-axis crossbeam is made of 2.5mm thick steel plate bent with a 20mm thick guide rail mounting plate, and is subjected to annealing and vibration aging treatment. The structure is relatively symmetrical in the Y/Z plane, and the external force is mainly in the Y/Z plane, and the deformation mainly occurs in the Y/Z plane.

(2) The dimensions of the chamfers and threaded holes relative to the Y-axis crossbeam are small and can be ignored. Components such as the cushion plate and connecting transition plate help increase the stiffness of the crossbeam. Ignoring them will not affect the actual requirements in engineering.

(3) When the cutting machine is in operation, the Y-axis crossbeam mainly bears the effects of concentrated force and inertia force.

The solid model is created using SolidWorks, and then simplified before importing into Simulation for meshing. Based on the complex nature of the actual structure, the mesh is adjusted manually after automatic meshing. Figure 3 shows the actual mesh structure after meshing, with a total of 35,388 elements and 55,241 nodes.

Example name | Application analysis |

Mesher used | standard grid |

Automatic transition | close |

Include mesh auto ring | close |

Jacobi point | four point |

Jacobi inspection of shell | open |

Cell size | 41.9985mm |

Tolerance | 2.09992mm |

Grid quality | high |

Total number of nodes | 55241 |

Total number of units | 35388 |

Time to complete the grid (hour: minute: second) | 00:00:41 |

The Y-axis crossbeam is fixed and connected to the transition plate using M10 bolts, which move together with the sliding saddle in the X-axis direction. According to the mechanical properties of the load and its distribution in the structure, the load can be divided into the following categories:

**(1) Concentrated load.** This load is caused by the weight of the Z-axis component on the crossbeam, and its point of application varies with the position of the Z-axis component on the crossbeam. Therefore, the weight of the Z-axis component can be treated as a concentrated load, and several cross-sectional positions can be analyzed. The concentrated load acting on the Y-axis crossbeam is F_concentrated = m_Zg = 80 × 10 = 800N.

**(2) Distributed load.** This load is mainly due to the weight of the Y-axis. The center of mass of the crossbeam is always at 0.5L, so the weight can be loaded as a distributed load. The distributed load acting on the Y-axis crossbeam is F_distributed = m_Yg = 181.91 × 10 = 1819.1N.

**(3) Inertia load.** The movements of the CNC laser cutting machine in the three directions are controlled by the motor. When the motor is started, the Y-axis crossbeam will produce X-axis acceleration, and the Z-axis component will produce inertia loads in the Y- and Z-axis directions. The formula for calculating inertia load is F_inertia = m(Y+Z)ax = (181.91+80) × 15 = 3928.65N.

Based on the above conditions, a mechanical model of the Y-axis crossbeam is established, as shown in Figure 4. The concentrated load is applied to the central position when loaded. The X-axis acceleration’s inertia force on the Y-axis is loaded as a surface load. According to the principle of force translation, the weight of the Z-axis component is simplified as a force and a moment acting on the center of the crossbeam.

## Strain analysis of the Y-axis crossbeam

Finite element analysis of the Y-axis crossbeam was performed using Simulation to obtain the strain distribution within the operating range of the laser cutting machine, which was used to verify the forming quality under the following two working conditions:

- Load distribution settings. Finite element analysis was performed at three positions within the full length L: 0.5L, 0.25L, and 0.125L.
- Acceleration impact analysis. The lateral deformation (in the Z direction) caused by the inertia force along the Y-axis during startup is negligible. The inertia force along the Z-axis has been treated as a concentrated load. Therefore, the main focus is on the effect of the inertia force caused by the startup acceleration along the X-axis on the deformation of the Y-axis crossbeam, to obtain the deformation of the Y-axis crossbeam under the worst working condition.

The calculation results are presented in both table and contour map formats, as shown in Table 2 and Figure 5.

Table 2: Maximum deformation values (mm) of the crossbeam with concentrated load at different positions.

Position | 0.125L | 0.25L | 0.5L |

Maximum deformation | 6.893e-002 | 7.097e-002 | 7.178e-002 |

## Finite element modal analysis of Y-Axis crossbeam

Modal analysis refers to the process of solving eigenvalues and eigenvectors, also known as mode extraction. The inherent frequency and vibration mode of the crossbeam were obtained by using simulation frequency analysis. The frequency number was set to 5, which represents the 5th order mode. The direct sparse solver (sparse matrix solver) was selected to accelerate the solving speed. The parameters of the first five modes are shown in Table 3. The crossbeam vibration mode deformation diagram for each mode with different frequencies is shown in Figure 6.

Table 3 Modal solution results

Modal order | 1 | 2 | 3 | 4 | 5 |

Natural frequency /Hz | 47.183 | 133.04 | 157.67 | 173.92 | 211.85 |

## Conclusion

The deformation of the Y-axis crossbeam is related to the position of the Z-axis components. The closer the Z-axis components are to the center of the crossbeam, the greater the deformation. The maximum deformation occurs at the center position and is less than 0.3mm, which meets the engineering requirements of controlling the deformation within 2mm.