KR101251632B1 - Gerotor oil pump and method for designing the same - Google Patents

Abstract

The present invention is configured in the form of the combination of the hypocycloid-polycircle-epi cycloid of the inner rotor, and the shape of the outer rotor from the inner rotor shape can further reduce the noise and wear resistance during operation The present invention relates to a rotor rotor pump and a method of designing the same, wherein the rotor rotor pump according to the present invention includes an outer rotor having a plurality of robes formed on an inner circumferential surface thereof, and an eccentric rotation in an inner space of the outer rotor. In a GROTOR oil pump having an inner rotor, from P ₀ to P ₁ for the inner rotor half pitch section based on the inner rotor center point O ₁ = (e, 0) where the eccentricity is e ₁₎ is in the hypo-cycloid curve, from P ₁ as poly circle curve which is a combination of the circle center point of the plurality of different continuous to _{P 2 (β 2), P} 2 or more (β _3/2) four epi It is characterized by being a large Lloyd curve.

Description

Gerotor Oil Pump and Method for Designing the Same}

The present invention relates to a gerotor oil pump and a method of designing the same, and more particularly to a polycircle-epi cycloid in which the inner rotor is a combination of a plurality of consecutive circles having different hypocycloid-center points. It relates to a gyro oil pump and a method of designing the combination consisting of.

Automotive engine lubrication is essential for smooth engine operation and long life. One of the components of the lubrication system is an internal gear pump which is advantageous in terms of flow rate, durability, noise and miniaturization.

The oil pump is an essential functional part of an engine that is mounted and driven in an automobile engine, and converts mechanical energy supplied from the engine into pressure energy and speed energy of the engine oil to lubricate each sliding part of the engine. This part is to prevent abnormal wear and sintering of parts. Components constituting the oil pump is composed of an electric motor, a key, an inner rotor, a rotor case, an O-ring, a screw, and the like. . In addition to the other standard products in the oil pump, the rotor case is produced by die casting according to the specifications of the oil pump, and the outer rotor and the inner rotor are produced by powder forging.

Meanwhile, a gerotor oil pump and a motor having an arbitrarily generated rotor are composed of an inner rotor and an outer rotor, so the structure is simple and the shape is complicated as the precision of processing increases due to the development of manufacturing technology of sintered products. It is easy to process, easy to assemble, and there is little relative movement between two teeth, so there is little change of efficiency even in long-term use, and it has excellent suction performance. In addition, it is widely used as a pump that gives suction and resistance to a tandem pump combined with a piston pump, and is especially used as a source of lubricating oil for engine lubrication or an hydraulic source of an automatic transmission due to less noise than other pumps. . In addition, it has an advantage that the discharge amount per one revolution is larger than the vane or the gear pump compared to the total volume. For this reason, it is widely used in hydraulic systems, and recently, with the development of processing technology, the applicability is gradually expanding.

Therefore, many techniques have been performed in connection with the rotor tooth design of the girder type oil pump / motor. Colbourne ("Gear Shape and Theoretical Flow Rate in Internal Gear Pumps," Trans. Of the CSME, Vol. 3, No. 4 pp. 215-223, 1975) simulates the contact of the internal and external rotors to simulate internal rotor teeth. We calculated the coordinates of and calculated the area in the chamber that is closed by the tooth curves of the inner and outer rotors. Sae-gusa ("Development of Oil-Pump Rotor with a Trochoidal Tooth Shape," Tran. SAE, 840454. pp. 359-364, 1984), etc., secured the inner rotor and rotated the outer rotor to form a circular arc. The trajectory of the center of the rotor is calculated, and the equation of the inner rotor teeth is derived from the bite characteristics of the inner and outer rotors. Beard ("Hypotrochoidal versus Epitrochoidal Gerotor Type Pumps with Special Attention to Volume Change Ratio and Size," ASME Proceedings, Design Automation conferance, Boston, Mass. The flow rate change between) is compared and the mathematical relationship is shown. Tsay ("Gerotor Pumps-Design Simulation And Contact Analysis," pp. 349-356. 1992) presented a method to simulate the cutting process and obtain the teeth of an internal rotor. On the other hand, Lee Sung-cheol ("Journal of KSTLE, Vol. 11, No 2, pp 63-70. 1995), uses the family of curves to induce the equation of the teeth of the internal rotor and target the hydraulic motor. Characteristic analysis, such as flow rate and torque calculation, was performed.

However, the contents published so far have focused on theoretical analysis, and there are many problems in actual design because there is no computerized example. In addition, there is a need for the technology of designing the rotor shape, which is the most important in the oil pump design technology, and the technology for the new teeth of high performance, high efficiency, low noise and low vibration is urgently needed. In particular, by analyzing the factors related to the performance, vibration, and efficiency of the oil pump, geometric geometry, computational fluid dynamics (CFD), and system sumulation approaches were required.

As a conventional technology for solving such a problem, the Gerotor oil pump disclosed in Korean Patent Application Publication No. 10-2011-0113541 (registered on October 17, 2011) proposed by the present applicant is disclosed. The GROTOR oil pump of this patent discloses an inner rotor by inserting an arc curve between a hypocycloid curve and an epi cycloid curve, and creates an outer rotor trajectory from the inner rotor to form an outer rotor. have.

However, the GROTOR oil pump of the above-mentioned patent publication has a significant advantage in terms of flow rate, abrasion resistance, and noise compared to the conventional GROTOR oil pump, but the circular path between the hypocycloid and the epicycloid of the inner rotor There was a limit to reduce the noise.

The present invention is to solve the above problems, an object of the present invention is a combination of a polycircle-epi cycloid consisting of a combination of a plurality of consecutive circles different from the hypocycloid-center point of the inner rotor shape The present invention provides a GROTOR oil pump and its design method which can further reduce noise and wear resistance during operation by deriving the shape of the external rotor from the internal rotor shape.

The rotor rotor pump according to the present invention for achieving the above object is an outer rotor in which a plurality of rovers (lobe) is formed on the inner peripheral surface, and the inner rotor eccentrically rotating in the inner space of the outer rotor ( In a rotor rotor pump with an inner rotor, P ₀ to P ₁ (β ₁ ) for a half pitch section of the inner rotor, based on the inner rotor center point O ₁ = (e, 0) with eccentricity e in the cycloid curve, from P ₁ as poly circle curve which is a combination of up to P ₂ (β ₂₎ is a source of a plurality of center points of different continuous, P ₂ or more (β _3/2) is characterized by being a epi-cycloid curve do.

According to another aspect of the present invention, there is provided a method of designing a gerotor oil pump, comprising: designing an inner rotor by combining a hypocycloid curve, a polycircle curve, and an epicycloid curve; The design method of the rotor rotor pump is provided, comprising the step of calculating the trajectory of the outer rotor from the shape of the inner rotor to design the outer rotor.

According to the present invention, it is possible to improve the noise and wear resistance by applying a poly circle and a cycloid shape which is advantageous for the sliding rate between the inner rotor and the outer rotor.

에서 접선기울기(Tangential gradient)를 나타내는 도면이다.
도 20은 외부로터의 변형(modification) 방법을 나타내는 도면이다.
도 21은 본 발명에 의해 설계된 내부로터와 외부로터의 형상(profile)을 나타내는 도면이다. 1 is a view showing a profile of one pitch angle section of the inner rotor of the rotor rotor pump according to an embodiment of the present invention.
2 is a diagram showing a hypocycloid curve section for deriving the constitutive equation of the hypocycloidic curve according to the present invention.
3 is a view showing the coordinates of the poly circle curve for deriving the constitutive equation of the poly circle according to the present invention.
4 is a diagram showing an epicycloid curve section for deriving the constitutive equation of the epicycloid curve according to the present invention.
5 is a view showing a profile of one pitch section of the inner rotor for the curve boundary guidance according to the present invention.
FIG. 6 is a diagram illustrating coordinates of a curved section of a polycircle for deriving a curve boundary at a point P ₁ of the inner rotor.
FIG. 7 is a diagram illustrating coordinates of a curved section of a polycircle for deriving a curve boundary at a point P ₂ of the inner rotor.
FIG. 8 is a diagram illustrating an effect of cost function convergence for the design of an internal rotor.
9 is a view showing an internal rotor profile.
10 is a view showing a rotation simulation rotated by changing the center of the inner rotor.
11 is a view showing a group of curves of the inner rotor rotation traces obtained by the rotational simulation of the inner rotor fixing method.
12 is a diagram illustrating an example of an interference phenomenon between an internal rotor and an external rotor.
FIG. 13 is a diagram illustrating a state in which an external rotor curve is modified by an interference avoiding equation.
14 is a diagram illustrating an interference phenomenon between the inner rotor and the outer rotor.
15 is a diagram illustrating an interference phenomenon according to a rotation angle.
16 is a diagram illustrating coordinates of a polycircle curve.
17 is a view showing the maximum interference interval of the inner rotor and the outer rotor.
18 is a diagram illustrating an offset movement of a point on a polycircle curve.
19 is the point

It is a diagram showing a tangential gradient in.
20 is a diagram illustrating a modification method of an external rotor.
Figure 21 is a view showing the profile (profile) of the inner rotor and the outer rotor designed by the present invention.

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the gyrotor oil pump and its design method according to the present invention.

1 to 21 illustrate a method of designing a rotor of a gerotor oil pump using a tooth curve formed of a hypocycloidic-polycircle-epicycloidic curve according to an embodiment of the present invention. As described above, the method of designing the gerotor oil pump includes inserting a polycircle composed of a combination of a plurality of consecutive circles having different center points between the hypocycloid curve and the epicycloid curve, so as to first insert the inner rotor. After the configuration is a method for creating a trajectory of the outer rotor in the inner rotor.

First, in designing the rotor rotor pump according to the present invention, it will be described in detail the geometric analysis of the inner rotor.

1 to 4, when a rolling circle rolls around a pitch circle without sliding, a curve drawn by a point on the rolling circle is called a cycloid curve, which is a curve generated when the rolling circle touches and rolls around the pitch circle. Hypocycloids are called, and the curves that occur when rolling out of contact around the pitch circle are called epicycloids. In this way it may be composed of a combination of a half pitch intervals _{(β 1, β 2, β} 3/2) to sequentially Hypocycloid, poly as shown in Fig circles and epi-cycloidal curve of the inner rotor.

과 일치하며 각각의 반경 r_bh, r_be는 아래의 수학식 1과 같이 구할 수 있다.Referring to the process of designing the teeth of the inner rotor using the configuration equation of the hypocycloidoid, polycircle and epicycloid curve, first, as shown in FIG. 1, the base circle center of the hypocycloid and epicycloid curve is the inner rotor. Focus

And each radius r _bh , r _be can be obtained as in Equation 1 below.

의 기울기와 같다. 따라서 도 1에서와 같이 하이포 사이클로이드 및 에피 사이클로이드 곡선 사이에 폴리서클 곡선을 삽입하기 위해 곡선 연결점 P₁, P₂는 사이클로이드 곡선의 기초원 위에 있지 않다. 그러므로

,

라 하면 수학식 2의 관계식이 성립한다.On the other hand, due to the nature of the cycloid curve, the tangent slope of the hypocycloid and epi cycloid curves at point P ₁ of FIG.

Is equal to the slope of. Thus, in order to insert the polycircle curve between the hypocycloid and epi cycloid curves as in FIG. 1, the curve connection points P ₁ , P ₂ are not on the base circle of the cycloid curve. therefore

,

Then, the relation of Equation 2 is established.

In FIG. 1 O _p (O _px , O _py ) is the midpoint of the polycircle. In the inner rotor half pitch angle section, β ₁ is the section of the hypocycloid curve, β ₂ is the section of the polycircle curve, 0.5β ₃ is the section of the epicycloid curve. Further, when the point on the hypocycloid curve cloud circle is located at P ₁ , if the midpoint of the cloud circle is O _h1 , φ ₁ is equal to ∠P ₁ O ₁ O _h1 . Likewise, when the point on the epicycloid curve cloud circle is located at P ₂ , the midpoint of the cloud source is O _e2 , φ ₂ is equal to ∠P ₂ O ₁ O _e2 . θ _p1 and θ _p2 are the range angles at points P ₁ and P ₂ in the polycircle curve, respectively.

이고, 회전각은 θ_h1이다. 이를 이용하여 하이포 사이클로이드 곡선의 궤적을 구하면 수학식 3과 같다.The constitutive equation of the hypocycloid curve is obtained as follows. As shown in Fig. 2, the midpoint of the rolling circle at the point P on the hypocycloid curve is O _h , and the rolling circle moving angle at this time is β and the rotation angle is θ _h . When the point P is located at P ₁ , the rolling angle of the rolling circle is

And the rotation angle is θ _h1 . Using this, the trajectory of the hypocycloid curve can be obtained from Equation 3.

Fig up at point P ₀ on the 2 In the generating circle P, when moving from P ₀ to P _1, since the arcuate length of the base circle of the rolled without generating circle slide corresponds to the distance and the original moving each cloud same each other, Equation (4) Hold.

및

에 대해 제2코사인 법칙을 적용하면 θ_h1 및 φ₁은 아래의 수학식 5와 6과 같이 구할 수 있다.ΔP ₁ O ₁ O _h1 in FIG. 2

And

When the second cosine law is applied to θ _h1 and φ ₁ can be obtained as Equations 5 and 6 below.

는 수학식 7과 같고, 수학식 6과 7을 이용하면 β₁은 수학식 8과 같이 구할 수 있다.Using Equations 4 and 5

Is equal to Equation 7, and using Equations 6 and 7, β ₁ can be obtained as Equation 8.

Therefore, when Equation 3 is arranged using Equation 4, the configuration equation of the hypocycloid curve may be obtained as Equation 9.

Next, the configuration equation of the polycircle curve is obtained with reference to FIG. 3.

의 궤적으로 표현할 수 있다.The polycircle curve is a point of Equation 10 as shown in FIG.

It can be expressed as the trajectory of.

이므로 수학식 11이 성립하며,

및

를 φ에 대해 미분하면 수학식 12와 같다.The radius of curvature that decreases as φ increases in Equation 10 is

Since Equation 11 holds,

And

Differentiating with respect to φ is as follows.

Using Equation 12, the tangent slope at point P ⁽¹⁾ of FIG. 3 can be obtained as shown in Equation 13.

가

으로 옮겨진다면 점 P⁽¹⁾는 도 4의

에 위치한다. 수학식 10을 이용하여 점 P⁽²⁾의 좌표를 구하면 다음과 같다.The coordinate system of FIG. 3 rotates clockwise by θ and the point

end

Is moved to the point P ⁽¹⁾ of FIG.

Located in By using Equation 10, the coordinates of the point P ⁽²⁾ are obtained as follows.

In FIG. 1, when φ values at the points P ₁ and P ₂ are θ _p1 and θ _p2 , the constitutive equation of the polycircle curve can be obtained as shown in Equation 15.

이다. And,

to be.

Next, the configuration equation of the epicycloid curve is obtained with reference to FIG. 4.

,

라 하면, 이 때의 구름원 이동각은

, 회전각은 (θ_e-θ_e2)으로 정의하였다. 이를 이용하여 에피 사이클로이드 곡선의 궤적을 구하면 수학식 16과 같다.As shown in FIG. 4, the midpoint of the cloud circle at point P on the epicycloid curve is denoted by O _e ,

,

In this case, the cloud circle moving angle is

, The rotation angle was defined as (θ _e -θ _e2 ). Using this, the trajectory of the epicycloid curve can be obtained from Equation 16.

In FIG. 4, when the point on the cloud circle moves from P ₂ and P to the inner rotor half pitch angle point, the distance that the cloud circle rolls without slip and the arc length of the base circle corresponding thereto are equal to each other.

에서

및

에 대해 제2코사인 법칙을 적용하면 θ_e2 및 φ₂는 수학식 18 및 19와 같이 구할 수 있다.4

in

And

When the second cosine law is applied to, θ _e2 and φ ₂ can be obtained as Equations 18 and 19.

Β ₃ can be obtained as in Equation 20, and the relation of Equation 21 holds for β ₁ , β _2, and β ₃ .

By using Equations 19 and 21, (β ₁ + β ₂ + φ ₂ ) can be obtained as shown in Equation 22.

Therefore, by arranging Equation 16 using Equation 17, the constitutive equation of the epicycloid curve can be obtained as Equation 23 below.

Next, the curve boundary condition is derived.

Curves having different configuration equations of Equations 9, 15, and 23, respectively, should be smoothly connected with the same coordinate values and instantaneous tangent slopes at connection points P ₁ and P ₂ as shown in FIG.

일 때, 하이포 사이클로이드 곡선 상의 점 P₁에서 O₁까지의 거리는 수학식 24와 같이 구할 수 있다. 또한 도 1에서 ∠P₁O₁P₀= β₁이므로 하이포 사이클로이드 곡선 상의 점 P₁의 좌표는 수학식 25와 같이 구할 수 있다.First, the coordinates at point P ₁ must be the same. In Equation (9)

When the distance from the point P ₁ to the O ₁ on the hypocycloid curve can be obtained as shown in Equation 24. In addition, it coordinates of the point P ₁ on the hypo-cycloid curve, so _{∠P 1 O 1 P 0 = β} 1 in Figure 1 can be obtained as shown in equation (25).

일 때, 폴리서클 곡선 상의 점 P₁의 좌표가 수학식 25의 좌표값과 같아야 하므로 수학식 26 및 27이 성립한다.In equation (15)

When the coordinates of the point P ₁ on the polycircle curve should be equal to the coordinate value of the equation (25) equations (26) and (27) hold.

Second, the instantaneous tangential slope at point P ₁ must be the same. In Equation 9, when β = θ ₁ , the instantaneous tangential slope of the hypocycloid curve is shown in Equation 28.

Using Equation 25, the coordinates of the point on the hypocycloid curve can be expressed as Equation 29.

When Equation 28 is arranged using Equation 29, Equation 30 is expressed as follows.

라고 정의하였다. 따라서 수학식 31과 같이 내부로터 곡선에서 점 P₁에서의 순간 접선기울기를 구할 수 있다.On the other hand, and also the focus O _1, as shown in 5 the tangent point and hypo acute angle to each other forming a tangent at P ₁ in the cycloid curve at the point P ₁ in the radius r _p1 circle

It is defined as. Therefore, as shown in Equation 31, the instantaneous tangent slope at the point P ₁ can be obtained from the internal rotor curve.

Equation 32 must be established because the values of Equations 30 and 31 must be the same.

은 직교한다. 따라서 P₁에서의 접선의 기울기각도를 θ_t1라 하고 수학식 31을 이용하면 수학식 33의 관계식이 성립한다.When the curvature radius of the extension and the reference axis that meets at the point P ₁ on the poly-circle curve in Figure 6 have been called F _1, P ₁ and the tangent line at the

Is orthogonal. Therefore, when the inclination angle of the tangent line in P ₁ is θ _t1 and Equation 31 is used, the relation of Equation 33 is established.

Third, the coordinate values at the point P ₂ must be the same. When β = β ₁ + β ₂ + φ ₂ = θ ₂ in the constitutive equation of Equation 23, the distance from the point P ₂ on the epicycloid curve to O ₁ can be obtained as shown in Equation 34. In addition, in FIG. 1, since ∠P ₂ O ₁ P ₀ = β ₁ + β ₂ , the coordinate of the point P ₂ on the epicycloid curve is expressed by Equation 35.

When φ = θ _p2 in Equation 15, Equations 36 and 37 hold since the coordinates of the point P ₂ on the polycircle curve must be the same as the coordinate values of Equation 35.

Finally, the instantaneous tangent slopes at point P ₂ must be equal to each other. When β = θ ₂ in Equation 23, the instantaneous tangential slope of the epicycloid curve is shown in Equation 38.

Using Equation 35, the coordinates of the point P ₂ on the epicycloid curve can be expressed as Equation 39.

When Equation 38 is arranged using Equation 39, Equation 40 is expressed as follows.

는 직교한다. 따라서 P₂에서의 접선의 기울기각도를 θ_t2라 하고 수학식 33을 이용하면 수학식 41의 관계식이 성립한다. 따라서, 폴리서클 곡선 상의 점 P₂에서의 순간 접선기울기는 수학식 42와 같이 구할 수 있다.When the curvature radius of the extension and the reference axis that meets at the point P ₂ on poly-circle curve in Figure 7 that have F _2, tangent at P ₂ and

Is orthogonal. Therefore, when the inclination angle of the tangent line in P ₂ is θ _t2 and Equation 33 is used, the relation of Equation 41 is established. Therefore, the instantaneous tangent slope at the point P ₂ on the polycircle curve can be obtained as shown in Equation 42.

Equation 43 must be established because the values of Equations 40 and 42 must be the same.

On the other hand, when Equations 26 and 36 are combined, Equation 44 is established.

Similarly, when Equations 27 and 37 are combined, Equation 45 is established.

Equations 44 and 45 can be expressed by Equations 46 and 47, respectively, for r and μr.

로, 수학식 47을

로 정의하면, r와 μr는 수학식 48과 같이 구할 수 있다.Equation 46

Equation 47

R and μr can be obtained as in Equation 48.

In Equation 48, P = CE-BF, Q = AF-CD, and R = AE-BD can be arranged as Equations 49, 50, and 51 using Equations 33, 46, and 47, respectively.

Therefore, using Equations 49-51, r, μ can be obtained as Equation 52.

In addition, using Equation 52, O _px and O _py in Equations 26 and 27 can be obtained as Equations 53 and 54, respectively.

Therefore, in the constitutive equations of Equations 9, 15 and 23, the unknowns are equal to r _h , r _e , r _p1 , r _p2 , θ _p1 and θ _p2 . If p _2max , e, r _h , r _e , r _p1 and r _p2 are all k (≠ 0) times as in Eq. 55 at θ ' _p1 = θ _p1 and θ' _p2 = θ _p2 , It can be seen that Equation 56 holds.

Substituting Equation 56 into the boundary condition equations of Equations 32 and 43 is the same as Equations 57 and 58, respectively.

인 경우

를 계산하여 6개의 미지수를 도출할 수 있다. 한편, 수학식 2를 6개의 부등식으로 분리하고 수학식 11을 이용하면 수학식 59의 설계 제약조건을 얻을 수 있다.Since equation 57, as in 58 ρ _2max, e, r _h, r _e, r _p1 and r _p2 are both k (≠ 0) times may be satisfied with a curved boundary condition equation, in the case of ρ _2max = 12 the boundary condition Construct a database of satisfactory unknowns r _h , r _e , r _p1 , r _p2 , θ _p1, and θ _p2 ,

If

We can derive six unknowns by calculating. Meanwhile, if Equation 2 is divided into six inequalities and Equation 11 is used, a design constraint of Equation 59 may be obtained.

By designing the actual inner rotor using the configuration equation and the curve boundary equation as described above, and calculating the tip width of the inner rotor is as follows.

및

값은 수학식 61 및 63과 같다.The boundary condition equations of Equations 32 and 43 are defined as f ₁ = 0 and f ₂ = 0, respectively. Here, when Z ₁ = 9, ρ _2max = 12, e = 1.31, and γ = 71 °, the unknown r _h , r _e , r _p1 , r _p2 , θ _p1 and θ _p2 are represented by Equations 60 or 62 Assuming a value for each

And

The values are as shown in Equations 61 and 63.

이며, 내부로터를 설계하면 도 8과 같이 곡선 연결점에서 원활하게 연결되지 못한다. 따라서 수학식 32, 43의 경계조건식에 대한 수렴조건을

로 설정하여 수학식 64와 같이 미지수에 대한 해를 구하였다.For both Equations 60 and 62

If the inner rotor is designed, it may not be smoothly connected at the curved connection point as shown in FIG. Therefore, the convergence condition for the boundary condition equations

The solution to the unknown was obtained as shown in Equation 64.

의 수렴조건 및 설계 제약조건 수학식 59를 만족하면서

을 최소화하는 미지수 r_h, r_e, r_p1, r_p2, θ_p1 및 θ_p2 의 값을 도출하였다.When Z ₁ = 9 and ρ _2max = 12, e increases by 0.01 at 1.26 ≦ e ≦ 1.41, and γ increases by 1 ° at 65 ° ≦ γγ 79 °,

While satisfying the convergence and design constraints of

The values of unknown values r _h , r _e , r _p1 , r _p2 , θ _p1 and θ _p2 are minimized.

The internal rotor receives β in Equation 9 by Δβ _h based on the values of r _h , r _e , r _p1 , r _p2 , θ _p1 and θ _p2 calculated by receiving e and γ, It is designed by connecting the construction points generated while increasing φ by Δφ _n and β in Equation 23 by Δβ _e . Here, the point-to-point distance in the polycircle curve is defined as distance between points (DBP). On the other hand, using equations (9) and (23), as shown in Fig. 9, the distance f _h (β) of the hypocycloid curve is maximum when β = 0, and the distance f _e (β) of the epicycloid curve is β = π. Maximum when / Z ₁ Therefore, the maximum point-to-point distance of each curve is set equal to DBP.

이므로 수학식 65의 초기값에서 수학식 66의 방정식을 풀이하여 △β_h를 구할 수 있다.First, a point when the △ β = β _h in Equation 9 P _h la and la the y-coordinate value y _{h, △ β = βh.} In addition, the coordinate of P ₀ in FIG.

Δβ _h can be obtained by solving the equation of Equation 66 from the initial value of Equation 65.

범위에서 φ는

으로 증분된다고 하면, 증분각

는 수학식 67과 같이 구할 수 있다.Next, the expression (15)

Φ in the range

If we increment by, the incremental angle

Can be obtained as shown in Equation 67.

Finally, in Equation 23, the coordinates of the points P _e1 and P _e2 when the cloud circle moving angle β is β _e1 and β _{e2 in} Equation 68 are as shown in Equations 69 and 70.

Therefore, by using Equations 69 and 70, Δβ _e can be obtained by solving the equation of Equation 72 from the initial value of Equation 71.

For Z ₁ = 9, e = 1.31, γ = 71 °, DBP = 0.005, ρ _2max = 12, the incremental angles of the hypo and epicycloid curves are calculated as Δβ _h = 0.01693 °, Δβ _e = 0.01412 ° . In this case, after the inner rotor is designed to the half pitch angle section, the inner rotor may be symmetrical by the straight line of the half pitch angle and arranged by Z ₁ based on the point O ₁ to design the inner rotor as shown in FIG. 9. Here the two concentric circles with the center O ₁ and the radius r _p1 , r _p2 represent the polycircle curve range inserted between the hypo and epi cycloid curves.

의 길이와 같으며, 수학식 20을 이용하면 수학식 73과 같이 구할 수 있다.In FIG. 9, the inner rotor tooth width w _i is a line segment connecting the inflection points P ₂ and P ₃ .

Equation 20 is the same as, and using Equation 20 can be obtained as Equation 73.

Next, the process of deriving the external rotor configuration equation and designing the external rotor will be explained.

First, we derive an external rotor approximation through rotation simulation.

,

라 하고, 도 10의 (b)와 같이 O₂가 중점이고 반경 e인 원과

축의 교점을 중심으로

를 시계방향으로 α(Z₁/Z₂)만큼 회전시킨 결과를 각각

,

라 한다. The inner rotor and the outer rotor rotate in the same direction with the angular velocity ratio of Z ₂ : Z ₁ around the center of gravity O ₁ (e, 0) and O ₂ (0,0), respectively. This is the same as the following external rotor fixed rotation simulation. As shown in (a) of FIG. 10, the results of rotating the x and y reference axes of the internal rotor and the internal rotor counterclockwise with respect to O ₂ , respectively, are shown.

,

La, and the O ₂ source is focused and the radius e as shown in FIG. 10 (b) and

Around the intersection of the axes

Are rotated clockwise by α (Z ₁ / Z ₂ )

,

It is called.

Figure 11 shows a group of curves and the inner rotor of the inner rotor rotor trace obtained by the rotational simulation of the outer rotor fixing method of the inner rotor.

In FIG. 11, the outer rotor can be designed by connecting the outermost component points of the inner rotor rotation curve group (Sumitomo, 2006), but the derivation of the configuration equation is very difficult, so the outer rotor is designed in the following manner.

과

의 교점의 집합이 외부로터를 형성하고 있음이 관찰되었다. 내부로터 및 외부로터 곡선 상의 점을 각각 (x, y), (X,Y)라고 하면 이의 관찰결과는 수학식 74와 같이 표현할 수 있으며, (X, Y)를 소거하면 수학식 75를 얻을 수 있다.In the rotation simulation of Figure 10

and

It was observed that the set of intersections forms the outer rotor. If the points on the inner rotor and outer rotor curves are (x, y) and (X, Y), respectively, the observation result can be expressed as Equation 74. If (X, Y) is eliminated, Equation 75 can be obtained. have.

Therefore, by using the internal rotor configuration equation and the equations of Equations 74 and 75, an external rotor approximation equation up to the external rotor half pitch angle can be obtained as shown in Equations 76, 77 and 78.

을 사용하여 외부로터 구성점의 좌표값을 감소시켰다.Next, design an interference avoidance method of the inner rotor and the outer rotor. That is, since the external rotor approximation equations of Equations 76 to 78 are approximations derived from the results of the rotor rotation simulation observation, interference is generated as shown in FIG. Therefore, in order to avoid interference of the inner and outer rotors, the correction width factor is expressed as in Equation 79.

The coordinate values of the external rotor configuration point are reduced by using.

FIG. 13 expresses a modification of Equation 79. FIG. In FIG. 12, P _i (x, y) is a point on the inner rotor curve, and P ₀ (X, Y) is a curve expressed as an external rotor approximation equation before modification in the internal rotor configuration equation using Equations 74 and 75. It's a point. P _{o, m} (X _m , Y _m ) is the point on the outer rotor curve modified using Equation 79.

The correction width coefficient and the construction equation are derived as follows.

As shown in FIG. 14, when the area indicated by the dotted rectangular area for each rotor rotation angle is observed, interference occurs in the direction of the inner rotor polycircle curve at the point on the outer rotor curve before correction, which is derived from the outer rotor approximation equation, and the interference amount as shown in FIG. 15. The size of is gradually increased and decreased with the rotation angle of the external rotor.

Therefore, as shown in FIG. 15, the external rotor is modified as follows so that the inner rotor and the outer rotor fall by the tip gap at the rotation angle at which the maximum amount of interference occurs for avoiding the internal and external rotor interference.

,

이 수학식 76을 이용하여 변환된 수정 전의 외부로터 곡선 상의 점

가 도 15에서와 같이 외부로터 회전각 α에 따라 회전된 점을

라 하면 점

,

,

의 좌표는 수학식 80~82와 같이 구할 수 있다.First, considering the area indicated by the dotted line circle in FIG. 14, the maximum interference amount occurs in the radius of curvature of the polycircle curve of the inner rotor at a point on the outer rotor curve before modification derived by the outer rotor approximation equation (Equation 76). Point on the inner rotor hypocycloid curve of Figure 1

,

Point on the external rotor curve before modification modified using this equation (76)

Is rotated according to the rotation angle α of the outer rotor as shown in FIG.

Point

,

,

The coordinate of can be obtained as Equation 80 ~ 82.

, 점

을 내부로터 반 피치각도 직선에 의해 대칭시킨 점

가 도 15에서와 같이 회전된 점을

라 하면, 점

,

,

의 좌표는 수학식 83, 84, 85와 같이 구할 수 있다.Meanwhile, as shown in FIG. 16, the center of curvature of the inner rotor polycircle curve of FIG.

, Point

Of the inner rotor half pitch angle

Is rotated as shown in FIG.

Speaking of points

,

,

The coordinate of can be obtained as Equation 83, 84, 85.

와 같다. 따라서 도 17과 같이 내부로터 및 외부로터의 간섭량

을 곡률반경 ρ에서

의 길이를 뺀 값으로 정의하였다. 최대 간섭량은 α, β 및 φ에 대한 수학식 86의 초기값 및 범위에서 수학식 87의

을 최대로 하는 α, β 및 φ 값을 수학식 88에서와 같이 도출함으로써 계산한다.In Fig. 16, the radius of curvature ρ is

Same as Therefore, the interference amount of the inner rotor and the outer rotor as shown in FIG.

At the radius of curvature ρ

Defined as minus the length of. The maximum amount of interference is expressed by Equation 87 at the initial value and range of Equation 86 for α, β and φ.

It is calculated by deriving the values of α, β and φ that maximizes as shown in Equation 88.

For Z ₁ = 9, ρ _2max = 12, e = 1.31, γ = 71 °, DBP = 0.005, the values in Eq. 88 are α _Inf = 20.2711 °, β _Inf = 5.93420 °, and φ _Inf = 0.620999 °, respectively. Is calculated.

을 t_p만큼 옵셋시킨 점을

라 한다. 수학식 15에서

의 좌표는 수학식 89와 같다.Next, find the point on the inner rotor polycircle curve and the center of curvature considering the tip gap t _p . Point on the polycircle curve of FIG. 3

The point offset by t _p

It is called. In equation (15)

Is the same as (89).

와

는 동일 직선 상에 놓여있으며, 두 점 사이의 거리는 t_p이므로 수학식 90의 관계식이 성립한다. 수학식 90을 연립하면 수학식 91과 같이

에 관한 2차방정식으로 정리할 수 있다.As in Figure 18

Wow

Lie on the same straight line, and the distance between two points is t _p, so the relation of Equation 90 is established. If you combine Equation 90,

Can be summed up as a quadratic equation for.

의 좌표는 수학식 90 및 수학식 92의

에 관한 초기값을 바탕으로 수학식 93의 목적함수의 제곱을 최소화하여 구한다.therefore

The coordinates of Equation 90 and Equation 92 are

The square of the objective function of Equation 93 is obtained based on the initial value of

을 t_p만큼 옵셋시킨 점을

라 하고, 점

를 내부로터 반 피치각도 직선에 의해 대칭시킨 점

이 도 15에서 수학식 88의

만큼 회전된 점을

이라 한다. 먼저, 수학식 83을 이용하면

의 좌표는 수학식 94와 같이 구할 수 있다.Similarly, the center of curvature in the polycircle curve of FIG.

The point offset by t _p

Let's point

Of the internal rotor half pitch angle

In FIG. 15, Equation 88

Rotated by

Quot; First, using Equation 83

The coordinate of can be obtained as in Equation 94.

의 좌표는 수학식 92, 93을 이용하면 수학식 95 및 96의

에 관한 초기값을 바탕으로 수학식 97의 목적함수의 제곱을 최소화하여 구한다.

For the coordinates of Equations 92 and 93,

The square of the objective function of Equation 97 is minimized based on the initial value of.

및

의 좌표는 수학식 98, 99와 같이 구할 수 있다.point

And

The coordinate of can be obtained as shown in Equations 98 and 99.

는 수학식 (100)과 같이 구할 수 있다. Also, the radius of curvature in the inner rotor polycircle curve considering the tip gap t _p

Can be obtained as in Equation (100).

라 하고,

가 수학식 76을 이용하여 변환된 외부로터 곡선 상의 점

가 수학식 79를 이용하여 수정된 점을

라 한다. 점

,

,

의 좌표는 수학식 101~103과 같이 구할 수 있다.Meanwhile, the points on the inner rotor hypocycloid curve

,

Points on the outer rotor curve converted using Equation 76

Is modified using Equation 79

It is called. point

,

,

The coordinate of can be calculated as Equation 101 ~ 103.

가 도 15에서 수학식 88의

만큼 회전된 점을

라 하면 점

의 좌표는 수학식 104와 같이 구할 수 있다.point

15 in Equation 88

Rotated by

Point

Can be obtained as shown in Equation 104.

에서의 접선기울기는 수학식 105와 같다. Meanwhile, in FIG. 19

The tangential slope at is equal to (105).

,

를 β에 관해 미분하면 수학식 106과 같다.In Equation 102

,

Differentiating with respect to β is as in Equation 106.

,

및 수학식 102에서의 α^*를 β에 관해 미분하면 수학식 107, 108과 같다.Also in Equation 101

,

And differentiating [alpha] ^* in Equation 102 with respect to [beta].

는 수학식 109와 같이 구할 수 있다.Therefore, using Equations 105 to 108,

Can be obtained as shown in Equation 109.

가 점

에서의 접선과 수직이며,

의 길이를 갖도록 설정함으로써 수정폭 계수 n을 결정하였다. 따라서 β 및 φ에 대한 수학식 110의 초기값 및 범위에서 수학식 93, 97, 111의 목적함수 제곱을 최소화하는 β 및 φ을 수학식 113과 같이 도출할 수 있다.Interference avoidance of the inner rotor and the outer rotor is at the rotation angle of the maximum interference amount as shown in FIG.

Point

Perpendicular to the tangent to

The correction width coefficient n was determined by setting to have a length of. Accordingly, β and φ that minimize the square of the objective function of Equations 93, 97, and 111 in the initial value and range of Equation 110 for β and φ can be derived as shown in Equation 113.

At this time, by substituting Equations 99 and 104 into Equation 112, the correction width coefficient n can be obtained as in Equation 114.

,

,

,

으로 계산되며 이때, 수정폭 계수는 n=2.38003이다.For Z ₁ = 9, ρ _2max = 12, e = 1.31, γ = 71 °, DBP = 0.005, the values in

,

,

,

Where the correction width factor is n = 2.38003.

On the other hand, in order for the distance from the outer rotor half pitch angle point to the point O ₂ to be equal to ρ _2max , the correction width factor must be n = 0. Therefore, when the external rotor is modified by converting it from the hypocycloid and polycircle curves of the inner rotor as shown in Equations 76 and 77, the correction is performed by using the correction width coefficient n as shown in Equation 79. In this case, the modified width coefficient n 'is changed by changing the modified width coefficient in the form of a cubic polynomial according to the rolling circle β of the epicycloid curve as shown in Equation 115. In Equation 115 below, the symbol [] is a Gaussian symbol.

Therefore, the constitutive equation up to half the pitch angle of the outer rotor can be obtained as Equations 116 to 118.

Next, design the external rotor and calculate the tip width.

Design the external rotor using the external rotor configuration equations of Eqs. 116-118, symmetrically by a half-pitch angle line, and arrange by Z ₂ with respect to the point O _2. Z ₁ = 9, e = 1.31, γ = In the case of 71 °, DBP = 0.005, ρ _2max = 12, and t _p = 0.025, the inner rotor and the outer rotor can be designed as shown in FIG. 21. At this time, the size of the rotor outer diameter is the same as (29).

The outer rotor tip width w _o is equal to the value of (2Y _p ) when φ = θ _p1 in Equation 117. By using Equations 26 and 27, w _o can be obtained as in Equation 119.

The GROTOR oil pump of the present invention as described above is designed by applying a polycircle and a cycloid shape, which is advantageous for the sliding ratio between the inner rotor and the outer rotor, and the internal rotor and the existing hypocycloid-one-epi cycloid shape applied to the test results. The noise and abrasion resistance were improved compared to the rotor rotor oil pump having an external rotor.

Table 1 below shows a conventional Gerotor oil pump (Comparative Example 1) to which the hypocycloid-one-epi cycloid shape is applied, and a Gerotor Oil Pump to which the Hypocycloid-polycircle-Epi cycloid according to the present invention is applied (Example 1). The theoretical flow rate of the flow rate and the flow rate pulsation and the CFD analysis results are shown, and Table 2 shows a comparison of the average flow rate performance test results of the conventional giraffe oil pump and the gyro oil pump of the present invention.

Eccentricity Flow rate (cc / rev) Flow rate pulsation (%) Flow rate-CFD
(cc / rev) Flow Pulsation-CFD
(%) Comparative Example 1 1.16 1.1221 2.3382 0.972 97.22 Example 1 1.28 1.2736 7.0819 1.1109 69.59

Metric flux electric current RPM Comparative Example 1 Early 207.7 6.92 4451 After 20 hours 196.6 6.66 4385 Example 1
Early 210.8 8.96 3825 After 20 hours 221.5 7.49 4042

As can be seen from Table 1 and Table 2, the GROTOR oil pump of the present invention is improved by about 5% compared to the conventional GROTOR oil pump, flow rate pulsation is also improved about 10 to 20% The noise is lowered.

While the present invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiments. In addition, it is apparent that any person having ordinary knowledge in the technical field to which the present invention belongs may make various modifications and imitations without departing from the scope of the technical idea of the present invention.

: 내부로터의 중점
r_bh : 하이포사이클로이드의 반경
r_be: 에피사이클로이드의 반경

: Center of inner rotor
r _bh : radius of hypocycloid
r _be : Radius of epicycloid

Claims (4)

In a rotor rotor pump having an outer rotor having a plurality of rovers formed on an inner circumferential surface, and an inner rotor eccentrically rotating in an inner space of the outer rotor,
P ₀ to P ₁ (β ₁ ) is a hypocycloid curve, P ₁ to P ₂ (β ₂ ) for the inner rotor half pitch interval based on the inner rotor center point O ₁ = (e, 0) with eccentricity e ) is a central point as the other poly-circle curve which is a combination of a series of a plurality of sources, over P ₂ (β _3/2) in the Gerotor oil pump which is characterized by being a epi-cycloid curve. As a design method of the rotor rotor pump according to claim 1,
Designing an inner rotor by combining a hypocycloid curve, a polycircle curve, and an epicycloid curve;
And calculating a trajectory of the outer rotor from the shape of the inner rotor to design the outer rotor. The method of claim 2, wherein the designing the inner rotor,
Deriving a constitutive equation of a hypocycloidic curve for a section β ₁ from any one point P ₀ to one set point P ₁ based on the half pitch section of the inner rotor, and setting another one at the point P ₁ . and for a period β ₂ to the point P ₂ further comprising: deriving the configuration manner of the polyacrylic circle curve and deriving the constitutive equation of the epi-cycloid curve with respect to the point P ₂ or more legs β _3/2, the hypo-cycloid curve and poly-circle configuration of the attachment point of P ₁ and the poly circle curve and the epitaxial cycloid curve connecting the point of phase with, the curve leading to the coordinate value and the instantaneous curve boundary condition equation to a slope of the match in the P ₁ of the curve equation And designing the overall shape of the inner rotor from the curved boundary condition equation and calculating the tip width. Method of designing a rotor rotor pump. The method of claim 3, wherein the designing the external rotor,
Deriving an approximation equation of an external rotor through rotation simulation, calculating a correction width coefficient (n) for avoiding interference between the internal rotor and the external rotor, calculating an external rotor configuration equation, and calculating the correction width coefficient And designing the overall shape of the external rotor from the external rotor configuration equation and calculating the tip width.

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