Calculation method and calculation device for mass of elliptical head and storage medium

Abstract

The invention discloses a method and device for calculating the mass of an elliptical head and a storage medium, and the method comprises the steps: obtaining an outer surface generatrix parameter equation for the elliptical head according to an inner surface generatrix parameter equation; and according to the volume formula of the ellipsoid, calculating the volume of the three-dimensional body obtained by rotating the inner surface parameter equation and the outer surface parameter equation around the y axis by adopting a numerical calculation method, subtracting the volume of the three-dimensional body and adding the volume of the straight section to obtain the volume of the ellipsoidal head, and multiplying the volume by the density to obtain the mass of the ellipsoidal head. According to the method, tedious three-dimensional model drawing and subsequent quality extraction processes are avoided, and the quality of the elliptical head can be accurately, quickly and conveniently calculated.

Description

Technical Field

[0001] The invention relates to the field of pressure vessels, and in particular to a method for calculating the mass of an elliptical head, a calculating device and a storage medium. Background Art

[0002] Elliptical heads are commonly used in the pressure vessel industry. Accurate calculation of the quality of elliptical heads is a key reference for the blanking process of head manufacturing companies.

[0003] At present, the quality of elliptical heads can be accurately calculated by using CAD software such as AutoCAD, UG NX and Solidworks, drawing entities according to the diameter and thickness of the heads, and then querying the volume or quality in the entity properties. However, the process is complicated, and in production enterprises, general designers and plane drafting personnel do not know how to draw three-dimensional entity drawings.

[0004] The national standards "JB / T 4746-2002 Heads for Steel Pressure Vessels" and "GB / T 25198-2010 Heads for Pressure Vessels" both provide tables for the mass of elliptical heads. The national standard GB / T 25198 also provides a formula (A.7) for calculating the mass of an EHA elliptical head based on the inner diameter. The formula is:

[0005]

[0006] Where W is the mass, ρ is the density of the head material, π is the circumference, a and b are the long and short semi-axes of the inner wall ellipse of the elliptical head, respectively, and δ n is the nominal thickness of the elliptical head, and h is the height of the straight edge section.

[0007] According to the formula in standard GB / T 25198, the mass (volume) of the head body calculated in this standard is calculated based on the outer surface of the head being an ellipsoid, and the generatrix of this ellipsoid is an elliptical curve (ellipse major semi-axis = a + δ n , minor semi-axis = b + δ n ) is the surface of revolution formed by rotating around the minor axis. If the inner surface generatrix of the EHA elliptical head is an elliptical curve, the equidistant curve from the inner surface generatrix is ​​not an elliptical curve. Therefore, the outer surface cannot be calculated using the semi-ellipsoid volume formula, and formula (1) It is the volume formula given based on the outer surface being a semi-ellipsoid.

[0008] Therefore, the existing elliptical head mass calculation method has the above-mentioned shortcomings and deficiencies, and it is urgent to propose an accurate, fast and convenient calculation method. Summary of the invention

[0009] The present invention provides a method, a device and a storage medium for calculating the mass of an elliptical head to solve the problems existing in the prior art. In order to achieve the above object, the present invention adopts the following technical solutions:

[0010] A method for calculating the mass of an elliptical head, comprising:

[0011] For the EHA elliptical head, the inner surface generatrix f(x) parameter equation is:

[0012]

[0013] Where: a and b are the long and short semi-axes of the inner wall ellipse of the elliptical head respectively;

[0014] By making the distance between the outer surface and the inner surface equal everywhere, the parameter equation of the outer surface generatrix g(x) of the EHA elliptical head is obtained as follows:

[0015]

[0016] According to the volume formula of the ellipsoid, the cubic volume formulas obtained by rotating the f(x) curve around the y axis are:

[0017]

[0018] According to the parametric equation g(x), we can integrate y from 0 to b+t to get the volume V of the solid obtained by rotating g(x) around the y axis. g :

[0019]

[0020] Where: t is the thickness of the elliptical head;

[0021] By substitution method we get:

[0022]

[0023] The integrand in the above equation

[0024]

[0025] Denoted as w(θ); numerical calculation method is used to solve V g ;

[0026] According to the cylinder volume calculation method, the volume formula of the straight edge segment is:

[0027] V skirt =π[(a+t) 2 ha 2 h]

[0028] Where, h is the length of the straight edge segment;

[0029] Elliptical head mass W T The calculation formula is:

[0030] W T =ρ(V g -V f +V skirt )

[0031] Among them, ρ is the density of the head material.

[0032] A further improvement of the present invention is to solve V g In the process of , the complex trapezoidal integral method is used to calculate The integrand is w, and the integration interval [a, b] is divided into n parts. Then the n equally divided V g The complex trapezoidal integral formula is:

[0033]

[0034] Among them, α = (ba) / n is the step size;

[0035] The truncation error of the complex trapezoidal integral formula is:

[0036]

[0037] Where: a≤ξ≤b.

[0038] A further improvement of the present invention is to solve V g In the process of , the complex Simpson integral and the complex Cotes integral are used to calculate

[0039] A further improvement of the present invention is that the function in Excel software is used to calculate the mass W of the elliptical head according to the calculation formula T Perform calculations.

[0040] The present invention also provides a device for calculating the mass of an elliptical head, comprising:

[0041] A memory for storing computer executable instructions; and

[0042] A processor is used to execute the computer executable instructions to implement the above-mentioned method for calculating the mass of the elliptical head.

[0043] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores executable instructions, and when a computer executes the executable instructions, the above-mentioned method for calculating the mass of an elliptical head can be implemented.

[0044] The beneficial effects of the present invention include:

[0045] 1. The present invention avoids the tedious three-dimensional model drawing and subsequent quality extraction process, and can accurately, quickly and conveniently calculate the quality of the elliptical head.

[0046] 2. The present invention provides an analytical solution to the mass calculation formula of an elliptical head, and uses a numerical calculation method to obtain an approximate solution expressed by an elementary function. The method is simple and has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of an elliptical head. DETAILED DESCRIPTION

[0048] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0049] It should be noted that the illustrations provided in the following embodiments are only used to illustrate the basic concept of the present invention in a schematic manner, and thus the illustrations only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0050] Example 1: Figure 1 As shown, an embodiment of the present invention provides a method for calculating the mass of an elliptical head, which includes:

[0051] For the EHA elliptical head, the inner surface generatrix f(x) parameter equation is:

[0052]

[0053] Where: a and b are the long and short semi-axes of the inner wall ellipse of the elliptical head respectively;

[0054] By making the distance between the outer surface and the inner surface equal everywhere, the parameter equation of the outer surface generatrix g(x) of the EHA elliptical head is obtained as follows:

[0055]

[0056] According to the volume formula of the ellipsoid, the cubic volume formulas obtained by rotating the f(x) curve around the y axis are:

[0057]

[0058] According to the parametric equation g(x), we can integrate y from 0 to b+t to get the volume V of the solid obtained by rotating g(x) around the y axis. g :

[0059]

[0060] Where: t is the thickness of the elliptical head;

[0061] By substitution method we get:

[0062]

[0063] The integrand in the above equation

[0064]

[0065] Denoted as w(θ); In this embodiment, the complex trapezoidal integral of the numerical calculation method is used for calculation The integrand is w, and the integration interval [a, b] is divided into n parts. Then the n equally divided V g The complex trapezoidal integral formula is:

[0066]

[0067] Among them, α = (ba) / n is the step size;

[0068] The truncation error of the complex trapezoidal integral formula is:

[0069]

[0070] Where: a≤ξ≤b;

[0071] According to the cylinder volume calculation method, the volume formula of the straight edge segment is:

[0072] V skirt =π[(a+t) 2 ha 2 h]

[0073] Where, h is the length of the straight edge segment;

[0074] Elliptical head mass W T The calculation formula is:

[0075] W T =ρ(V g -V f +V skirt )

[0076] Among them, ρ is the density of the head material.

[0077] In some embodiments, the function function in Excel software is used to calculate the mass W of the elliptical head according to the calculation formula T Perform calculations.

[0078] An embodiment of the present invention further provides a device for calculating the mass of an elliptical head, comprising:

[0079] A memory for storing computer executable instructions; and

[0080] A processor is used to execute the computer executable instructions to implement the above-mentioned method for calculating the mass of the elliptical head.

[0081] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores executable instructions, and when a computer executes the executable instructions, the above-mentioned method for calculating the mass of an elliptical head can be implemented.

[0082] Embodiment 2: The main difference between the present invention and embodiment 1 is that a numerical calculation method is used to solve V g In the process of , the complex Simpson integral or the complex Cotes integral is used to calculate

[0083] Specific application examples:

[0084] (1) In this example, the treatment object is an EHA elliptical head, and the head density is ρ = 7850 kg / m 3 ;

[0085] (2) According to the elliptical head size data, the inner diameter D i =1000mm, thickness t=16mm, diameter-to-height ratio a / b=2, straight edge length h=25mm, calculated according to the method in this patent, the volume V obtained by rotating the generatrix of the inner surface of the head around the y-axis f =130899693.9mm 3 , the volume V obtained by rotating the generatrix of the outer surface of the head around the y-axis g =148941926.2mm 3 , the volume of the straight edge section of the head V skirt =1276743.254mm 3 .

[0086] (3) Calculate the head mass W using Excel T =151.65kg.

[0087] In this example, the quality of two elliptical heads of different sizes is calculated using the method in this patent, UG NX software, and the method in GB / T 25198 standard. i=

[0088] 600mm, thickness t=16mm, diameter-to-height ratio a / b=2, straight edge length h=25mm, the patented method calculates the mass to be W T =58.4kg, using UG NX software to calculate the mass, we get W UG =58.4kg, using the method in GB / T 25198 standard to calculate the mass, we get W 25198 =56.65kg, at this time W T With W UG The deviation is 0.0%, W 25198 With W UG The deviation is -3.0%. The second elliptical head, inner diameter D i =5000mm, thickness t=24mm, diameter-to-height ratio a / b=3, straight edge length h=40mm, the patented method calculates the mass to get W T =4647.3kg, using UG NX software to calculate the mass, we get W UG =4645.68kg, using the method in GB / T 25198 standard to calculate the mass, we get W 25198 =4284.66kg, at this time W T With W UG The deviation is 0.0%, W 25198 With W UG The deviation is -7.8%.

[0089] The applicant uses the patent method and the method in UG NX software to calculate and statistically analyze the mass of elliptical heads of various sizes: the deviation between the method in this patent and the calculation result of UG NX software does not exceed 0.4%. Therefore, the present invention has high accuracy and is easy to operate, and the technical effect is very significant.

[0090] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A method for calculating the mass of an elliptical head, characterized in that include: For the EHA elliptical head, the inner surface generatrix f(x) parameter equation is: Where: a and b are the long and short semi-axes of the inner wall ellipse of the elliptical head respectively; By making the distance between the outer surface and the inner surface equal everywhere, the parameter equation of the outer surface generatrix g(x) of the EHA elliptical head is obtained as follows: According to the volume formula of the ellipsoid, the cubic volume formulas obtained by rotating the f(x) curve around the y axis are: According to the parametric equation g(x), we can integrate y from 0 to b+t to get the volume V of the solid obtained by rotating g(x) around the y axis. g : Where: t is the thickness of the elliptical head; By substitution method we get: The integrand in the above equation Denoted as w(θ); numerical calculation method is used to solve V g ; According to the cylinder volume calculation method, the volume formula of the straight edge segment is: V skirt =π[(a+t) 2 h-a 2 h] Where, h is the length of the straight edge segment; Elliptical head mass W T The calculation formula is: W T =ρ(V g -V f +V skirt ) Among them, ρ is the density of the head material.

2. The method for calculating the mass of an elliptical head according to claim 1, characterized in that: Solving for V g In the process of , the complex trapezoidal integral method is used to calculate The integrand is w, and the integration interval [a, b] is divided into n parts. Then the n equally divided V g The complex trapezoidal integral formula is: Among them, α = (ba) / n is the step size; The truncation error of the complex trapezoidal integral formula is: Where: a≤ξ≤b.

3. The method for calculating the mass of an elliptical head according to claim 1, characterized in that: Solving for V g In the process of , the complex Simpson integral and the complex Cotes integral are used to calculate 4. The method for calculating the mass of an elliptical head according to claim 1, characterized in that: Using the function in Excel software, the mass W of the elliptical head is calculated according to the calculation formula T Perform calculations.

5. A device for calculating the mass of an elliptical head, characterized in that: include: A memory for storing computer executable instructions; and A processor, wherein the processor is used to execute the computer executable instructions to implement the method for calculating the mass of an elliptical head according to any one of claims 1-4.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores executable instructions, and when a computer executes the executable instructions, the method for calculating the mass of an elliptical head according to any one of claims 1-3 can be implemented.

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