The boom is the most important working part of a crane. The design of the boom directly affects the lifting performance of the crane. The quality of the jib structure generally accounts for 13% to 15% of the overall machine quality, and with the development of large-tonnage truck cranes, this proportion will be higher. How to reduce the boom quality and improve the performance of the whole crane without affecting the lifting performance is a key issue for designing the boom. At present, there are mainly two methods adopted in the industry: (1) the application of high-strength materials; (2) the improvement of the boom structure, the use of polygonal (or even large arc, elliptical) boom to replace the quadrilateral boom.
With the continuous development of large-tonnage crane products, high-strength steel plates have been used in a large number of applications, and the boom strength has also increased significantly. However, if all materials are used, the deformation of the boom structure will increase. As a result of the increased deformation, the bending moment caused by the axial force of the boom becomes an indispensable factor. Therefore, under the non-linear condition, it is necessary to apply a new algorithm and re-design the boom in consideration of the deformation of the boom.
Design of non-linear design of the jib 1. Geometry modeling In order to realize proceduralization and universalization of the jib, it is necessary to parameterize the geometry and physical state of the jib. This mainly includes the following three parts: (1) Geometry of the cross section of the jib, through Determine the dimensions such as angle and side length; (2) Determine the mass, length, and center of gravity of each arm; (3) Determine the performance parameters, including single rope lifting speed, lifting pulley group magnification, and so on.
2. The non-linear iterative calculation process is calculated using the Liugong QY70 crane crane arm as an example. The main lifting arm of the crane is composed of an arm and four telescopic arms. The telescopic mode is the sequential and synchronous telescopic mode.
The force of the boom is analyzed firstly for the cement production process drying equipment. In the luffing plane, the loads on the jib are: (1) the weight of the jib; (2) the weight of the jib; and (3) the lifting force of the lifting rope. When calculating the bending moment of each dangerous section on the jib, the product of the force in the axial direction and the product of the axial force arm should be added.
Force analysis in the plane of rotation. The loads on the jib are: (1) the yaw load of the hoist; (2) the wind load; (3) the weight of the jib; and (4) the hoisting mechanism. Similarly, when calculating the bending moment of each dangerous section of the jib, the bending moment due to the axial component of the above load must also be considered.
The iterative process assumes that the boom's elevation angle does not change, and feedback is provided by changes in arm deflection.
By assigning the initial value, the bending moment and lateral force at each dangerous section are first calculated, and then the deflection and rotation angle formulas of the material mechanics are used to obtain the deflection and rotation angle of each section of the arm. The total deflection of the boom can be obtained by accumulating. This deflection is compared with the initial deflection. If the set conditions are satisfied, the bending moment, lateral force, and axial force of each section are output. If not, the deflection is assigned to the previous deflection and the bending moment is recalculated. , lateral force, and find the new total deflection. In this cycle, until the deflection obtained from the two cycles before and after meets the conditions set by us, the boom is considered to have been balanced and the value obtained is the value after the boom has been deformed and balanced. The slewing plane calculation idea is the same as the amplitude change plane.
In the cyclic process, the change of the total deflection is used as the determination condition, and the total deflection is obtained by calculating the deflection and the rotation angle of each joint. The calculation formula of the deflection and the rotation angle is obtained by deriving the physical model from the material mechanics formula. .
3. Check the strength, local stability The nonlinear moments, lateral forces, and axial forces of each dangerous section are obtained by a nonlinear iterative method. From this, the stress values ​​at each point on the boom section can be calculated. In strict accordance with the relevant contents of the crane design specification GB/T3811, the local stability and strength of the jib were calculated and checked with the respective allowable stress.
Finite Element Analysis Calculation 1. The establishment of a finite element model for the establishment of a finite element model requires not only faithfully reflecting structural features but also minimizing the complexity of the model. Based on this principle, we simplified the boom. Because the boom is mainly subjected to bending, we modeled it with the beam element beam181. According to the actual arm length, overlap length, and slider position of each joint arm, then the previously established two-section section properties of each joint arm are assigned to each joint arm. Both the jib head and the pulleys are simplified. Defining unit types, material properties, etc., then meshing the model.
2. Load and add constraints are loaded into the boom according to the actual force of the load, including axial and lateral lifting forces, wire rope tension and gravity. The freedom of the x, y, and z directions is coupled between the arm and the arm, and the rear hinge point of the jib is constrained. In addition to the freedom in the y direction, the other five degrees of freedom are constrained. In addition, the lower hinges and wire ropes of the luffing cylinder are also constrained. After loading the constraint, solve it with the universal solver and get the result of the calculation.
3. Comparing the calculation results with the finite element calculation results Two conditions are selected for comparison. One is the full extension, that is, the arm length is 44.2m, the elevation angle is 79°, the lifting weight is 10t, and the lifting pulley group magnification is 3; The other is the full extension of the first section of the fuel tank, the second section of the fuel tank stretch 1/3, ie, the arm length is 27.5m, the elevation angle is 79°, the lifting weight is 20t, and the lifting pulley group magnification is 4 (see Table 1 for the comparison results). Table 2 shows). By comparison, it can be found that the nonlinear calculation methods and finite element simulations have similar results, indicating that the calculation results are accurate.
Experimental verification When testing in the field, selective strain gages should be placed on the jib to measure the strain of the jib. The strain gage layout is consistent with the calculation of selected points on the selected hazard cross section (actual test results and calculation results. For comparison, see Table 3). The maximum error is less than 20%. Consider the accumulation of various error factors such as wind load, weight weight, boom upturn, and the full accuracy of the strain gauge during the actual test. The measured results are acceptable, indicating that the calculation results of the program are true and reliable, which greatly contributes to the design and development.
In this paper, a crane crane design software developed with a non-linear iterative algorithm is used to calculate the boom of the Liugong QY70 crane product. The finite element simulation is performed under the same conditions and the final results are compared. The error between the two is about 5%. Verified by field tests, the results are also consistent. This shows that this calculation method is feasible.
With the continuous development of large-tonnage crane products, high-strength steel plates have been used in a large number of applications, and the boom strength has also increased significantly. However, if all materials are used, the deformation of the boom structure will increase. As a result of the increased deformation, the bending moment caused by the axial force of the boom becomes an indispensable factor. Therefore, under the non-linear condition, it is necessary to apply a new algorithm and re-design the boom in consideration of the deformation of the boom.
Design of non-linear design of the jib 1. Geometry modeling In order to realize proceduralization and universalization of the jib, it is necessary to parameterize the geometry and physical state of the jib. This mainly includes the following three parts: (1) Geometry of the cross section of the jib, through Determine the dimensions such as angle and side length; (2) Determine the mass, length, and center of gravity of each arm; (3) Determine the performance parameters, including single rope lifting speed, lifting pulley group magnification, and so on.
2. The non-linear iterative calculation process is calculated using the Liugong QY70 crane crane arm as an example. The main lifting arm of the crane is composed of an arm and four telescopic arms. The telescopic mode is the sequential and synchronous telescopic mode.
The force of the boom is analyzed firstly for the cement production process drying equipment. In the luffing plane, the loads on the jib are: (1) the weight of the jib; (2) the weight of the jib; and (3) the lifting force of the lifting rope. When calculating the bending moment of each dangerous section on the jib, the product of the force in the axial direction and the product of the axial force arm should be added.
Force analysis in the plane of rotation. The loads on the jib are: (1) the yaw load of the hoist; (2) the wind load; (3) the weight of the jib; and (4) the hoisting mechanism. Similarly, when calculating the bending moment of each dangerous section of the jib, the bending moment due to the axial component of the above load must also be considered.
The iterative process assumes that the boom's elevation angle does not change, and feedback is provided by changes in arm deflection.
By assigning the initial value, the bending moment and lateral force at each dangerous section are first calculated, and then the deflection and rotation angle formulas of the material mechanics are used to obtain the deflection and rotation angle of each section of the arm. The total deflection of the boom can be obtained by accumulating. This deflection is compared with the initial deflection. If the set conditions are satisfied, the bending moment, lateral force, and axial force of each section are output. If not, the deflection is assigned to the previous deflection and the bending moment is recalculated. , lateral force, and find the new total deflection. In this cycle, until the deflection obtained from the two cycles before and after meets the conditions set by us, the boom is considered to have been balanced and the value obtained is the value after the boom has been deformed and balanced. The slewing plane calculation idea is the same as the amplitude change plane.
In the cyclic process, the change of the total deflection is used as the determination condition, and the total deflection is obtained by calculating the deflection and the rotation angle of each joint. The calculation formula of the deflection and the rotation angle is obtained by deriving the physical model from the material mechanics formula. .
3. Check the strength, local stability The nonlinear moments, lateral forces, and axial forces of each dangerous section are obtained by a nonlinear iterative method. From this, the stress values ​​at each point on the boom section can be calculated. In strict accordance with the relevant contents of the crane design specification GB/T3811, the local stability and strength of the jib were calculated and checked with the respective allowable stress.
Finite Element Analysis Calculation 1. The establishment of a finite element model for the establishment of a finite element model requires not only faithfully reflecting structural features but also minimizing the complexity of the model. Based on this principle, we simplified the boom. Because the boom is mainly subjected to bending, we modeled it with the beam element beam181. According to the actual arm length, overlap length, and slider position of each joint arm, then the previously established two-section section properties of each joint arm are assigned to each joint arm. Both the jib head and the pulleys are simplified. Defining unit types, material properties, etc., then meshing the model.
2. Load and add constraints are loaded into the boom according to the actual force of the load, including axial and lateral lifting forces, wire rope tension and gravity. The freedom of the x, y, and z directions is coupled between the arm and the arm, and the rear hinge point of the jib is constrained. In addition to the freedom in the y direction, the other five degrees of freedom are constrained. In addition, the lower hinges and wire ropes of the luffing cylinder are also constrained. After loading the constraint, solve it with the universal solver and get the result of the calculation.
3. Comparing the calculation results with the finite element calculation results Two conditions are selected for comparison. One is the full extension, that is, the arm length is 44.2m, the elevation angle is 79°, the lifting weight is 10t, and the lifting pulley group magnification is 3; The other is the full extension of the first section of the fuel tank, the second section of the fuel tank stretch 1/3, ie, the arm length is 27.5m, the elevation angle is 79°, the lifting weight is 20t, and the lifting pulley group magnification is 4 (see Table 1 for the comparison results). Table 2 shows). By comparison, it can be found that the nonlinear calculation methods and finite element simulations have similar results, indicating that the calculation results are accurate.
Experimental verification When testing in the field, selective strain gages should be placed on the jib to measure the strain of the jib. The strain gage layout is consistent with the calculation of selected points on the selected hazard cross section (actual test results and calculation results. For comparison, see Table 3). The maximum error is less than 20%. Consider the accumulation of various error factors such as wind load, weight weight, boom upturn, and the full accuracy of the strain gauge during the actual test. The measured results are acceptable, indicating that the calculation results of the program are true and reliable, which greatly contributes to the design and development.
In this paper, a crane crane design software developed with a non-linear iterative algorithm is used to calculate the boom of the Liugong QY70 crane product. The finite element simulation is performed under the same conditions and the final results are compared. The error between the two is about 5%. Verified by field tests, the results are also consistent. This shows that this calculation method is feasible.
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