Method for optimizing cross section shape of cross beam of laser cutting machine based on constrained torsion

Abstract

The invention provides a laser cutting machine cross beam section shape optimization method based on constrained torsion, which comprises the following steps: establishing a laser cutting machine cross beam CAE model according to a to-be-optimized laser cutting machine cross beam; evaluating the rigidity performance of the cross beam, and if the beam rigidity meets the performance requirement, completing the cross section shape optimization of the cross beam; if the rigidity of the beam does not meet the performance requirement, extracting geometric information of a cross section contour line of the beam; calculating the sensitivity of a plurality of nodes of the cross beam section contour line according to the geometric information of the cross beam section contour line; sensitivity analysis is carried out according to the sensitivity of the multiple nodes, and sensitive area nodes are selected; setting optimization variables, and performing shape optimization on the sensitive area nodes; an optimized laser cutting machine beam CAE model is established, and beam rigidity performance evaluation is conducted again; therefore, the weight of the cross beam can be reduced on the premise of meeting the rigidity requirement of the cross beam.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of beam cross section optimization, and specifically relates to a laser cutting machine beam cross section shape optimization method based on constraint torsion. BACKGROUND

[0002] The laser cutting machine generally comprises a bed body, a beam, a Z assembly, a laser emitter, a sliding block, a rack and the like; the laser cutting machine is used to cut materials by focusing a laser beam emitted by a laser emitter into high-density energy to irradiate a material surface, so that the material reaches its melting point or boiling point, thereby being melted or gasified, and the laser beam is moved to cut the material into a required shape.

[0003] The laser cutting requires that the machine tool of the laser cutting machine has good dynamic performance, that is, the vibration of the machine tool is small under the high dynamic response of the laser head, and the cutting precision is not affected. The laser cutting machine head and the cutting machine beam that bears the machine head require light weight and good rigidity, and the performance of the beam is particularly important, and the cross section shape and size of the beam mainly determine the stability of the beam.

[0004] Therefore, there is an urgent need for a laser cutting machine beam cross section shape optimization method to optimize the cross section of the laser cutting machine beam to meet the rigidity requirement of the beam and reduce the weight of the beam. SUMMARY

[0005] In view of the above problems in the prior art, the technical problem to be solved by the present application is to provide a laser cutting machine beam cross section shape optimization method to optimize the cross section of the laser cutting machine beam to meet the rigidity requirement of the beam and reduce the weight of the beam.

[0006] To solve the above technical problems, the present application adopts the following technical scheme: a laser cutting machine beam cross section shape optimization method based on constraint torsion, comprising:

[0007] A CAE model of the laser cutting machine beam is established according to the laser cutting machine beam to be optimized;

[0008] The rigidity performance of the beam is evaluated, if the rigidity of the beam meets the performance requirement, the cross section shape optimization of the beam is completed, and if the rigidity of the beam does not meet the performance requirement, the geometric information of the cross section contour line of the beam is extracted;

[0009] According to the geometric information of the cross section contour line of the beam, the sensitivity of multiple nodes of the cross section contour line of the beam is calculated;

[0010] According to the sensitivity of the multiple nodes, sensitivity analysis is performed, and the sensitive area nodes are selected;

[0011] The optimization variables are set, and the shape optimization of the sensitive area nodes is performed;

[0012] The optimized laser cutting machine beam CAE model is established, and the beam stiffness performance is evaluated again.

[0013] Preferably, according to the laser cutting machine beam to be optimized, a laser cutting machine beam CAE model is established, including:

[0014] According to the laser cutting machine beam to be optimized, the beam is discretized by shell plate shell element, and the Z component is discretized by solid entity element;

[0015] A MASS concentrated mass element is established at the laser emission hole to simulate the mass of the laser head;

[0016] Simple support displacement constraints are applied at the contact sliding blocks of the two ends of the beam and the bed;

[0017] The connection between the Z-axis component and the beam is simulated by a contact element;

[0018] The hypermesh software is used to obtain the laser cutting machine geometric cross-section beam CAE model.

[0019] Preferably, according to the cross-sectional profile line geometric information of the beam, the sensitivity of multiple nodes of the cross-sectional profile line of the beam is calculated, including:

[0020] According to the cross-sectional profile line geometric information of the beam, the perpendicular distance ρ(s) from the torsion center to the tangent line of the node M(z,s) on the cross-sectional profile line of the beam, the free torsional inertia moment J d And the warping coefficient γ are obtained;

[0021] The sensitivity of multiple nodes of the cross-sectional profile line of the beam is calculated And the sensitivity

[0022] Wherein, z is the normal direction of the beam cross section, and s is the circumferential coordinate of the beam cross section.

[0023] Preferably, according to the cross-sectional profile line geometric information of the beam, the sensitivity of multiple nodes of the cross-sectional profile line of the beam is calculated, including:

[0024] By calculating The free torsional inertia moment J d is obtained.

[0025] Wherein, Ω is twice the so-called area of the contour line, and δ(s) is the thickness of the thin-walled beam plate.

[0026] Preferably, according to the cross-sectional profile line geometric information of the beam, the sensitivity of multiple nodes of the cross-sectional profile line of the beam is calculated, including:

[0027] By calculating Ω = ∮ ρ(s)ds, Ω is obtained.

[0028] Preferably, according to the beam cross-section profile line geometric information, the sensitivity of multiple nodes of the beam cross-section profile line is calculated, including:

[0029] By calculating The warping coefficient γ is obtained.

[0030] Wherein, J p Is the directional inertia moment.

[0031] Preferably, according to the beam cross-section profile line geometric information, the sensitivity of multiple nodes of the beam cross-section profile line is calculated, including:

[0032] By calculating J p = ∮ ρ 2 (s)δ(s)ds, the directional inertia moment J p Is obtained.

[0033] Preferably, the optimization variable is set, and the shape of the sensitive area node is optimized, including:

[0034] The value of the node ρ(s) is taken as the change amount, the beam structure stiffness performance is taken as the optimization constraint, and the minimization of the beam mass is taken as the optimization target, and a shape optimization model is established.

[0035] The value of the sensitive area node ρ(s) is input, the method of grid deformation and model reconstruction is adopted by Hypermorph to change the beam cross-section shape parameter, and shape optimization is performed.

[0036] Compared with the prior art, the present application has at least the following advantages:

[0037] In the present application, according to the laser cutting machine beam to be optimized, a CAE model of the laser cutting machine beam is established; the cross-section profile line geometric information of the beam is extracted; the sensitivity of multiple nodes of the beam cross-section profile line is calculated according to the cross-section profile line geometric information of the beam; the sensitive area node is selected, and the shape of the sensitive area node is optimized; thereby the weight of the beam can be reduced under the premise of meeting the rigidity requirement of the beam. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to more clearly illustrate the specific embodiments of the present application, the drawings needed in the specific embodiments will be briefly introduced below. In all the drawings, the elements or parts are not necessarily drawn according to the actual scale.

[0039] Figure 1 The beam cross-section optimization flowchart provided by the present application.

[0040] Figure 2 The beam torsion analysis simplified model diagram provided by the present application.

[0041] Figure 3 The beam constraint torsion mechanical model diagram provided by the present application.

[0042] Figure 4 Schematic diagram of geometric meaning of thin-walled beam cross section parameter provided by the present application

[0043] Figure 5 Schematic diagram of geometric information of beam cross section provided by the present application.

[0044] Figure 6 Sensitivity of node 24-14 provided by the present application Figure.

[0045] Figure 7 Sensitivity of node 24-14 provided by the present application Figure.

[0046] Figure 8 Schematic diagram of cross section shape optimization variable based on p(s) provided by the present application.

[0047] Figure 9 Schematic diagram of cross section shape optimization variable based on node normal bias provided by the present application.

[0048] Figure 10 Comparison diagram of beam cross section optimization scheme provided by the present application.

[0049] Figure 11 Original structure displacement diagram provided by the present application

[0050] Figure 12 Optimized structure displacement diagram provided by the present application.

[0051] Figure 13 Original structure first-order modal vibration mode diagram provided by the present application

[0052] Figure 14 Optimized structure first-order modal vibration mode diagram provided by the present application DETAILED DESCRIPTION

[0053] The embodiments of the technical solutions of the present application will be described in detail below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and therefore only serve as examples, and cannot limit the present application. It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present application should be the usual meaning understood by the skilled in the art to which the present application belongs. The terms "first", "second", etc. in the specification and claims of the present disclosure and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily describe a specific order or sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances in order to implement the embodiments of the present disclosure described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. Unless otherwise specified, the term "multiple" means two or more. In the present disclosure, the character " / " represents a "or" relationship between the objects before and after. For example, A / B means: A or B. The term "and / or" is a description of the association between objects, which means that there can be three relationships. For example, A and / or B means: A or B, or, A and B, the three relationships. The term "corresponding" can refer to an association or binding relationship, A corresponding to B means that there is an association or binding relationship between A and B.

[0054] Referring to Figure 1 The present application provides an embodiment: a laser cutting machine beam cross section shape optimization method based on constraint torsion, comprising:

[0055] According to the laser cutting machine beam to be optimized, a laser cutting machine beam CAE model is established;

[0056] The stiffness performance of the beam is evaluated, and if the beam stiffness meets the performance requirements, the beam cross section shape optimization is completed;

[0057] If the beam stiffness does not meet the performance requirements, the beam cross section contour line geometric information is extracted;

[0058] According to the beam cross section contour line geometric information, the sensitivity of multiple nodes of the beam cross section contour line is calculated;

[0059] According to the sensitivity of multiple nodes, sensitivity analysis is performed, and sensitive area nodes are selected;

[0060] The optimization variables are set, and the shape optimization of the sensitive area nodes is performed;

[0061] The optimized laser cutting machine beam CAE model is established, and the beam stiffness performance evaluation is performed again.

[0062] Further, referring to Figure 2According to the laser cutting machine beam to be optimized, a CAE model of the laser cutting machine beam is established, including: according to the laser cutting machine beam to be optimized, shell plate shell elements are discretized, and solid body elements are discretized for structures such as Z assemblies, sliders, and racks; MASS concentrated mass elements are established at the laser emission holes to simulate the mass of the laser head; simple support displacement constraints are applied at the contact sliders of the two ends of the beam and the bed; contact elements are used to simulate the connection between the Z-axis assembly and the beam; the hypermesh software is used to obtain the CAE model of the laser cutting machine geometric cross-section beam; and the X and Y direction concentrated forces are applied at the laser emission holes through rigid connection elements to simulate the eccentric force generated by the Z-axis assembly. Among them, the horizontal concentrated force Fx represents the horizontal inertia force generated when the beam is running, and the vertical concentrated force Fy represents the gravity generated by the Z-axis assembly, which is initially set to 100 N.

[0063] participate Figure 3 According to the structure of the laser cutting machine beam, the eccentric force generated by the Z-axis assembly is simplified as a concentrated torque applied to the middle of the beam, and the beam can be regarded as a thin-walled beam constraint torsion mechanics model with simple support at both ends.

[0064] Under the action of the torque H, shear flow is generated on the cross-section Where z is the normal direction of the beam cross-section, and s is the circumferential coordinate of the beam cross-section. Since the normal stress is not 0 when the constraint torsion is performed, the torque can be represented as:

[0065]

[0066] Where p(s) is the perpendicular distance from the torsion center to the tangent line of a point M(z, s) on the contour line; δ(s) is the thickness of the thin-walled beam, see Figure 4 .

[0067] Further, see Figure 5 , the cross-sectional geometric information of the beam is obtained in hyperbeam, the line segments ①-⑤ are the installation and running areas of the Z-axis assembly and the beam, and the line segment ⑥ is the installation and running area of the beam and the bed. The cross-sectional shapes of the above line segments cannot be changed; only the line segments ⑦ and ⑧ are free areas and can be optimized in shape. According to the cross-sectional contour line geometric information of the beam, the sensitivity of the cross-sectional contour line nodes of the beam is calculated, including: according to the cross-sectional contour line geometric information of the beam, the perpendicular distance p(s) from the torsion center to the tangent line of the node M(z, s) on the cross-sectional contour line of the beam, the free torsion inertia moment J d , and the warping coefficient γ are obtained; the sensitivity of the cross-sectional contour line node 24-14 of the beam is calculated , and the sensitivity See Figure 6 and Figure 7 .

[0068] Furthermore, based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including:

[0069] Through calculation Obtain the free torsional moment of inertia J d ;

[0070] Wherein, Ω is twice the area of ​​the outline.

[0071] Furthermore, based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including:

[0072] Ω is obtained by calculating Ω=∮ρ(s)ds.

[0073] Furthermore, based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including:

[0074] Through calculation Obtain the warping coefficient γ; the warping coefficient γ is a parameter that reflects the degree of warping of the cross section; the larger the value of the warping coefficient γ, the more severe the warping, which in turn affects the Z-axis positioning accuracy of the laser emission aperture.

[0075] Among them, J p Let be the directional moment of inertia.

[0076] Furthermore, based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including:

[0077] By calculating J p =∮ρ 2 (s)δ(s)ds, to obtain the directional moment of inertia J p .

[0078] Torque θ′ represents the change in angle of rotation of the beam under torque. The smaller the torque θ′, the smaller the free torsional moment of inertia J. d The larger the crossbeam, the greater its torsional stiffness, and the smaller the rotation angle around the Z-axis generated by the laser head's emission aperture, thus resulting in higher positioning accuracy in the X and Y directions.

[0079] Through calculation Obtain the torque θ′;

[0080] Where G is the shear modulus.

[0081] Depend on Figure 6 As can be seen, nodes 17, 11, and 14 The sensitivity value is significantly higher than that of the other nodes, meaning that increasing the ρ(s) value of these three nodes easily leads to increased warping, and should be reduced. The sensitivity values ​​of the other nodes... The sensitivity values ​​are all relatively small, indicating that changes in the ρ(s) value have little effect on warpage.Figure 7 As can be seen, nodes 17, 11, and 14 A negative sensitivity value indicates that increasing the ρ(s) value of the three nodes mentioned above is detrimental to improving the torsional stiffness of the beam. Meanwhile, the sensitivity values ​​of nodes 16-10... The sensitivity value is high, and increasing the ρ(s) value of the above nodes helps to improve the torsional stiffness of the beam. Therefore, to improve the torsional stiffness of the beam, the ρ(s) values ​​of nodes 17, 11, and 14 should be decreased, and the ρ(s) values ​​of nodes 16-10 should be increased.

[0082] Furthermore, optimization variables are set in Hypermorph to optimize the shape of nodes in sensitive areas. This includes: establishing a shape optimization model with the change in node ρ(s) as the variable, the structural stiffness performance of the beam as the optimization constraint, and minimizing the mass of the beam as the optimization objective; inputting the ρ(s) values ​​of nodes in sensitive areas, and using Hypermorph to change the cross-sectional shape parameters of the beam through mesh deformation and model reconstruction to optimize the shape; as the cross-sectional shape parameter ρ(s) increases, i.e., the cross-section increases, the warping of the beam will also increase; if the sensitivity at a certain node of the cross-section... The larger the value, the greater the contribution of the node's ρ(s) to the beam warping; therefore, the value of ρ(s) at that node should be reduced. See also... Figure 7 , Figure 7 The direction of the middle arrow indicates the direction of change of the ρ(s) value at each node, and the length of the arrow is the distance of change of the ρ(s) value at each node, which is determined by the sensitivity value.

[0083] according to Figure 2 The CAE model of the laser cutting machine beam was established, with the constraint that the node displacement d1 at the laser emission hole after shape optimization should not be greater than the node displacement d0 at the laser emission hole in the initial model. Figure 2 Minimizing the total mass of the crossbeam model is taken as the shape optimization objective. The mathematical model for crossbeam shape optimization is established in HyperMogh as follows:

[0084] Find: f(ρ(s))

[0085] std1≤d0

[0086] min:mass

[0087] To compare with the optimization process of the beam section to be optimized, Figure 6 The normal directions of midline segments ⑦ and ⑧ are used as the offset directions for all nodes in this region, with an offset distance of 50mm, thus establishing shape optimization variables (see below). Figure 9 Under the premise that the optimization constraints and optimization objectives remain unchanged, the beam cross sections obtained by the two optimization schemes are shown in the figure. Figure 10 .

[0088] according to Figure 4The calculation results of the laser emission hole displacement and the beam modal natural frequency of the two optimization schemes under the indicated analysis conditions are shown in Table 1.

[0089] Table 1 Comparison of calculation results of optimization schemes

[0090]

[0091] As shown in Table 1, the mass of the first scheme and the second scheme is reduced by about 3 kg and 2 kg respectively, the laser emission hole displacement is reduced by 26.86% and 16.76% respectively, and the first order natural frequency is increased by 19.97% and 11.25% respectively. It is shown that both schemes have certain lightweight effect and help to improve the stiffness of the beam. Therefore, further analysis and verification are made on the performance of the laser cutting machine based on the beam cross-section shape optimization model obtained in the first scheme.

[0092] Under the condition of considering the gravity, the laser emission hole displacement is calculated as Figure 11 and Figure 12 The first order modal shape of the beam is shown in Figure 13 and Figure 14 The calculation results of the two are compared in Table 2.

[0093] Table 2 Comparison of performance of the laser cutting machine before and after optimization

[0094]

[0095] As shown in Table 2, after the cross-section optimization, the weight of the laser cutting machine beam is reduced by 5.3 kg, the laser emission hole displacement is reduced by 48.21%, and the first order natural frequency of the overall structure of the beam is increased by 27.21%. The optimization effect is very obvious, which shows that the beam cross-section optimization method has good engineering practical value for improving the processing performance of the laser cutting machine.

[0096] The above examples are only used to illustrate the technical solutions of the present application, but not to limit it; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the specification of the present application.

Claims

1. A method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion, characterized in that, include: Based on the crossbeam of the laser cutting machine to be optimized, a CAE model of the laser cutting machine crossbeam is established. Evaluate the beam stiffness performance. If the beam stiffness meets the performance requirements, then complete the beam cross-section shape optimization; if the beam stiffness does not meet the performance requirements, then extract the geometric information of the beam cross-section outline. Based on the geometric information of the cross-section profile of the beam, calculate the sensitivity of multiple nodes of the cross-section profile of the beam; Based on the sensitivity of multiple nodes, sensitivity analysis is performed to select nodes in sensitive areas; Set optimization variables to optimize the shape of nodes in sensitive areas; An optimized CAE model of the laser cutting machine beam was established, and the beam stiffness performance was evaluated again.

2. The method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion according to claim 1, characterized in that, Based on the crossbeam of the laser cutting machine to be optimized, a CAE model of the crossbeam is established, including: Based on the crossbeam of the laser cutting machine to be optimized, the crossbeam is discretized using shell plate elements, and the Z component is discretized using solid elements. A MASS lumped mass element is established at the laser emission aperture to simulate the laser head mass; Simply supported displacement constraints are applied at the points where the crossbeam contacts the bed at both ends of the slider. The connection between the Z-axis assembly and the crossbeam is simulated using contact elements. Use HyperMesh software to obtain the CAE model of the cross-section of the laser cutting machine beam.

3. The method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion as described in claim 1, characterized in that, Based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including: Based on the geometric information of the crossbeam cross section profile, obtain the perpendicular distance ρ(s) from the torsion center to the node M(z,s) on the crossbeam cross section profile, and the free torsional moment of inertia J. d and warpage coefficient γ; Calculate the sensitivity of multiple nodes on the cross-sectional profile of the beam. and sensitivity Where z is the normal direction of the beam cross section and s is the circumferential coordinate of the beam cross section.

4. The method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion according to claim 3, characterized in that, Based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including: Through calculation Obtain the free torsional moment of inertia J d ; Where Ω is twice the area of ​​the outline, and δ(s) is the thickness of the thin-walled beam.

5. The method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion according to claim 4, characterized in that, Based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including: Ω is obtained by calculating Ω=∮ρ(s)ds.

6. The method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion according to claim 4, characterized in that, Based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including: Through calculation Obtain the warpage coefficient γ; Among them, J p Let be the directional moment of inertia.

7. The method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion according to claim 6, characterized in that, Based on the geometric information of the beam cross-section profile, the sensitivity of multiple nodes of the beam cross-section profile is calculated, including: By calculating J p =∮ρ 2 (s)δ(s)ds, to obtain the directional moment of inertia J p .

8. The method for optimizing the cross-sectional shape of a laser cutting machine beam based on constrained torsion according to claim 1, characterized in that, Set optimization variables to optimize the shape of nodes in sensitive areas, including: A shape optimization model is established with the node ρ(s) value as the variable, the stiffness performance of the beam structure as the optimization constraint, and the minimization of the beam mass as the optimization objective. Input the node ρ(s) value of the sensitive area, and use Hypermorph to change the cross-sectional shape parameters of the beam through mesh deformation and model reconstruction to optimize the shape.

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