Multi-source load induced portal frame assembly stress resolving method under pose constraint

Abstract

The invention discloses a multi-source load induced portal frame assembly stress resolving method under pose constraint, and belongs to the technical field of numerically-controlled machine tool high-performance assembly. Comprising the following steps: establishing a portal frame pretilt angle model, and proposing a double-upright-column tilt angle error equivalent modeling method; defining the pre-tilt angle error and the top beam-stand column connection coupling effect as pose constraints, and establishing an additional load model caused by the bias load under the pose constraints at the end part of the top beam; analyzing the stress condition of the portal frame, and constructing a portal frame assembly stress characterization model under the combined action of the assembly pretightening force, the bias load and the additional load; numerical calculation and verification are carried out on the model through refined finite element simulation, and it is revealed that the pose constraint additional load is a remarkable cause for inducing non-uniform distribution of portal frame assembly stress. According to the method, the forming mechanism of the portal frame assembly stress is clarified, an assembly stress resolving method combining a theoretical model and a refined finite element is formed, and method support is provided for improvement of assembly performance and optimization of a low-stress assembly process.

Description

Technical Field

[0001] The invention belongs to the field of high-performance assembly of CNC machine tools, and in particular relates to a method for solving gantry assembly stress induced by multi-source loads under posture constraints, which is particularly suitable for assembly stress analysis of gantry machining centers. Background Art

[0002] Gantry machining centers must meet the high-precision machining requirements of core, critical and complex parts in fields such as aerospace and wind power / nuclear power. As the load-bearing component of the crossbeam and spindle system, the gantry is mainly composed of columns and crossbeams. Its assembly stress level and distribution state have become the main factors affecting the accuracy and machining stability of the whole machine. However, the gantry is subject to multi-source loads such as assembly preload, offset load and additional load under posture constraints, and the assembly stress is often difficult to reach an ideal state. Therefore, revealing the formation mechanism of gantry assembly stress is an important bottleneck in the field of high-performance assembly of gantry machine tools, and solving it has important engineering value.

[0003] At present, the research on gantry assembly stress mostly relies on experimental measurement and finite element simulation methods. For example, existing experimental studies have obtained stress changes during the assembly process through equipment such as loading devices and strain gauges, but the complexity of the test environment and the uncontrollability of the assembly process limit the promotion of experimental methods. Existing finite element simulation methods often assume that stress is uniformly distributed or ignore small geometric errors, and fail to fully consider the actual constraints and load action modes during the assembly process, making it difficult to accurately predict the stress distribution of the gantry under actual working conditions. For this reason, it is urgent to propose a method for solving gantry assembly stress induced by multi-source loads under posture constraints, which can provide a theoretical basis for assembly stress analysis and control, and thus improve the assembly quality of the whole machine. Summary of the invention

[0004] The purpose of the present invention is to provide a method for solving gantry assembly stress induced by multi-source loads under posture constraints, so as to solve the problems of uniform assembly stress distribution of the gantry structure under the action of multi-source loads, insufficient accuracy of traditional simulation models and difficulty in stable control of assembly quality.

[0005] The method for solving the gantry assembly stress induced by multi-source loads under posture constraints described in the present invention can comprehensively consider multi-source loads such as column inclination error, component deadweight and bolt preload, and realize the visualization of stress distribution and identification of non-uniform stress areas during the assembly process by establishing an analytical model of the gantry assembly stress and combining it with refined finite element simulation. The method includes establishing a pre-tilt angle model, constructing an assembly stress characterization model under the influence of multi-source loads, performing refined finite element simulation and assembly stress verification, which can effectively optimize the gantry assembly quality and improve the stability of the overall structure.

[0006] The present invention provides a method for calculating the stress distribution of threaded connections by combining numerical and real elements, which specifically includes the following steps:

[0007] S10. Establish the gantry pre-tilt angle model and propose the equivalent modeling method of double column tilt angle error

[0008] Through the geometric analysis of the column-beam structure, the pre-tilt angle error θ function of the gantry double column posture relationship is established to describe the geometric relationship between the column tilt angle caused by gravity, processing error or assembly process and the beam during the assembly process. Through theoretical calculation, the quantitative relationship between the pre-tilt angle error θ and the assembly stress is obtained, providing a theoretical basis for subsequent stress solution.

[0009] S20. Clarify the mapping relationship between the pre-tilt angle error θ and multi-source loads under the gantry posture constraint

[0010] Under the condition of posture constraints, the mapping relationship between the pre-tilt angle error θ and the multi-source additional loads is analyzed to clarify the mechanism of these loads on the stress distribution of the joint surface. Through this mapping relationship, a mathematical model is established to accurately describe the influence of multi-source loads on the assembly stress distribution, thus providing a basis for subsequent optimization.

[0011] S30. Construction of a stress characterization model for gantry assembly under multi-source loads

[0012] According to the actual working conditions in the assembly process, a stress characterization model of the gantry assembly under multi-source loads is constructed. Through a systematic analysis of loads such as the deadweight of the column, the deadweight of the beam, the deadweight of the top beam and the deadweight of the spindle, a stress distribution model of the column-beam structure is established. Based on the mathematical methods of mechanical analysis and error transfer, this model quantitatively describes the distribution of internal stress of the machine tool gantry under multi-source load conditions, laying the foundation for the analysis and optimization of assembly stress.

[0013] S40. Assembly stress calculation method combining formation mechanism model with refined finite element simulation

[0014] Based on the aforementioned stress analysis model, combined with the refined finite element simulation method, a method for solving assembly stress is proposed. Through finite element simulation, the range of pre-tilt angle error is further optimized and adjusted, forming a comprehensive solution method of mechanism model and finite element simulation to ensure the accuracy and reliability of stress solution. This method has been verified by experiments and can be used to ensure its feasibility and effectiveness in actual assembly.

[0015] Furthermore, the pre-tilt angle error in step S10 is defined as θ. Considering that the angle θ is difficult to measure accurately, a method of indirectly solving θ by using the horizontal and vertical displacement components of the center point of the top beam-column joint surface is proposed. The geometric relationship model is:

[0016] Δ l =(hh1 )sinθ-(a / 2)(1-cosθ) (1)

[0017] Δ v =(hh 1 )(cosθ-1)+(a / 2)sinθ (2)

[0018] Among them, Δ l is the horizontal displacement of the center point of the joint surface, Δ v is the vertical displacement of the center point of the joint surface, h is the height of the column, and h 1 is the distance from the center point of the joint surface to the top of the column, and a is the length of the joint surface along the x direction.

[0019] Furthermore, the bias load in step S20 refers to the weight of the y-axis feed system G S , Spindle system deadweight G M , Top beam deadweight G H , Column deadweight G C .

[0020] Furthermore, the additional load in step S20 is the overturning moment, i.e., torque M, which is expressed as:

[0021] M=(G S L CS +G M L CM -G H L ZH )cosθ-(G C H Z +G S H S +C M H S +G H H H )sinθ (3)

[0022] Among them, L CS , L CM and L ZH are the horizontal distances from the center of gravity of the y-axis feed system, spindle system, top beam to the center of gravity of the column; H Z , H M , H S , H H They are the height of the center of gravity of the column, y-axis feed system, spindle system, and top beam respectively.

[0023] Furthermore, in step 30, the gantry is simplified to a physical model with a single column fixed constraint and a top beam as a cantilever beam. The additional load caused by the offset load under the posture constraint, the assembly preload and the deadweight of the top beam are added to the physical model. By establishing the equilibrium equation, the mathematical model of each load can be derived, that is,

[0024] T=GI D,P I L,p θ / (L·I L,p +Y d I D,P ) (4)

[0025] F x =K Fx Δ 1 +b Fx ,M z =K Mz Δ 1 +b Mz (5)

[0026] F z =K Fz Δ 2 (6)

[0027] M x =K Mx Δ 2 (7)

[0028] Where T is the shear force at the top of the gantry, I D,p is the polar moment of inertia of the top beam around its own axis, I L,p is the moment of inertia of the column around the Z direction, G is the shear modulus of the column, L is the length of the beam, and Y d is the axis offset, F x is the force along the X direction, K Fx is the stiffness coefficient along the X direction, b Fx Indicates that F x Force-related constant term; M z is the bending moment about the Z direction, K Mz is the bending moment stiffness coefficient about the Z direction, b Mz For M z Related constant terms or external influences; F z is the force along the Z direction, K Fz is the stiffness coefficient along the Z direction, M x is the bending moment about the X direction, K Mx is the bending moment stiffness coefficient about the X direction.

[0029] Furthermore, the characterization models of the horizontal and vertical directions and the tangential stress limit values ​​in step 30 are respectively

[0030]

[0031]

[0032]

[0033] The equivalent stress at the dangerous point in step 30 is:

[0034]

[0035] Furthermore, in step S40, a refined finite element model of the gantry is established taking into account the thread geometry, the bottom of the column is set as a fixed constraint and the assembly preload, offset load, and additional load are set, and a stress cloud diagram is obtained to verify the validity of the theoretical model and realize the solution of the assembly stress. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Flow chart of the method for solving stress of gantry assembly induced by multi-source loads under posture constraints.

[0037] Figure 2 Schematic diagram of the double columns and top beam of the gantry when the pre-tilt angle error θ exists.

[0038] Figure 3 Schematic diagram of the influence of multi-source loads on the overturning moment when the pre-tilt angle error θ exists and does not exist.

[0039] Figure 4 This is the stress distribution cloud diagram when there is a pre-tilt angle error in the column.

[0040] Figure 5 The simulation result diagram is used to compare the pre-tilt angle error of the column with the theoretical calculation result. DETAILED DESCRIPTION

[0041] Combine the following Figure 1 The flowchart of a method for solving gantry assembly stress induced by multi-source loads under posture constraints is shown to describe the technical solution in the embodiment of the present invention in more detail. It should be understood that the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without proposing creative labor are all within the scope of protection of the present invention.

[0042] A numerical-real combined method for solving threaded connection stress distribution, the steps of implementing the method include:

[0043] S10. Establish a gantry pre-tilt angle model and propose an equivalent modeling method for the double-column inclination angle error. According to the assembly process requirements, establish a pre-tilt angle error θ function of the gantry double-column posture relationship to describe the influence of the column posture change on the assembly stress. Figure 2 The figure shows the schematic diagram of the double columns and top beam of the gantry when the pre-tilt angle error θ exists. The geometric relationship function is:

[0044] Horizontal displacement difference of the center point of the joint surface at both ends of the top beam Δ 1 for:

[0045] Δ 1 =(h-h1)sinθ-(a / 2)(1-cosθ)

[0046] Vertical displacement difference of the center point of the joint surface at both ends of the top beam Δ 2 for:

[0047] Δ 2 =(h-h1)(cosθ-1)+(a / 2)sinθ

[0048] Where h is the height of the column, h 1 is the distance from the center point of the top beam-column joint surface to the top of the column, and a is the length of the top beam-column joint surface along the X direction.

[0049] S20. Clarify the mapping relationship between the pre-tilt angle error θ and multi-source loads under the gantry posture constraint. Use the mechanical analysis method to clarify the mapping relationship between the pre-tilt angle error θ and multi-source loads such as the deadweight of the column. Figure 3 The figure shows the effect of multi-source loads on the overturning moment when the pre-tilt angle error θ exists and does not exist. The mechanical analytical model is:

[0050] M=(G S L CS +G M L CM -G H L ZH )cos-(G C H Z +G S H S +G M H M +G H G H )sinθ

[0051] In the formula, G S , G M , G H , G C They are the deadweight of the moving beam, the main axis system, the top beam, and the column; L CS , L CM , L ZH H is the horizontal distance from the center of gravity of the moving beam, the main shaft system, and the top beam to the center of gravity of the column; Z , H M , H S , H H They are the center of gravity heights of the column, moving beam, main axis system, and top beam respectively.

[0052] S30 analyzes the stress condition of the gantry and constructs a gantry assembly stress characterization model with the combined effects of assembly preload, offset load, and additional load.

[0053] The assembly stress model under multi-source loads is constructed to analyze the stress distribution characteristics under different load conditions. The force balance relationship is characterized by the following equation:

[0054] Top beam torque

[0055]

[0056] Where, T is the shear force at the top of the gantry, G is the shear modulus of the column, and I D,P is the polar moment of inertia of the top beam around its own axis, I L,P is the moment of inertia of the column around the Z direction, L is the length of the beam, Y d is the axis offset.

[0057] Horizontal shear force on top beam

[0058] F x =K Fx Δ 2 +b Fx

[0059] Among them, K Fx is a constant related to the machine tool itself, b Fx is a variable linearly related to θ.

[0060]

[0061] Among them, I L,Y is the moment of inertia of the column around the Y direction, and λ is the Poisson’s ratio of the material.

[0062]

[0063] Bending moment of top beam in horizontal direction

[0064] M z =K Mz Δ 1 +b Mz

[0065] Among them, K Mz , b Mz These are constants related to the machine tool itself.

[0066]

[0067]

[0068] Shear force on the top beam in the vertical direction

[0069] F z =K Fz Δ 2

[0070] Among them, K Fz These are constants related to the machine tool itself.

[0071]

[0072] Among them, A L is the cross-sectional area of ​​the column perpendicular to the axial direction, I D,X is the moment of inertia of the top beam around the X direction.

[0073] Bending moment of the top beam in the vertical direction

[0074] M x =K Mx Δ 2

[0075] Among them, K Mx These are constants related to the machine tool itself.

[0076]

[0077] Bending stress

[0078]

[0079] Shear stress

[0080]

[0081]

[0082] Torque

[0083]

[0084] Maximum tensile stress caused by horizontal displacement

[0085] σ y,z =σ y,z2 -σ y,z1

[0086] Maximum tensile stress caused by vertical displacement

[0087] σ y,x =σ y,x2 -σ y,x1

[0088] The torque with the beam axis as the axis generates shear stress on the top beam. The maximum value appears on the four axial edges of the top beam farthest from the neutral axis. The shear stress value is

[0089]

[0090] According to the bending stress intensity theory, the equivalent stress at the dangerous point is

[0091]

[0092] S40. Assembly stress calculation method combining formation mechanism model with refined finite element simulation

[0093] The accuracy of the stress solution model is verified by combining finite element simulation. Finite element analysis is used to simulate the stress distribution of pre-tilt angle error under multi-source loads, and a stress field cloud map is generated to reveal the stress concentration areas that may occur during the assembly process. Figure 4 The stress distribution cloud diagram is shown when there is a pre-tilt angle error in the column. Based on the simulation results, the pre-tilt angle error of the column is adjusted and compared with the theoretical calculation results, such as Figure 5 As shown, the stress distribution of the gantry structure during the assembly process is ensured to be more uniform, thereby significantly improving the assembly accuracy and structural stability. By optimizing the assembly process, adjusting the bolt preload and pre-tilt angle error, and optimizing the distribution of assembly stress, the uniformity of stress during the assembly process and the improvement of assembly quality are ensured.

Claims

1. A method for solving gantry assembly stress induced by multi-source loads under posture constraints, characterized in that: The following steps are involved: S10, establish the gantry pre-tilt angle model and propose the equivalent modeling method of double column tilt angle error; S20, defining the pre-tilt angle error and the coupling effect of the top beam-column connection as posture constraints, and establishing an additional load model caused by the offset load at the end of the top beam under the posture constraint; S30, analyzing the stress condition of the gantry and constructing a gantry assembly stress characterization model with the combined effects of assembly preload, offset load, and additional load; S40, the model was numerically solved and verified through refined finite element simulation, and it was revealed that the additional load of posture constraint was a significant cause of the non-uniform distribution of stress in the gantry assembly.

2. The method for solving gantry assembly stress induced by multi-source loads under posture constraints according to claim 1 is characterized in that: The pre-tilt angle error in step S10 is defined as θ. Considering that it is difficult to accurately measure the angle θ, a method of indirectly solving θ by using the horizontal and vertical displacement components of the center point of the top beam-column joint surface is proposed. The geometric relationship model is: D l =(h-h1)sinθ-(a / 2)(1-cosθ) (1) D v =(h-h1)(cosθ-1)+(a / 2)sinθ (2) Among them, Δ l is the horizontal displacement of the center point of the joint surface, Δ v is the vertical displacement of the center point of the joint surface, h is the height of the column, h1 is the distance from the center point of the joint surface to the top of the column, and a is the length of the joint surface along the x direction.

3. The method for solving gantry assembly stress induced by multi-source loads under posture constraints according to claim 1 is characterized in that: The bias load in step S20 refers to the weight of the y-axis feed system G S , Spindle system deadweight G M , Top beam deadweight G H , Column deadweight G C .

4. The method for solving gantry assembly stress induced by multi-source loads under posture constraints according to claim 1 or 2, characterized in that: The additional load in step S20 is the overturning moment, i.e., torque M, which is expressed as M=(G S L CS +C M L CM -G H L ZH )cosθ-(G C H Z +G S H S +G M H S +G H H H )sinθ (3) Among them, L CS , L CM and L ZH are the horizontal distances from the center of gravity of the y-axis feed system, spindle system, top beam to the center of gravity of the column; H Z , H M , H S , H H They are the height of the center of gravity of the column, y-axis feed system, spindle system, and top beam respectively.

5. The method for solving gantry assembly stress induced by multi-source loads under posture constraints according to claim 1 or 4, characterized in that: In step 30, the gantry is simplified to a physical model with a single column fixed constraint and a cantilever beam as the top beam. The additional load caused by the offset load under the posture constraint, the assembly preload and the deadweight of the top beam are added to the physical model, and the mathematical model of each load is derived by establishing the equilibrium equation, that is, T=GI D,P I L,p θ / (L·I L,p +Y d ·I D,P ) (4) F x =K Fx Δ1+b Fx ,M z =K Mz Δ1+b Mz (5) F z =K Fz Δ2 (6) M x =K Mx ·Δ2 (7) Where T is the shear force at the top of the gantry, I D,p is the polar moment of inertia of the top beam around its own axis, I L,p is the moment of inertia of the column around the Z direction, G is the shear modulus of the column, L is the length of the beam, and Y d is the axis offset, F x is the force along the X direction, K Fx is the stiffness coefficient along the X direction, b Fx Indicates that F x Force-related constant term; M z is the bending moment about the Z direction, K Mz is the bending moment stiffness coefficient about the Z direction, b Mz For M z Related constant terms or external influences; F z is the force along the Z direction, K Fz is the stiffness coefficient along the Z direction, M x is the bending moment about the X direction, K Mx is the bending moment stiffness coefficient about the X direction.

6. The method for solving gantry assembly stress induced by multi-source loads under posture constraints according to claim 1 or 5, characterized in that: The characterization models of the horizontal, vertical and tangential stress limit values ​​in step 30 are:

7. The method for solving gantry assembly stress induced by multi-source loads under posture constraints according to claim 1 or 6, characterized in that: The equivalent stress at the dangerous point in step 30 is:

8. The method for solving gantry assembly stress induced by multi-source loads under posture constraints according to claim 1 is characterized in that: In step S40, a refined finite element model of the gantry is established taking into account the thread geometry, the bottom of the column is set as a fixed constraint, and the assembly preload, offset load, and additional load are set, and a stress cloud diagram is obtained to verify the validity of the theoretical model and realize the solution of the assembly stress.

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