CN101266206B - Enwinding fibre and mandrel surface friction coefficient measurement method - Google Patents

Abstract

The invention provides a measuring method of the frictional coefficient between the winding fiber and core formwork surface, belonging to fibre winding moulding composite material manufacturing technology, in order to solve the problem that there is a big frictional coefficient error between the winding fiber and core formwork surface. The measuring process comprises: producing the core formwork;measuring the frictional coefficient u(r) between the fiberous belt and outer surface of the core formwork, and mounting the designed core formwork on the fiber winding machine; winding the fiberous belt on the core formwork along the direction of the generating line by fiber winding machine performing the uniform rate rotary motion and the fiber spout performing the uniform rate rectilinear motion, when the fiberous belt winds on one site and skids, the numerical value at the said site R is determined and inserted into the above formula to obtain the frictional coefficient u(r) of the site. The invention measures the frictional coefficient using the core formwork designed in advance and the stability can be ensured only by simply mechanical control and the error is reduced.

Description

Twine the measuring method of friction factor between fiber and mandrel surface

Technical field

The present invention relates to fiber winding forming manufacture technology of composite material field, be specifically related to a kind of measuring method of twining friction factor between fiber and mandrel surface.

Background technology

Since nineteen forty-six U.S.'s invention continuous fiber winding shaping process technology, the winding process goods have obtained constantly improving and development.This initial at aerospace field composite applications goods, nowadays be widely used in each big field.Divide from the fiber winding path, winding product can be divided into substantially: geodesic line winding product and non-geodesic curve winding product two big classes.Geodesic line winding process fiber track length is the shortest, and quality of item is lighter relatively.But owing to be subjected to the influence of goods geometric configuration, geodesic line winding shaping process limitation is bigger.By contrast, the relative design space of non-geodesic curve winding product is just more wide, except being fit to general rotational symmetry solid of revolution, can also some specific (special) requirements of moulding and the goods of complicated shape, such as the transition section winding of isostension pressure vessel, cylindrical pressure vessel, bend pipe etc., and biggest advantage is the optimal design that can carry out varied angle according to load-up condition to winding product.Yet, the planning and design that non-geodesic curve twines fiber track require will have between winding fiber and core clear and definite friction co-efficient value reliably, judge whether stable, the slip not of non-geodesic curve winding path with this, and then the calculating of carrying out winding angle is found the solution and the planning and design of line style.

Therefore how to obtain reliable practical again friction factor, will directly have influence on design, the moulding of non-geodesic curve winding product.Consult domestic and international pertinent literature, as can be known at present about the friction coefficient measurement method between fiber and core of twining summarize mainly contain following several: 1. adopt cylindrical core, obtain friction factor by changing winding angle up to the fiber slip in the measuring process.Make this method complex operation owing to will constantly change winding angle, error is bigger, and the final friction co-efficient value error that obtains is bigger; 2. adopt the broadening formation core, apply two different power in the measuring process, increase one of them power value, obtain friction factor until the fiber slip.Owing to be difficult to apply the winding process parameter, make that this method and actual winding process gap are bigger, and operate and waywardly make that the measured value precision is difficult to control; 3. adopt board device or slope method, core is constantly tilted, after reaching certain angle, cause fiber to skid and obtain friction factor.This method is carried out the measurement of friction factor from the angle of physics, equally also is to be difficult to apply the winding process parameter, makes itself and actual winding process gap bigger, and measuring error is bigger.

Summary of the invention

The objective of the invention is to solve existing method and measure the big problem of friction factor error between winding fiber and the mandrel surface, design a kind of measuring method of twining friction factor between fiber and mandrel surface.

Measuring process of the present invention is:

One, make core, process is as follows:

Step 1 is decided the numerical value of the maximum latitude circle radius R of core according to actual needs;

Step 2 is asked the numerical value of constant C:

During r=0, μ (r)=1 is with this group numerical value substitution formula

In, try to achieve constant C;

Step 3 is asked the value of L, and when f (r)=0, r=L is with f (r)=0, constant C substitution formula

In try to achieve L;

Step 4 is according to formula

Whenever getting a r tries to achieve corresponding latitude circle radius f (r) (0≤r≤L), the bus track of core is determined like this, makes core;

R is the maximum latitude circle radius of core;

C is a constant;

F (r) is the core outside surface latitude circle radius of any arbitrarily;

R is that radius is the latitude circle of f (r) and the distance between the maximum latitude circle;

L is that radius is a distance between zero latitude circle and the maximum latitude circle;

μ (r) for fabric strip when the latitude circle radius is f (r) and the friction factor between the core outside surface;

Two, the coefficientoffriction (r) between measurement fabric strip and the core outside surface, its step is poly-as follows:

Step 1 with the core clamping that designs the scroll chuck of fiber winding machine and top between;

The step 2 fiber winding machine is the uniform speed rotation, the silk mouth is done linear uniform motion from the maximum latitude circle side direction opposite side of core, direction of motion is parallel to the axial line of core, and the fabric strip hoop that applies certain winding tension and be soaked with resin is wound on the core, and this moment, winding angle θ got pi/2;

When step 3 was wound into certain point when the fabric strip that applies certain winding tension, the fiber on the core began to skid, and determines the numerical value of this some r of place, the substitution formula

Try to achieve the coefficientoffriction (r) of this point, this friction factor is that fabric strip is along the minimized friction coefficient between winding of core generatrix direction and mandrel surface.

Advantage of the present invention is: core of the present invention is under the situation of fixing winding angle, and fabric strip is along satisfying linear relationship apart from r between the coefficientoffriction (r) of core generatrix direction arbitrfary point and this place's latitude circle and the maximum latitude circle.The advantage of utilizing this core to carry out friction coefficient measurement is only to need just can guarantee measuring stability by simple machinery control, reduces error.

Description of drawings

Fig. 1 is a structural representation of the present invention, and Fig. 2 is a solid of revolution curved surface Representative Volume Element synoptic diagram.

Embodiment

Embodiment one: present embodiment is described below in conjunction with Fig. 1, the present invention designs a novel core, provide a kind of and can accurately measure the method for twining friction factor between fiber and mandrel surface, for non-geodesic curve fiber winding forming technology provides design parameter, and cost is low, and is simple and easy to do.

Measuring process of the present invention is:

One, make core 1, process is as follows:

Step 1 is decided the numerical value of core 1 maximum latitude circle radius R according to actual needs;

Step 2 is asked the numerical value of constant C:

During r=0, μ (r)=1 is with this group numerical value substitution formula

In, try to achieve constant C;

Step 3 is asked the value of L, and when f (r)=0, r=L is with f (r)=0, constant C substitution formula

In try to achieve L;

Step 4 is according to formula

Whenever getting a r tries to achieve corresponding latitude circle radius f (r) (0≤r≤L), the bus track of core 1 is determined like this, makes core 1;

R is the maximum latitude circle radius of core 1;

C is a constant;

F (r) is the core 1 outside surface latitude circle radius of any arbitrarily;

R is that radius is the latitude circle of f (r) and the distance between the maximum latitude circle;

L is that radius is a distance between zero latitude circle and the maximum latitude circle;

μ (r) for fabric strip 2 when the latitude circle radius is f (r) and the friction factor between core 1 outside surface;

Two, the coefficientoffriction (r) between measurement fabric strip 2 and core 1 outside surface, its step is poly-as follows:

Step 1 with core 1 clamping that designs the scroll chuck of fiber winding machine and top between;

The step 2 fiber winding machine is the uniform speed rotation, silk mouth 3 is done linear uniform motion from the maximum latitude circle side direction opposite side of core 1, direction of motion is parallel to the axial line of core 1, fabric strip 2 hoops that apply certain winding tension and be soaked with resin are wound on the core 1, and this moment, winding angle θ got pi/2;

When step 3 was wound into certain point when the fabric strip 2 that applies certain winding tension, the fiber on the core 1 began to skid, and determines the numerical value of this some r of place, the substitution formula

Try to achieve the coefficientoffriction (r) of this point, this friction factor is that fabric strip 2 is along the minimized friction coefficient between winding of core 1 generatrix direction and core 1 surface.

If adopt the numerical control fiber winding machine, the coordinate of the point of slippage obtains easily according to numerical control program, determines the numerical value of r afterwards; If do not adopt the numerical control fiber winding machine, the r value of the point of slippage can be by obtaining with the yardstick amount.

The model that above-mentioned fiber winding machine is selected for use is a HG-2 jet pipe large-sized numerical control fiber winding machine.

Silk mouth 3 be fiber winding machine from tape member, it is along the orbital motion that is parallel to core 1 axial line, its major function is to allow fabric strip 2 pass therethrough, with location fabric strip 2 to the line direction.

Core design concept of the present invention:

Twine for the non-geodesic curve fiber, the stable not condition of slip of fiber track is

$\mathrm{\μ}\≥\left|\frac{k_g}{k_n}\right|$ Formula one

Wherein, μ---friction factor;

k _g---the geodesic curvature of core 1 curved surface;

k _n---the normal direction curvature of core 1 curved surface.

By differential geometric knowledge as can be known, the parametric equation for any solid of revolution curved surface S (as shown in Figure 2) is

S (r, v)={ f (r) cosv, f (r) sinv, r} formula two

Wherein, and S (r, v)---any solid of revolution curved surface;

R, v---surface coordinates, wherein r is that radius is the latitude circle of f (r) and the distance between the maximum latitude circle, v is the projection of bus f (r) in x, y plane and the angle of x axle;

F (r)---solid of revolution bus equation, f (r)＞0 is again the core 1 outside surface latitude circle radius of any arbitrarily;

The first kind fundamental quantity of trying to achieve this surface of revolution is:

E=1+f ²(r) F=0 G=f ²(r) formula three

The second class fundamental quantity is:

$L=\frac{f^{\′\′}\left(r\right)}{\sqrt{E}}$ M＝0 $N=\frac{-f\left(r\right)}{\sqrt{E}}$ Formula four

E, F, the first kind fundamental quantity of G---parametric surface;

L, M, the second class fundamental quantity of N---parametric surface;

According to Euler's formula

$k_n=\frac{\mathrm{<figure-callout\; id="2"\; label="L\; E\; cos"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">L</figure-callout>}}{E}{\cos }^{}{}^2\mathrm{\&theta;}+\frac{\mathrm{<figure-callout\; id="2"\; label="N\; g\; sin"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">N</figure-callout>}}{g}{\sin }^{}{}^2\mathrm{\&theta;}$ Formula five

Trying to achieve its normal direction curvature is

$k_n=\frac{f^{\&prime;\&prime;}\left(r\right){\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&theta;}}{{\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">E</figure-callout>}}^{3/2}}-\frac{{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&theta;}}{f\left(r\right){\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">E</figure-callout>}}^{1/2}}$ Formula six

Geodesic curvature is arranged again

$k_g=-\frac{\cos \mathrm{\&theta;}}{\sqrt{E}}\&CenterDot;\frac{\mathrm{d\&theta;}}{\mathrm{du}}-\frac{f^{\&prime;}\left(r\right)}{f\left(r\right)\&CenterDot;\sqrt{E}}\sin \mathrm{\&theta;}$ Formula seven

Formula six and formula seven substitution formula one are obtained

$\frac{|f^{\&prime;}\left(r\right)\sin \mathrm{\&theta;}+f\left(r\right)\cos \mathrm{\&theta;}\frac{\mathrm{d\&theta;}}{\mathrm{dr}}|}{{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\mathrm{\&theta;}-\frac{f^{\&prime;\&prime;}\left(r\right)f\left(r\right){\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="H2008100644554E00011.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&theta;}}{1+f^{\&prime;2}\left(r\right)}}=\mathrm{\&mu;}\left(r\right)$ Formula eight

In the formula, θ---winding angle, radius are angle between the latitude circle place fiber track of f (r) and bus;

F ' (r), f " (r)---be respectively first order derivative and the second derivative of asking bus equation f (r).

Make winding angle θ=pi/2, under the situation that this hoop twines, formula eight is simplified.So just directly set up the relation between the coefficientoffriction (r) between core 1 latitude circle radius f (r) and this latitude circle place fabric strip 2 and core 1 outside surface, promptly

-f ' (r)=μ (r) formula nine

By coefficientoffriction (r) ∈ (0,1] interval, correspondingly f (r) ∈ (R, 0] (R is the maximum latitude circle radius of core 1).So have:

$-f^{\&prime;}\left(r\right)=1-\frac{f\left(r\right)}{R}$ Formula ten

Find the solution

$f\left(r\right)=R-e^{(\frac{r}{R}+C)}$ Formula 11

$\mathrm{\&mu;}\left(r\right)=1-\frac{R-e^{(\frac{r}{R}+C)}}{R}$ Formula 12

In the formula, the distance between r---the latitude circle of radius f (r) and the maximum latitude circle of core 1;

C---constant.

Fabric strip 2 is along satisfying linear relationship apart from r between the coefficientoffriction (r) of core 1 generatrix direction arbitrfary point and this place's latitude circle and the maximum latitude circle.

Claims (1)

1. twine the measuring method of friction factor between fiber and mandrel surface, it is characterized in that its measuring process is:

One, make core (1), process is as follows:

Step 1 is decided the numerical value of the maximum latitude circle radius R of core (1) according to actual needs;

Step 2 is asked the numerical value of constant C:

During r=0, μ (r)=1 is with this group numerical value substitution formula

In, try to achieve constant C;

Step 3 is asked the value of L, and when f (r)=0, r=L is with f (r)=0, constant C substitution formula

In try to achieve L;

Step 4 is according to formula

Whenever getting a r tries to achieve corresponding latitude circle radius f (r) (0≤r≤L), the bus track of core (1) is determined like this, makes core (1);

R is the maximum latitude circle radius of core (1);

C is a constant;

F (r) is core (1) the outside surface latitude circle radius of any arbitrarily;

R is that radius is the latitude circle of f (r) and the distance between the maximum latitude circle;

L is that radius is a distance between zero latitude circle and the maximum latitude circle;

μ (r) for fabric strip (2) when the latitude circle radius is f (r) and the friction factor between core (1) outside surface;

Two, the coefficientoffriction (r) between measurement fabric strip (2) and core (1) outside surface, its step is poly-as follows:

Step 1 with core (1) clamping that designs the scroll chuck of fiber winding machine and top between;

The step 2 fiber winding machine is the uniform speed rotation, silk mouth (3) is done linear uniform motion from the maximum latitude circle side direction opposite side of core (1), direction of motion is parallel to the axial line of core (1), fabric strip (2) hoop that applies certain winding tension and be soaked with resin is wound on the core (1), and this moment, winding angle θ got pi/2;

When step 3 was wound into certain point when the fabric strip that applies certain winding tension (2), the fiber on the core (1) began to skid, and determines the numerical value of this some r of place, the substitution formula Try to achieve the coefficientoffriction (r) of this point, this friction factor is that fabric strip (2) is along the minimized friction coefficient between winding of core (1) generatrix direction and core (1) surface.

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