CN115758511A - Arching design method for heavy-load large-span cross beam - Google Patents
Arching design method for heavy-load large-span cross beam Download PDFInfo
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Abstract
The invention relates to the technical field of beams, in particular to an arching design method of a heavy-load large-span beam, which comprises the following steps: determining parameters of the cross beam; constructing an initial geometric model of the beam according to parameters of the beam, and processing the geometric model through meshing to form a finite element model of the beam; carrying out deformation analysis on the finite element model of the beam, and calculating coordinate values of the beam after deformation of a plurality of point positions; drawing a beam deflection curve according to the coordinate values of the deformed point positions; obtaining a target geometric model of the beam according to the deflection curve of the beam; the invention provides an arching design method for a heavy-load large-span crossbeam, which can improve the straightness of the constructed crossbeam after deformation.
Description
Technical Field
The invention relates to the technical field of beams, in particular to an arching design method for a heavy-load large-span beam.
Background
The heavy-load large-span cross beam is used as an important supporting structural member and widely applied to equipment such as hoisting machinery, heavy machine tools and the like, and the performance of the heavy-load large-span cross beam has important influence on the running stability of the hoisting equipment and the processing quality of the machine tools. The heavy-load large-span cross beam is easy to bend and deform under the action of gravity and external load, so that the straightness of the cross beam is poor.
In the related technology, deformation deflection is obtained by adopting one-time finite element simulation analysis, and the deflection is used as an arching deformation value to design the crossbeam to offset the bending deformation of the crossbeam, but the continuous action of gravity and external load on the crossbeam is not considered during one-time finite element simulation analysis, so that the straightness of the arched crossbeam after being stressed and deformed is still poor.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art. Therefore, the embodiment of the invention provides an arching design method for a heavy-load large-span crossbeam, which can improve the straightness of the constructed crossbeam after deformation.
The arch camber design method of the heavy-load large-span beam comprises the following steps:
determining parameters of the cross beam;
constructing an initial geometric model of the beam according to the parameters of the beam, and processing the geometric model through meshing to form a finite element model of the beam;
carrying out deformation analysis on the finite element model of the beam, and calculating coordinate values of the deformed beam at a plurality of point positions;
drawing a beam deflection curve according to the coordinate values of the plurality of point positions after deformation;
and obtaining a target geometric model of the beam according to the beam deflection curve.
The arching design method of the heavy-load large-span crossbeam provided by the embodiment of the invention can improve the straightness of the constructed crossbeam after deformation.
In some embodiments, processing the geometric model by meshing to form a finite element model of the beam comprises:
carrying out grid division on the initial geometric model and determining Y-direction initial coordinate values of a plurality of point positions;
and setting load parameters, and carrying out deformation analysis on the beam finite element model according to the load parameters.
In some embodiments, calculating the coordinate values of the deformed plurality of point locations of the beam comprises:
calculating a Y-direction displacement value of each point location;
and drawing a beam deflection curve according to the Y-direction displacement value of the point location.
In some embodiments, the calculating the coordinate values of the deformed point locations of the beam further includes determining whether a Y-direction coordinate value of the point location meets a preset requirement, and if so, outputting the Y-direction point location coordinate value of the beam deflection curve.
In some embodiments, the determining whether the Y-coordinate value of the point location meets a preset requirement includes:
adding the Y-direction displacement value of the point location and the Y-direction initial coordinate value of the point location or the Y-direction coordinate value of the last iteration to obtain an output coordinate value, and drawing a deflection curve model according to the output coordinate value, wherein the deflection curve model is as follows:
wherein i is each point position of the cross beam,
is the Y-direction coordinate value of each point position i after the k-1 iteration,
for the Y-bit displacement value of each bit i,
the coordinate value of each point position i after the kth iteration is the Y-direction coordinate value;
and judging whether the output coordinate value meets a preset requirement or not.
In some embodiments, determining whether the output coordinate value satisfies a preset requirement includes:
calculating Y-direction coordinate values of all point positions after the kth iteration
Standard deviation of (d);
judging whether the standard deviation meets a preset tolerance or not;
if so, obtaining an output coordinate value, otherwise, adjusting the parameters of the beam and carrying out finite element deformation analysis again.
In some embodiments, the Y-coordinate values of all point locations after the kth iteration
The standard deviation of (d) is expressed as:
wherein N is the number of point positions, the value of N is positive number,
as Y-coordinate values of all point positions
Is calculated as the arithmetic mean of (1).
In some embodiments, adjusting the parameter of the beam comprises:
correcting the deformed Y-direction coordinate value which does not meet the preset requirement;
and taking the corrected Y-direction coordinate value as the Y-direction coordinate value of each point position in the next finite element deformation analysis and calculation.
In some embodiments, the modification of the deformed Y-coordinate value that does not meet the preset requirement may be represented as:
w is the width dimension of the beam as the Y coordinate value of each point position after correction,
and the coordinate value of each point position i in the Y direction after the k-1 iteration.
In some embodiments, determining parameters of the beam includes determining dimensions and material parameters of the beam.
Drawings
Fig. 1 is a schematic flow chart of an arching design method for a heavy-duty large-span beam according to an embodiment of the present invention.
FIG. 2 is a schematic view of an initial geometric model of a beam of an embodiment of the present invention.
FIG. 3 is a flow chart illustrating deformation analysis of a finite element model according to an embodiment of the present invention.
FIG. 4 is a schematic view of a beam deflection curve variation according to an embodiment of the present invention.
Fig. 5 is an enlarged schematic view at a in fig. 4.
FIG. 6 is a schematic diagram illustrating the variation of the standard deviation of the Y-coordinate values of all points according to an embodiment of the present invention.
FIG. 7 is a schematic view of a target geometric model of a beam of an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
As shown in fig. 1, the arching design method for a heavy-load large-span beam according to the embodiment of the present invention includes: parameters of the beam are determined. And constructing an initial geometric model of the beam according to the parameters of the beam, and processing the geometric model through meshing to form a finite element model of the beam. And carrying out finite element deformation analysis on the beam model, and calculating coordinate values of the beam after deformation of a plurality of point positions. And drawing a beam deflection curve according to the coordinate values of the deformed point positions. And obtaining a target geometric model of the beam according to the deflection curve of the beam.
Specifically, the beam is divided into a plurality of sections with the same length in the length direction of the beam through the determined parameters of the beam, the top end point of each section is used as the point position of the beam, and coordinate values of a plurality of point positions are set to combine with the size parameters of the beam to construct an initial geometric model of the beam.
As shown in fig. 2, when the coordinate values of the coordinates are set, the X-axis direction is set as the longitudinal direction of the beam, and the Y-axis direction is set as the width direction of the beam, with the left lower end of the beam as the origin of coordinates, to construct the coordinate system of the beam. Dividing the beam into a plurality of sections with the same length along the X-axis direction, taking the top end point of each section as the point position of the beam, determining the coordinate value of each point position as an initial coordinate value, and constructing an initial geometric model of the beam.
For example, the beam may be divided into 50, 100, and 200 segments of the same length in the X-axis direction.
In the arching design method of the heavy-load large-span crossbeam, parameters of the crossbeam are determined according to the actual use environment of the heavy-load large-span crossbeam, a finite element model is constructed on an initial geometric model of the crossbeam constructed according to the parameters of the crossbeam, coordinate values of all point positions after deformation are obtained through finite element deformation analysis, a crossbeam deflection curve is drawn according to the coordinate values of all point positions after deformation, the deflection curve of the crossbeam after deformation is closer to a horizontal line along with the progress of iterative calculation, the standard difference of the point position Y-direction coordinate values after deformation of the crossbeam is compared with a preset tolerance, the termination condition of iteration is determined, and a target geometric model of the crossbeam is obtained when the iteration is terminated.
The target geometric model of the beam constructed by the embodiment of the invention can reduce the straightness error of the deformed beam under the action of gravity and external load, namely the straightness of the deformed beam meets the requirement of preset straightness.
It can be understood that the embodiment of the invention automatically searches for the optimal arching design curve through the finite element modeling of the cross beam and the iterative computation, thereby saving a great deal of time cost.
In some embodiments, processing the geometric model by meshing to form a finite element model of the beam comprises: carrying out grid division on the initial geometric model and determining Y-direction initial coordinate values of a plurality of point positions; and setting load parameters, and carrying out deformation analysis on the beam finite element model according to the load parameters.
Specifically, after the constructed initial geometric model of the beam is subjected to meshing by adopting finite element units, displacement constraints are added to the beam, namely all degrees of freedom at two ends of the beam are constrained, and meanwhile, the determined load parameters are applied to the beam, so that the finite element model of the beam is constructed and deformation analysis is carried out.
It is understood that the load parameters include gravity applied to the beam and external load applied to the beam, wherein the gravity load is simulated by gravity acceleration and applied to the beam, the external load is applied to the top of the beam and is applied to the middle position of the beam in the length direction of the beam, namely the top middle of the beam, the direction of the external load is vertical downward, and the external load is set to be FY, for example, FY = -5 × 10 4 N。
As shown in fig. 3, calculating the coordinate values of the deformed plurality of point positions of the beam includes: calculating the Y-direction displacement value of each point location; and drawing a beam deflection curve according to the Y-direction displacement value of the point location.
Specifically, the constructed finite element model of the beam is submitted to a solver for calculation, so that a Y-direction displacement value of each point location after a load is applied to the beam can be obtained, a coordinate value after deformation is obtained by adding the Y-direction displacement value of each point location and a current coordinate value, and a beam deflection curve is drawn according to the coordinate value after deformation.
In some embodiments, the calculating the coordinate values of the deformed plurality of point locations of the beam further includes determining whether a Y-direction coordinate value of the point location meets a preset requirement, and if so, outputting the Y-direction coordinate value of the beam deflection curve.
Specifically, the calculated standard deviation of the Y-coordinate values of all the point locations is compared with a preset tolerance, if the standard deviation is within the preset tolerance, the Y-coordinate value of each point location of the beam before current iterative computation is output, and the geometric model of the beam is drawn according to the output Y-coordinate value of each point location.
In some embodiments, the determining whether the Y-coordinate value of the point location meets the preset requirement includes: adding the Y-direction displacement value of the point location and the Y-direction initial coordinate value of the point location or the Y-direction coordinate value of the last iteration to obtain an output coordinate value, and drawing a deflection curve model according to the output coordinate value, wherein the deflection curve model is as follows:
wherein i is each point position of the cross beam,
is the Y-direction coordinate value of each point position i after the k-1 iteration,
for the Y-bit displacement value of each bit i,
the coordinate value of each point position i after the kth iteration is the Y-direction coordinate value; and judging whether the output coordinate value meets the preset requirement or not.
Specifically, the Y-direction displacement value of the point location after the load is applied to the beam is added to the current Y-direction coordinate value of the point location to obtain an output coordinate value to draw the beam deflection curve model, wherein the current coordinate value is the initial Y-direction coordinate value or the point location Y-direction coordinate value after the last iteration.
It can be understood that, when the first iteration is performed, the current Y-coordinate value is a Y-initial coordinate value, that is, the Y-initial coordinate value of each point location is added to the Y-displacement value of each point location after the load is applied, so as to obtain a Y-coordinate value of each point location on the top of the beam after the first iteration. And when the second iterative calculation is carried out, the current Y-direction coordinate value is the Y-direction coordinate value of each point position on the top of the beam after the first iterative calculation, namely the Y-direction coordinate value of each point position on the top of the beam after the first iterative calculation is added with the Y-direction displacement value of each point position after the load is applied, so that the Y-direction coordinate value of each point position on the top of the beam after the second iterative calculation is obtained.
As shown in fig. 4 and 5, the diagrams are schematic diagrams of deflection curve changes of the cross beam, and as iterative calculation is performed, the deflection curve after the cross beam is deformed becomes more and more gentle, that is, becomes closer to a horizontal line, which indicates that the straightness error after the cross beam is deformed becomes smaller and smaller, the deflection curve with the smallest straightness error is selected, and a corresponding cross beam target geometric model is output and constructed, so that the straightness of the constructed cross beam under the load action is improved.
In some embodiments, the determining whether the output coordinate value satisfies the preset requirement includes: calculating Y-direction coordinate values of all point positions after the kth iteration
Standard deviation of (d); judging whether the standard deviation meets a preset tolerance or not; if so, obtaining an output coordinate value, otherwise, adjusting the parameters of the beam and carrying out finite element deformation analysis again.
Specifically, with the progress of iterative computation, the standard deviation of the Y-direction coordinate values of the beam is compared with a preset tolerance, and an end condition of the iteration is determined, that is, the standard deviation of the Y-direction coordinate values of all the point locations after each iteration is compared with the preset tolerance, and if the standard deviation of the Y-direction coordinate values of all the point locations after the current iteration is within the preset tolerance, it is determined that the Y-direction coordinate values of the point locations after the current iteration meet the requirements, and the Y-direction coordinate values after the last iteration are output as output coordinate values.
It can be understood that the smaller the standard deviation is, the smaller the dispersion of the Y-direction coordinate values of all the point positions after the deformation of the cross beam is, the smaller the straightness error of the deformed cross beam is, and the better the straightness of the deformed cross beam is. As shown in fig. 6 and 7, in the iteration process, after each iteration, the standard deviation of the Y-direction coordinate values of each point location at the top of the beam is smaller and smaller, after 15 times of iterative calculations, the standard deviation of the Y-direction coordinate values of all the point locations of the beam is smaller than a preset tolerance, until the iteration is terminated, the Y-direction coordinate value after the 14 th iteration is output, and the beam curve is drawn according to the output coordinate value to obtain the target geometric model of the beam, i.e., the arching geometric model of the beam.
For example, the preset tolerance value is 10 -4 The value of the preset tolerance can be determined according to the requirement, and the smaller the preset tolerance is, the better the straightness of the corresponding beam is.
In some embodiments, the Y-coordinate values of all point locations after the kth iteration
The standard deviation of (d) is expressed as:
wherein N is the number of point positions, the value of N is positive number,
for all point location Y-coordinate values
Is calculated as the arithmetic mean of (1).
Specifically, calculating the standard deviation of the Y-direction coordinate values of all the point locations after each iteration, comparing the calculated standard deviation of the Y-direction coordinate values of the point locations after the current iteration with a preset tolerance to determine whether the Y-direction coordinate values of the point locations after the current iteration meet the requirements, terminating the iteration calculation if the standard deviation of the Y-direction coordinate values of all the point locations after the current iteration is less than or equal to the preset tolerance to obtain output coordinate values, wherein the output coordinate values are the Y-direction coordinate values of all the point locations after the last iteration, and constructing the target geometric model of the beam according to the output coordinate values.
It can be understood that the smaller the standard deviation is, the smaller the dispersion of the Y-direction coordinate values of the point positions of the deformed beam is, and the better the straightness of the beam after deformation is, the standard deviation of the Y-direction coordinate values of all the point positions after each iteration is compared with a preset tolerance, so that a reference value of the straightness of the deformed beam after current iteration can be obtained, the standard deviation of the Y-direction coordinate values of all the point positions after iteration is less than or equal to the preset tolerance is used as an iteration termination condition, and the Y-direction coordinate values of the point positions of the beam before current deformation calculation are output and used as output coordinate values, so as to improve the straightness of the target geometric model of the constructed beam.
In some embodiments, adjusting the parameters of the beam comprises: correcting the deformed Y-direction coordinate value which does not meet the preset requirement; and taking the corrected Y-direction coordinate value as the Y-direction coordinate value of each point position in the next finite element deformation analysis and calculation.
Specifically, if the standard deviation of the Y-direction coordinate values of all the point locations at the top of the beam after the current iteration is greater than the preset tolerance, it is indicated that the straightness of the beam after the current iteration is deformed is poor, the Y-direction coordinate values of the point locations at the top of the beam after the current iteration, which are greater than the preset tolerance, are corrected, and the corrected Y-direction coordinate values of the point locations are used as the Y-direction coordinate values of the point locations of the next iteration.
In some embodiments, the modification of the deformed Y-coordinate value that does not meet the preset requirement may be represented as:
w is the width dimension of the beam as the Y coordinate value of each point position after correction,
and the coordinate value of each point position i in the Y direction after the k-1 iteration.
Optionally, since the positions of the point locations change after the beam deforms, in order to ensure that the size parameter of the beam design does not change, the Y-direction coordinate values of the point locations at the top of the beam after the current iteration, which are greater than the preset tolerance, are corrected, and the Y-direction size of the beam is ensured to be unchanged through correction, that is, the width value of the beam is kept unchanged. Keeping the X-direction coordinate value of each point position of the beam unchanged, and taking the obtained corrected Y-direction coordinate value of each point position of the beam as the Y-direction coordinate value of the next iterative computation to perform finite element modeling of the next iterative computation.
When iterative computation is carried out on the initial coordinate value, the current coordinate value is the initial coordinate value, namely the initial coordinate value is added with the Y-direction displacement value of each point of the beam after the load is applied, and the Y-direction coordinate value of each point of the top of the beam after iteration is obtained. And if the standard deviation of the Y-direction coordinate values of each point position after iteration is still not within the preset tolerance range, continuously correcting the Y-direction coordinate values of each point position after iteration, taking the Y-direction coordinate values of each point position after correction as new Y-direction coordinate values for finite element modeling of next iteration calculation, wherein the current coordinate values are new Y-direction coordinate values, namely adding the new Y-direction coordinate values and the Y-direction displacement values of each point position of the beam after the load is applied to obtain the Y-direction coordinate values of each point position at the top of the beam after iteration.
According to the embodiment of the invention, through analyzing the finite element model constructed by the beam, the optimal arching design curve can be automatically searched through iterative calculation, a large amount of time is saved, and the standard deviation of the Y-direction coordinate value of each point position after the beam is deformed is compared with the preset tolerance, so that the point position coordinate value of the beam meeting the straightness requirement can be obtained, and further the target geometric model of the beam can be obtained.
In some embodiments, determining the parameters of the beam includes determining dimensions and material parameters of the beam.
In particular, the dimensional parameters of the beam include determining beam structure dimensional parameters such as length, width and height of the beam. The material parameters of the beam include the material and model number of the beam.
For example, the length of the cross beam is 1000mm, the width of the cross beam is 40mm, the degrees of freedom of two ends of the cross beam are restrained, and the cross beam is made of steel.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and are therefore not to be considered limiting of the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to implicitly indicate the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless explicitly specified otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; may be mechanically coupled, may be electrically coupled or may be in communication with each other; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood according to specific situations by those of ordinary skill in the art.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "above," and "over" a second feature may mean that the first feature is directly above or obliquely above the second feature, or that only the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the present disclosure, the terms "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" and the like mean that a specific feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present disclosure. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
It should be understood that the above-described embodiments are exemplary and should not be construed as limiting the present invention, and those skilled in the art may make variations, modifications, substitutions and alterations to the above-described embodiments within the scope of the present invention.
Claims (10)
1. An arching design method for a heavy-load large-span cross beam is characterized by comprising the following steps:
determining parameters of the cross beam;
constructing an initial geometric model of the beam according to the parameters of the beam, and processing the geometric model through meshing to form a finite element model of the beam;
carrying out deformation analysis on the finite element model of the beam, and calculating coordinate values of the deformed beam at a plurality of point positions;
drawing a beam deflection curve according to the coordinate values of the plurality of point positions after deformation;
and obtaining a target geometric model of the beam according to the beam deflection curve.
2. The arching design method of a heavy-duty large-span crossbeam of claim 1, wherein processing the geometric model through meshing to form a finite element model of the crossbeam comprises:
carrying out grid division on the initial geometric model and determining Y-direction initial coordinate values of a plurality of point positions;
and setting load parameters, and carrying out deformation analysis on the beam finite element model according to the load parameters.
3. The arching design method of the heavy-load large-span crossbeam according to claim 2, wherein calculating the coordinate values of the crossbeam after deformation of a plurality of point positions comprises:
calculating a Y-direction displacement value of each point location;
and drawing a beam deflection curve according to the Y-direction displacement value of the point location.
4. The arching design method of the heavy-load large-span crossbeam according to claim 3, wherein the step of calculating coordinate values of the crossbeam after deformation further comprises the step of judging whether Y-direction coordinate values of the point positions meet preset requirements, and if yes, outputting Y-direction point position coordinate values of the crossbeam deflection curve.
5. The arching design method of the heavy-load large-span crossbeam according to claim 4, wherein judging whether the Y-direction coordinate value of the point position meets the preset requirement comprises:
adding the Y-direction displacement value of the point location and the Y-direction initial coordinate value of the point location or the Y-direction coordinate value of the last iteration to obtain an output coordinate value, and drawing a deflection curve model according to the output coordinate value, wherein the deflection curve model is as follows:
wherein i is each point position of the cross beam,
is the Y-direction coordinate value of each point position i after the k-1 iteration,
for the Y-bit displacement value of each bit i,
the coordinate value of each point position i after the kth iteration is determined;
and judging whether the output coordinate value meets a preset requirement or not.
6. The arching design method of the heavy-load large-span crossbeam of claim 5, wherein judging whether the output coordinate values meet preset requirements comprises:
calculating Y-direction coordinate values of all point positions after the kth iteration
Standard deviation of (d);
judging whether the standard deviation meets a preset tolerance or not;
if so, obtaining an output coordinate value, otherwise, adjusting the parameters of the beam and carrying out finite element deformation analysis again.
7. The arching design method for heavy-load large-span cross beams according to claim 6, wherein Y-direction coordinate values of all point positions after the kth iteration are determined
The standard deviation of (d) is expressed as:
wherein N is the number of point positions, the value of N is positive number,
as Y-coordinate values of all point positions
Is calculated as the arithmetic mean of (1).
8. The arching design method of a heavy-duty large-span crossbeam of claim 7, wherein adjusting parameters of the crossbeam comprises:
correcting the deformed Y-direction coordinate value which does not meet the preset requirement;
and taking the corrected Y-direction coordinate value as the Y-direction coordinate value of each point position in the next finite element deformation analysis calculation.
9. The arching design method of the heavy-duty large-span crossbeam of claim 8, wherein the modification of the deformed Y-coordinate value which does not meet the preset requirement can be expressed as:
w is the width dimension of the beam as the Y coordinate value of each point position after correction,
and the coordinate value of each point position i in the Y direction after the k-1 iteration.
10. The arching design method of a heavy-duty large-span crossbeam of claim 1, wherein determining parameters of the crossbeam comprises determining dimensions and material parameters of the crossbeam.
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