CN2381839Y - Energy storing flywheel with section of normal distribution curves - Google Patents

Abstract

The utility model relates to an energy storing flywheel, the section of which is a normal distribution curve, the contour line of the section of the flywheel is the normal distribution curve, the shape of the section is that z is equal to (z0e minus p) dividing by 20 (wr) square and z is equal to 0, the r is more or equal to and the r is smaller or equal to the R and the R is smaller than the r, z0 is half of the thickness of the rotating shaft of the fly wheel, R is the radius of the maximum outer edge, and the size of the flywheel accords with the following relational expression: z0 dividing by R is equal to (2 to 10) dividing by 100 and w0 is equal to 1 dividing by the R multiplying by the route of (S minus 8) multiplying Q dividing by P. The energy storage flywheel which is provided with the shape of the utility model is provided with high specific energy, and the design and calculation of the flywheel are simple.

Description

The cross section is the accumulated energy flywheel of normal distribution curve

The utility model relates to the accumulated energy flywheel that a kind of cross section is a normal distribution curve, belongs to technical field of vehicle manufacture.

The flywheel energy storage that utilizes high speed rotating is a very ancient topic.But be not easy because the mechanical energy of flywheel energy storage converts other forms of energy to, therefore, the twentieth century previous decades is very big technological break-through and practicability never.

The seventies later stage in this century, because the development of permagnetic synchronous motor and power inverter technology is very easy to the conversion of mechanical energy and electric energy, and practicability.Permagnetic synchronous motor is connected with flywheel, electric energy is inputed or outputed flywheel, make the mechanical energy of the flywheel of rotation be transformed into the electric energy that is easy to use by permagnetic synchronous motor.Now, utilize flywheel energy storage to become a reality.Flywheel energy storage is a kind of mechanical energy storing device, also is flying wheel battery or flywheel power supply (mechanical energy battery).Because flying wheel battery does not pollute, therefore energy storage has boundless application prospect than high.For example, at wind-power electricity generation, energy storage device is made in the solar electrical energy generation aspect.Electric bicycle, the energy storage device of electric vehicle.Replace various lead-acid batteries, especially among the UPS.Since 1980's, about the existing a large amount of application of the patent of the manufacture view of flywheel energy storage and flywheel, as U.S. US4408500, US5695584, US5566588 or the like.The spy of Japan opens flat 6-210748

The basic principle of flywheel energy storage is to utilize the kinetic energy of rotary article In the formula 1: E: the kinetic energy of flywheel

J: the rotary inertia of flywheel, relevant with the sectional shape of the quality of flywheel material and flywheel.

ω: flywheel rotational angular.

The size of the energy of flywheel storage is directly proportional with the rotary inertia J of flywheel and square ω 2 of flywheel rotational angular.Flywheel in case make is finished, and its rotary inertia just determined, the rotating speed that improves flywheel can make flywheel improve the mechanical energy that stores with the speed of rotating speed square.But the rotating speed of flywheel can not unlimited raising.This is because rotating speed is high more, the stress that material bore is caused by centrifugal force in the flywheel also with the rotating speed of flywheel with rotating speed square rule increase.When the rotating speed of flywheel was brought up to internal stress that flywheel causes by centrifugal force greater than the limit allowable stress of the material of flywheel, flywheel can destroy.At this moment flywheel rotating speed is destroying rotating speed (flywheel).When the rotating speed of flywheel was very high, the energy of flywheel was very big, and unexpected destruction can set off an explosion.The sectional shape of flywheel has not only determined the size of the rotary inertia of flywheel, but also the internal stress of decision flywheel distributes.Good sectional shape can make flywheel under certain rotating speed, and internal stress distributes more even, and maximum internal stress is less.That is to say that under the condition that the maximum permissible stress of flywheel material is determined, good sectional shape can make flywheel be operated in high rotational speed, stores bigger energy.So the maximum permissible stress of flywheel material and the sectional shape of flywheel will determine the energy storage size of flywheel.

For the size of the object stored energy of comparative unit quality (weight), can utilize the notion of specific energy, that is: $e=E/M----\left(2\right)$ E wherein: unit mass (weight) specific energy, unit: watt-hour/kilogram.W.h/kg

E: the total energy that the energy storage object is stored, unit: joule.Jr

M: the gross mass that the energy storage object is comprised, unit: kilogram.kg

Formula 2 is applicable to the object of various energy storage modes, as the flywheel energy storage, and chemical energy storage, heat accumulation and accumulator are put or the like.

For example: the specific energy of lead-acid battery is at present: 30-50W.h/kg

The air-depolarized zinc type button cell specific energy is: 400W.h/kg

Flywheel energy storage needs to satisfy:

1, specific energy e is big as far as possible.

2, strength of materials height, design easily, processing.

3, the shape of flywheel is convenient to connect, and installs.

At present, the material that most of patents are used is the carbon fiber mixed material, or Kev draws nylon material (kevlar), and the shortcoming of this class material is to process, and mechanical property is a non-isotropy, and distortion is bigger during the flywheel high speed rotating.And the flywheel sectional shape with above-mentioned material scarcely is the sectional shape of optimum specific energy.Though the patent that has has adopted isotropic material, as US4408500, sectional shape complexity, and the made flywheel of employing unlike material are made complexity, and the joint of the material of unlike material is separation or the like problem easily.The specific energy of the sectional shape in the patent neither optimum sectional shape.When changing radius size simultaneously,, also to carry out complicated designing and calculating because stress does not have geometrical similarity.

The utility model purpose is that a kind of cross section of design is the accumulated energy flywheel of normal distribution curve, with the most frequently used isotropy metal is material, the sectional shape of flywheel is normal distribution curve (hereinafter to be referred as Stodola), makes flywheel have bigger specific energy, and design easily.

The cross section of the utility model design is the accumulated energy flywheel of normal distribution curve, and the cross section contour of flywheel is a normal distribution curve, sectional shape: , establish z ₀For the thickness on the flywheel center of rotation half, R is the maximum outer rim radius of flywheel, then the size conforms following relationship formula of flywheel: $\frac{z_0}{R}=\frac{2~10}{100}$ ${\mathrm{\ω}}_0=1/R\·\sqrt{\frac{(5~8){\mathrm{\σ}}_0}{\mathrm{\ρ}}}$ In the following formula, ω ₀The flywheel angular velocity of selecting when being the design flywheel, ρ are the density of making the flywheel material therefor, σ ₀It is the maximum permissible stress of making the flywheel material therefor.

Accumulated energy flywheel with the utility model shape has higher specific energy, and flywheel design is calculated simple.

Illustrate that accompanying drawing is as follows:

Fig. 1 is that the cross section is the structural representation of the accumulated energy flywheel of normal distribution curve.Fig. 2 is the coordinate diagram that flywheel design is calculated usefulness.

Below in conjunction with accompanying drawing, introduce content of the present utility model in detail.The Stodola cross section is with rotatingshaft center symmetrical section shape:

Wherein: ω ₀The angular velocity of the flywheel of choosing when being design.

σ ₀It is the maximum permissible stress that given flywheel uses material.

ρ is the density (proportion) that given flywheel uses material.

z ₀Be half of thickness on the flywheel center of rotation.

R is the maximum outer rim radius of flywheel.

Specific energy $=\frac{{\mathrm{\ω}}^2}{2}\·\frac{\underset{0}{\overset{R}{\∫}}{r}^3\·e^{-C^2\·r^2}\·\mathrm{dr}}{\underset{0}{\overset{R}{\∫}}r\·e^{-C^2\·r^2}\·\mathrm{dr}}----\left(4\right)$ Wherein,

As seen, the center thickness H of specific energy and flywheel is irrelevant from formula (4).(actual because the maximum speed of flywheel and the thickness z of flywheel ₀Relevant, so the specific energy of flywheel is still relevant with the center thickness of flywheel.) specific energy and the R of flywheel, ω, ω ₀, ρ, σ ₀, , value choose relevant.For the flywheel of Stodola sectional shape, its specific energy is: $=\frac{{\mathrm{\ω}}^2}{{\mathrm{\ω}}_0^2}\·\frac{{\mathrm{\σ}}_0}{\mathrm{\ρ}}\·(1-\frac{C^2{R}^2\·e^{-C^2{R}^2}}{1-e^{-C^2{R}^2}})----\left(6\right)$ Order

$e=\frac{{\mathrm{\ω}}^2\·{\mathrm{\σ}}_0}{{\mathrm{\ω}}_0^2\·\mathrm{\ρ}}\·(1-\frac{\mathrm{\τ}\·e^{-\mathrm{\τ}}}{1-e^{-\mathrm{\τ}}})----\left(8\right)$ $e=\frac{{\mathrm{\ω}}^2\·{\mathrm{\σ}}_0}{{\mathrm{\ω}}_0^2\·\mathrm{\ρ}}\·(1-\frac{\mathrm{\τ}}{e^{\mathrm{\τ}}-1})----\left(9\right)$ Formula (9) shows that specific energy e is With

Long-pending function.

It is monotonic increasing function.Its limiting value is in τ=∝, maximum value at this moment In addition, specific energy still Function, if Greater than 1, specific energy might greater than For example,

Be 0.75,

Be 1.4, then specific energy can greater than The following formula explanation, ω is greater than ω ₀, and be the bigger the better.This need pass through the program repeat tentative calculation.Can find the high specific energy.Because in reality is made, flywheel radius R, working strength σ ₀And quality (weight proportion) density all is given, so flywheel rotational angular ω is big more, specific energy is also big more.

In the ordinary course of things.Common given R, ρ, σ ₀, ask specific energy e at z ₀And ω ₀Be the maximum value under the situation of variable.Set z ₀And ω ₀Initial value, just can obtain the shape in Stodola cross section.Utilize finite element method, obtain flywheel under different ω circle data, the actual maximum stress σ of flywheel.Usually require σ＜σ ₀, and requirement

(precision is decided as requested).By repeatedly tentative calculation, can find the flywheel angular velocity omega in the EE Error Excepted precision, angular velocity omega at this moment is exactly under given material, given z ₀And ω ₀The time the maximum angular rate ω of flywheel.Same method changes z ₀And ω ₀Numerical value, repeat above-mentioned tentative calculation process, can obtain optimum z ₀And ω ₀Numerical value.At this moment ω is exactly the actual maximum angular rate of flywheel.Also obtain simultaneously the sectional shape curve with high specific energy in Stodola cross section.

The ratio of the characteristic size of flywheel is as follows: $\frac{z_0}{R}=\frac{2~10}{100}----\left(10\right)$ ${\mathrm{\ω}}_0=1/R\·\sqrt{\frac{(5~8){\mathrm{\σ}}_0}{\mathrm{\ρ}}}----\left(11\right)$

She Ji flywheel sectional shape is the flywheel sectional shape with big specific energy according to the above ratio.

Usually, given parameter ρ, σ ₀, behind the R,, in given scope, can determine ω according to formula (10) (11) ₀, z ₀ρ has been arranged, σ ₀, R, ω ₀, z ₀, the shape in Stodola cross section has just been decided.Utilize finite element method,, obtain at maximum permissible stress σ by tentative calculation ₀Condition under, maximum flywheel angular velocity omega.If remove R in the formula (10) (11), beyond the H, other parameter constants, under given maximum permissible stress condition, this Stodola cross section has geometrical similarity under the garden radius condition outside difference.Promptly when finding behind the optimum Stodola sectional shape under the radius (original calculation), can be by the size (similar calculating) of the Stodola sectional shape of other radiuses of principle design of geometric similarity, thereby, can simplify the designing and calculating of flywheel.

Under the given condition of the maximum permissible stress of material, have to the flywheel size and the rotating speed of similar calculating with rotating speed for the flywheel size of original calculation: $\frac{{\mathrm{\ω}}_1}{{\mathrm{\ω}}_0}=\frac{R_0}{R_1}----\left(12\right)$

ω ₀: the flywheel rotational angular of original calculation.

R ₀: the outer rim radius of the flywheel of original calculation.

ω ₀: the flywheel rotational angular of similar calculating.

R ₁: the outer rim radius of the flywheel of similar calculating.

When the radius of the flywheel that will design was greater than or less than the flywheel radius of original calculation, the sectional dimension of flywheel was by aforementioned 2 designs, and the maximum (top) speed of flywheel is (12) design then by formula.

Introduce two embodiments of the present utility model below.

Embodiment 1: select homemade alloyed steel for use: code name 651-1, the Maraging steel of 350ksi level.Its density p=8 * 10 ³Kg/m ³, maximum permissible stress σ ₀=2400 * 10 ⁶Pa.Set the maximum outer rim radius R=0.095m of flywheel.According to formula (10), can obtain z ₀=0.0019m～0.0095m.The present is got z ₀=0.006m.According to formula (11), can get

Radian per second.Get ω ₀=15000 radian per seconds.In view of the above, sectional shape can obtain according to formula (3):

Formula (13) is exactly the cross section curve of the actual normal distribution of our resulting accumulated energy flywheel.

According to formula (13), by calculating, the actual maximum speed that can obtain accumulated energy flywheel is 144410 rev/mins.The high specific energy is: 74.64W.h/kg.With same thickness, the accumulated energy flywheel of the polygonal cross-section of same radius is compared, and the specific energy of the accumulated energy flywheel in normal distribution curve cross section is bigger than the specific energy of the accumulated energy flywheel of polygonal cross-section: 7～20%.

Embodiment 2: choose the made accumulated energy flywheel the same with example 1.With the flywheel in the example 1 is that this routine accumulated energy flywheel of original calculation energy storage is similar flywheel.Given similar accumulated energy flywheel outer rim maximum radius R ₁=0.0475m.According to geometrical similarity principle, z then ₀₁=0.003m.According to formula (12), the design corner speed of this similar accumulated energy flywheel

Radian per second.The cross section curve of the accumulated energy flywheel of this moment is

At this moment the actual maximum speed of accumulated energy flywheel is: 288810 rev/mins, specific energy is identical with example 1.

If use Maraging steel, allowable stress is 2400 MPas, and density p is 8 * 10 ³Kg/m ³, then the maximum speed of example (1) is: 144410 rev/mins.The high specific energy is: 74.64W.h/kg.By FEM (finite element) calculation, the specific energy of Stodola sectional shape is greater than the specific energy 7～20% of polygonal cross-section shape.Example (2) is used and example (1) same material, and sectional dimension ratio (1) is little, but specific energy is the same.The maximum (top) speed of example (2) flywheel is the twice of example (1).

Claims (1)

1, a kind of cross section is the accumulated energy flywheel of normal distribution curve, it is characterized in that, the cross section contour of this flywheel is a normal distribution curve, sectional shape: , establish z ₀For the thickness on the flywheel center of rotation half, R is the maximum outer rim radius of flywheel, then the size conforms following relationship formula of flywheel: $\frac{z_0}{R}=\frac{2~10}{100}$ ${\mathrm{\ω}}_0=1/R\·\sqrt{\frac{(5~8){\mathrm{\σ}}_0}{\mathrm{\ρ}}}$ In the following formula, ω ₀The flywheel angular velocity of selecting when being the design flywheel, ρ are the density of making the flywheel material therefor, σ ₀It is the maximum permissible stress of making the flywheel material therefor.

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