CN105003026A - Method for calculating stiffness of web of rectangular recessed cavity structure - Google Patents

Abstract

The invention discloses a method for calculating the stiffness of a web of a rectangular recessed cavity structure. The invention aims to provide a method for precisely calculating the stiffness of the web and determining the degree of the rigidity of the web so as to provide theoretical bases for component clamping and quality control. According to the geometrical structure and machining characteristics of a rectangular recessed cavity, the geometric center of the web of the rectangular recessed cavity structure is determined as a point with weakest rigidity; if the rigidity of the point meets clamping and processing requirements, the rigidity of the other areas of the web certainly meets the requirements. The web is finely divided into innumerable simply-supported beam models, with the point as the center of each simply-supported beam and the edges of the web as two ends of each simply-supported beam; and on the basis of a mechanical model of bending deformation of the simply-supported beam, analytical expression of flexural rigidity of the midpoint of any finely-divided beam is calculated, the length functions of the finely-divided beams are integrated along the edges of the web, so the flexural rigidity of the web of the rectangular recessed cavity is calculated.

Description

A kind of computational methods of web rigidity of rectangle curved cavity

Technical field

The present invention relates to a kind of computational methods of web rigidity of rectangle curved cavity, particularly relate to the computational methods of the web rigidity of the rectangle cavity that all side seals close.

Background technology

A class part is had to have multiple rectangle curved cavity feature in structural member, when formulating processing method and the fixture scheme of this kind of part, usually need the rigidity considering part strong and weak, especially the rigidity of rectangle cavity floor and web will be considered, engineering practice shows, the rigidity power of web is the primary factor affecting parts fixation and quality.Judgement at present to the web rigidity of rectangle cavity, mainly contain two kinds of methods, one is engineers and technicians by the basic structure of observation analysis cavity and size, and incorporation engineering experience is assessed, this method limitation is very large, cannot carry out quantitatively evaluating to the rigidity of groove web; Two is rely on finite element emulation software to analyze, and this method complicated operation, needs technical professional to perform, and also cannot provide accurate analytical expression and reliably calculate web rigidity.Cannot the rigidity of accurate Calculation web, also just can not provide theoretical foundation and guidance for the fixture scheme design of part and the process strategies taked, affect the control of part crudy.

Summary of the invention

Cannot the rigidity of accurate Calculation web for solving the part with rectangle curved cavity feature that prior art exists, theoretical foundation and guidance can not be provided for the fixture scheme design of part and the process strategies taked, affect the problem of the control of part crudy, the invention provides a kind of computational methods of web rigidity of rectangle curved cavity.The computational methods of the web rigidity of a kind of rectangle curved cavity of the present invention, is characterized in that, described rectangle cavity week side seal closes and web uniform thickness everywhere, comprises the steps:

1) according to the geometry feature of rectangle, determine that the geometric center point of the web of rectangle cavity is the weakest point of its rigidity;

2) web differential is become countless differential beams, described differential beam take geometric center point as mid point, and be two ends with boundary of web, the cross section of described differential beam is rectangle, described differential beam, based on simply supported beam flexural deformation mechanical model, calculates the bending rigidity k of any differential beam mid point by formula (1) _i,

$K_i=48\·\frac{E}{l^3\left(x\right)}\·\frac{1}{12}{t}^3\·dx---\left(1\right)$

3) along boundary of web, integration is carried out to the bending rigidity of differential beam, calculates the bending rigidity K of the web of rectangle cavity,

The present invention has following good effect compared to prior art, the computational methods of the web rigidity of a kind of rectangle curved cavity of the present invention, theoretical based on simply supported beam bending die, and combines with engineering practice, makes engineering problem can by accurate expression; The computational methods of web rigidity of the present invention need by analysis software such as finite elements, only from the feature of rectangle curved cavity be starting point, quick calculating part web rigidity, owing to calculating the rigidity of web the weakest point, therefore other region one of part meets rigidity requirement surely; Utilize the web rigidity calculated, can control to provide theoretical foundation to the fixture scheme of part in process and part quality, thus crudy is controlled; Special tooling can be reduced according to calculating in addition, shortening the frock manufacturing cycle, reduce costs, raise the efficiency.

Accompanying drawing explanation

Below in conjunction with accompanying drawing, specific embodiments of the invention are described in further detail.

Fig. 1 is the simply supported beam schematic diagram of the computational methods foundation of the web rigidity of a kind of rectangle curved cavity of the present invention.

Fig. 2 is the simply supported beam schematic cross-section of Fig. 1.

Fig. 3 is the stressed schematic diagram of simply supported beam of the computational methods foundation of the web rigidity of a kind of rectangle curved cavity of the present invention.

Fig. 4 is that the web differential of the computational methods foundation of the web rigidity of a kind of rectangle curved cavity of the present invention simplifies structural representation.

Fig. 5 is the differential beam schematic diagram of the web of the computational methods foundation of the web rigidity of a kind of rectangle curved cavity of the present invention.

Detailed description of the invention

The computational methods of the web rigidity of a kind of rectangle curved cavity of the present invention, is characterized in that, described rectangle cavity week side seal closes and web uniform thickness everywhere, comprises the steps:

1) according to the geometry feature of rectangle, determine that the geometric center point of the web of rectangle cavity is the weakest point of its rigidity;

2) web differential is become countless differential beams, described differential beam take geometric center point as mid point, and be two ends with boundary of web, the cross section of described differential beam is rectangle, described differential beam, based on simply supported beam flexural deformation mechanical model, calculates the bending rigidity k of any differential beam mid point by formula (1) _i,

$K_i=48\·\frac{E}{l^3\left(x\right)}\·\frac{1}{12}{t}^3\·dx---\left(1\right)$

3) along boundary of web, integration is carried out to the bending rigidity of differential beam, calculates the bending rigidity K of the web of rectangle cavity,

Fig. 1 is the simply supported beam schematic diagram of the computational methods foundation of the web rigidity of a kind of rectangle curved cavity of the present invention, Fig. 2 is the A-A sectional view of Fig. 1, cross section is rectangle, and wherein Z is diastrophic neutral axis, then the moment of inertia I design formulas of simply supported beam cross section centering axle is as (1-1):

$I=\frac{1}{12}{\mathrm{mn}}^3---(1-1)$

In formula (1-1),

I: beam section to the moment of inertia of neutral bending axis,

M: rectangle length,

N: rectangle width,

Fig. 3 is the stressed schematic diagram of simply supported beam of the computational methods foundation of the web rigidity of a kind of rectangle curved cavity of the present invention.The concentrated load F that simply supported beam is subject at mid point, produces amount of deflection ω, by simply supported beam flexural deformation mechanical model, calculates the amount of deflection ω of simply supported beam mid point with formula (1-2),

$\mathrm{\ω}=\frac{{\mathrm{Fl}}^3}{48EI}=\frac{F}{\frac{48EI}{l^3}}=\frac{F}{K_i}---(1-2)$

(1-2) in formula:

ω: simply supported beam length direction mid point, the amount of deflection of rigidity the weakest point;

F: the concentrated load that simply supported beam is subject to;

E: Young's model;

I: the moment of inertia of simply supported beam cross section centering axle;

L: simply supported beam length;

K _i: the bending rigidity of simply supported beam mid point.

When simply supported beam cross section is rectangle, then substitute into the design formulas (1-3) that formula (1-1) draws the bending rigidity of simply supported beam mid point

$K_l=\frac{48EI}{l^3}---(1-3)$

Fig. 4 is that the web differential of the computational methods foundation of the web rigidity of a kind of rectangle curved cavity of the present invention simplifies structural representation, the length of web ABCD is a, width is b, thickness is t, geometric center is Ο point, is also rigidity the weakest point, and FGHI is wherein arbitrary differential beam, wherein O is the mid point of differential beam, and Fig. 5 is differential beam section schematic diagram.The cross section of this differential beam is rectangle, and wherein dx is the length of rectangle, and t is the wide of rectangle, according to the design formulas (1-3) of the bending rigidity of above-mentioned simply supported beam mid point, draws the analytical expression of the bending rigidity of any differential beam mid point

$K_i=48\·\frac{EI}{l^3\left(x\right)}\·ds=48\·\frac{E}{l^3\left(x\right)}\·\frac{1}{12}{t}^3\·dx---\left(1\right)$

Wherein l (x) represents the length function of differential beam

Along boundary of web, integration is carried out to the length function of differential beam, obtain the bending rigidity design formulas (2) of rectangle cavity web

(2) in formula:

K: web the most weak rigidity place rigidity;

E: Young's model;

T: web thickness;

A: web length;

B: web width.

The computational methods of the web rigidity of a kind of rectangle curved cavity of the present invention, aim to provide a kind of accurate Calculation web rigidity, determine the method for web rigidity power, thus provide theoretical foundation for parts fixation, quality control.According to geometry and the processing characteristic of rectangle cavity, determine that the geometric center of rectangle cavity web is the weakest point of its rigidity, if the weakest point rigidity meets clamping and processing request, then other region of web necessarily meets the demands, with the center that this is simply supported beam, boundary of web is the two ends of simply supported beam, web differential is become countless simply supported beam models, based on simply supported beam flexural deformation mechanical model, solve the analytical expression of the bending rigidity of any differential beam mid point, along boundary of web, integration is carried out to the bending rigidity of differential beam, solve the bending rigidity of rectangle cavity web.

Claims (1)

1. computational methods for the web rigidity of rectangle curved cavity, is characterized in that, described rectangle cavity week side seal closes and web uniform thickness everywhere, comprises the steps:

1) according to the geometry feature of rectangle, determine that the geometric center point of the web of rectangle cavity is the weakest point of its rigidity;

2) web differential is become countless differential beams, described differential beam is mid point with geometric center point, and is two ends with boundary of web, and the cross section of described differential beam is rectangle, described differential beam, based on simply supported beam flexural deformation mechanical model, calculates the bending rigidity k of any differential beam mid point _i,

$K_i=48\·\frac{E}{l^3\left(x\right)}\·\frac{1}{12}{t}^3\·dx;$

3) along boundary of web, integration is carried out to the length function of differential beam, calculates the bending rigidity K of the web of rectangle cavity,