CN106769476A - The prestressed axle loading measuring method of film in prestressing force circular membrane structure - Google Patents

Abstract

The invention discloses the prestressed axle loading measuring method of film in prestressing force circular membrane structure：In the prestressing force circular membrane center that periphery fixes to clamp, one transverse load F is applied to prestressing force circular membrane by a smooth flat cylinder loading axis, wherein, the Young's modulus of elasticity of prestressing force circular membrane is E, Poisson's ratio is ν, thickness is h, radius is a, the radius of smooth flat cylinder loading axis is b, standing balance analysis based on this On Axisymmetric Deformation of A, using transverse load F and film maximum defluxion w_mMeasured value, then can determine that the prestressing force σ of film in the prestressing force circular membrane structure₀。

Description

The prestressed axle loading measuring method of film in prestressing force circular membrane structure

Technical field

The present invention relates to the prestressed measuring method of film in prestressing force circular membrane structure.

Background technology

Circular membrane structure has a wide range of applications in fields such as machinery, electronics, bioengineering.In fact, due to temperature, The influence of the factors such as the change of humidity and manufacture craft, in the circular membrane structure after making shaping, in most cases Certain prestressing force can be there is in film.Prestressed presence will change the mechanical behavior of circular membrane structure, therefore need It is measured.However, to measure the prestressing force in film, the solution of prestressing force circular membrane structure just must be in advance obtained Analysis solution.Using loading axis in prestressing force circular membrane center imposed load, it will usually make loading, measurement work more convenient, But from terms of the result of document Investigation, the axisymmetric deformation of the lower circular membrane fixed to clamp with prestressed periphery of axle loading is asked Topic, is not resolved also solves so far, thus has influence on the prestressing force measurement work in circular membrane structure.

The content of the invention

This invention address that the analysis research of film problem, the prestressing force that Analytical Solution axle loading following peripheral fixes to clamp The On Axisymmetric Deformation of A of circular membrane, obtains the analytic solutions of the problem, and it is thin to give prestressing force circle on this basis The prestressed axle loading measuring method of film in membrane structure.

The prestressed axle loading measuring method of film in prestressing force circular membrane structure：In the prestressing force that periphery fixes to clamp Circular membrane center, a transverse load is applied by a smooth flat cylinder loading axis to prestressing force circular membrane F, wherein, the Young's modulus of elasticity of prestressing force circular membrane is E, Poisson's ratio is that ν, thickness are that h, radius are a, smooth flat circle The radius of cylinder loading axis is b, then based on the standing balance analysis to this On Axisymmetric Deformation of A, the prestressing force circle is thin The prestressing force σ of film in membrane structure₀Can be expressed as

Wherein, π is pi,

And c₀And c₁Value by equation

With

It is determined that, wherein, w_mIt is the maximum defluxion of prestressing force circular membrane,

Wherein, all parameters all use the International System of Units.

So, as long as measuring the value and corresponding film maximum defluxion w of transverse load F_mValue, it is possible to it is determined that Go out the prestressing force σ of film in the prestressing force circular membrane structure₀。

Brief description of the drawings

Fig. 1 loads organigram for the prestressing force circular membrane that periphery fixes to clamp, wherein, 1- prestressing force circles are thin Film, 2- smooth flat cylinder loading axis, 3- clamping devices, and a represents that the inside radius and prestressing force of clamping device are circular The radius of film, b represents the radius of smooth flat cylinder loading axis, and F represents that loading axis is applied to prestressing force circular membrane Plus transverse load, w_mRepresent the maximum defluxion of prestressing force circular membrane.

Specific embodiment

Technical scheme is described in further detail with reference to Fig. 1：

At the prestressing force round rubber thin film center that periphery fixes to clamp, loaded by a smooth flat cylinder Axle applies a transverse load F to prestressing force round rubber film, wherein, the Young's modulus of elasticity of prestressing force round rubber film E=7.84MPa, Poisson's ratio ν=0.47, thickness h=1mm, radius a=50mm, the radius b of smooth flat cylinder loading axis =5mm.Measure transverse load F=5N, corresponding film maximum defluxion w_m=6.8847mm.Using the side given by the present invention Method, by equation

With

Wherein,

C can then be obtained₀=1.339882, c₁=2.262485.Then, then by formula

The prestressing force σ of film in the prestressing force circular membrane structure can then be obtained₀=0.1MPa.

Claims (1)

1. the prestressed axle of film loads measuring method in prestressing force circular membrane structure, it is characterised in that：In periphery geometrical clamp Tight prestressing force circular membrane center applies one by a smooth flat cylinder loading axis to prestressing force circular membrane Individual transverse load F, wherein, the Young's modulus of elasticity of prestressing force circular membrane is E, Poisson's ratio is that ν, thickness are that h, radius are a, light The radius of sliding flat cylinder loading axis is b, measures the value and corresponding film maximum defluxion w of transverse load F_m's Value, the prestressing force σ of film in the prestressing force circular membrane structure is determined by below equation₀：

${\mathrm{\σ}}_0=\frac{E^{1/3}}{2(1-v)}{\left(\frac{F}{2\mathrm{\π}ah}\right)}^{2/3}\[2\underset{i=1}{\overset{8}{\Σ}}{\mathrm{ic}}_i{\left(\frac{a^2-b^2}{2a^2}\right)}^{i-1}-(1+v)\underset{i=0}{\overset{8}{\Σ}}{c}_i{\left(\frac{a^2-b^2}{2a^2}\right)}^i\],$

Wherein, π is pi,

$c_2=-\frac{1}{2c_0^2},$

$c_3=\frac{c_1}{3c_0^3},$

$c_4=-\frac{1}{12c_0^5}(1+3c_0{c}_1^2),$

$c_5=\frac{c_1}{60c_0^6}(11+12c_0{c}_1^2),$

$c_6=-\frac{1}{360c_0^8}(11+102c_0{c}_1^2+60c_0^2{c}_1^4),$

$c_7=\frac{c_1}{1260c_0^9}(146+477c_0{c}_1^2+180c_0^2{c}_1^4),$

$c_8=-\frac{1}{10080c_0^{11}}(4716c_0^2{c}_1^4+1260c_0^3{c}_1^6+2745c_0{c}_1^2+146),$

And c₀And c₁Value by equation

$w_m={\left(\frac{a^{2}F}{2\mathrm{\π}hE}\right)}^{1/3}\[\underset{i=1}{\overset{8}{\Σ}}{d}_i{\left(\frac{b^2-a^2}{2a^2}\right)}^i-\underset{i=1}{\overset{8}{\Σ}}{d}_i{\left(\frac{a^2-b^2}{2a^2}\right)}^i\]$

With

$\underset{i=0}{\overset{8}{\Σ}}{c}_i{\left(\frac{b^2-a^2}{2a^2}\right)}^i-\frac{b^2}{a^2}\underset{i=1}{\overset{8}{\Σ}}{\mathrm{ic}}_i{\left(\frac{b^2-a^2}{2a^2}\right)}^{i-1}=0$

It is determined that, wherein

$d_1=-\frac{1}{c_0},$

$d_2=\frac{1}{2}\frac{c_1}{c_0^2},$

$d_3=-\frac{1}{6}\frac{(1+2c_0{c}_1^2)}{c_0^4},$

$d_4=\frac{1}{12}\frac{c_1(4+3c_0{c}_1^2)}{c_0^5},$

$d_5=-\frac{1}{60}\frac{(4+29c_0{c}_1^2+12c_0^2{c}_1^4)}{c_0^7},$

$d_6=\frac{1}{180}\frac{c_1(43+111c_0{c}_1^2+30c_0^2{c}_1^4)}{c_0^8},$

$d_7=-\frac{1}{1260}\frac{(43+927c_0^2{c}_1^4+677c_0{c}_1^2+180c_0^3{c}_1^6)}{c_0^{10}},$

$d_8=\frac{1}{10080}\frac{c_1(1784+8496c_0^2{c}_1^4+9801c_0{c}_1^2+1260c_0^3{c}_1^6)}{c_0^{11}},$

All parameters all use the International System of Units.