A method for calculating the weight of a machine beam suitable for concentrating large load action

Abstract

This application provides a method for calculating the weight of machined beams subjected to concentrated large loads. The method includes: obtaining the total web weight Q corresponding to the initial beam height H1 based on the initial beam height H1. f1 Based on the initial beam height H1, the total flange weight Q corresponding to the initial beam height H1 is obtained. t1 According to the total weight Q of the web f1 Take any beam height H2, and obtain the total web weight Q corresponding to the arbitrary beam height H2. f2 According to the total weight Q of the flange t1 Take any beam height H2 and obtain the total flange weight corresponding to the initial beam height H2; then take the total web weight Q. f2 Total weight of flange Q t2 Add them together to get the total weight of the machined beam corresponding to the arbitrary beam height H2.

Description

TECHNICAL FIELD

[0001] The application belongs to the professional field of comprehensive strength design, and particularly relates to a weight calculation method of a machine-added beam suitable for concentrated large load action. BACKGROUND

[0002] The machine-added beam structure is generally adopted in a helicopter main load-bearing beam structure, which mainly bears and diffuses large concentrated load and is widely used in a helicopter structure. As known, weight control is of great significance to an aircraft, especially to the weight control of a main load-bearing structure. Therefore, the machine-added beam structure as the main load-bearing structure takes the minimum weight as the primary target of optimization design in the scheme design stage.

[0003] The main size affecting the weight of the machine-added beam structure is the web height, and the weight-optimal design scheme is given through the optimization design of the beam height. In the size design of the machine-added beam suitable for bearing large concentrated load, the finite element method is often used, that is, the finite element models of machine-added beams with different heights are established, the machine-added beams with different web heights are respectively defined in size according to the finite element calculation results, and then the size-optimal scheme is selected. This method is time-consuming and labor-consuming, and a series of web height beams need to be modeled and calculated, which is large in workload and low in efficiency. Therefore, it is of great practical value to propose a method for quickly obtaining the weight-optimal scheme of the machine-added beam in the early scheme design stage. SUMMARY

[0004] The application provides a weight calculation method of a machine-added beam suitable for concentrated large load action, which can quickly give the weight corresponding to beams with different heights, so as to select the machine-added beam with optimal height.

[0005] In order to solve the above technical problems, the application provides a weight calculation method of a machine-added beam suitable for concentrated large load action, which comprises the following steps:

[0006] According to the initial beam height H1, the total weight Q f1 of the web corresponding to the initial beam height H1 is obtained.

[0007] According to the initial beam height H1, the total weight Q t1 of the flange corresponding to the initial beam height H1 is obtained.

[0008] According to the total weight Q f1 of the web and the arbitrary beam height H2, the total weight Q f2 of the web corresponding to the arbitrary beam height H2 is obtained.

[0009] According to the total weight Q t1 of the flange and the arbitrary beam height H2, the total weight of the flange corresponding to the initial beam height H2 is obtained.

[0010] The total weight Q f2 of the web and the total weight Qt2 Add them together to get the total weight of the machined beam corresponding to the arbitrary beam height H2.

[0011] Specifically, the total web weight Q corresponding to the initial beam height H1 is obtained based on the initial beam height H1. f1 Specifically, it includes:

[0012] Based on the initial beam height H1, using Obtain the total web weight Q corresponding to the initial beam height H1. f1 Where H1 is the initial beam height, ρ is the material density, L is the length between the two support frame segments, δ is the beam web thickness, and H j b1 is the transverse height of the reinforcement bars in the beam web, and b1 is the smaller value between the width between two reinforcement bars and the beam height after the reinforcement bars are placed.

[0013] Specifically, the total flange weight Q corresponding to the initial beam height H1 is obtained based on the initial beam height H1. t1 Specifically, it includes:

[0014] Based on the initial beam height H1, using The total flange weight Q corresponding to the initial beam height H1 is obtained. t1 Among them, b f1 The value is half the width of the beam flange, and its value is taken as half the width of the beam flange, δ f1 The thickness is the beam flange.

[0015] Specifically, based on the total weight Q of the web... f1 Take any beam height H2, and obtain the total web weight Q corresponding to the arbitrary beam height H2. f2 Specifically, it includes:

[0016] Based on the total weight Q of the web f1 Take any beam height H2, and use the formula Obtain the total web weight Q corresponding to the arbitrary beam height H2. f2 Where H2 is an arbitrary beam height, H j The transverse height of the reinforcement bars in the beam web.

[0017] Specifically, based on the total flange weight Q t1 Take any beam height H2 and obtain the total flange weight corresponding to the initial beam height H2, specifically including:

[0018] Based on the total flange weight Q t1 Take any beam height H2, and use the formula Obtain the total flange weight Q corresponding to the arbitrary beam height H2. t2 Among them, b f1 The value is half the width of the beam flange, and its value is taken as half the width of the beam flange, δ f1 The thickness is the beam flange.

[0019] Specifically, when the initial beam height H1=200mm, the beam height H2=300mm is taken at random, the total weight of the web corresponding to the beam height H2 is

[0020] When the initial beam height H1=200mm, the beam height H2=400mm is taken at random, the total weight of the web corresponding to the beam height H2 is

[0021] When the initial beam height H1=500mm, the beam height H2=500mm is taken at random, the total weight of the web corresponding to the beam height H2 is

[0022] Specifically, when the initial beam height H1=200mm, the beam height H2=300mm is taken at random, the total weight of the flange corresponding to the beam height H2 is obtained

[0023] When the initial beam height H1=200mm, the beam height H2=400mm is taken at random, the total weight of the flange corresponding to the beam height H2 is obtained

[0024] When the initial beam height H1=200mm, the beam height H2=500mm is taken at random, the total weight of the flange corresponding to the beam height H2 is obtained

[0025] Specifically, the beam height H2 is taken in the range of 200mm-600mm.

[0026] In summary, the application proposes a machining beam optimization design method suitable for concentrated large load action, and the weight corresponding to different beam heights can be quickly obtained from the above method according to the initial beam web height size definition result, the optimal weight scheme is given, which is consistent with the conclusion of the finite element method, so the above method has important practical value in the machining beam scheme design stage. DETAILED DESCRIPTION

[0027] The application takes the shear stability of the beam web and the compression strength of the flange as constraint conditions, gives the web and flange size corresponding to the initial beam height H1, and obtains the weight of the initial height machining beam. On this basis, the general formula for calculating the weight of the beam of any height based on the initial beam height size is obtained by fitting the weight data of the beams of different heights, and the rapid optimization of the machining beam scheme for bearing concentrated large load is realized.

[0028] Example 1

[0029] The application proposes a machining beam weight calculation method suitable for concentrated large load action, which comprises the following steps:

[0030] Step 101: according to the initial beam height H1, using get the total weight of the web Q f1 corresponding to the initial beam height H1

[0031] Where H1 is the initial beam height; p is the material density; L is the length between the two support frame sections; d is the beam web thickness; H j is the transverse height of the beam web arranged with ribs; b1 is the smaller value between the width between the two ribs arranged with ribs and the beam height.

[0032] In practical applications, the initial value of H1 is generally 200mm according to design experience. The value of b1 is calculated according to the initial height and the shear stability requirement of the beam web. The beam web rib mainly plays the role of increasing the shear stability of the web, and the transverse height H j of the beam web rib is a constant.

[0033] It should be noted that d is the beam web thickness, which is the minimum value according to the machining requirement of the machined part, and is a constant in this calculation method; in the calculation of the shear stability of the beam web, the Poisson's ratio is taken as 0.3; the unit system of the above-mentioned variables is: mm, Kg.

[0034] Step 102: according to the initial beam height H1, using get the total weight of the flange Q t1 corresponding to the initial beam height H1

[0035] Where H1 is the initial beam height; p is the material density; L is the length between the two support frame sections; b f1 is the half width of the beam flange, which is half of the width of the beam flange; d f1 is the thickness of the beam flange.

[0036] In practical applications, the initial value of H1 is generally 200mm according to design experience. The values of b f1 , d f1 are given according to the initial height and the corresponding value according to the requirement of the beam flange compression damage.

[0037] It should be noted that the thickness of the beam flange d f1 is a constant; the unit system of the above-mentioned variables is: mm, Kg.

[0038] Step 103: according to the total weight of the web Q f1 , and the beam height H2, using the formula

[0039] get the total weight of the web Q f2 corresponding to the beam height H2

[0040] Where H1 is the initial beam height; H2 is the arbitrary beam height; ρ is the material density; L is the length between the two support frame segments; δ is the beam web thickness; H j b1 represents the transverse height of the reinforcement bars in the beam web; b1 is the smaller value between the two reinforcement bars and the beam height after the reinforcement bars are placed.

[0041] In practical applications, the initial value of H1 is generally set to 200mm based on design experience. The value of b1 is calculated according to the initial height and the shear stability requirements of the beam web. The web reinforcement mainly serves to increase the shear stability of the web, and the transverse height H of the web reinforcement is... j It is an invariant.

[0042] It should be noted that δ is the thickness of the beam web, which is taken as the minimum value according to the machining requirements of the machined parts, and is an invariant in this calculation method; in the calculation of the shear stability of the beam web, Poisson's ratio is taken as 0.3; the unit system of the variables involved above is: mm, Kg.

[0043] Step 104: Based on the total flange weight Q t1 Take any beam height H2, and use the formula The total flange weight Q corresponding to the initial beam height H2 is obtained. t2 ;

[0044] Where H1 is the initial beam height; H2 is the arbitrary beam height; ρ is the material density; L is the length between the two support frame segments; b f1 δ is half the width of the beam flange, and its value is taken as half the width of the beam flange; f1 The thickness is the beam flange.

[0045] In practical applications, the initial value of H1 is generally set to 200mm based on design experience. f1 δ f1 The value is given according to the initial height and the requirements for beam flange compression damage.

[0046] It should be noted that the beam flange thickness δ f1 The variables are invariants; the unit system for the variables mentioned above is: mm, Kg.

[0047] Step 105: The total weight Q of the web plate f2 Total weight of flange Q t2 Adding them together, we get the total weight of the machined beam corresponding to the arbitrary beam height H2, that is: Q2 = Q f2 +Q t2 .

[0048] Example 2

[0049] The invention will be further described in detail below with reference to examples of calculating the weight of machined beams of different heights under concentrated heavy loads on a certain type of machine.

[0050] The main idea of the method is to minimize the weight of the beam under the strength design requirements, and to optimize the beam height and its corresponding flange cross-sectional area. It mainly includes the following steps:

[0051] 1. Beam web and flange load

[0052] Under the same external load of different beam heights, assume that the beam section mainly bears the transverse load P, which generates the transverse bending moment M (the selected I-beam section is a symmetric section, the load passes through the section centroid, and there is no additional torsional moment).

[0053] Let the cross-sectional upper and lower flange area be A, the upper and lower flange centroid height be H, the web thickness be δ, the material yield stress σ s , the shear yield stress τ s , and ρ be the material density. Since the flange failure mode is compression failure and the web is shear instability, the corresponding yield strength of the material is taken.

[0054] The axial load on the flange is:

[0055] The axial stress on the flange is:

[0056] The length L of beams of different heights is the same.

[0057] The unit weight of the upper and lower flanges is: t = 2ρA

[0058] The shear flow on the web is:

[0059] The shear stress on the web is:

[0060] The unit weight of the web is: f = ρHδ + Q j Q j is the weight of the arranged rib.

[0061] Based on the analysis of the stresses obtained above, the flange area of beams of different heights, the flange compression failure strength, and the web stability strength are analyzed, and the weight of beams of different heights under the strength design requirements is given.

[0062] 2. Analysis of the web weight of beams of different heights:

[0063] Since the I-beam is a whole machine beam, to meet the requirements of machine manufacturing, it is assumed that the web thickness of beams of different heights is the same, which is δ.

[0064] The web stability calculation formula is:

[0065] Since the reinforced beam is a metal material, generally take μ = 0.3,

[0066] Where b is the short side length.

[0067] Let the initial beam height be H1(200mm) and the web shear stress be τ1. Because the distance between the two frames is large, the shear stability needs to be improved by arranging bars on the beam.

[0068] The value of K in the formula is related to the ratio of b / H1(assuming that the plate is simply supported on four sides), so as to make τ1<τ cr , the corresponding short side width b1 is selected, the corresponding shear critical stress coefficient is K1, and the web stability critical stress is:

[0069]

[0070] In this case, the web weight is calculated as:

[0071] The beam length between the two frames is L, and the number of bars arranged is L / b1. The bar size is thickness δ, and the cross-sectional height is H j (the bar cross-sectional height is the same for beams of different heights). Therefore, the total weight of the web is:

[0072] When the beam height is changed from H1(200mm) to H2(300mm), the beam height is increased by 1.5 times.

[0073] The shear stress on the web is:

[0074] The corresponding stability critical stress should satisfy:

[0075]

[0076] If b2=1.5b1, i.e.

[0077] Substituting the above formula does not meet the requirements, but it can be obtained that b2<1.5b1 to meet the above formula requirements, and under the assumption

[0078] K2=K1, According to the specific load-bearing requirements of the beam, the beam needs to bear large concentrated load or distributed load, so the length-width ratio of the beam web is generally required to be less than 0.5. According to the solution of K in the “Aircraft Design Manual (Volume 9)”, when the length-width ratio is less than 0.5, the value of K remains basically unchanged, so based on the above analysis, it can be obtained that b2=1.22b1.

[0079] Therefore, when the beam height is H2(300mm), the total weight of the web is:

[0080]

[0081] Based on the same analysis, when the beam height from H1 (200mm) to H3 (400mm), the beam height increased 2 times.

[0082] Shear stress on the web:

[0083] Corresponding to its stability critical stress should meet:

[0084]

[0085] K3 = K1,

[0086] Thus, when the beam height is H3 (400mm), the total weight of the web is:

[0087]

[0088] When the beam height from H1 (200mm) to H4 (500mm), the beam height increased 2.5 times.

[0089] Shear stress on the web:

[0090] Corresponding to its stability critical stress should meet:

[0091]

[0092] K4 = K1,

[0093] Thus, when the beam height is H4 (500mm), the total weight of the web is:

[0094]

[0095] According to the above different height beam web weight calculation method, using data fitting method to give the arbitrary height beam web weight, that is

[0096] H r is the arbitrary height of the beam.

[0097] 3. Analysis of the weight of the flange of the beam of different heights:

[0098] The flange pressure loss strength calculation uses the following calculation method:

[0099] The initial beam height is H1 (200mm), the flange half width is b f1 , the thickness is δ f1 .

[0100] The axial load on the flange:

[0101] The axial stress on the flange:

[0102] According to the figure 21-28 on page 379 of the Aircraft Design Manual (Volume 9), according to b f1 / δ f1 The pressure loss strength coefficient K f1 is obtained, and the pressure loss strength is obtained:

[0103] (the flange is left and right half width)

[0104] The length of the beam between the two frames is L, so the total weight of the flange (including the upper and lower flanges) is:

[0105]

[0106] When the beam height changes from H1 (200mm) to H2 (300mm), the beam height increases by 1.5 times.

[0107] The axial load on the flange:

[0108] The axial stress on the flange:

[0109] Make σ z2 = σ z1 , then A1 = 1.5A2, keep the flange thickness δ f1 unchanged in this state, then the flange half width:

[0110] The ratio of its thickness to H1 in the state is obtained:

[0111]

[0112] By taking the pressure loss strength coefficient K f1 The figure shows that as the side length thickness ratio decreases, the pressure loss strength coefficient increases, that is, the pressure loss strength in the H2 state is greater than that in the H1 state, but the critical value of the pressure loss strength is σ s Therefore, it is conservative to consider that the pressure loss strength in the H2 state is equal to that in the H1 state.

[0113] The total weight of the flange in this state is:

[0114]

[0115] Similarly:

[0116] When the beam height changes from H1 (200mm) to H3 (400mm), the beam height increases by 2 times.

[0117] The total weight of the flange in this state is:

[0118]

[0119] When the beam height changes from H1(200mm) to H4(500mm), the beam height is increased by 2.5 times.

[0120] The total weight of the flange in this state is:

[0121]

[0122] According to the above weight calculation method of the flange of the beam of different heights, the weight of the flange of the beam of any height is given, that is,

[0123]

[0124] In the formula, H r is the height of the beam.

[0125] 4. Beam total weight calculation

[0126] The weight of the beam of different heights is calculated according to the above, and the weight of the beam of several heights is given as follows.

[0127]

[0128]

[0129] According to the size calculation result of the initial beam height(200mm), the weight of the beam of any height can be quickly obtained according to the above table, so as to obtain the weight optimal beam height scheme.

[0130] As described above, the application proposes a machining beam weight calculation method suitable for concentrated large load action. According to the size definition result of the initial beam web height, the weight corresponding to different beam heights can be quickly obtained by the above method, and the weight optimal scheme is given. The conclusion is consistent with the finite element method, so the above method has important practical value in the design stage of the machining beam scheme.

Claims

1. A method for calculating the weight of a machine beam suitable for concentrating the action of a large load, characterized in that, The method comprises: Based on the initial beam height The initial beam height was obtained. Corresponding total weight of web Specifically, this includes: based on the initial beam height. ,use The initial beam height was obtained. Corresponding total weight of web ,in, For the initial beam height, For material density, The length between the two support frame segments, For the thickness of the beam web, The transverse height of the reinforcement bars in the beam web, The smaller value between the width of two reinforcing bars and the beam height should be used after the reinforcement bars are arranged. Based on the initial beam height The initial beam height was obtained. Corresponding total flange weight Specifically, this includes: based on the initial beam height. ,use The initial beam height was obtained. Corresponding total flange weight ;in, This is half the width of the beam flange, and its value is taken as half the width of the beam flange. The thickness of the beam flange; According to the total weight of the web , the height of the arbitrary beam , the total weight of the web corresponding to the height of the arbitrary beam is obtained; specifically comprising: according to the total weight of the web , the height of the arbitrary beam , the formula , the total weight of the web corresponding to the arbitrary beam height ; wherein, is the arbitrary beam height, is the transverse height of the web arranged with the bars According to the total weight of the flange , the total weight of the flange corresponding to the arbitrary beam height is obtained .​ The total weight of the web and the flange is added to give the total weight of the machined beam corresponding to the arbitrary beam height .

2. The method of claim 1, wherein, According to the total weight of the flange , the total weight of the flange corresponding to the arbitrary beam height is obtained, specifically comprising: , the total weight of the flange corresponding to the arbitrary beam height is obtained, specifically comprising: , the total weight of the flange corresponding to the arbitrary beam height is obtained, specifically comprising: According to the total weight of the flange , the total weight of the flange corresponding to the arbitrary beam height is obtained by using the formula ; wherein, the total weight of the flange corresponding to the arbitrary beam height ; wherein, is the half width of the beam flange, which is half of the width of the beam flange, is the thickness of the beam flange.

3. The method of claim 1, wherein, When initial beam height = 200 mm, take beam height = 300 mm, take beam height Corresponding total weight of web = ; When initial beam height = 200 mm, take beam height = 400 mm, take beam height Corresponding total weight of web = ; When initial beam height = 500 mm, take beam height = 500 mm, take beam height Corresponding total weight of web = .

4. The method of claim 1, wherein, When the initial beam height = 200 mm, the beam height = 300 mm, the beam height correspondingly, the total weight of the flange correspondingly, the total weight of the flange = ; When the initial beam height = 200 mm, the arbitrary beam height = 400 mm, the arbitrary beam height corresponding to the arbitrary beam height corresponding flange total weight = ; When initial beam height = 200 mm, take beam height = 500 mm, take beam height Corresponding to take beam height Corresponding flange total weight = .

5. The method of claim 1, wherein, Ren Qu Liang Gao The value range is 200mm-600mm.

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