Calculation method of maximum stress of parallel equal length welds subjected to plane torque

Abstract

The embodiment of the present invention provides a method for calculating the maximum stress of parallel equal-length welds subjected to plane torque, which relates to the technical field of steel rolling mills. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque includes: using the following formula 1 to calculate the maximum stress of two parallel equal-length welds subjected to plane torque: τ1=3M[√(l 2 +h 2 )] / [al(l 2 +3h 2 )], where τ1 is the maximum stress in MPa; M is the planar torque applied to the weld in Nmm; a is the effective weld surface width in mm; l is the effective weld surface length in mm; and h is the distance between two parallel welds in mm. The derivation method used in this invention can be used to calculate the maximum stress at a specific point in a weld subjected to planar torque, avoiding the large errors caused by simplified approximate formulas, reducing potential manufacturing risks, improving the safety factor of welds, and enhancing the design level of machine manufacturing.

Description

Technical Field

[0001] The invention relates to the technical field of steel rolling mills, and in particular to a method for calculating the maximum stress of parallel equal-length welds subjected to plane torque. Background Art

[0002] At present, the "Machinery Design Handbook" (published by Chemical Industry Press in 2004, Chapter 1 Common Design Data, page 289) uses a simplified approximate formula to calculate the maximum stress of two parallel and equal-length welds subjected to plane torque:

[0003] τ0=M / [al(h+a)],when h﹤﹤l,τ0=M / (0.33al 2 )

[0004] Where, τ0 is the stress calculated by the simplified approximate formula, MPa;

[0005] M——plane torque on the weld, Nmm;

[0006] a——effective welding surface width of the weld, mm;

[0007] l——effective welding surface length of weld, mm;

[0008] h is the distance between two parallel welds, mm.

[0009] The derivation process of the formula is as follows:

[0010] al is the effective weld area of the weld, and the torque acting on one weld is alτ0. Therefore, the planar torque M acting on the weld is M = alτ0(h + a), where h + a is the average moment arm between the torques acting on the two welds. This yields a simplified approximate formula. As can be seen from this derivation, it implicitly assumes that stress is uniform across the effective weld area. Therefore, the calculated result, τ0, is actually the average stress acting on the weld.

[0011] When h﹤﹤l, τ0=M / (0.33al 2 )=3M / (0.99al 2 )≈3M / (al 2 The formula for calculating the strength of a single weld is τ=6M / (al 2 ), two welds are superimposed, that is, τ=3M / (al 2 ). Therefore, τ0=M / (0.33al 2 ) can be derived from the formula for calculating the strength of a single weld.

[0012] As shown above, the simplified approximate formula can only calculate the average stress in the weld, but it cannot determine the maximum stress at a specific point in the weld subjected to in-plane torque, nor can it indicate the most likely location of weld failure. Based on the theory of elastic deformation of welds, it is not difficult to derive a precise formula for calculating the maximum stress in two parallel welds of equal length subjected to in-plane torque.

[0013] Compared to the precise calculation results, the error exceeds 10% within the commonly used field range (l / h = 0.8 to 1.78); when l / h = 3.8, the error reaches as high as 18%. Furthermore, within the commonly used field range (l / h = 0.8 to 1.78), the value calculated using the simplified approximate formula is smaller than the precise value, meaning the safety factor is reduced by more than 10%, which undoubtedly poses a hidden danger to the machinery manufacturing industry.

[0014] Therefore, it is necessary to propose an accurate calculation formula for the maximum stress calculation of two parallel welds of equal length when subjected to plane torque, so as to improve the design level of mechanical manufacturing. Summary of the Invention

[0015] Technical problem to be solved: Currently, the simplified approximate formula used in calculations has large calculation errors and low safety factors, while the precise calculation formula is complex.

[0016] In order to solve the above technical problems, the present invention provides a method for calculating the maximum stress of parallel and equal-length welds subjected to plane torque, which includes:

[0017] The maximum stress of two parallel welds of equal length subjected to plane torque is calculated using the following formula 1:

[0018] τ1=3M[√(l 2 +h 2 )] / [al(l 2 +3h 2 )] Formula 1

[0019] Where, τ1 is the maximum stress, MPa;

[0020] M——plane torque on the weld, Nmm;

[0021] a——effective welding surface width of the weld, mm;

[0022] l——effective welding surface length of weld, mm;

[0023] h is the distance between two parallel welds, mm.

[0024] In an optional embodiment, the calculation formula 1 for the maximum stress of two parallel welds of equal length subjected to plane torque is derived from the following formula 2:

[0025] τ max =3M[√(l2 +h 2 )] / [a(l 3 +3lh 2 )] Formula 2

[0026] Among them, τ max ——Stress at the four end points of the weld, τ max =τ1.

[0027] In an optional embodiment, Formula 2 is derived from the following Formula 3:

[0028] τ max =Eθ√(l 2 / 4+h 2 / 4) Formula 3

[0029] Where, E is the elastic modulus of the weld; θ is the torsional deformation angle of the weld.

[0030] In an optional embodiment, the torsional deformation angle θ of the weld is equal to the relative movement angle of the two steel plates.

[0031] In an optional embodiment, Eθ is calculated using the following formula 4:

[0032] M=Eθa(l 3 / 6+lh 2 / 2) Formula 4.

[0033] In an optional embodiment, the calculation formula 4 of M is derived from the following formula 5:

[0034] M=2∫ l / 2 -l / 2 Eθa(x 2 +h 2 / 4)dx formula 5

[0035] Among them, dx is to establish a rectangular coordinate system with the centroid of the weld as the origin, and take the length of a section of the weld at the horizontal coordinate x.

[0036] In an optional embodiment, Formula 5 is derived from the following Formula 6:

[0037] dM=τadx√(x 2 +h 2 / 4) Formula 6

[0038] Where τ is the stress at point dx.

[0039] In an optional embodiment, the stress τ at dx is calculated using the following formula 7:

[0040] τ=Eθ√(x 2 +h 2 / 4) Formula 7.

[0041] In an optional embodiment, the method for calculating the maximum stress of parallel equal-length welds subjected to planar torque further includes:

[0042] Program formula 1 into a computer program and input the values of M, l, h, and a to obtain the value of τ1.

[0043] In an optional embodiment, the steps of programming Formula 1 into a computer program and inputting the values of M, l, h, and a to obtain the value of τ1 include:

[0044] Enter the values of M, l, h, a and formula 1 into Excel, and change the values of M, l, h, a to get the corresponding value of τ1.

[0045] The beneficial effects of the method for calculating the maximum stress of parallel equal-length welds subjected to planar torque provided by the embodiment of the present invention include:

[0046] 1. The derivation method used in this embodiment can calculate the maximum stress at a certain point of the weld under plane torque, indicating the location where the weld is most likely to fail, avoiding the large errors caused by using simplified approximate formulas, reducing potential mechanical manufacturing hazards, increasing the safety factor of the weld, and improving the design level of mechanical manufacturing;

[0047] 2. The calculation formula provided in this embodiment can be used to derive a single weld strength calculation formula, thereby unifying the calculation formulas for the strength of two equal-length parallel welds and a single weld. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0049] Figure 1 Schematic diagram of parallel welds of equal length. DETAILED DESCRIPTION

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0051] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0052] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0053] In the description of the present invention, it should be noted that if the terms "upper", "lower", "inside", "outside", etc. appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the accompanying drawings, or is the orientation or position relationship in which the product of the invention is usually placed when in use. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be understood as a limitation on the present invention.

[0054] It should be noted that, in the absence of conflict, the features in the embodiments of the present invention may be combined with each other.

[0055] Please refer to Figure 1 This embodiment provides a method for calculating the maximum stress of parallel equal-length welds subjected to plane torque. In this method, the maximum stress of two parallel equal-length welds subjected to plane torque is calculated using the following formula 1:

[0056] τ1=3M[√(l 2 +h 2 )] / [al(l 2 +3h 2 )]Formula 1

[0057] Where, τ1 is the maximum stress, MPa;

[0058] M——plane torque on the weld, Nmm;

[0059] a——effective welding surface width of the weld, mm;

[0060] l——effective welding surface length of weld, mm;

[0061] h is the distance between two parallel welds, mm.

[0062] The derivation process of the above formula 1 is as follows:

[0063] The width of the steel plate is much larger than the effective width of the weld, so the stiffness of the steel plate is much larger than the stiffness of the weld. The steel plate can be regarded as a rigid body and the weld as an elastic body. Under the action of the plane torque M on the weld, the weld will be torsional deformed around the centroid, and the torsional deformation angle is equal to the relative motion angle θ of the two steel plates. A rectangular coordinate system is established with the centroid as the origin. A micro-segment of the weld dx is taken as the research object at the horizontal coordinate x. The deformation at dx is θ√(x 2 +h 2 / 4), assuming the elastic modulus of the weld is E, the calculation formula 7 for the stress at dx is as follows:

[0064] τ=Eθ√(x 2 +h 2 / 4) Formula 7

[0065] The moment generated by torsional deformation at dx is dM, and the calculation formula of dM is as follows:

[0066] dM=τadx√(x 2 +h 2 / 4)Formula 6

[0067] Substituting Formula 7 into Formula 6 and considering the two welds, the integral gives the moment generated by the torsional deformation of the two welds. This moment is balanced with the action of M, so the calculation formula 5 for M is as follows:

[0068] M=2∫ l / 2 -l / 2 Eθa(x 2 +h 2 / 4)dx formula 5

[0069] The calculation formula 4 for M is as follows:

[0070] M=Eθa(l 3 / 6+lh 2 / 2) Formula 4

[0071] According to formula 7, the maximum stress is generated at the four ends of the weld, and its value τ max The calculation formula 3 is as follows:

[0072] τ max =Eθ√(l 2 / 4+h 2 / 4) Formula 3

[0073] Eliminating Eθ from Formula 3 and Formula 4, we obtain Formula 2 as follows:

[0074] τ max =3M[√(l 2 +h 2 )] / [a(l 3 +3lh 2)] Formula 2

[0075] From the above derivation process, it can be seen that the stress in the effective welding area of the weld is not equal at all places, which is related to the distance from that place to the centroid, which is in line with reality.

[0076] Let h=0, then τ1=3M / (al 2 ), which is equivalent to the strength of a weld with an effective welding surface width of 2a, and the strength calculation formula of a single weld is τ=6M / (al 2 ), which shows that Formula 2 is correct.

[0077] τ1 can be determined by calculating using Formula 1. Formula 1 can be programmed into a computer program, and the values of M, l, h, and a can be input to obtain the value of τ1.

[0078] Specifically, as shown in Table 1, by entering the values of the relevant parameters M, l, h, and a, along with Formula 1, into Excel, and changing the values of the parameters M, l, h, and a, the value of τ1 for various conditions can be instantly obtained. This fully utilizes the powerful computing power of computers, making the use of precise calculation formulas as simple and convenient as using simplified approximate formulas.

[0079] Table 1 Comparison of the maximum stress formula of two parallel welds subjected to plane torsion and the calculation results of the formula in the Mechanical Design Manual

[0080]

[0081]

[0082] As shown in Table 1, the simplified approximate formula and the error value formula of τ1 and τ0 (τ0-τ1)*100 / τ1 are input into Exel, and the h value, that is, the l / h value, are changed to obtain different τ1, τ0 values, and the error values between the two.

[0083] It can be seen that when l / h = 0.8 to 1.78, the error between the two exceeds -10%;

[0084] When l / h=1.25, the error reaches the highest value of -12.3%;

[0085] When l / h=3.8, the error reaches the maximum value of 18%.

[0086] From this, we can also clarify the meaning of h﹤﹤l: when l / h>5, the simplified approximate formula should be τ0=M / [0.33al 2 ], using τ0=M / [al(h+a)], the error exceeds 37%, which can be considered as wrong.

[0087] The beneficial effects of the method for calculating the maximum stress of parallel equal-length welds subjected to planar torque provided in this embodiment include:

[0088] 1. The derivation method used in this embodiment can calculate the maximum stress at a certain point of the weld under plane torque, indicating the location where the weld is most likely to fail, avoiding the large errors caused by using simplified approximate formulas, reducing potential mechanical manufacturing hazards, increasing the safety factor of the weld, and improving the design level of mechanical manufacturing;

[0089] 2. The calculation formula provided in this embodiment can be used to derive a single weld strength calculation formula, thus unifying the calculation formulas for the strength of two equal-length parallel welds with that for a single weld.

[0090] 3. It can make full use of the powerful computing power of computers, making the use of precise calculation formulas as simple and convenient as using simplified approximate formulas.

[0091] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for calculating the maximum stress of parallel equal-length welds subjected to plane torque, characterized in that: The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque includes: The maximum stress of two parallel welds of equal length subjected to plane torque is calculated using the following formula 1: τ1=3M[√(l 2 +h 2 )] / [al(l 2 +3h 2 )] Formula 1 Wherein, τ1 is the maximum stress, MPa; M is the plane torque of the weld, Nmm; a is the effective welding surface width of the weld, mm; l is the effective welding surface length of the weld, mm; h is the distance between two parallel welds, mm; The calculation formula 1 for the maximum stress of two parallel welds of equal length subjected to plane torque is derived from the following formula 2: τ max =3M[√(l 2 +h 2 )] / [a(l 3 +3lh 2 )] Formula 2 Among them, τ max ——Stress at the four end points of the weld, τ max =τ1; Formula 2 is derived from the following formula 3: τ max =Eθ√(l 2 / 4+h 2 / 4) Formula 3 Where, E is the elastic modulus of the weld; θ is the torsional deformation angle of the weld.

2. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque according to claim 1, characterized in that: The torsional deformation angle θ of the weld is equal to the relative movement angle of the two steel plates.

3. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque according to claim 1, characterized in that: Eθ is calculated using the following formula 4: M = Eθa(l 3 / 6 + lh 2 / 2) Equation 4.

4. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque according to claim 3, characterized in that: The calculation formula 4 of M is derived from the following formula 5: M=2∫ l / 2 -l / 2 Eθa(x 2 +h 2 / 4) dx formula 5 Among them, dx is to establish a rectangular coordinate system with the centroid of the weld as the origin, and take the length of a section of the weld at the horizontal coordinate x.

5. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque according to claim 4, characterized in that: Formula 5 is derived from the following formula 6: dM=τadx√(x 2 +h 2 / 4) Formula 6 Where τ is the stress at point dx.

6. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque according to claim 5, characterized in that: The stress τ at dx is calculated using the following formula 7: τ=Eθ√(x 2 +h 2 / 4) Formula 7.

7. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque according to claim 1, characterized in that: The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque also includes: Program formula 1 into a computer program and input the values of M, l, h, and a to obtain the value of τ1.

8. The method for calculating the maximum stress of parallel equal-length welds subjected to plane torque according to claim 7, characterized in that: The steps of programming Formula 1 into a computer program and inputting the values of M, l, h, and a to obtain the value of τ1 include: Enter the values of M, l, h, a and formula 1 into Excel, and change the values of M, l, h, a to get the corresponding value of τ1.

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