CN111695207A - Crane test model design method based on similarity theory - Google Patents

Crane test model design method based on similarity theory Download PDF

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CN111695207A
CN111695207A CN202010374104.4A CN202010374104A CN111695207A CN 111695207 A CN111695207 A CN 111695207A CN 202010374104 A CN202010374104 A CN 202010374104A CN 111695207 A CN111695207 A CN 111695207A
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CN111695207B (en
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靳慧
陈加军
丁克勤
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Southeast University
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Abstract

The invention provides a crane test model design method based on a similar theory, which comprises the steps of firstly deducing a similar proportional relation according to the similar theory and a dimension analysis method, selecting a reasonable model according to a reasonable similarity ratio by combining practical conditions such as a test purpose and the like, then respectively establishing finite element models of a prototype and the model by utilizing software, analyzing the similar relation of stress, displacement and first two-stage frequency of the prototype and the model under a certain load condition, and finally verifying whether a calculation result conforms to the deduced similar proportional relation. By applying the method, the similar model design of a general hoisting mechanical structure can be realized, the characteristics of prototype work can be truly reflected, and a prototype test is replaced by a model test, so that the research on the actual operation characteristics of the hoisting mechanical structure is facilitated.

Description

Crane test model design method based on similarity theory
The technical field is as follows:
the invention relates to a crane test model design method based on a similar theory, and belongs to the technical field of mechanical equipment model tests.
Background art:
the similarity theory is used to guide model experiments to determine the degree of similarity between the model and the prototype. The similarity theory is a process of establishing a similarity model of an original model and researching the similarity model in the practical application process of engineering, and using the similarity model for guidance and application to the original model after a relevant rule is obtained. The core content of the similarity theory is the three similar theories, namely the first, second and third theories.
The similarity first theorem is that the questions studied are similar to each other (the model is similar to the prototype) and the two single-valued conditions (the system geometry, the medium physical properties, etc.) are the same, then the similarity criteria of the questions are equal. The similarity second theorem (II theorem) is that the problem under study comprises M physical quantities (N basic quantities), and then the M physical quantities can be similar to the criterion II1、∏2、……∏M-NIs expressed by functional relation between the two. The third theorem of similarity is that the single values of the geometry, physical properties, etc. of the problem under study are similar, and the similarity criterion derived from the single value conditions, etc., then the problems are similar to each other. In the three similar theorems, the similar first and second theorems regard the existing similar phenomenon as the known condition for solving the problem. The third theorem of similarity makes it clear that the result of the phenomenon that has been or is being studied can be restored to the original phenomenon as long as the phenomenon that has been or is being studied has the same single-valued condition and similarity criterion as the original phenomenon.
At present, the design methods of the similar theory are mainly divided into 3 methods such as a law analysis method, an equation analysis method and a dimension analysis method. The law analysis method and the equation analysis method need to be based on an accurate physical relation or a mathematical model, the two methods are strict in derivation theory, and generally used on a simple structure or a structure with known physical equation relation, and the designed model is accurate. The dimension analysis method is based on the mathematical theory of a dimension homogeneous equation, and the dimension homogeneous principle is as follows: the terms in any one physical equation must have the same dimension. Only quantities with equal dimensions can be equal, and the property is called dimension homogeneous principle. This method provides the possibility to solve the problem by knowing only the physical quantities related to the problem under study. The current model design method is mainly applied to bridges, large-scale building structure earthquake-resistant research and the like, and rarely utilizes models to replace prototypes for mechanical equipment such as cranes and the like to carry out tests, so that it is necessary to apply a similar theory to carry out model tests on the hoisting mechanical equipment.
Disclosure of Invention
Aiming at the existing problems, the invention provides a crane test model design method based on a similar theory, which mainly considers the stress displacement state of hoisting machinery equipment during working, designs a similar model capable of reflecting the real stress displacement characteristics of a prototype according to the similar theory and a dimension analysis method, and can manufacture the similar model to be placed in a laboratory for model test.
The above purpose is realized by the following technical scheme:
a crane test model design method based on a similar theory comprises the following steps:
the first step is as follows: according to a similarity theory and a dimension analysis method, defining a similarity proportional relation between the prototype and each physical parameter of the model;
the second step is that: comprehensively considering according to the actual situation of the test purpose, and setting the similar proportion of the geometric length between the prototype and the model;
the third step: selecting a material for manufacturing a model, and calculating the medium similarity proportion of the prototype and the model;
the fourth step: establishing a finite element model of a prototype, determining the load condition of the prototype, and calculating the stress, the displacement and the first two-order frequency of the prototype;
the fifth step: establishing a finite element model of the model, determining the proportional relation between the prototype and the model, and calculating the stress, the displacement and the first two-order frequency of the model under the load borne by the proportional relation model;
and a sixth step: comparing the stress, displacement and first two-stage frequency results of the prototype and the model respectively calculated in the fourth step and the fifth step to determine whether the similar proportional relationship is satisfied;
stress similarity ratio: cσ＝σp/σm＝CE；
Displacement similarity ratio: c＝p/m＝Cl；
The first two orders of frequency similarity ratio:
Figure BDA0002479489040000021
in the formula: cσFor the prototype to model stress similarity ratio, σpStress of the prototype, σmIs the stress of the model; cIs the displacement similarity proportion of the prototype and the model,pis a displacement of the prototype and is,mis the displacement of the model; cωFrequency similarity ratio of prototype to model, ωpFrequency of the prototype, ωmIs the frequency of the model; clGeometric similarity ratio of prototype to model, CEThe ratio of the elastic modulus of the prototype to that of the model is similar, CρIs the similar ratio between the densities of the prototype and the model;
if yes, the design method is feasible; if not, resetting the similar proportion of the geometric length between the prototype and the model and the selection of the model material, and repeating the second step to the fifth step until the stress similar proportion, the displacement similar proportion and the first two-order frequency similar proportion between the prototype and the model meet the similar proportion relation.
According to the crane test model design method based on the similar theory, in the first step, the similar proportional relation between the defined prototype and each physical parameter of the model is as follows:
geometric similarity ratio of prototype and model: cl＝lp/lm；
The elastic modulus of the prototype and the model are in similar proportion: cE＝Ep/Em；
Similar ratio of poisson ratio of prototype to model: cμ＝μp/μm；
Similar proportions of prototype to model density: cρ＝ρp/ρm；
The similar proportion of the stresses of the prototype and the model: cσ＝σp/σm；
Displacement similarity ratio of prototype and model: c＝p/m；
The first two orders of frequency similarity ratio of the prototype and the model: cω＝ωp/ωm；
The section moments of inertia of the prototype and the model are similar in proportion: cI＝Ip/Im；
The prototype and the model have similar load proportion: cF＝Fp/Fm；
In the formula IpIs the geometric length of the prototype, /)mIs the geometric length of the model, EpElastic modulus of the prototype, EmAs modulus of elasticity, μ of the modelpPoisson ratio, μ, of the prototypemPoisson's ratio, p, for the modelpDensity of the prototype, pmIs the density of the model, σpStress of the prototype, σmIs the stress of the model and is,pis a displacement of the prototype and is,mis the displacement of the model; omegapFrequency of the prototype, ωmIs the frequency of the model; i ispIs the cross-sectional moment of inertia of the prototype, ImIs the section moment of inertia, F, of the modelpFor prototype loads, FmModel loads.
In the method for designing the crane test model based on the similar theory, in the second step, the similar proportion C of the geometric length between the prototype and the model is setlTaking 1 (5-50).
In the method for designing the crane test model based on the similar theory, in the third step, the materials for manufacturing the model are selected, and the medium similarity proportion of the prototype and the model is calculated, wherein the medium similarity comprises the elastic modulus similarity proportion of the prototype and the model, the Poisson ratio similarity proportion of the prototype and the model and the similarity proportion between the densities of the prototype and the model.
The crane test model design method based on the similar theory establishes a finite element model of a prototype in the fourth step, determines the stress, the displacement and the first two-order frequency of the prototype under the load of the prototype, and specifically comprises the following steps:
4.1 determining the load F of the prototypepEqual to the rated lifting capacity of the crane:
4.2 establishing a finite element model of a prototype:
4.3 input in finite element model of prototypeModulus of elasticity E of entry typepDensity of prototype ρpConstraint of the prototype, load of the prototype FpExtracting the stress sigma of the prototype from the calculation result output by the finite element model of the prototypepDisplacement of the prototypepAnd the first two frequencies omega of the prototypep。
The crane test model design method based on the similar theory comprises the following steps of establishing a finite element model of the model in the fifth step, determining the proportional relation between a prototype and the model, and calculating the stress, the displacement and the first two-order frequency of the model under the load borne by the proportional relation model, wherein the method specifically comprises the following steps:
5.1 calculating the load to which the model is subjected based on the ratio of the geometric length between the prototype and the model, and the material of the selected model
Figure BDA0002479489040000041
In the formula: fpLoad of the prototype, CEThe ratio of the elastic modulus of the prototype to that of the model is similar, ClIs the geometric similarity ratio of the prototype and the model
5.2 establishing a finite element model of the model:
5.3 inputting the modulus of elasticity E of the model in the finite element model of the modelmDensity of model ρmConstraint mode of model, load of model FmExtracting the stress sigma of the model from the calculation result output by the finite element model of the modelmDisplacement of the modelmAnd the first two orders frequency omega of the modelm。
Has the advantages that:
the invention provides a crane model test design method by combining a similarity theory and a dimension analysis method. When the method is used for designing the model, the similarity of three important characteristics of the crane during working, namely the similarity of stress, displacement and first two-order frequency with the prototype, is mainly considered, so that the characteristics of the prototype during working can be truly reflected through the characteristics of the model. The test model designed by the model design method can greatly save the cost required by prototype test.
Drawings
FIG. 1 is a flow chart of a crane test model design method based on similar theory.
Detailed Description
In order to make the technical means for carrying out the invention apparent, the invention is further illustrated below with reference to specific examples. The existing bridge crane is made of Q345 steel and has a box-shaped beam structure, the length is 20 meters, the width is 2.6 meters, the height is 2 meters, and the maximum bearing capacity is 200 tons. It is now designed as a similar model to replace the prototype for testing.
A design method of a crane test model based on a similar theory includes the steps of firstly deducing a similar proportional relation according to the similar theory and a dimension analysis method, designing a reasonable model by selecting a reasonable similar ratio according to practical conditions such as a test purpose and the like, then respectively establishing finite element models of a prototype and the model by utilizing software, analyzing the similar relation of stress, displacement and first two-order frequency of the prototype and the model under a certain load condition, and finally verifying whether a calculation result accords with the deduced similar proportional relation. The method specifically comprises the following steps:
the first step is as follows: according to a similarity theory and a dimension analysis method, defining a similarity proportional relation between the prototype and each physical parameter of the model, wherein the similarity proportional relation between the prototype and each physical parameter of the model is as follows:
geometric similarity ratio of prototype and model: cl＝lp/lm；
The elastic modulus of the prototype and the model are in similar proportion: cE＝Ep/Em；
Similar ratio of poisson ratio of prototype to model: cμ＝μp/μm；
Similar proportions of prototype to model density: cρ＝ρp/ρm；
The similar proportion of the stresses of the prototype and the model: cσ＝σp/σm；
Displacement similarity ratio of prototype and model: c＝p/m；
The first two orders of frequency similarity ratio of the prototype and the model: cω＝ωp/ωm；
The section moments of inertia of the prototype and the model are similar in proportion: cI＝Ip/Im；
The prototype and the model have similar load proportion: cF＝Fp/Fm；
In the formula IpIs the geometric length of the prototype, /)mIs the geometric length of the model, EpElastic modulus of the prototype, EmAs modulus of elasticity, μ of the modelpPoisson ratio, μ, of the prototypemPoisson's ratio, p, for the modelpDensity of the prototype, pmIs the density of the model, σpStress of the prototype, σmIs the stress of the model and is,pis a displacement of the prototype and is,mis the displacement of the model; omegapFrequency of the prototype, ωmIs the frequency of the model; i ispIs the cross-sectional moment of inertia of the prototype, ImIs the section moment of inertia, F, of the modelpFor prototype loads, FmModel loads.
The second step is that: and comprehensively considering actual conditions such as test purposes and the like, and setting the length similarity relation between the prototype and the model. In this example, assume that Cl＝lp/lm10, i.e. according to the geometric dimensions 10: 1, and designing the geometric dimension of the model. The size of the model is 2 meters long, 0.23 meters wide and 0.2 meters high.
The third step: selecting the material for making the model, and calculating the similar proportion between the elastic modulus, Poisson's ratio and density of the prototype and the model. The model and the prototype are made of the same material, namely Q345 steel, and the material parameters of the prototype and the model are the same, namely CE＝Ep/Em＝1；Cμ＝μp/μm＝1；Cρ＝ρp/ρm＝1；
Fourthly, establishing a finite element model of the prototype, wherein the maximum bearing load of the finite element model is 2 × 106N, inputting the elastic model of the prototype in the finite element model of the prototypeQuantity EpDensity of prototype ρpConstraint of the prototype, load of the prototype FpThe prototype stress, displacement and first two frequencies are obtained.
The fifth step: establishing a finite element model of the model, and calculating the load of the model according to the similar proportion of the geometric length between the prototype and the model and the material of the selected model
Figure BDA0002479489040000051
The maximum load of the model can be obtained as 2 × 104N, the model in the embodiment is the same as the prototype material, and the elastic modulus E of the model is input in the finite element model of the modelmDensity of model ρmConstraint mode of model, calculated load F of modelmIs 2 × 104And N, extracting the stress, the displacement and the first two-order frequency data from the output data of the finite element model of the model.
And a sixth step: comparing the results of the stress, the displacement and the first two-order frequency calculated by the prototype and the model, and analyzing whether the similar relation of the stress, the displacement and the frequency is required to be satisfied or not, namely whether the following similar proportional relation is satisfied or not, namely:
stress similarity ratio: cσ＝σp/σm＝CE；
Displacement similarity ratio: c＝p/m＝Cl；
The first two orders of frequency similarity ratio: cω＝ωp/ωm＝Cl -1(Cρ/CE)1/2；
Through data comparison, if the error is within an allowable range, the design of the model is completed, and the allowable range of the error is generally not more than 20%.
In this embodiment:
Cσ＝σp/σm＝0.98,CE＝1；
C＝p/m＝9.7,Cl＝10；
Cω＝ωp/ωm＝0.098,Cl -1(Cρ/CE)1/2＝0.1。
therefore, in the model designed in the embodiment, the similarity relation between the prototype of the embodiment and the stress, displacement and frequency of the model is found through calculation, and the error of the similarity proportional relation is within an allowable range, so that the model design can be completed according to the parameters.
The above-described specific implementation operation method, the technical solutions and the advantages of the present invention are further described in detail, it should be understood that the above-described specific implementation mode of the present invention should be included in the scope of the present invention, and any modifications, equivalent substitutions, improvements, and the like, which are within the spirit and principle of the present invention, should be made.

Claims (6)

1. A crane test model design method based on a similar theory is characterized in that: the method comprises the following steps:
the first step is as follows: according to a similarity theory and a dimension analysis method, defining a similarity proportional relation between the prototype and each physical parameter of the model;
the second step is that: comprehensively considering according to the actual situation of the test purpose, and setting the similar proportion of the geometric length between the prototype and the model;
the third step: selecting a material for manufacturing a model, and calculating the medium similarity proportion of the prototype and the model;
the fourth step: establishing a finite element model of a prototype, determining the load condition of the prototype, and calculating the stress, the displacement and the first two-order frequency of the prototype;
the fifth step: establishing a finite element model of the model, determining the proportional relation between the prototype and the model, and calculating the stress, the displacement and the first two-order frequency of the model under the load borne by the proportional relation model;
and a sixth step: comparing the stress, displacement and first two-stage frequency results of the prototype and the model respectively calculated in the fourth step and the fifth step to determine whether the similar proportional relationship is satisfied;
stress similarity ratio: cσ＝σp/σm＝CE；
Displacement similarity ratio: c＝p/m＝Cl；
The first two orders of frequency similarity ratio: cω＝ωp/ωm＝Cl -1(Cρ/cE)1/2；
In the formula: cσFor the prototype to model stress similarity ratio, σpStress of the prototype, σmIs the stress of the model; cIs the displacement similarity proportion of the prototype and the model,pis a displacement of the prototype and is,mis the displacement of the model; cωFrequency similarity ratio of prototype to model, ωpFrequency of the prototype, ωmIs the frequency of the model; clGeometric similarity ratio of prototype to model, CEThe ratio of the elastic modulus of the prototype to that of the model is similar, CρIs the similar ratio between the densities of the prototype and the model;
if yes, the design method is feasible; if not, resetting the similar proportion of the geometric length between the prototype and the model and the selection of the model material, and repeating the second step to the fifth step until the stress similar proportion, the displacement similar proportion and the first two-order frequency similar proportion between the prototype and the model meet the similar proportion relation.
2. The crane test model design method based on the similar theory as claimed in claim 1, wherein: in the first step, the similar proportion relation between the prototype and each physical parameter of the model is defined as follows:
geometric similarity ratio of prototype and model: cl＝lp/lm；
The elastic modulus of the prototype and the model are in similar proportion: cE＝Ep/Em；
Similar ratio of poisson ratio of prototype to model: cμ＝μp/μm；
Similar proportions of prototype to model density: cρ＝ρp/ρm；
The similar proportion of the stresses of the prototype and the model: cσ＝σp/σm；
Displacement similarity ratio of prototype and model: c＝p/m；
The first two orders of frequency similarity ratio of the prototype and the model: cω＝ωp/ωm；
The section moments of inertia of the prototype and the model are similar in proportion: cI＝Ip/Im；
The prototype and the model have similar load proportion: cF＝Fp/Fm；
In the formula IpIs the geometric length of the prototype, /)mIs the geometric length of the model, EpElastic modulus of the prototype, EmAs modulus of elasticity, μ of the modelpPoisson ratio, μ, of the prototypemPoisson's ratio, p, for the modelpDensity of the prototype, pmIs the density of the model, σpStress of the prototype, σmIs the stress of the model and is,pis a displacement of the prototype and is,mis the displacement of the model; omegapFrequency of the prototype, ωmIs the frequency of the model; i ispIs the cross-sectional moment of inertia of the prototype, ImIs the section moment of inertia, F, of the modelpFor prototype loads, FmModel loads.
3. The crane test model design method based on the similar theory as claimed in claim 1, wherein: in a second step, the similarity ratio C of the geometric length between the prototype and the model is setlTaking 1 (5-50).
4. The crane test model design method based on the similar theory as claimed in claim 1, wherein: and in the third step, selecting materials for manufacturing the model, and calculating the medium similarity proportion of the prototype and the model, wherein the medium similarity comprises the elastic modulus similarity proportion of the prototype and the model, the Poisson ratio similarity proportion of the prototype and the model and the similarity proportion between the densities of the prototype and the model.
5. The crane test model design method based on the similar theory as claimed in claim 1, wherein: and fourthly, establishing a finite element model of the prototype, and calculating the stress, the displacement and the first two-order frequency of the prototype under the load of the prototype, wherein the method specifically comprises the following steps:
4.1 determining the load F of the prototypepEqual to the rated lifting capacity of the crane:
4.2 establishing a finite element model of a prototype:
4.3 inputting the elastic modulus E of the prototype in the finite element model of the prototypepDensity of prototype ρpConstraint of the prototype, load of the prototype EpExtracting the stress sigma of the prototype from the calculation result output by the finite element model of the prototypepDisplacement of the prototypepAnd the first two frequencies omega of the prototypep。
6. The crane test model design method based on the similar theory as claimed in claim 1, wherein: and fifthly, establishing a finite element model of the model, determining a proportional relation between the prototype and the model, and calculating the stress, the displacement and the first two-stage frequency of the model under the load borne by the proportional relation model, wherein the method specifically comprises the following steps:
5.1 calculating the load to which the model is subjected based on the ratio of the geometric length between the prototype and the model, and the material of the selected model
Figure FDA0002479489030000031
In the formula: fpLoad of the prototype, CEThe ratio of the elastic modulus of the prototype to that of the model is similar, ClIs the geometric similarity ratio of the prototype and the model
5.2 establishing a finite element model of the model:
5.3 inputting the modulus of elasticity E of the model in the finite element model of the modelmDensity of model ρmConstraint mode of model, load of model FmExtracting the stress sigma of the model from the calculation result output by the finite element model of the modelmDisplacement of the modelmAnd the first two orders frequency omega of the modelm。
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CN115795926A (en) * 2023-02-08 2023-03-14 太原理工大学 Method for constructing barreling and polishing machining test model based on similarity theory

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CN115795926B (en) * 2023-02-08 2023-05-09 太原理工大学 Method for constructing barreling finishing processing test model based on similarity theory

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