CN106769477A - Axle loads the determination method of lower prestress circular membrane maximum stress - Google Patents

Abstract

The invention discloses the determination method that axle loads lower prestress circular membrane maximum stress：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 be E, Poisson's ratio be ν, prestressing force be σ₀, thickness be h, radius be a, the radius of smooth flat cylinder loading axis is b, standing balance analysis based on this On Axisymmetric Deformation of A, using the measured value of transverse load F, then can determine that maximum stress σ of the prestressing force circular membrane under transverse load F effects_m。

Description

Axle loads the determination method of lower prestress circular membrane maximum stress

Technical field

The determination method of the prestressing force circular membrane maximum stress under axle loading fixed to clamp the present invention relates to periphery.

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.Generally, adopt With loading axis in circular membrane center imposed load, loading, measurement work can be made more convenient, but from the knot of document Investigation Fruit sees that axle loads the analytic solutions of the On Axisymmetric Deformation of A of the prestressing force circular membrane that following peripheral fixes to clamp, there is presently no It is presented, thus has influence on the work that prestressing force circular membrane maximum stress is determined based on load measurement value.

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 solid to shaft loading following peripheral on this basis The determination method of the maximum stress of the tight prestressing force circular membrane of clamp.

Axle loads the determination method of lower prestress circular membrane maximum stress：The prestressing force circle fixed to clamp on periphery is thin At center membrane, a transverse load F is applied to prestressing force circular membrane by a smooth flat cylinder loading axis, its In, the Young's modulus of elasticity of prestressing force circular membrane is E, Poisson's ratio is that ν, prestressing force are σ₀, thickness be h, radius be a, it is smooth The radius of flat cylinder loading axis be b, the standing balance analysis based on this On Axisymmetric Deformation of A, the prestressing force is circular The maximum stress σ of film_mParsing relation with transverse load F can be expressed as

Wherein, π is pi,

And c₀And c₁Value by equation

With

It is determined that, all parameters all use the International System of Units.

So, as long as measuring the value of transverse load F, it is possible to determine the prestressing force circular membrane in transverse load F Maximum stress σ under effect_m。

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, prestressing force σ₀=0.2MPa, thickness h=1mm, radius a=50mm, smooth flat circle The radius b=5mm of cylinder loading axis.Measure transverse load F=15N.Using the method given by the present invention, by equation

With

Wherein,

C can then be obtained₀=1.330249489, c₁=2.239081372.Finally, by formula

Can then obtain, as transverse load F=15N, the maximum stress σ of the prestressing force round rubber film_m= 1.509MPa。

Claims (1)

1. axle loads the determination method of lower prestress circular membrane maximum stress, it is characterised in that：Periphery fix to clamp it is pre- A transverse direction is applied to prestressing force circular membrane by a smooth flat cylinder loading axis at stress circle thin film center Load F, wherein, the Young's modulus of elasticity of prestressing force circular membrane is E, Poisson's ratio is that ν, prestressing force are σ₀, thickness be h, radius It is a, the radius of smooth flat cylinder loading axis is b, measures the value of transverse load F, and the prestressing force is determined by below equation Maximum stress σ of the circular membrane under transverse load F effects_m：

${\mathrm{\σ}}_m=\frac{1}{2^{5/3}}\frac{E^{1/3}}{b^2}{\left(\frac{a^{2}F}{\mathrm{\π}h}\right)}^{2/3}\underset{i=0}{\overset{8}{\Σ}}{c}_i{\left(\frac{b^2-a^2}{2a^2}\right)}^i,$

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

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

With

$2\underset{i=1}{\overset{8}{\mathrm{\Σ}}}{\mathrm{ic}}_i{\left(\frac{a^2-b^2}{2a^2}\right)}^{i-1}-\left(1+v\right)\underset{i=0}{\overset{8}{\mathrm{\Σ}}}{c}_i{\left(\frac{a^2-b^2}{2a^2}\right)}^i=\frac{2^{5/3}{\mathrm{\σ}}_0}{E^{1/3}}{\left(\frac{\mathrm{\π}ah}{F}\right)}^{2/3}\left(1-v\right)$

It is determined that, all parameters all use the International System of Units.