KR101101610B1 - Method for designing the gerotor pump - Google Patents

Abstract

The present invention provides an automated system capable of creating and designing a rotor having a high flow characteristic to satisfy a required flow rate even if the size of the rotor is reduced, and also provides a flow rate pulsation for noise reduction when driving the rotor. We will implement a rotor design automation system for a GROTOR oil pump using various tooth curves that can design a small rotor.

Description

Rotor design method of Gerotor oil pump using various tooth curves {METHOD FOR DESIGNING THE GEROTOR PUMP}

The present invention relates to an internal gear pump for use in an oil pump and the like, and more particularly, to a method of designing a rotor of a gerotor oil pump using various tooth curves such as hypocycloid, arc and epicycloid.

As is well known, the lubricator of an automobile engine is an essential device for smooth engine operation and long life, and one of the components of the lubricator is an internal gear pump which is advantageous in terms of flow rate, durability, noise and miniaturization. Mainly used.

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 pump and a motor having an arbitrarily generated rotor are composed of an inner rotor and an outer rotor, so that the structure is simple and the processing is complicated even when the shape is complicated due to the increase in the precision of processing due to the development of the manufacturing technology of the sintered product. Easy to assemble, easy to assemble and less relative movement between two teeth, less change in efficiency even long-term use, 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, much research has been carried out with respect to the rotor tooth design of the gerotor 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, it is necessary to study the design of the rotor shape which is the most important in the oil pump design technology, and the study of new teeth of high performance, high efficiency, low noise, and low vibration is urgently needed. In particular, analysis of factors related to the performance, vibration, and efficiency of the oil pump requires geometric, computational fluid dynamics (CFD), and system sumulation approaches.

On the other hand, as a conventional technology for solving such a problem is a Korean Patent No. 10-0940980 (name of the invention: rotor design automation system for the rotor rotor pump, registration date: January 29, 2010).

The prior application registration invention is configured to build the automation of the rotor design by performing the kinematic analysis in consideration of the design variables of the outer rotor having a circular or elliptical rover shape. Specifically, an input module for inputting design variable values for automating tooth design, flow rate and flow rate pulsation calculation, and generates the trajectory of the internal rotor and the external rotor by the tooth equation from the input design variable values. It consists of a design module that calculates the flow rate and pulsation of the created tooth after correcting the offset amount between the internal rotor and the external rotor, and an output module that performs tooth modeling, rotation simulation, instantaneous flow curve and data file storage. Technical features of the rotor design automation system for the rotor oil pump.

It is clear that such an invention is useful as it is to realize the automation of the rotor design and to realize that the lobe shape of the external rotor can be combined in various curves to have good performance in terms of flow rate and flow rate pulsation.

However, since the registered invention creates an inner rotor after designing the lobe shape of the outer rotor, if the eccentric amount is continuously increased to increase the flow rate, the tip width of the inner rotor becomes smaller than the design limit condition. There was a disadvantage in that there is a limit amount of eccentricity that cannot increase the flow rate.

The present invention is to solve the above problems, to provide a method for designing a rotor of a gyro oil pump using a variety of tooth curves such as hypocycloid, arc and epicycloid so that the eccentricity is not constrained under the design limit conditions The purpose is.

In addition, the present invention, by designing and analyzing the trajectory of the external rotor based on the internal rotor configuration equation, the rotor of the GROTOR oil pump using a variety of tooth curves to derive the configuration equation and perform kinematics, kinematic analysis of the teeth Its purpose is to provide a method of designing.

In addition, the present invention is to determine the characteristics of the rotor rotor pump by deriving the flow rate and the flow rate pulsation value discharged when the inner rotor and the outer rotor rotates by using the area calculation method based on the rotor configuration equation The purpose is to provide.

The present invention is a method for designing a rotor of a rotor rotor oil pump using a variety of tooth curves, the process of configuring the inner rotor by inserting an arc curve between the hypocycloid curve and epi cycloid curve, and the internal rotor configuration equation It is characterized by consisting of the process of creating the trajectory of the external rotor based on this.

At this time, based on the more preferably the eccentricity is e the inner rotor center point of the Gerotor O ₁ (e, 0), in the region of the pitch angle β ₁ and β ₅ as hypo-cycloid curve, β ₃ by epitaxial cycloid curve In addition, it is characterized by consisting of a process of deriving the constitutive equation of the internal rotor combined by an arc curve by β ₂ and β ₄ .

In addition, when the inner rotor and the outer rotor rotate together, the area between the inner rotor and the outer rotor is reduced in order to derive the discharge flow rate and thus the flow rate pulsation value that form the periodic curve for each rotation angle of one pitch angle of the outer rotor. Characterized in that the process of automatically calculating the area change amount of the rotation angle of the chamber.

According to the present invention, when the arc curve is inserted between the hypocycloid curve and the epi cycloid curve of the inner rotor, the slope of the hypocycloid curve and the arc curve can be arbitrarily adjusted, thereby connecting only the hypocycloid curve and the epi cycloid curve. Compared to one rotor, there is an advantage that there is no limit on the setting of the eccentricity for the flow increase and the internal and external rotor tip width design.

In addition, the present invention has the advantage that can automatically calculate the tip width of the inner rotor and the outer rotor without the occurrence of peaks and loops when designing the rotor compared to the prior art, unlike the conventional technology between the inner and outer rotor Since the contact point of is formed less than the number of external rotor teeth, it has more advantages in terms of wear and noise, and derives theoretical discharge flow rate and flow rate pulsation value by its own method, and thus the performance factor of the pump using the same or similar type of rotor as the present invention. There is an advantage that can be derived more effectively.

1 is a view showing one pitch section of the inner rotor according to an embodiment of the present invention.
Figure 2 is a view showing the tooth width of the inner rotor according to an embodiment of the present invention.
3 is a view showing one pitch section of the inner rotor for induction of the configuration equation of the inner rotor according to the present invention.
4 and 8 are diagrams showing the hypocycloid curve section for the derivation of the constitutive equation of the hypocycloid curve according to the present invention.
5 and 7 is a view showing a circular arc curve section for deriving the constitutive equation of the circular arc curve according to the present invention.
6 is a diagram showing an epicycloid curve section for deriving the constitutive equation of the epicycloid curve according to the present invention.
9 is a view showing the teeth of the inner rotor according to the present invention.
10 is a view showing a rotation simulation state of the rotor according to the prior art.
11 is a view showing the interference phenomenon of the inner and outer rotor according to the present invention.
12 is a view showing the teeth of the inner and outer rotor according to the present invention.
Figure 13 shows the chamber between the inner and outer rotor according to the present invention.
14 shows an input window on a computer monitor according to the present invention.
15 is a graph showing the discharge amount according to the present invention.

Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. In the following detailed description, exemplary embodiments of the present invention will be described in order to accomplish the above-mentioned technical problems. And other embodiments that can be presented with the present invention are replaced by the description in the configuration of the present invention.

In the present invention, as one of methods for reducing the oil pump energy loss rate, the flow rate (discharge amount) is not reduced together when reducing the size of the rotor used in the gerotor oil pump. Specifically, even if the size of the rotor is reduced, the required flow rate is reduced. To satisfy, we propose an automated method to create and design a rotor with high flow characteristics. In addition, to reduce the noise generated when driving the rotor to implement a rotor design method of the rotor rotor pump using a variety of teeth curves that can design a rotor with a small flow rate pulsation.

To this end, an automatic method of designing and analyzing the trajectory of the external rotor in the internal rotor should be specifically disclosed. Preferably, the internal rotor of the method in which the circular arc is inserted between the hypocycloid curve and the epi cycloid curve is first constructed. From this, a concrete plan for creating an external rotor should be disclosed.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 to 15 illustrate a method of designing a rotor of a gerotor oil pump using various tooth curves such as hypocycloid, arc and epicycloid curve according to an embodiment of the present invention. As described above, the design method of the rotor rotor pump of the present invention is a method of inserting an arc curve between a hypocycloid curve and an epicycloid curve to construct an inner rotor first, and then create a trajectory of the outer rotor in the inner rotor. .

First, in designing the rotor rotor pump according to the present invention, the geometrical analysis of the inner rotor will be described in detail with reference to FIGS. 1 to 9.

1 to 9, 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. Is called a cyclocycloid, and the curve generated when it is rolled out of contact around the pitch circle is called epicycloid. In this manner, one pitch section of the inner rotor may be combined as shown in FIG. 1.

That is, since the pitch circle radius of the inner rotor is γ ₁ and the number of teeth is Z ₁ , considering the sum of the distances rolled on each pitch circle on the pitch circle, Equation 1 is established.

If here the value low hardness outer rotor ρ _2max, the inner rotor diameter value ρ _1max, the tip clearance of the inner and outer rotor t _p and d refer to the <Equation 1> is established that <Equation 2> below.

In addition, considering the distance each rolling circle rolled on the pitch circle, it is as shown in <Equation 3>.

In FIG. 1, the width t _i of the inner rotor may be calculated as a distance between the points P ₁ and P ₂ , which are inflection points, and the result is expressed by Equation 4 below.

In this case, when the outer diameter of the rotor is 29, ρ _2max = 12 (unit: mm), and Z ₁ = 9, the <Equation 4> is derived as shown in the following <Equation 5> Same as FIG.

E _lim here T _i if = 1.134 It can be seen that it is = 2, which corresponds to the limit condition of the rotor manufacturing. In general, when the amount of eccentricity is increased, the flow rate increases, but the amount of eccentricity cannot be increased than that of e _lim . Thus, in the same manner as in FIG.

However, by inserting an arc between the hypocycloid curve and the epi cycloid curve as shown in FIG. 3, a factor other than the amount of eccentricity is added to adjust the width of the tip of the inner rotor and is not limited by the adjustment of the amount of eccentricity to increase the flow rate. can do.

On the other hand, a hypocycloid curve by β ₁ and β ₅ of the pitch angle with respect to the internal rotor center point O ₁ = ( e , 0) of the gyro rotor having an eccentricity e , an arc curve by β ₂ and β ₄ , and β ₃ As a result, the constitutive equation of the inner rotor combined with the epicycloid curve is derived.

는 점 P ₁에서 반경 γ _{p 1}인 원에의 접선과 C _{h 1} 곡선에의 접선이 이루는 각도이다.The cloud circle radii of the hypocycloid curve and the epicycloid curve are γ _h and γ _e , respectively, and the rotation angles of the cloud sources are θ _{h 1} , θ _{h 2,} and θ _e as shown in FIG. 3. Also, from the x-axis, the first hypocycloid curve C _{h 1} , the second arc curve C _{a 1} , the third epi cycloid curve C _e , the fourth arc curve C _{a 2} , and the last hypocycloid curve C _{h 2} do. In FIG. 3, the centers of the base circles of the hypocycloid curve and the epicycloid curve are both coincident with O _1, and the radius of each base circle is γ _bh and γ _be . Also in FIG. 3 above

Is the angle between the tangent to the circle with radius γ _{p 1} and the tangent to the C _{h 1} curve at point P ₁ .

Equal to the value the height H = 2 e of the inner rotor, the points of each curve are met around the point O ₁ to d P _1, P _2, P _3, P _4, and the point source passing through P ₁ and P ₄ If the radius of γ _{p 1} , and the radius of the circle passing through the points P ₂ and P ₃ is γ _{p 2} , the relational expression is as follows.

In the following, the configuration equation of the internal rotor according to the present invention will be described in detail.

(1) C _{h 1} curve

If the point on the C _{h 1} curve in FIG. 4 is ( x _{h 1} , y _{h 1} ), the following Equation 7 is established.

As shown in FIG. 4, the relationship between the base circle radius and the cloud circle moving angle of the hypocycloid curve when the cloud circle is moved is represented by Equation (8).

By arranging <Equation 16> using the following <Equation 17>, the following <Equation 9> can be obtained.

The relation between the radius of the rolling circle and the elementary circle radius of the hypocycloid curve at the point P ₁ of FIG. 4 is as shown in <Equation 10>.

Further, when applying a second cosine law for Δ P _h O ₁ O ₁ can be obtained the following <Equation 11>.

If the above <Equation 9> is summarized using the above <Equation 10> and <Equation 11>, the following <Equation 12> can be obtained.

On the other hand, when applying a second cosine law for the Δ O O _{h 1} P ₁ equal to the <Equation 13>.

(2) C _{a 1} curve

As shown in FIG. 5, if the point on the C _{a 1} curve is ( x _{a 1} , y _{a 1} ), the following <Equation 14> is established.

Here, the point O _{a 1} ( O _{1 x} , O _{1 y} ) is the coordinate of the center point of the circle having the radius γ _a , and the coordinates of the points P ₁ and P ₂ are obtained as shown in <Equation 15>.

Meanwhile, referring to FIG. 5 described above, the coordinates of the points P ₁ and P ₂ may be obtained through Equation 16 below.

In the above <Equation 15> and <Equation 16>, since the x and y coordinate values of the points P ₁ and P ₂ are the same, a relational expression such as the following <Equation 17> and <Equation 18> can be obtained.

As shown in FIG. 5, since the tangent of the C _{a 1} curve at the point P ₁ is perpendicular to the radial line segment, δ ₁ is expressed by Equation 19 according to the properties of the tangent of the circle.

Β ₁ can be obtained from Equation 12 and Equation 13 as shown in Equation 20 below.

In addition, between β _1, β ₂ and β ₃ is established a relationship such as the <Equation 21>.

Β ₃ is represented by the following <Equation 30>.

(3) C _e curve

In the aforementioned FIG. 6, when the point on the C _e curve is ( x _e , y _e ), the following <Equation 22> is established.

As shown in FIG. 6, when the cloud circle moves, a relationship as shown in Equation 23 is established between the base circle radius of the epicycloid curve and the cloud circle moving angle.

Referring to <Equation 21>, <Equation 23> is summarized as in <Equation 24> below.

In addition, in the C _e curve near the point P ₂ , a relational expression such as <Equation 25> is established between the moving angle and the rotation angle of the rolling circle.

By substituting <Equation 24> into the above <Equation 25>, the following <Equation 26> can be obtained.

On the other hand, when applying a second cosine law in Δ O ₁ P ₂ O _e can be obtained the following <Equation 27>.

In addition, a relational expression such as &lt; Equation 28 &gt; holds between the rolling circle and the base circle radius of the C _e curve.

Similarly, by applying the second cosine law in Δ O _e O ₁ P ₂ , the following <Equation 29> can be obtained.

At this time, since cos (π- θ _e ) =-cos θ _e , the equations (19) and (20) above can be combined to obtain β ₃ as shown in <Equation 30).

Therefore, the structural equation of the C _e curve is expressed as in <Equation 31>.

(4) C _{a 2} curve

As shown in FIG. 7, when the point on the C _{a 2} curve is ( x _{a 2} , y _{a 2} ), the following <Equation 32> is established.

Here, ( O _{2 x} , O _{2 y} ) is the coordinate of the center point of the circle C ₂ whose radius is γ _i , and the coordinates of the points P ₃ and P ₄ are obtained as shown in Equation 33.

Meanwhile, referring to FIG. 6, the coordinates of the points P ₃ and P ₄ can be obtained as shown in Equation 34 below.

In the above <Equation 33> and <Equation 34>, the x and y coordinate values of the points P ₃ and P ₄ are the same, so that the following <Equation 35>, <Equation 36>, and <Equation 37> We can get each relation.

In addition, as shown in FIG. 3, the center points of circles C ₁ and C ₂ are symmetrical by a straight line passing through the point O ₁ and having a half pitch angle, and thus the center point O _{a 2} ( O _{2 x} , O _{2 y} ) is It is represented by <Equation 38>, and the values of O _{1 x} and O _{1 y} are the same as in <Equation 17>.

(5) C _{h 2} curve

Referring to FIG. 8, the point on the C _{h 2} curve is ( x _{h 2} , y _{h 2} ), and the following Equation 39 is established.

As shown in FIG. 3, when the rolling circle moves, the relationship between the base circle radius of the hypocycloid curve and the rolling circle moving angle is expressed by Equation 40 below.

Using <Equation 40>, <Equation 39> is summarized as in <Equation 41> below.

Next, a method of deriving the variable setting and the boundary condition equation according to the present invention will be described in detail.

, ρ _2max값에 대해 상기 5개 곡선의 구성방정식을, 바람직하게는 위에서 언급한 C _{h 1} 곡선, C _{a 1} 곡선, C _e 곡선, C _{a 2} 곡선, C _{h 2} 곡선의 구성방정식을 도출하기 위해 γ _a , γ _h , γ _e , γ _{p 1}, γ _{p 2}를 변수로 설정하고 아래와 같은 5개의 경계 조건식을 유도하였다.First, Z ₁ , e ,

_Deriving the constitutive equations of the above five curves for the value of ρ _2max , preferably the constitutive equations of the above mentioned C _{h 1} curve, C _{a 1} curve, C _e curve, C _{a 2} curve, C _{h 2} curve For this, γ _a , γ _h , γ _e , γ _{p 1} , γ _{p 2} were set as variables and five boundary condition equations were derived.

(1) First boundary condition equation

Since the tangent slope of the C _{h 1} curve at the point P ₁ is the same as the tangent slope of the C _{a 1} curve, the relation shown in Equation 42 is established.

In addition, the x coordinate value of the C _{h 1} curve at the point P ₁ is equal to the following Equation 43, and the equation for the y coordinate value is the same.

If the above <Equation 42> and <Equation 43> are combined and arranged, the following <Equation 44> can be obtained.

(2) second boundary condition equation

Since the tangential slope of the C _e curve at the point P ₂ is the same as the tangential slope of the C _{a 1} curve, the following relational expression is established.

The x coordinate value of the C _e curve at point P ₂ is equal to <Equation 46>, and the equation for the y coordinate value is equivalent thereto.

If the above <Equation 45> and <Equation 46> are combined and arranged, the following <Equation 47> can be obtained.

(3) Third boundary condition equation

In the above-described <Equation 17> and <Equation 18>, the x coordinate values of the points P ₁ and P ₂ are the same as the following <Equation 48>.

If the above <Equation 48> is combined and arranged, the following <Equation 49> can be obtained.

(4) Fourth boundary condition equation

In the above-described <Equation 35> and <Equation 36>, the x coordinate values of the points P ₁ and P ₂ are the same as the following <Equation 50>.

If the above <Equation 50> is combined and rearranged, the following <Equation 51> can be obtained.

(5) Fifth boundary condition equation

의 기울기는 δ ₁와 δ ₂의 산술평균과 같으며, 이는 도 7에서도 대칭적으로 성립한다. 이와 관련된 ＜수학식 52＞는 다음과 같다.5 described above

The slope of is equal to the arithmetic mean of δ ₁ and δ ₂ , which holds symmetrically in FIG. 7. Equation 52 related to this is as follows.

Next, a method for setting a range for a variable according to the present invention will be described in detail.

First, as shown in FIG. 3 described above, a relationship of γ _{p 1} < γ _bh < γ _be < γ _{p 2} is established, which can be considered by dividing into the following cases.

And, the remaining γ _{p 1} < γ _{p 2} and γ _bh < γ _be are established by themselves if an arc curve is inserted. Further, the curve point C _{h 1} P ₁ is present and, as a C _e to, if point P ₂ is on the curve <Equation 56> relational expression above is satisfied.

In addition, for all arccos ( k ) values, | k | <1 must be satisfied.

Next, in the present invention, the internal rotor was designed using Visual Basic, Auto LISP, and Auto CAD.

, ρ _2max값에 대하여 위에서 언급한 '변수 설정 및 경계 조건식 유도' 및 '변수에 대한 범위 설정'의 조건을 만족하면서 5개의 경계 조건식의 해인 5개의 변수 γ _a , γ _h , γ _e , γ _{p 1}, γ _{p 2}의 값을 도출해낸 다음, 하기의 ＜수학식 57＞을 이용하여 원호 곡선을 구성하는 점간거리(도 14에서의 DBP)로부터 원호 곡선에서의 증분각 Δδ을 계산하고, 사이클로이드 곡선을 구성하는 점간거리를 DBP와 동일하게 하기 위해 C _{h 1} 곡선을 원호로 가정한 후 사이클로이드 곡선에서의 증분각 Δβ을 계산할 수 있다.That is, the input Z ₁ , e ,

, 5 variables γ _a , γ _h , γ _e , and γ _p that satisfy the conditions of 'parameter setting and derivation of boundary condition' and 'range of variables' mentioned above for the value of ρ _2max . _After deriving the value of ₁ , γ _{p 2} , the incremental angle Δ δ in the arc curve is calculated from the point-to-point distance (DBP in FIG. 14) constituting the arc curve using the following Equation 57, and the cycloid In order to make the point-to-point distance constituting the curve equal to DBP, it is possible to calculate the incremental angle Δ β in the cycloid curve after assuming the C _{h 1} curve as an arc.

=69˚, ρ _2max =12이며 2개의 동심원은 하이포 사이클로이드 곡선과 에피 사이클로이드 곡선 사이에 원호(Arc) 곡선이 삽입된 범위를 나타내며, 내부로터 이끝폭 w _i 는 도 3에서 변곡점 P ₂ 및 P ₃ 사이의 거리,

와 같다.Accordingly, the inner rotor was generated as shown in FIG. 9. Where Z ₁ = 9, e = 1.35,

= 69˚, ρ _2max = 12 and the two concentric circles represent the range in which the arc curve is inserted between the hypocycloid and epicycloid curves, and the inner rotor tip width w _i is the inflection point P ₂ and P ₃ in FIG. Distance between,

Same as

Meanwhile, in the present invention, a method of creating an external rotor using data obtained through geometrical analysis of the internal rotor as described above will be described in detail with reference to FIGS. 10 to 12.

만큼 회전시킴으로써 수행할 수 있다.First, the rotor rotation simulation revolves the inner rotor by the angle α in the CCW direction about the center of the outer rotor O ₂ (0, 0) and rotates the inner rotor back in the CW direction around the center of the revolved inner rotor.

This can be done by rotating as much as possible.

That is, as a result of the rotation simulation analysis of FIG. 10, the reference axis (x-axis) revolving like the inner rotor generates an intersection with the inner rotor after rotation, and a point away from the intersection by t _p in the axial direction constitutes the outer rotor. Able to know. This may be expressed as Equation 58. Here, the coordinates of the points constituting the external rotor ( X , Y ) and the coordinates of the points constituting the internal rotor are ( x , y ).

Since the intersection with the revolving reference axis constitutes the external rotor, the following relational expression is established.

When the above formulas (58) and (59) are combined and solved, the following formula (60) can be obtained.

As described above, the internal rotor was generated based on the configuration equation of the internal rotor, and the external rotor was created using Equation 58 and Equation 60, as shown in FIG.

As a result of the rotor rotation simulation, overall interference occurred in the hypocycloid curve and the arc curve portion of the inner rotor, and partial interference occurred in the epicycloid curve portion, as shown in the top view of FIG. In addition, as shown in the bottom view of FIG. 11, the inner and outer rotors are rotated by CCW by a half pitch angle around each midpoint, and then the points on the inner rotors in which the points P ₁ of FIG. 3 are symmetrical to the x-axis are converted ( The maximum amount of interference occurred at P ₁ ′). Therefore, after defining the correction width coefficient n and the correction range coefficient k , the distance between the point P ₁ ′ and the point on the inner rotor having the closest point distance is defined as the tip clearance in Fig. 14 ( t _p : tip clearance). Set.

Also, since the total interference occurred in the hypocycloid and arc curve parts of the inner rotor, the correction width coefficient n was applied, and the partial width interference occurred in the epicycloid curve portion, so the correction width coefficient n was applied to the range where the correction range coefficient k was applied. After that, a modified width coefficient with variable differential intervals was applied from the range angle to the half pitch angle of the external rotor.

At this time, the outer rotor curve composed of the points transformed on the epicycloid curve of the inner rotor should have the shape of a convex function outwardly based on the point O ₁ (0,0) for smooth sliding between the inner and outer rotors. Representative quadratic polynomials among the convex functions in the entire interval have convex characteristics when the quadratic coefficient, that is, the sign of the second derivative is positive.

In order to use this characteristic, four continuous points on the outer rotor curve were extracted, and a correction width coefficient having a fixed width coefficient n and a variable differential interval was applied. In the case of the convex function, the slope (first derivative) of three lines connecting each of the four points is increased (second derivative) or the slope angle from the positive x-axis increases when the slope is negative. Accordingly, the external rotor configuration equation for each section up to the external rotor half pitch angle section using Equations 58 and 60 is derived from Equations 61 to 65 as follows.

As described above, convert the outer rotor to the point corresponding to the half pitch section of the inner rotor and symmetrically at the half pitch point of the outer rotor to form the outer rotor of one pitch section, and then arrange the outer rotor by the number of teeth of the outer rotor. It produced as shown in FIG. At this time, the outer rotor tip width w _o is equal to twice the value of Y _{a 1} when δ = δ ₁ in Equation 62 where the point P ₁ of FIG. 3 is converted.

As seen from above, in the present invention, a system for designing a rotor of a rotor rotor oil pump by creating a trajectory of an outer rotor in the inner rotor, preferably an inner rotor in which an arc curve is inserted between a hypocycloid curve and an epicycloid. First, we explained the system that can design the rotor of the GROTOR oil pump by constructing the external rotor and creating an external rotor from it.

In the following, it will be described in detail how to calculate the performance factors of the internal and external rotor based on this. Specifically, the description will be divided into (1) flow rate and flow rate pulsation calculation and (2) Gerotor pump design considering the limit conditions.

(1) Flow rate and flow pulsation calculation

The instantaneous flow rate ( Q ㎣ / rad ) means the change in area compared to the rotation angle in which the area of the chamber between the inner and outer rotor decreases as the inner and outer rotors rotate, and the unit ( cc / rev ) or r decreases. (Cm 3 / sec) or the like. At this time, the thickness of the rotor was set to 7.2.

As shown in FIG. 13-1, the chamber of which the area decreases as the inner and outer rotors of FIG. 12 rotate in the CCW direction by a half pitch angle around each center point and then rotate in the CCW direction among the chambers generated between the inner and outer rotors. Are shaded. At this time, the boundary region of the chamber was designated as an inner and outer rotor shape connecting the points on the inner and outer rotors having the closest point distance in a predetermined section and then connecting them.

When the outer rotor rotates in the CCW direction by Δ α around O ₂ (0,0), the inner rotor rotates in the same direction by ( Z ₂ / Z ₁ ) Δ α around O ₁ ( e , 0). Accordingly, the area of the chamber shaded as shown in FIG. 13-2 is reduced. Therefore, even in the shape of the outer rotor 13-1 is changed to the shape of the chamber 13-3 also rotates by half a pitch angle, and this Δ α S _{k +} S _k in the area of the chamber as the outer rotor rotates as indicated by the shaded If it is changed to ₁ , the instantaneous flow rate is calculated by the following formula (66).

In addition, the average flow rate q _av can be obtained as the average value of the instantaneous flow rate in the outer rotor half pitch section, and the relationship thereof is expressed by Equation 67 below.

Among the instantaneous flow rate values in the outer rotor half pitch section of FIG. 13, if the maximum value is q _max and the minimum value is q _min , the flow rate pulsation value I (%) is calculated by the following equation (68).

, 내외부로터 이끝폭, 외부로터 수정폭 계수 및 평균유량, 유량맥동, 챔버면적 회귀분석 결정계수 γ ²값을 출력한 결과 도 15와 같다. 이때 결정계수가 1에 가까울수록 회귀분석의 신뢰도는 증가한다.In the rotor shape of FIG. 13-3, if the inner and outer rotor rotation continues, the shape of FIG. 13-1 changes to the shape of FIG. 13-1, which rotates the outer rotor since the area of the chamber shaded in the region 13-1 to FIG. The instantaneous flow rate change pattern according to the change of angle is symmetrical with respect to FIG. 13-1. Based on this, the result of plotting the change pattern of the flow rate with respect to the external rotor rotation angle is shown in FIG. Since the instantaneous flow rate oscillates based on an arbitrary width, as a result of regression analysis of S _k in <Equation 66> by the third-order polynomial, the coefficient of determination has a value of 1, and the change of flow rate using the regression analysis chamber area At the same time, the eccentricity of the internal and external rotors,

The output widths of the inner and outer rotor teeth, the outer rotor correction width coefficient and average flow rate, flow rate pulsation, and chamber area regression analysis coefficient γ ² are shown in FIG. 15. At this point, the closer the coefficient of determination is to 1, the greater the reliability of the regression analysis.

(2) Gerotor pump design considering limit conditions

를 79˚부터 69˚까지 변화시키면서 유량 및 유량맥동 값을 계산하였다. 이때 γ ²은 모두 1으로 계산되었다.Due to manufacturing limitations, the width of the inner and outer rotor teeth ( w _i / w _o ) should not be less than 2mm. Referring to FIG. 14, when Z ₁ = 9 , DBP = 0.005, ρ _2max = 12 , w = 7.2 , t _p = 0.025 and e is 1.32,

The flow rate and flow rate pulsation values were calculated while changing from 79 ° to 69 °. At this time, γ ² was all calculated as 1.

Table 1 below shows the output values in this case.

를 1˚씩 감소시킬 때마다 내부로터 이끝폭은 증가하고 외부로터 이끝폭은 감소하는 경향을 가지며, 유량은 평균 0.036％ 증가하고 유량맥동은 평균 1.37％ 감소함을 알 수 있다. 여기에서 임의의 편심량 값에서 외부로터의 이끝 폭에 대해 제작상의 한계조건을 고려하였을 때 한계

값이 존재함을 알 수 있다. 또한 이러한 한계

값에서 유량 및 유량맥동 측면에서 볼 때 해당 편심량에서 가장 좋은 성능의 로터라고 할 수 있다.Fixed e in Table 1 above

It is found that the tip width of the inner rotor increases and the tip width of the outer rotor decreases with each decrease of 1˚. The flow rate increases by 0.036% and the flow pulsation decreases by 1.37%. Limits here, considering manufacturing limit conditions for the tip width of the external rotor at any eccentric value

You can see that the value exists. Also these limitations

In terms of flow rate and flow rate pulsation, the rotor is the best performing eccentric.

에 대한 유량 및 유량맥동을 계산해보았으며, 그 결과는 표 2에 나타내었다.Based on this trend, the amount of eccentricity is changed from 1.26 to 1.41 in 0.01 units and the limit in 0.1˚ unit

For the flow rate and flow rate pulsation was calculated, the results are shown in Table 2.

In Table 2, as the eccentricity increases, the average flow rate and flow rate pulsation value increase, so that the flow rate characteristics are improved, but the flow rate pulsation is worsened. Table 3 shows the shapes of six of the rotors shown in Table 2 when the eccentricity is 1.26, 1.29, 1.32, 1.35, 1.38, and 1.41.

Claims (4)

In the method of designing the rotor of the Gerotor oil pump using various tooth curves,
Inserting an arc curve between the hypocycloid curve and the epi cycloid curve to construct the inner rotor,
Rotor design method of a rotor rotor oil pump using a variety of teeth curve characterized in that the process of creating a trajectory of the outer rotor in the inner rotor. The method of claim 1,
The eccentricity of e is not the inner rotor center O ₁ = the pitch angle based on the (e, 0) β ₁ and β ₅ as hypo-cycloid curve of the rotor, the β ₂ and β ₄ as the arcuate curve, β ₃ by epi Rotor design method of the rotor rotor pump using a variety of tooth curves characterized in that the process consisting of inducing the configuration equation of the internal rotor combined by the cycloid curve. The method of claim 2,
The radius of curvature of the arcuate curve is γ _a, the hypo-cycloid curve and epi cycloid, and that each of γ _h, γ _e a generating circle radius of the curve, the inner rotor center O ₁ (e, 0) centered in the hypo-cycloid curve and the circular arc curve of The radius of the circle passing through the connection point of γ _{p 1 is} called γ _{p 2} , and the radius of the circle passing through the connection point of the arc and epicycloid curves is called γ _{p 2} . Also, from the x-axis, the first hypocycloid curve C _{h 1} , the second arc curve C _{a 1} , the third epi cycloid curve C _e , the fourth arc curve C _{a 2} , and the last hypocycloid curve C _{h 2} when doing;
The hypocycloid curve C _{h 1} is determined by the following Equations 7 to 13,
The arc curve ( C _{a 1} ) is determined by the following Equations 14 to 21,
The epicycloid curve C _e is determined by the following Equations 22 to 31,
The arc curve C _{a 2} is determined by the following Equations 32 to 38,
The hypocycloid curve ( C _{h 2} ) is determined by the equations (39) to (41).
&Quot; (7) &quot;

&Quot; (8) &quot;

[Equation 9]

[Equation 10]

[Equation 11]

[Equation 12]

[Equation 13]

[Equation 14]

[Equation 15]

[Equation 16]

[Equation 17]

Equation 18

[Equation 19]

[Equation 20]

[Equation 21]

[Equation 22]

[Equation 23]

[Equation 24]

[Equation 25]

[Equation 26]

[Equation 27]

[Equation 28]

[Equation 29]

Equation 30

Equation 31

Equation 32

[Equation 33]

[Equation 34]

[Equation 35]

[Equation 36]

[Equation 37]

[Equation 38]

[Equation 39]

[Equation 40]

[Equation 41]

The method according to any one of claims 1 to 3,
The rotor design method of the rotor rotor pump using a variety of teeth curve, characterized in that the external rotor according to the inner rotor is determined by the following formula (Equation 61) to <Equation 65>.
Equation 61

Equation 62

Equation 63

Equation 64

[Equation 65]

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