CN115034018A - Optimal design method for shape and size parameters of elastic hydraulic oil tank shell - Google Patents

Optimal design method for shape and size parameters of elastic hydraulic oil tank shell Download PDF

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CN115034018A
CN115034018A CN202210753346.3A CN202210753346A CN115034018A CN 115034018 A CN115034018 A CN 115034018A CN 202210753346 A CN202210753346 A CN 202210753346A CN 115034018 A CN115034018 A CN 115034018A
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oil tank
hydraulic oil
wall
elastic hydraulic
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CN115034018B (en
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姚静
王定煜
何蔼雯
张昊
郝金鹿
赵志成
张熙堃
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Yanshan University
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Abstract

The invention provides an optimal design method for shape and size parameters of an elastic hydraulic oil tank shell, which comprises the following specific steps: obtaining the optimal shape of the oil tank shell according to the oil tank volume and the working pressure; establishing a mathematical model of the oil tank shell; analyzing the oil tank shell to obtain three performance index parameter models of hoop stress, axial stress and mass, determining parameters to be optimized, and taking the minimum hoop stress, axial stress and mass as an optimization objective function; under the constraints of the machining size and the volume of the oil tank, performing multi-objective optimization on the structure of the oil tank by adopting a multi-objective optimization algorithm to obtain an optimal parameter solution set; and obtaining an optimal structure of the oil tank according to the comprehensive evaluation function, and obtaining optimal shape and size parameters after strength check. The invention can satisfy the oil liquid requirement and the allowable pressure of the oil tank, not only can satisfy the strength of the oil tank shell, but also can reduce the weight of the oil tank shell, effectively reduce the design and processing cost of the oil tank shell, and can obtain the high-performance elastic hydraulic oil tank shell with different requirements.

Description

Optimal design method for shape and size parameters of elastic hydraulic oil tank shell
Technical Field
The invention relates to the technical field of hydraulic oil tanks, in particular to an optimization design method for shape and size parameters of an elastic hydraulic oil tank shell.
Background
In actual engineering, a hydraulic oil tank is a container for storing oil required by a hydraulic system during operation. The elastic hydraulic oil tank is applied to a closed hydraulic system and is used for compensating the volume difference of an asymmetric hydraulic cylinder in the hydraulic system. In the related elastic hydraulic oil tank research, the oil tank shell generally utilizes the flexibility of rubber to realize the volume change of the oil tank. In addition, the oil tank shell needs to have a pressure-bearing performance, and under a certain specific shell shape, the wall thickness of the oil tank shell is increased to meet the normal use of the oil tank, so that the mass of the oil tank is heavier, and the material cost is increased.
Therefore, under the conditions of certain pressure strength and meeting the requirement of the volume of the oil tank, the design of the oil tank shell with extremely light weight has very important significance, and different series of corresponding optimal oil tank structures can be obtained under the conditions of different pressure and volume requirements.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an optimal design method for the shape and size parameters of the shell of the elastic hydraulic oil tank, which obtains the optimal shape of the shell of the oil tank by analyzing the stress of the shell of the elastic hydraulic oil tank and ensures that the shell of the oil tank obtains better working performance under the required volume; by establishing a mathematical model of the oil tank in an optimal shape, taking the annular stress of the shell, the axial stress of the shell and the mass of the shell as an optimization objective function, taking the volume and the machining size of the shell of the elastic hydraulic oil tank as constraint conditions, and optimizing the shell of the elastic hydraulic oil tank by using a multi-objective optimization algorithm, the optimal structural parameters of the shell of the elastic hydraulic oil tank are obtained, so that the oil tank can bear certain working strength, the oil tank has lighter mass, and the design and machining cost of the shell of the oil tank is effectively reduced.
The invention provides an optimal design method for shape and size parameters of an elastic hydraulic oil tank shell, which comprises the following specific implementation steps of:
s1, determining the shape of the elastic hydraulic oil tank shell according to the structural volume and the internal working pressure of the elastic hydraulic oil tank:
s11, respectively establishing three-dimensional models of a triangular shell, a cylindrical shell and an elliptical shell of the elastic hydraulic oil tank under the condition that the volume of the elastic hydraulic oil tank is fixed;
s12, taking the maximum working pressure of the elastic hydraulic oil tank in the working state as a constraint condition, and carrying out fluid-solid coupling analysis on the elastic hydraulic oil tanks in the three different shapes established in the S11 to respectively obtain three parameters of the maximum deformation, the maximum stress and the maximum strain of the elastic hydraulic oil tanks in the different shapes;
s13, comparing the maximum deformation parameter, the maximum stress parameter and the maximum strain parameter of the elastic hydraulic oil tank in different shapes obtained in the S12, and obtaining the optimal shape of the oil tank shell by taking the minimum value of the three parameters in different shapes as a constraint condition;
s2, establishing a mathematical model of the volume of the elastic hydraulic oil tank shell:
s21, determining the volume of the elastic hydraulic oil tank shell according to the basic parameters and the geometric relationship of the elastic hydraulic oil tank shell, wherein the volume expression is as follows:
Figure BDA0003719032930000021
wherein r is the radius of the arc of the inner wall of the shell, h is the half height of the inner wall of the shell, and A is the distance between the arc dot of the inner wall of the shell and the central axis;
s22, according to independent variables in the mathematical model of the elastic hydraulic oil tank shell, taking the wall thickness t of the shell, the half included angle theta of the arc of the inner wall of the shell, the radius R of the arc of the inner wall of the shell and the radius R of the sealing end face circle of the shell as optimization parameters of the shape of the elastic hydraulic oil tank shell;
s3, establishing an elastic hydraulic oil tank shell performance index parameter model and establishing an optimization objective function according to shell circumferential stress, shell axial stress and shell mass;
s4, respectively establishing constraint conditions according to the volume and the machining size of the elastic hydraulic oil tank shell;
s5, under the constraint conditions of the multi-objective optimization function of S3 and S4, optimizing the elastic hydraulic oil tank shell by using a multi-objective optimization algorithm to obtain an optimal solution set of the elastic hydraulic oil tank shell under three optimization targets of minimum shell hoop stress, minimum shell axial stress and minimum shell mass;
s6, establishing a comprehensive evaluation function of the elastic hydraulic oil tank shell according to the annular stress of the shell, the axial stress of the shell and the quality of the shell, and analyzing the optimal solution set of the elastic hydraulic oil tank shell to obtain the optimal structural parameters of the elastic hydraulic oil tank shell;
s7, performing strength check on the optimal structure parameters of the elastic hydraulic oil tank shell obtained in the S6, and if the strength is qualified, obtaining the optimal structure and the optimal structure parameters of the elastic hydraulic oil tank shell; if the strength fails, the process returns to S6.
Preferably, in S21, the basic parameters of the elastic hydraulic oil tank include a sealing end face circle radius R, an inner wall arc radius R, an arc length L of the ellipse part, a distance a between the inner wall arc dots and the central axis, and a difference B between the distance B between the inner wall arc dots and the central axis and the sealing end face circle radius.
It is preferable that in S22, the variation range of the casing wall thickness t is 4mm to 10mm, the variation range of the half angle θ of the arc of the casing inner wall is 15 to 90 °, the variation range of the radius R of the arc of the casing inner wall is 20 to 130mm, and the variation range of the radius R of the circle of the casing sealing end face is 40 to 140 mm.
Preferably, the specific step of step S3 includes:
s31, establishing an expression of the hoop stress of the shell expressed by optimized parameters according to the stress of the cross section of the elastic hydraulic oil tank shell after the shell is longitudinally cut, wherein the expression comprises the following steps:
Figure BDA0003719032930000031
wherein σ θ The circumferential stress of the shell is represented as p, the maximum working pressure of the oil tank shell is represented as R, the radius of a sealing end face of the shell is represented as t, the wall thickness of the shell is represented as t, the radius of an arc of the inner wall of the shell is represented as R, and theta is a half included angle of the arc of the inner wall of the shell;
s32, according to stress analysis of a cross section of the elastic hydraulic oil tank shell after transverse cutting at the center axis, establishing an expression of shell axial stress expressed by optimized parameters as follows:
Figure BDA0003719032930000032
wherein σ z Is the shell axial stress; p is the maximum working pressure of the oil tank shell, R is the radius of the sealing end face of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell;
s33, establishing an expression of the mass of the elastic hydraulic oil tank shell according to the volume of the elastic hydraulic oil tank shell and the density of the material of the oil tank shell as follows:
Figure BDA0003719032930000033
wherein m is rubber Rho is the shell mass, rho is the density of the shell material of the oil tank, R is the circular radius of the sealed end face of the shell, t is the shell wall thickness, R is the circular arc radius of the inner wall of the shell, theta is the half included angle of the circular arc of the inner wall of the shell, a is the circular ring width, and b is the circular ring thickness;
s34, according to the expressions established by S31, S32 and S33, establishing the expression of the multi-objective optimization function of the elastic hydraulic oil tank shell as follows:
f＝min(f 1 ,f 2 ,f 3 )。
preferably, in step S4, the volume constraint conditional expression is as follows:
Figure BDA0003719032930000041
v is the volume of the oil tank shell, R is the radius of the sealing end face circle of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell;
the processing size constraint conditional expression is as follows:
Figure BDA0003719032930000042
wherein R is the radius of the sealing end face circle of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, theta is the half included angle of the arc of the inner wall of the shell, and a is the width of the ring.
Preferably, in step S6, the expression of the comprehensive evaluation function is as follows:
Figure BDA0003719032930000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003719032930000044
is a function of the circumferential stress of the oil tank shell,
Figure BDA0003719032930000045
as a function of axial stress of the tank shell, f m As a function of the mass of the tank shell,
Figure BDA0003719032930000046
f m0 is an initial acceptable value, λ i Is a relative coefficient, and is a coefficient related to the fuel tank shell performance index weighting coefficient.
Compared with the prior art, the invention has the following advantages:
1. the invention solves the problems of the selection of the optimal shell shape of the elastic hydraulic oil tank and the selection of the optimal parameters thereof, is beneficial to the design of the oil tank shell under different volumes and oil tank pressures, and meets the high-efficiency design of the oil tank shell of different series and related performance indexes.
2. The invention solves the problem of selecting the optimal shape of the shell of the traditional elastic oil tank; the design and processing cost of the oil tank is reduced, the lightest weight is obtained under the condition of the same strength, and the oil tank has the advantage of light weight.
3. The invention has important significance in designing the oil tank shell with extremely light weight under the conditions of certain pressure strength and meeting the volume requirement of the oil tank, and can obtain different corresponding series of optimal oil tank structures under the conditions of different pressure and volume requirements.
Drawings
FIG. 1 is a flow chart of the method for optimally designing the shape and the size parameters of the shell of the elastic hydraulic oil tank;
FIG. 2 is a comparison graph of results of simulation of triangular, cylindrical and elliptical shells in the method for optimizing the shape and size parameters of the shell of the elastic hydraulic oil tank of the present invention;
FIG. 3 is a dimension parameter diagram of the cross section of an elliptical shell in the optimized design method for the shape and dimension parameters of the shell of the elastic hydraulic oil tank;
FIG. 4 is a parameter diagram of the cross-sectional area of the hydraulic oil tank shell in the method for optimizing the shape and size parameters of the elastic hydraulic oil tank shell according to the invention;
FIG. 5 is a schematic diagram of the hoop stress of the hydraulic oil tank shell in the optimal design method for the shape and the size parameters of the elastic hydraulic oil tank shell according to the invention;
FIG. 6 is a schematic view of the axial stress of the hydraulic oil tank shell in the optimized design method for the shape and the size parameters of the elastic hydraulic oil tank shell;
FIG. 7 is a schematic diagram of the overall structural parameters of the oil tank shell in the optimization design method for the shape and the size parameters of the elastic hydraulic oil tank shell;
FIG. 8 is a graph of the relationship between the circumferential stress and the axial stress of the shell and the wall thickness respectively in the method for optimally designing the shape and the size parameters of the shell of the elastic hydraulic oil tank;
FIG. 9 is a graph showing the relationship between the mass and the wall thickness of the housing in the method for optimizing the shape and the dimensional parameters of the housing of the elastic hydraulic oil tank according to the present invention;
FIG. 10 is an optimal solution diagram of the circumferential stress, the axial stress and the mass of the hydraulic oil tank shell in the optimal design method for the shape and the size parameters of the elastic hydraulic oil tank shell.
Detailed Description
The invention will be described in detail with reference to the accompanying drawings for describing the technical content, the achieved purpose and the efficacy of the invention.
As shown in FIG. 1, the optimal design method for the shape and the size parameters of the elastic hydraulic oil tank shell is realized by the following steps:
and S1, determining the shape of the elastic hydraulic oil tank shell according to the structural volume and the internal working pressure of the elastic hydraulic oil tank.
And S2, establishing a mathematical model of the volume of the elastic hydraulic oil tank shell.
And S3, establishing an elastic hydraulic oil tank shell performance index parameter model and establishing an optimization objective function according to the shell circumferential stress, the shell axial stress and the shell mass.
And S4, establishing constraint conditions according to the volume and the machining size of the elastic hydraulic oil tank shell respectively.
In a preferred implementation of the invention, the volume constraint expression is as follows:
Figure BDA0003719032930000061
v is the volume of the oil tank shell, R is the radius of the sealing end face circle of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell;
the machining size constraint expression is as follows:
Figure BDA0003719032930000062
wherein R is the radius of the sealing end face circle of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, theta is the half included angle of the arc of the inner wall of the shell, and a is the width of the ring.
And S5, under the constraint conditions of the multi-objective optimization function of S3 and S4, optimizing the elastic hydraulic oil tank shell by using a multi-objective optimization algorithm to obtain an optimal solution set of the elastic hydraulic oil tank shell under three optimization targets of minimum shell hoop stress, minimum shell axial stress and minimum shell mass.
S6, establishing a comprehensive evaluation function of the elastic hydraulic oil tank shell according to the annular stress of the shell, the axial stress of the shell and the quality of the shell, and analyzing the optimal solution set of the elastic hydraulic oil tank shell to obtain the optimal structural parameters of the elastic hydraulic oil tank shell.
Specifically, the expression of the comprehensive evaluation function is as follows:
Figure BDA0003719032930000063
in the formula (I), the compound is shown in the specification,
Figure BDA0003719032930000071
as a function of the hoop stress of the fuel tank shell,
Figure BDA0003719032930000072
as a function of axial stress of the tank shell, f m As a function of the mass of the tank shell,
Figure BDA0003719032930000073
f m0 is an initial acceptable value, λ i The relative coefficient is a coefficient related to the weighting coefficient of the performance index of the fuel tank shell.
S7, performing strength check on the optimal structure parameters of the elastic hydraulic oil tank shell obtained in the S6, and if the strength is qualified, obtaining the optimal structure and the optimal structure parameters of the elastic hydraulic oil tank shell; if the strength fails, the process returns to S6.
Preferably, the concrete step of determining the shape of the elastic hydraulic oil tank case at step S1 includes,
and S11, respectively establishing three-dimensional models of triangular, cylindrical and elliptical shells of the elastic hydraulic oil tank under the condition that the volume of the elastic hydraulic oil tank is fixed.
And S12, taking the maximum working pressure of the elastic hydraulic oil tank in the working state as a constraint condition, and carrying out fluid-solid coupling analysis on the elastic hydraulic oil tanks in the three different shapes established in the S11 to obtain three parameters, namely the maximum deformation, the maximum stress and the maximum strain of the elastic hydraulic oil tanks in the different shapes.
Specifically, the smaller the maximum deformation parameter is, the minimum deformation of the elastic hydraulic oil tank in the working state is indicated, the reasonable parameter obtained under the condition can enable the volume and the mass of the elastic hydraulic oil tank shell to be optimal, and the smaller the maximum stress and the maximum strain parameter is, the best working performance of the elastic hydraulic oil tank in the working state of the elastic hydraulic oil tank is indicated.
And S13, comparing the maximum deformation parameter, the maximum stress parameter and the maximum strain parameter of the elastic hydraulic oil tank in different shapes obtained in the S12, and obtaining the optimal shape of the oil tank shell by taking the minimum three parameters in different shapes as constraint conditions.
Further, the step S2 of establishing a mathematical model of the volume of the elastic hydraulic tank casing includes,
s21, calibrating the internal volume of the shell according to the basic parameters and the geometric relationship of the elastic hydraulic oil tank shell to obtain partial parameters of the shell under a certain specific volume, and determining the volume of the elastic hydraulic oil tank shell according to the parameters, wherein the volume expression is as follows:
Figure BDA0003719032930000074
wherein r is the arc radius of the inner wall of the shell; h is the half height of the inner wall of the shell; a is the distance between the arc dots on the inner wall of the shell and the central axis.
Specifically, the basic parameters of the elastic hydraulic oil tank shell comprise a sealing end face circle radius R, an inner wall arc radius R, an arc length L of an ellipse part, a distance A between an inner wall arc dot and a central axis, and a difference B between the distance between the inner wall arc dot and the central axis and the sealing end face circle radius.
And S22, according to independent variables in the mathematical model of the elastic hydraulic oil tank shell, taking the wall thickness t of the shell, the half included angle theta of the arc of the inner wall of the shell, the radius R of the arc of the inner wall of the shell and the radius R of the circle of the sealing end face of the shell as optimization parameters of the shape of the shell.
Specifically, the variable range of the shell wall thickness t is 4-10 mm, the variable range of the half included angle theta of the shell inner wall circular arc is 15-90 degrees, the variable range of the radius R of the shell inner wall circular arc is 20-130mm, and the variable range of the radius R of the shell sealing end face circle is 40-140 mm.
Further, step S3 is a specific process of establishing an elastic hydraulic oil tank shell performance index parameter model and establishing an optimization objective function as follows:
s31, establishing a circumferential stress expression of the oil tank shell expressed by the optimization parameters:
s311, on the basis of S2, establishing the cross section area of the elastic hydraulic oil tank shell after being longitudinally cut, wherein the mathematical expression of the cross section area of the oil tank shell after being longitudinally cut is as follows:
S θ ＝2(t 2 +2rt)θ
wherein S is θ The cross section area of the oil tank shell after longitudinal cutting is shown, t is the wall thickness of the shell, r is the arc radius of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell.
S312, on the basis of S311, through force analysis, the expression of the resultant force of the internal force at the cross section of the oil tank shell after being longitudinally cut is obtained as follows:
N θ ＝σ θ S θ ＝2σ θ (t 2 +2rt)θ
wherein N is θ The resultant force of internal forces, sigma, at the cross section of the fuel tank shell after longitudinal cutting θ Is the hoop stress of the casing, S θ The cross section area of the oil tank shell after longitudinal cutting is shown, t is the wall thickness of the shell, r is the arc radius of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell.
S313, the projection area expression of the oil tank shell after longitudinal cutting on the xoz plane is as follows:
S xoz ＝4Ah+2hB+2r 2 θ
wherein S is xoz The projection area of the oil tank shell longitudinally cut on the xoz plane is shown as A, the distance between an arc dot of the inner wall of the shell and a central axis is shown as h, the half height of the inner wall of the shell is shown as B, the difference value between the distance between the arc dot of the inner wall and the central axis and the radius of a circle of a sealing end face is shown as B, r is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell.
S314, the resultant force expression of the pressure inside the oil tank shell after longitudinal cutting along the y-axis direction is as follows:
F θ ＝pS xoz ＝p(4Ah+2hB+2r 2 θ)
wherein, F θ The resultant force of the internal pressure of the oil tank along the y-axis direction after the oil tank shell is longitudinally cut, p is the maximum working pressure of the oil tank shell, S xoz The projection area of the oil tank shell longitudinally cut on the xoz plane is shown as A, the distance between an arc dot of the inner wall of the shell and a central axis is shown as h, the half height of the inner wall of the shell is shown as B, the difference value between the distance between the arc dot of the inner wall and the central axis and the radius of a circle of a sealing end face is shown as B, r is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell.
S315, establishing a stress balance equation of the oil tank shell in the y-axis direction, namely F θ -N θ 0, the expression of the circumferential stress of the tank shell can be obtained as follows:
Figure BDA0003719032930000091
wherein σ θ The stress of the shell is circumferential stress, p is the maximum working pressure of the oil tank shell, A is the distance between an arc dot on the inner wall of the shell and a central axis, h is the half height of the inner wall of the shell, B is the difference value between the distance between the arc dot on the inner wall and the central axis and the radius of a circle on a sealing end surface, and r is the circumferential stress of the shellThe radius of the wall arc, theta is the half included angle of the shell inner wall arc, and t is the shell wall thickness.
S316, according to the geometrical relationship B of the basic parameters of the elastic hydraulic oil tank shell, i.e. rcos theta, h, i.e. rsin theta, A, i.e. R-B, expressing the expression of the hoop stress in the S315 by four optimization parameters of the shell wall thickness t, the half included angle theta of the shell inner wall arc, the radius R of the shell inner wall arc and the radius R of the shell sealing end face circle, and establishing the expression of the shell hoop stress expressed by the optimization parameters as follows:
Figure BDA0003719032930000092
wherein σ θ The method is characterized in that the annular stress of a shell is adopted, p is the maximum working pressure of the oil tank shell, R is the circular radius of the sealing end face of the shell, t is the wall thickness of the shell, R is the circular radius of the inner wall of the shell, and theta is the half included angle of the circular arc of the inner wall of the shell.
S32, establishing a shell axial stress expression expressed by optimization parameters:
s321, on the basis of S2, establishing the cross section area of the elastic hydraulic oil tank shell after the elastic hydraulic oil tank shell is transversely cut at the central axis, wherein the mathematical expression of the cross section area of the elastic hydraulic oil tank shell after the elastic hydraulic oil tank shell is transversely cut at the central axis is as follows:
S z ＝π[t 2 +2(r+A)t]
wherein S is z The cross section area of the middle axis after transverse cutting is shown, t is the wall thickness of the shell, r is the arc radius of the inner wall of the shell, and A is the distance between the arc dot of the inner wall of the shell and the central axis.
S322, on the basis of S321, through stress analysis, the expression of the resultant force of the internal force at the cross section after the transverse cutting at the center axis of the oil tank shell is obtained as follows:
N z ＝S z σ z ＝π[t 2 +2(r+A)t]σ z
wherein N is z The resultant force sigma of the internal forces at the cross section of the oil tank shell after the transverse cutting at the positive axis z Is the axial stress of the shell, S z The cross-sectional area of the cross section of the center shaft after transverse cutting, t is the wall thickness of the shell, and r isThe radius of the arc of the inner wall of the shell, A is the distance between the arc and the circular point of the inner wall of the shell and the central axis.
S323, the projection area expression of the oil tank shell after being transversely cut at the central axis on the xoy plane is as follows:
S xoy ＝π(A+r) 2
wherein S is xoy The projection area of the oil tank shell on the xoy plane is transversely cut at the right middle axis, A is the distance between an arc dot of the inner wall of the shell and the middle axis, and r is the arc radius of the inner wall of the shell.
S324, the expression of the acting resultant force of the internal pressure of the oil tank shell after being transversely cut at the central axis along the z-axis direction is as follows:
F z ＝pS xoy ＝pπ(A+r) 2
wherein, F z The resultant force of the internal pressure of the oil tank along the z-axis direction after the positive axis of the oil tank shell is transversely cut is shown, p is the maximum working pressure of the oil tank shell, S xoy The projected area of the xoy plane is transversely cut at the right middle axis of the oil tank shell, A is the distance between an arc dot of the inner wall of the shell and the middle axis, and r is the arc radius of the inner wall of the shell.
S325, establishing a stress balance equation of the oil tank shell in the z-axis direction, namely F z -N z 0, the expression for axial stress can be found as:
Figure BDA0003719032930000101
wherein σ z The axial stress of the shell is represented by p, the maximum working pressure of the oil tank shell is represented by A, the distance between an arc circular point of the inner wall of the shell and a central axis is represented by r, the radius of the arc of the inner wall of the shell is represented by t, and the wall thickness of the shell is represented by t.
S326, according to the geometrical relationship B of the basic parameters of the elastic hydraulic oil tank shell, namely rcos theta and A, namely R-B, expressing the axial stress expression in the S325 by four optimization parameters of the shell wall thickness t, the half included angle theta of the shell inner wall circular arc, the radius R of the shell inner wall circular arc and the radius R of the shell sealing end face circle, and establishing the expression of the shell axial stress expressed by the optimization parameters as follows:
Figure BDA0003719032930000102
wherein σ z Is the shell axial stress; p is the maximum working pressure of the oil tank shell, R is the radius of the sealing end face of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell.
S33, establishing an expression of the mass of the elastic hydraulic oil tank shell according to the volume of the elastic hydraulic oil tank shell and the density of the material of the oil tank shell:
s331, establishing a volume expression of the rubber shell of the oil tank according to the geometric relationship between the volume of the elastic hydraulic oil tank shell and basic parameters of the elastic hydraulic oil tank shell, wherein the volume expression comprises the following steps:
Figure BDA0003719032930000111
wherein, V shell The volume of the rubber shell of the oil tank is A, the distance between an arc dot of the inner wall of the shell and a central axis is A, the arc radius of the inner wall of the shell is R, the wall thickness of the shell is t, the half height of the inner wall of the shell is h, the circle radius of the sealing end face of the shell is R, the diameter of the port of the shell of the oil tank is d, and the thickness of a ring is b.
S332, establishing an expression of the mass of the elastic hydraulic oil tank shell according to the density of the oil tank shell material as follows:
Figure BDA0003719032930000112
wherein, V shell Is the volume of the rubber shell of the oil tank, m rubber ρ is the density of the tank shell material, which is the shell mass.
S333, according to the geometrical relation B (rcos theta), h (rsin theta), A (R-B) of the basic parameters of the elastic hydraulic oil tank shell,
Figure BDA0003719032930000113
Expressing the mass of the oil tank shell in S314 byThe method comprises the following steps of (1) expressing four optimized parameters of the wall thickness t of a shell, a half included angle theta of an arc of the inner wall of the shell, the radius R of the arc of the inner wall of the shell and the radius R of a circle of a sealing end face of the shell, and establishing an expression for establishing the quality of the shell of the elastic hydraulic oil tank expressed by the optimized parameters as follows:
Figure BDA0003719032930000114
wherein m is rubber The shell mass; rho is the density of the material of the oil tank shell, R is the radius of the circular end face of the shell seal, t is the wall thickness of the shell, R is the radius of the circular arc of the inner wall of the shell, theta is the half included angle of the circular arc of the inner wall of the shell, a is the width of the circular ring, and b is the thickness of the circular ring.
S34, according to the expressions established by S31, S32 and S33, establishing the expression of the multi-objective optimization function of the elastic hydraulic oil tank shell as follows:
f＝min(f 1 ,f 2 ,f 3 )。
the following describes the method for optimizing the shape and size parameters of the housing of the elastic hydraulic oil tank according to the present invention with reference to the following embodiments:
s1, determining the shape of the elastic hydraulic oil tank shell according to the structural volume and the internal working pressure of the elastic hydraulic oil tank:
and S11, under the condition that the volume of the elastic hydraulic oil tank is constant, building models in different shapes, and respectively building three-dimensional models of triangular, cylindrical and elliptical shells of the elastic hydraulic oil tank, as shown in figure 2.
And S12, taking the maximum working pressure of the elastic hydraulic oil tank in the working state as a constraint condition, and performing fluid-solid coupling simulation analysis on the elastic hydraulic oil tanks in the three different shapes established in the S11 by using fluid simulation software to obtain three parameters, namely the maximum deformation, the maximum stress and the maximum strain of the elastic hydraulic oil tanks in the different shapes.
S13, comparing the simulation results of the maximum deformation parameter, the maximum stress parameter and the maximum strain parameter of the elastic hydraulic oil tank in different shapes obtained in S12 as shown in Table 1, and obtaining the following results by comparing the simulation results of shells in different shapes: the maximum deformation, the maximum strain and the maximum stress of the oval shell are all minimum, the three parameters are respectively reduced by 78.5%, 55.9% and 28.1% compared with the triangular shell, and the three parameters are respectively reduced by 79.7%, 43.4% and 23.4% compared with the cylindrical shell, so that the working performance of the oval shell under the same volume can be determined to be optimal under the shells of three different shapes, and the shape of the shell is determined to be oval.
TABLE 1 simulation analysis results of shells of different shapes
Figure BDA0003719032930000121
S2, on the basis that the shape of the oil tank shell is determined to be oval at S1, as shown in figures 3 and 7, a mathematical model of the volume of the elastic hydraulic oil tank shell is established:
s21, determining the volume of the elastic hydraulic oil tank shell according to the basic parameters and the geometric relationship of the elastic hydraulic oil tank shell, wherein the volume expression is as follows:
Figure BDA0003719032930000122
wherein r is the radius of the arc of the inner wall of the shell, h is the half height of the inner wall of the shell, and A is the distance between the arc dot of the inner wall of the shell and the central axis;
s22, according to independent variables in the mathematical model of the elastic hydraulic oil tank shell, as shown in figures 8 and 9, taking the wall thickness t of the shell, the half included angle theta of the arc of the inner wall of the shell, the radius R of the arc of the inner wall of the shell and the radius R of the circle of the sealing end face of the shell as optimization parameters of the shape of the shell; determining the range of independent variables, wherein the variable range of the wall thickness t of the shell is 4-10 mm, the variable range of the half included angle theta of the arc of the inner wall of the shell is 15-90 degrees, the variable range of the radius R of the arc of the inner wall of the shell is 20-130mm, and the variable range of the radius R of the sealing end face circle of the shell is 40-140 mm.
S3, establishing an elastic hydraulic oil tank shell performance index parameter model and establishing an optimization objective function according to the shell circumferential stress, the shell axial stress and the shell quality:
s31, on the basis of S2, establishing an expression of the cross-sectional area of the elastic hydraulic oil tank shell after being longitudinally cut, as shown in FIG. 4. As shown in fig. 5, a circumferential stress diagram of the oil tank shell is established, and according to the geometrical relations B ═ rcos θ, h ═ rsin θ and a ═ R-B of the basic parameters of the elastic hydraulic oil tank shell, the expression of the circumferential stress is represented by four optimized parameters of the shell wall thickness t, the half included angle θ of the shell inner wall circular arc, the radius R of the shell inner wall circular arc and the radius R of the shell sealing end face circle, and the expression of the shell circumferential stress represented by the optimized parameters is established as follows:
Figure BDA0003719032930000131
wherein σ θ The circumferential stress of the shell is shown, p is the maximum working pressure of the oil tank shell, the value in the embodiment is 0.06MPa, R is the radius of the sealing end face circle of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell.
S32, on the basis of S2, a mathematical expression of the cross section area of the elastic hydraulic oil tank shell after being transversely cut at the right central axis is established. As shown in fig. 6, an axial stress diagram of the oil tank shell is established, according to the geometrical relationship B-rcos θ and a-R-B of the basic parameters of the elastic hydraulic oil tank shell, the expression of the axial stress is represented by four optimized parameters of the shell wall thickness t, the half included angle θ of the shell inner wall circular arc, the radius R of the shell inner wall circular arc and the radius R of the shell sealing end face circle, and the expression of the shell axial stress represented by the optimized parameters is established as follows:
Figure BDA0003719032930000132
wherein σ z In the embodiment, the axial stress of the shell is represented by p, the maximum working pressure of the oil tank shell is represented by 0.06MPa, R is the radius of the sealing end face of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell.
S33, according to the geometrical relation of the basic parameters of the elastic hydraulic oil tank shell, B is rcos theta, h is rsin theta, A is R-B,
Figure BDA0003719032930000141
The expression of the quality of the oil tank shell is expressed by four optimized parameters of the wall thickness t of the shell, a half included angle theta of an arc of the inner wall of the shell, the radius R of the arc of the inner wall of the shell and the radius R of a circle of a sealing end face of the shell, and the expression of the quality of the elastic hydraulic oil tank shell expressed by the optimized parameters is established as follows:
Figure BDA0003719032930000142
wherein m is rubber For the shell quality, ρ is the density of the shell material of the oil tank, R is the radius of the shell seal end face circle, t is the shell wall thickness, R is the radius of the shell inner wall arc, θ is the half included angle of the shell inner wall arc, a is the ring width, 27mm is taken in this embodiment, and b is the ring thickness, 21mm is taken in this embodiment.
S34, obtaining the expression of the multi-objective optimization function of the elastic hydraulic oil tank shell according to the expressions established by the S31, the S32 and the S33, wherein the expression of the multi-objective optimization function is as follows:
f＝min(f 1 ,f 2 ,f 3 )。
s4, respectively establishing constraint conditions according to the volume and the machining size of the elastic hydraulic oil tank shell:
the volume constraint condition expression of the elastic hydraulic oil tank shell is as follows:
Figure BDA0003719032930000143
wherein, V is the volume of the oil tank shell, and the volume of the embodiment is 7.2L; r is the circle radius of the sealing end surface of the shell; r is the arc radius of the inner wall of the shell; theta is a half included angle of the arc of the inner wall of the shell;
the machining size constraint expression is as follows:
Figure BDA0003719032930000144
wherein, R is casing sealing end face circle radius, t is casing wall thickness, and R is shells inner wall circular arc radius, and theta is shells inner wall circular arc half contained angle, and a is the ring width, takes 27mm in this embodiment.
S5, under the constraint conditions of the multi-objective optimization function of S3 and S4, optimizing the elastic hydraulic oil tank shell by using a multi-objective optimization algorithm to obtain an optimal solution set of the elastic hydraulic oil tank shell under three optimization targets of minimum shell hoop stress, minimum shell axial stress and minimum shell mass, as shown in FIG. 10.
S6, establishing a comprehensive evaluation function of the elastic hydraulic oil tank shell according to the annular stress of the shell, the axial stress of the shell and the quality of the shell, analyzing the optimal solution set of the elastic hydraulic oil tank shell by using the comprehensive evaluation function to obtain the optimal structural parameters of the elastic hydraulic oil tank shell, wherein the specific expression of the comprehensive evaluation function in the embodiment is as follows:
Figure BDA0003719032930000151
in the formula, λ 1 、λ 2 And λ 3 Respectively taking relative coefficients of circumferential stress, axial stress and mass, and respectively taking lambda 1 ＝0.3、λ 2 0.2 and λ 3 ＝0.5。
And evaluating the optimal solution in the Pareto frontier obtained after the multi-objective optimization by using the comprehensive evaluation function to finally obtain more proper design parameters of the oil tank shell. According to the expansion coefficient required by the oil tank shell and the analysis result of the rubber tensile experiment, taking
Figure BDA0003719032930000152
And f m0 The evaluation results of each scheme in the optimal solution can be obtained 2.5 kg. And analyzing the optimal solution of the oil tank shell according to the comprehensive evaluation function.
Satisfy the circumferential stress of the oil tank shell
Figure BDA0003719032930000153
And axial stress
Figure BDA0003719032930000154
At the same time less than 0.8MPa and a shell mass f m Under the condition that the thickness t of the shell is not more than 2.5kg, the optimal structural parameters obtained by comprehensive analysis are that the wall thickness t of the shell is 7.14mm, the half included angle theta of the arc of the inner wall of the shell is 76.8 degrees, the radius R of the arc of the inner wall of the shell is 61.94mm, and the radius R of the circle of the sealing end face of the shell is 101.79 mm.
S7, performing three-dimensional model modeling on the optimal structure parameters of the elastic hydraulic oil tank shell obtained in the S6, checking the strength by using simulation software, and if the strength is qualified, obtaining the optimal structure and the optimal structure parameters of the elastic hydraulic oil tank shell; if the strength fails, the process returns to S6.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope defined by the claims of the present invention.

Claims (6)

1. An optimal design method for shape and size parameters of a shell of an elastic hydraulic oil tank is characterized by comprising the following specific implementation steps:
s1, determining the shape of the elastic hydraulic oil tank shell according to the structural volume and the internal working pressure of the elastic hydraulic oil tank:
s11, respectively establishing three-dimensional models of a triangular shell, a cylindrical shell and an elliptical shell of the elastic hydraulic oil tank under the condition that the volume of the elastic hydraulic oil tank is fixed;
s12, taking the maximum working pressure of the elastic hydraulic oil tank in the working state as a constraint condition, and carrying out fluid-solid coupling analysis on the elastic hydraulic oil tanks in the three different shapes established in the S11 to respectively obtain three parameters of the maximum deformation, the maximum stress and the maximum strain of the elastic hydraulic oil tanks in the different shapes;
s13, comparing the maximum deformation parameter, the maximum stress parameter and the maximum strain parameter of the elastic hydraulic oil tank in different shapes obtained in the S12, and obtaining the optimal shape of the oil tank shell by taking the minimum value of the three parameters in different shapes as a constraint condition;
s2, establishing a mathematical model of the volume of the elastic hydraulic oil tank shell:
s21, determining the volume of the elastic hydraulic oil tank shell according to the basic parameters and the geometric relationship of the elastic hydraulic oil tank shell, wherein the volume expression is as follows:
Figure FDA0003719032920000011
wherein r is the radius of the arc of the inner wall of the shell, h is the half height of the inner wall of the shell, and A is the distance between the arc dot of the inner wall of the shell and the central axis;
s22, according to independent variables in the mathematical model of the elastic hydraulic oil tank shell, taking the wall thickness t of the shell, the half included angle theta of the arc on the inner wall of the shell, the radius R of the arc on the inner wall of the shell and the radius R of the circle on the sealing end face of the shell as optimization parameters of the shape of the elastic hydraulic oil tank shell;
s3, establishing an elastic hydraulic oil tank shell performance index parameter model and establishing an optimization objective function according to shell circumferential stress, shell axial stress and shell mass;
s4, respectively establishing constraint conditions according to the volume and the machining size of the elastic hydraulic oil tank shell;
s5, under the constraint conditions of the multi-objective optimization function of S3 and S4, optimizing the elastic hydraulic oil tank shell by using a multi-objective optimization algorithm to obtain an optimal solution set of the elastic hydraulic oil tank shell under three optimization targets of minimum shell hoop stress, minimum shell axial stress and minimum shell mass;
s6, establishing a comprehensive evaluation function of the elastic hydraulic oil tank shell according to the annular stress of the shell, the axial stress of the shell and the quality of the shell, and analyzing the optimal solution set of the elastic hydraulic oil tank shell to obtain the optimal structural parameters of the elastic hydraulic oil tank shell;
s7, performing strength check on the optimal structure parameters of the elastic hydraulic oil tank shell obtained in the S6, and if the strength is qualified, obtaining the optimal structure and the optimal structure parameters of the elastic hydraulic oil tank shell; if the strength fails, the process returns to S6.
2. The method as claimed in claim 1, wherein the basic parameters of the flexible hydraulic tank casing include a sealing end face circle radius R, an inner wall arc radius R, an arc length L of the ellipse part, a distance a between the inner wall arc and circular point and a central axis, and a difference B between the distance B between the inner wall arc and circular point and the central axis and the sealing end face circle radius at S21.
3. The method for optimizing shape and size parameters of a housing of an elastic hydraulic oil tank as claimed in claim 1, wherein in S22, the variable range of the wall thickness t of the housing is 4mm to 10mm, the variable range of the half included angle θ of the circular arc of the inner wall of the housing is 15 mm to 90 °, the variable range of the radius R of the circular arc of the inner wall of the housing is 20 mm to 130mm, and the variable range of the radius R of the circle of the sealing end face of the housing is 40mm to 140 mm.
4. The method for optimally designing the shape and the size parameters of the shell of the elastic hydraulic oil tank as claimed in claim 1, wherein the specific steps of the step S3 comprise the following steps:
s31, establishing an expression of the shell hoop stress expressed by optimized parameters according to the stress of the cross section of the elastic hydraulic oil tank shell after being longitudinally cut, wherein the expression is as follows:
Figure FDA0003719032920000021
wherein σ θ The method is characterized in that the annular stress of a shell is adopted, p is the maximum working pressure of the shell of an oil tank, R is the circular radius of the sealing end surface of the shell, t is the wall thickness of the shell, R is the circular radius of the inner wall of the shell, and theta is the half included angle of the circular arc of the inner wall of the shell;
s32, according to stress analysis of a cross section of the elastic hydraulic oil tank shell after transverse cutting at the center axis, establishing an expression of shell axial stress expressed by optimized parameters as follows:
Figure FDA0003719032920000022
wherein σ z Axial stress of the shell; p is the maximum working pressure of the oil tank shell, R is the radius of the sealing end face of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell;
s33, establishing an expression of the mass of the elastic hydraulic oil tank shell according to the volume of the elastic hydraulic oil tank shell and the density of the material of the oil tank shell as follows:
Figure FDA0003719032920000031
wherein m is rubber The mass of the shell is rho, the density of the shell material of the oil tank is rho, the radius of the sealing end face of the shell is R, the wall thickness of the shell is t, the radius of the arc of the inner wall of the shell is R, the included angle theta is the half included angle of the arc of the inner wall of the shell, a is the width of the ring, and b is the thickness of the ring;
s34, according to the expressions established by S31, S32 and S33, establishing the expression of the multi-objective optimization function of the elastic hydraulic oil tank shell as follows:
f＝min(f 1 ,f 2 ,f 3 )。
5. the optimum design method for shape and size parameters of elastic hydraulic oil tank shell according to claim 1, characterized in that in step S4, the volume constraint condition expression is as follows:
Figure FDA0003719032920000032
v is the volume of the oil tank shell, R is the radius of the sealing end face circle of the shell, R is the radius of the arc of the inner wall of the shell, and theta is the half included angle of the arc of the inner wall of the shell;
the processing size constraint conditional expression is as follows:
Figure FDA0003719032920000033
wherein R is the radius of the sealing end face circle of the shell, t is the wall thickness of the shell, R is the radius of the arc of the inner wall of the shell, theta is the half included angle of the arc of the inner wall of the shell, and a is the width of the ring.
6. The method for optimally designing the shape and the dimensional parameters of the elastic hydraulic oil tank shell according to the claim 1, wherein in the step S6, the expression of the comprehensive evaluation function is as follows:
Figure FDA0003719032920000034
in the formula (I), the compound is shown in the specification,
Figure FDA0003719032920000041
as a function of the hoop stress of the fuel tank shell,
Figure FDA0003719032920000042
as a function of axial stress of the tank shell, f m As a function of the mass of the tank shell,
Figure FDA0003719032920000043
f m0 is an initial acceptable value, λ i The relative coefficient is a coefficient related to the weighting coefficient of the performance index of the fuel tank shell.
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