CN103294852A - Linear variable-thickness pressing plate structure and its size optimization method and application - Google Patents

Abstract

The invention provides a linear variable-thickness pressing plate structure and its size optimization method and application. An optimization linear variable-thickness pressing plate parameter lambda<*> is provided, and according to the same, the central thickness and edge thickness of the pressing plate are obtained, so that the size of the linear variable-thickness pressing plate structure is optimized. The linear variable-thickness pressing plate structure and its size optimization method and application have the advantages that according to engineering practice, the linear variable-thickness pressing plate is used to replace a pressing plate in the same thickness, so that materials are saved, weight is reduced and the linear variable-thickness pressing plate is applicable to engineering; the derivation method is freed of mathematic difficulties by building a model, and the precision of the structure meets the engineering design requirements by using the energy principle in mechanics and the theory of calculating the variable thickness of the pressing plate; the method of optimizing the variable thickness parameter of the pressing plate is creative and novel and is significant both theoretically and economically.

Description

A kind of linear thickening degree rectangular platen structure and dimensionally-optimised methods and applications thereof

Technical field

The invention belongs to the structural dimension optimization technical field, be specifically related to a kind of linear thickening degree rectangular platen structure and dimensionally-optimised methods and applications thereof.

Background technology

Pressure wringing machine, the pressure filter used always on the engineering, its main pressing plate all is that main pressing plate is considered by equal thickness when design.In fact, from economizing the angle that material loss of weight and engineering are suitable for, should follow Optimum design of engineering structure, be replaced in the equal thickness plate to become thick plates.

There is the design of thickening degree in force structures such as existing pressing plate, if the design of existing thickening degree is with finite element and the finite difference numerical solution that grades, all be similar to, rather than represent with the function solution, be unfavorable for inquiring into the mutual relationship that exists between each amount, there is the problem of complex structure, difficult processing in She Ji structure simultaneously.

Summary of the invention

The object of the present invention is to provide a kind of linear thickening degree rectangular platen structure and dimensionally-optimised methods and applications thereof.

For achieving the above object, the present invention has adopted following technical scheme:

A kind of linear thickening degree rectangular platen structure, this pressure plate structure is the assembly that truncated rectangular pyramids and rectangular parallelepiped are formed, each incline equal in length of described truncated rectangular pyramids, the bottom surface of truncated rectangular pyramids links to each other with a side surface of rectangular parallelepiped, the corresponding coincidence with the edge on described surface in the edge of described bottom surface.

The angle that adjacent two sides of described truncated rectangular pyramids become with the bottom surface of truncated rectangular pyramids is respectively α and α ', and α and α ' satisfy following formula:

$\left.\begin{array}{c}\mathrm{tg}{\mathrm{\&alpha;}}^{\&prime;}=\frac{2\mathrm{\&lambda;}}{(1-\mathrm{\&lambda;})a}{h}_{2x}\\ \mathrm{tg\&alpha;}=\frac{2\mathrm{\&lambda;}}{(1-\mathrm{\&lambda;})b}{h}_{2y}\end{array}\right\}$

, wherein, h _2x, h _2yExpression pressure plate structure bound thickness, h _2x=h _2y, a, b represent half of the long limit of rectangular platen structure and bond length respectively, λ represents thickening degree parameter, 0≤λ≤0.5.

Described h _2xGet h _2x ^JustAnd h _2x ^{By force}In maximal value, h _2x ^JustBe shown below:

h _2x ^{By force}Be shown below:

, wherein, a 〉=b, μ represents the Poisson ratio of pressure plate structure material, and E represents the Young modulus of pressure plate structure material, and q represents to act on the lip-deep well-distributed pressure of pressure plate structure, the permission amount of deflection of [w] expression pressure plate structure, the permissible stress of [σ] expression pressure plate structure material.

The upper bottom surface of described truncated rectangular pyramids is to obtain after processing for the plane that installs and fixes spherical linkage by the place, summit at corresponding rectangular pyramid.

The adjacent side of described truncated rectangular pyramids connects at corresponding incline place rounding off.

The dimensionally-optimised method of above-mentioned linear thickening degree rectangular platen structure may further comprise the steps:

1) calculates the pressure plate structure bound thickness: get h _2x ^JustAnd h _2x ^{By force}In maximal value as bound thickness, h _2x ^JustBe shown below:

h _2x ^{By force}Be shown below:

Wherein, a 〉=b, a, b represent half of the long limit of rectangular platen structure and bond length respectively, μ represents the Poisson ratio of pressure plate structure material, and E represents the Young modulus of pressure plate structure material, and q represents to act on the lip-deep well-distributed pressure of pressure plate structure, the permission amount of deflection of [w] expression pressure plate structure, the permissible stress of [σ] expression pressure plate structure material;

2) calculate the pressure plate structure center thickness:

λ represents thickening degree parameter, 0≤λ≤0.5;

3) through step 2) after, process the plane that is used for installing and fixing spherical linkage at the place, summit of rectangular pyramid, make rectangular pyramid become truncated rectangular pyramids.

The application of above-mentioned linear thickening degree rectangular platen structure in center and fixedly spherical linkage is connected, the plate face is subjected to the well-distributed pressure effect pressing plate.

Beneficial effect of the present invention is:

The present invention is directed to actual engineering problem, adopt the energy principle of Elasticity, at the member even, continuous, that isotropic material is made, by finding the solution integral equation, carry out dimensionally-optimised design for the center with the pressure plate structure that fixedly spherical linkage is connected, the plate face is subjected to the well-distributed pressure effect, major advantage point of the present invention is as follows: 1) the present invention is from engineering reality, replace the equal thickness pressing plate with linear thickening degree pressing plate, economize the material loss of weight, simple in structure, be applicable to engineering.2) the present invention makes derivation method avoid mathematical difficulty by setting up model, utilizes the energy principle in the mechanics, and gained calculates the theory of pressing plate thickening degree, and its precision satisfies the engineering design requirement.3) the present invention provides optimization rectangular platen thickening degree parameter lambda intuitively ^*Method, λ ^*Be the upper limit of 0≤λ≤0.5, i.e. λ ^*=0.5, the intention novelty has double meaning theoretical and economically.

Description of drawings

Fig. 1 is the front view of pressure plate structure of the present invention;

Fig. 2 is the vertical view of pressure plate structure of the present invention;

Fig. 3 is one of schematic cross-section of Fig. 1;

Fig. 4 be Fig. 1 schematic cross-section two;

Fig. 5 is the one-piece construction synoptic diagram of pressing plate of the present invention;

Among the figure: 1 is rectangular parallelepiped, and 2 is truncated rectangular pyramids, and OX, OY and OZ represent with O to be the coordinate axis of the rectangular coordinate system of initial point, O ₁The Lian Liandian of expression spherical linkage.

Embodiment

The invention will be further described below in conjunction with drawings and Examples.

Referring to Fig. 1-Fig. 5, linear thickening degree rectangular platen structure of the present invention is the assembly that truncated rectangular pyramids and rectangular parallelepiped are formed, each incline equal in length of described truncated rectangular pyramids, the bottom surface of truncated rectangular pyramids links to each other with a side surface of rectangular parallelepiped, the corresponding coincidence with the edge on described surface in the edge of described bottom surface, the adjacent side of described truncated rectangular pyramids connects at corresponding incline place rounding off, and being used for eliminating stress concentrating influences.

Key issue of the present invention is: the energy principle of utilizing Elasticity, by finding the solution integral equation, released for the center and be connected with fixing spherical linkage, the plate face is subjected to the linear thickening degree rectangular platen structure optimization design theory of well-distributed pressure effect, and main innovate point is that optimization plate thickness variable element λ is provided intuitively ^*System of selection, calculate and lay a good foundation for further optimizing thickening degree pressure plate structure size.

(1) according to the Optimization of Mechanical Design theory, the function that is used for competition design quality is called objective function.Here select thickness of compressive plate h _2x, h _1x, tg α is objective function.

1) press rigidity condition: when a 〉=b,

$h_{2x}\&GreaterEqual;(1-\mathrm{\&lambda;})\mathrm{ab}{\left[\frac{0.8(1-{\mathrm{\&mu;}}^2)\mathrm{abq}}{E\left[w\right]{(a^2+b^2)}^2(0.25-0.05{\mathrm{\&lambda;}}^3+0.26{\mathrm{\&lambda;}}^2-0.3\mathrm{\&lambda;})}\right]}^{\frac{1}{3}}---\left(1\right)$

$h_{2x}=h_{2y},h_{1x}=h_{1y}=\frac{1+\mathrm{\&lambda;}}{1-\mathrm{\&lambda;}}{h}_{2x}=\frac{1+\mathrm{\&lambda;}}{1-\mathrm{\&lambda;}}{h}_{2y}$

In the formula (1), the Poisson ratio of μ---laminate material;

λ---pressing plate thickening degree parameter is generally got 0≤λ≤0.5, optimal value λ ^*=0.5;

2a---pressing plate is along ox direction of principal axis boundary length, and unit is mm;

2b---pressing plate is along oy direction of principal axis boundary length, and unit is mm;

The Young modulus of E---laminate material, unit is GPa;

Q---act on the well-distributed pressure on the clamp surface, unit is MPa;

The permission amount of deflection of [w]---pressing plate, unit is mm;

h _1x, h _1y---the thickness of pressing plate center, unit are mm, h _1x=h _1y

h _2x, h _2y---bound thickness around the pressing plate, unit is mm, h _2x=h _2y

2) press strength condition: when a 〉=b,

$h_{2x}\&GreaterEqual;\frac{(1-\mathrm{\&lambda;})\mathrm{ab}}{{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA00003186536000022.png"\; state="\{\{state\}\}">a</figure-callout>}}^2+b^2}{\left[\frac{(1-\mathrm{\&lambda;})(a^2+\mathrm{\&mu;}{b}^2)q}{\left[\mathrm{\&sigma;}\right](0.25-0.05{\mathrm{\&lambda;}}^3+0.26{\mathrm{\&lambda;}}^2-0.3\mathrm{\&lambda;})}\right]}^{\frac{1}{2}}---\left(2\right)$

$h_{2x}=h_{2y},h_{1x}=h_{1y}=\frac{1+\mathrm{\&lambda;}}{1-\mathrm{\&lambda;}}{h}_{2x}=\frac{1+\mathrm{\&lambda;}}{1-\mathrm{\&lambda;}}{h}_{2y}$

In the formula (2), the permissible stress of [σ]---laminate material, unit are MPa; Other is identical with formula (1).

3) physical significance and the span of pressing plate thickening degree parameter lambda

Known by Fig. 3 and 4:

$\left.\begin{array}{c}\mathrm{tg}{\mathrm{\&alpha;}}^{\&prime;}=\frac{h_{1x}-h_{2x}}{a}=\frac{\frac{1+\mathrm{\&lambda;}}{1-\mathrm{\&lambda;}}{h}_{2x}-h_{2x}}{a}=\frac{2\mathrm{\&lambda;}}{(1-\mathrm{\&lambda;})a}{h}_{2x}\\ \mathrm{tg\&alpha;}=\frac{h_{1y}-h_{2y}}{b}=\frac{\frac{1+\mathrm{\&lambda;}}{1-\mathrm{\&lambda;}}{h}_{2y}-h_{2y}}{b}=\frac{2\mathrm{\&lambda;}}{(1-\mathrm{\&lambda;})b}{h}_{2y}\end{array}\right\}---\left(3\right)$

λ shows that thickening degree thickness of compressive plate h is along the trend of x, y direction linear change, the i.e. physical quantity of horizontal piezometric plate gradient size.

In the process of derivation strength condition, utilized a precondition: considered that namely thickness of compressive plate h along x, y direction linear trends of change (gradient) relatively steadily, and the plane of dividing thickness equally still is the situation on plane, therefore in order to guarantee computational accuracy, from practical and in theory, regulation 0≤λ≤0.5 is o'clock satisfied, is implying the optimal selection problem of λ value here, the upper limit of 0≤λ in getting≤0.5, i.e. λ ^*=0.5 is optimum, also one of main innovate point of the present invention just.

During (2) when given laminate material (E, μ, [σ]), pressing plate length and width (2a, 2b), the stressed q of pressing plate with to the amount of deflection allowable [w] of pressing plate, border thickness h around the pressing plate then _2x=h _2y, pressing plate center thickness h _1x=h _1yReach pressing plate gradient tg α ', tg α, all can turn to the function h of λ _2x(λ), h _1x(λ), tg α ' (λ), tg α (λ), can prove: the higher limit λ that chooses variable element λ ^*=0.5 is optimum.

(3) with λ ^*Substitution formula (1) is obtained the h under rigidity condition _2x(h _2x ^Just).With λ ^*Substitution formula (2) is obtained the h under strength condition _2x(h _2x ^{By force}), select a wherein bigger h then _2x, calculate h then _1x, tg α (λ ^*) (note h _2x=h _2y, h _1x=h _1y), h like this _2x=h _2y, h _1x=h _1yOptimal value just determined.

Embodiment

1. draw pressing plate physique structure calculation diagram, referring to Fig. 1, Fig. 2.

2. according to 0≤λ≤0.5, preferred λ ^*Value.

3. the given known conditions of clear and definite pressing plate body: material (E, μ, [σ]), pressing plate length and width (2a, 2b), the stressed q of pressing plate and to the amount of deflection allowable [w] of pressing plate.

4. utilize formula (1) to calculate

Utilize formula (2) to calculate

5. select one group of bigger h _2x=h _2y, h _1x=h _1y, as optimal value.Tg α ' (λ), tg α (λ) can calculate, can be as the size of the reference gradient.

6. the back effect is optimized in evaluation.

Design example:

Common equipment ZQYC type four-column type oil pressure wringing machine in the papermaking experiment, the long limit 2a=370mm of known main frame pressurized rectangular slab, minor face 2b=290mm, the sheet material material is selected HT for use _20-40, get [σ]=40MPa, q=1MPa, μ=0.25, E=120GPa, [w]=0.5mm, λ ^*=0.5, examination estimation physical dimension.

h _2x=h _2y, h _1x=h _1yAnd gradient tg α ', tg α; Oblique angle α ', α.

The estimation result:

(1) presses rigidity condition

With a=185mm, b=145mm, q=1MPa, E=120 * 10 ³MPa, λ=λ ^*=0.5, μ=0.25, [W]=0.5mm substitution following formula:

(2) press strength condition

With a=185mm, b=145mm, q=1MPa, μ=0.25, λ=λ ^*=0.5, [σ]=40MPa substitution following formula:

(3) because 13.54mm〉11.86mm, 40.61〉35.58, for the safety meter is pressed the strength condition value

Satisfy the flat-plate theory requirement.

(4) gradient and oblique angle

As seen, the gradient is very little, is applicable to engineering.

Through check, prove that the plate structure of this design example design can satisfy the needs of practical application.

Claims (7)

1. linear thickening degree rectangular platen structure, it is characterized in that: this pressure plate structure is the assembly that truncated rectangular pyramids and rectangular parallelepiped are formed, each incline equal in length of described truncated rectangular pyramids, the bottom surface of truncated rectangular pyramids links to each other with a side surface of rectangular parallelepiped, the corresponding coincidence with the edge on described surface in the edge of described bottom surface.

2. according to the described a kind of linear thickening degree rectangular platen structure of claim 1, it is characterized in that: the angle that adjacent two sides of described truncated rectangular pyramids become with the bottom surface of truncated rectangular pyramids is respectively α and α ', and α and α ' satisfy following formula:

$\left.\begin{array}{c}\mathrm{tg}{\mathrm{\&alpha;}}^{\&prime;}=\frac{2\mathrm{\&lambda;}}{(1-\mathrm{\&lambda;})a}{h}_{2x}\\ \mathrm{tg\&alpha;}=\frac{2\mathrm{\&lambda;}}{(1-\mathrm{\&lambda;})b}{h}_{2y}\end{array}\right\}$

, wherein, h _2x, h _2yExpression pressure plate structure bound thickness, h _2x=h _2y, a, b represent half of the long limit of rectangular platen structure and bond length respectively, λ represents thickening degree parameter, 0≤λ≤0.5.

3. according to the described a kind of linear thickening degree rectangular platen structure of claim 2, it is characterized in that: described h _2xGet h _2x ^JustAnd h _2x ^{By force}In maximal value, h _2x ^JustBe shown below:

h _2x ^{By force}Be shown below:

, wherein, a 〉=b, μ represents the Poisson ratio of pressure plate structure material, and E represents the Young modulus of pressure plate structure material, and q represents to act on the lip-deep well-distributed pressure of pressure plate structure, the permission amount of deflection of [w] expression pressure plate structure, the permissible stress of [σ] expression pressure plate structure material.

4. according to the described a kind of linear thickening degree rectangular platen structure of claim 1, it is characterized in that: the upper bottom surface of described truncated rectangular pyramids is to obtain after processing for the plane that installs and fixes spherical linkage by the place, summit at corresponding rectangular pyramid.

5. according to the described a kind of linear thickening degree rectangular platen structure of claim 1, it is characterized in that: the adjacent side of described truncated rectangular pyramids connects at corresponding incline place rounding off.

6. the dimensionally-optimised method of linear thickening degree rectangular platen structure according to claim 1 is characterized in that, may further comprise the steps:

1) calculates the pressure plate structure bound thickness: get h _2x ^JustAnd h _2x ^{By force}In maximal value as bound thickness, h _2x ^JustBe shown below:

h _2x ^{By force}Be shown below:

Wherein, a 〉=b, a, b represent half of the long limit of rectangular platen structure and bond length respectively, μ represents the Poisson ratio of pressure plate structure material, and E represents the Young modulus of pressure plate structure material, and q represents to act on the lip-deep well-distributed pressure of pressure plate structure, the permission amount of deflection of [w] expression pressure plate structure, the permissible stress of [σ] expression pressure plate structure material;

2) calculate the pressure plate structure center thickness: λ represents thickening degree parameter, 0≤λ≤0.5;

3) through step 2) after, process the plane that is used for installing and fixing spherical linkage at the place, summit of rectangular pyramid, make rectangular pyramid become truncated rectangular pyramids.

7. the application of linear thickening degree rectangular platen structure in center and fixedly spherical linkage is connected, the plate face is subjected to the well-distributed pressure effect pressing plate according to claim 1.

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