Internal gear pump

Abstract

An internal gear pump wherein a diameter of a base circle is set to A mm, a diameter of a rolling circle is set to B mm, a radius of the rolling circle is set to b mm, a diameter of a locus circle is set to C mm, and an amount of a displacement is set to e mm, wherein a trochoidal curve (T) is drawn by rolling the rolling circle along the base circle without slippage and by applying a locus of a fixed point that is e away from a center of the rolling circle, wherein a tooth profile of an inner rotor (2) having n teeth is formed based on an envelope of a group of locus circles, each of which has a center on the trochoidal curve (T), wherein a pump rotor (1) is formed by combining the inner rotor (2) with an outer rotor (3) having (n+1) teeth, and where a tooth profile curve of the inner rotor (2) satisfies expression (1): K = C 6 ⋅ n + 2 n + 1 ⋅ n + 2 3 n ( b 2 − e 2 ) < 1 where, if a minimum radius of curvature ρ min the trochoidal curve (T) is determined by expression (2) and K1 = (2ρ min - C), 0.5 ≤ K1 ≤ 2 is satisfied: ρ min = 3 ⋅ n + 1 n + 2 ⋅ 3 n ( b 2 − e 2 ) n + 2

Description

Technical field

[0001] The present invention relates to an internal gear pump equipped with a pump rotor consisting of a combination of an inner rotor, the tooth profile of which is formed by applying a trochoidal curve, and an outer rotor which has one more tooth than the inner rotor. In particular, the present invention relates to an internal gear pump that achieves improved pumping performance by avoiding the formation of peaks on the protrusions of the inner rotor, and to a method for forming the tooth profile of the inner rotor. Technical background

[0002] An internal transmission pump is used, for example, as an oil pump to lubricate a vehicle drive system, for automatic transmission (AT), for continuous variable transmission (CVT), or to supply diesel fuel.

[0003] In a known type of this internal gear pump, the tooth profile of the inner rotor is formed by applying a trochoidal curve. As in Fig. As shown in Figure 8, first a diameter A of a base circle, a diameter B of a rolling circle, a displacement e, and a diameter C of a locus circle are defined. Then the rolling circle rolls along the base circle without slippage, and a trochoidal curve T, drawn through a point (by the displacement e) from the center of the rolling circle, is obtained. An envelope of a group of circular arcs obtained by moving a center C0 of the locus circle C along the trochoidal curve T serves as an inner rotor curve (tooth profile) TC (see Figure 8). Fig. 2 in patent specification 1).

[0004] An outer rotor has one more tooth than the inner rotor 2 (the number of teeth of the inner rotor: n, and the number of teeth of the outer rotor: n + 1). The tooth profile of the outer rotor is formed based on a method that uses a locus curve from a group of tooth profile curves of the inner rotor 2, obtained based on the method described above, or is formed based on another known method.For example, the previously described method, which utilizes a locus of a group of inner rotor tooth profile curves, involves rotating the center of the inner rotor one revolution along a circle centered on the center of the outer rotor and having a diameter of (2e + t) (e denotes the displacement between the inner rotor 2 and the outer rotor 3, and t denotes a tip distance between the inner rotor 2 and the outer rotor 3 at a theoretically eccentric position) and rotating the inner rotor 2 (1 / n) times during the revolution. As a result of the revolution and rotation of the inner rotor 2, an envelope of a group of inner rotor tooth profile curves is drawn, obtained when the inner rotor 2 rotates n times, and the envelope serves as the tooth profile of the outer rotor 3 (see ). Fig. 3, Fig. 4 to Fig. 5 in patent specification 1, and paragraph

[0044] and Fig.9 in patent specification 2).

[0005] A pump rotor is formed by combining the inner rotor 2 and the outer rotor 3, which are manufactured in this manner, and mounting these rotors eccentrically relative to each other. This pump rotor is housed within a rotor chamber of a casing that includes an intake port and a discharge port, thereby forming an internal gear pump (see Fig. 1 in the present application, and paragraph

[0048] and Fig. 10 in patent specification 2).

[0006] In the inner rotor 2, whose tooth profile is formed by applying the trochoidal curve, loops R ( Fig. 9(a)) form or points s at opposite corners of each bulge 2a ( Fig.9(b)) can form at the opposite corners of the bulge, depending, for example, on the choice of the diameter A of the base circle. A tooth profile shape that has the aforementioned loops R is not actually realizable, and since it is impossible for such loops R to form in a tooth profile, they become points s formed at the opposite corners of the bulge.

[0007] When a tooth profile that has the tips at the opposite corners of each bulge is used for a pump, the contact stress (i.e. Hertz load) increases at the tips (corners) and causes wear or yielding in these areas, consequently leading to a reduction in pump performance as well as an increase in vibration and noise. Citation list of patent specifications PTL 1: Japanese Approved Utility Model Registration Application Publication No. JP H06 - 39 109 Y2 PTL 2: Japanese Patent No. JP 4 600 844 B2

[0008] Document AT 35 848 E concerns an internal rotor for a centrifugal pump based on a trochoidal curve. The rotor dimensions – base and pitch circle diameters (A, B), rotational path diameter (C), eccentricity (e), and corresponding ratios – are selected such that the condition C / K0 ≤ fc / K1 ≤ 1.1 is met, thus ensuring optimal geometry.

[0009] Document JP 2008-157210A concerns an internal rotor for an oil pump with fine trochoidal teeth. The shoulders of the tooth heads are shaped with Bézier or other higher-grade curves to improve flow and efficiency.

[0010] Document WO 2010 / 016 473 A1 concerns an internal gear pump rotor that combines an inner and outer rotor with a one-tooth difference between them. The tooth height and number are optimized to increase the pump's delivery rate. The peak and base curves of the inner rotor are generated by tracking a point on moving circles that radiate away from the rotor center and rotate at a constant angular velocity.

[0011] Document DE 695 04 983 T2 relates to an internal gear pump with an inner rotor that meshes with an outer rotor having one more tooth. The tooth profiles are formed by moving circles along the trochoidal path and its envelope, which improves the meshing behavior and efficiency.

[0012] Document JP S61-223 283 A concerns a method for correcting the curve of the outer rotor to match a theoretical curve when it combs with a trochoidal inner rotor. This increases precision and performance. Summary of the invention; Technical task

[0013] In the related technique, a method for correcting peaks is used by applying an arc-curved surface (i.e., removing the peaks by forming an arc-curved surface) when peaks form. However, correction based on an arc-curved surface leads to an expansion of a tooth gap between the inner and outer rotors, resulting in reduced pumping performance (such as volumetric efficiency).

[0014] Furthermore, (1) the size of the rotors and (2) the minimum curvature of the inner rotor 2 and the minimum curvature of the outer rotor fluctuate depending on the diameter C of the locus circle. The fluctuations in (1) can lead to reduced mechanical efficiency of the rotor, and the fluctuations in (2) can lead to an increase in Hertz load.

[0015] Based on experience, a mechanical efficiency of 50% or higher and a Hertz load safety factor ((material contact fatigue limit) / (Hertz load)) of 1.5 or higher are required when the two rotors 2 and 3 mesh, and a product thereof (i.e., (mechanical efficiency) x (Hertz load safety factor)) must be 75% or greater.

[0016] To solve the aforementioned problem, a first objective of the present invention is to prevent the formation of peaks s at the opposite corners of each protrusion 2a of the tooth profile of the inner rotor 2. A second objective is to suppress a reduction in mechanical efficiency and an increase in Hertz load in the tooth profile of the inner rotor 2 that does not have peaks s. Solution to the problem

[0017] The above problem is solved by an internal gear pump according to claim 1 and a method for forming a tooth profile of an internal rotor of an internal gear pump according to claim 6.

[0018] Fig. 6(a), Fig. 6(b) and Fig.Figure 6(c) illustrates an envelope TC of a circle C obtained when the center of circle C is moved along a locus T connected by two lines formed by a circular arc having radius r. As in Fig. As shown in 6(a), an envelope TC can be drawn that is uniform on the upper and lower sides of the drawing relative to the locus line T if a radius c of circle C is smaller than the radius r of the circular arc of the locus line T (c < r). On the other hand, as shown in Fig.6(c) shows that when the radius c of circle C is larger than the radius r of the arc of the locus T (c > r), the envelope TC at the top of the drawing is uniform relative to the locus T, whereas the envelope TC at the bottom of the drawing has a crossing loop R. When the radius c of circle C and the radius r of the arc of the locus T are equal (c = r), as in Fig. As shown in Figure 6(b), the envelope TC has a point s at the bottom of the drawing.

[0019] In the case where the tooth profile of the inner rotor is formed by applying a trochoidal curve, an envelope on the inner side of a group of circular arcs obtained by moving the center C0 of the locus circle C along the trochoidal curve T serves as the inner rotor curve (tooth profile) TC, as shown in Fig.8 shown. In a case where there are sections where a radius of curvature ρ of the trochoidal curve is locally smaller than the radius (C / 2) of the locus circle C (ρ min < (C / 2)) is, the envelope TC of the group of circular arcs of the locus circle C crosses at each of these sections, resulting in the formation of loops R in the inner rotor curve (tooth profile) TC ( Fig. 9(a)). If there are sections where the curve radius ρ and the radius of the locus circle C are equal, cusps s are formed without any crossings ( Fig. 9(b)).

[0020] Accordingly, in the present invention, the radius (C / 2) of the locus circle C is set to be constantly smaller than the radius of curvature ρ of the trochoidal curve T. In other words, the radius (C / 2) of the locus circle C is smaller than the minimum radius of curvature ρ. min the trochoidal curve T (C / 2 < ρ min ).

[0021] As shown in Fig. 7(a) and Fig. 7(b), the following expression is satisfied: COS(π / 2−0)=sinθ=(x2+b2−e2) / 2bx where n denotes the number of teeth of the inner rotor 2, b denotes the radius of the rolling circle B (= B / 2), C denotes the diameter of the locus circle, and e denotes the magnitude of the displacement.

[0022] The radius of curvature ρ is expressed as follows, based on the Euler-Savary's formula: (1 / x+1 / (ρ−x))=sinθ=1 / a+1 / b.

[0023] Assuming that (1 / a + 1 / b) = γ, ρ=x+1 / (γ / sinθ−1 / x).

[0024] By substituting the aforementioned sinθ in this expression of ρ, assuming that α=b2−e2 and β=2bγ−1 is, ρ=x+(x3+αx) / (βx2−α.)

[0025] Furthermore, by differentiating ρ with respect to x, dρ / dx=1+((3x2+α)(βx2−α)−(x3+αx)(2βx)) / (βx2−α)2=((βx2−α)2+((3x2+α)(βx2−α)−(x3+αx)(2βx))) / (βx2−α)2, and the numerator of this is (β+1)x2(βx2−3α)

[0026] Based on e ≤ X ≤ 2b and β + 1 = 2bγ ≠ 0, the x that satisfies dp / dx = 0 is as follows: x=3α / β (x>0).

[0027] Therefore, if x=3α / β. The radius of curvature ρ is minimal (minimal radius of curvature ρ min ), so that ρmin=3⋅3 (b2−e2)2bγ−1⋅1+β2β.

[0028] Based on α = b 2 - e 2 , β = 2by - 1, and a / b = n, the following is obtained: ρmin=3⋅n+1n+2⋅3 n (b2−e2)n+2.

[0029] Assuming that the minimum radius of curvature ρ min is larger than the radius of the locus circle (ρ min > C / 2) will obtain the following: ρmin=3⋅n+1n+2⋅3 n (b2−e2)n+2>C / 2, C6⋅n+2n+1⋅n+23 n (b2−e2)<1

[0030] With the following expression: C6⋅n+2n+1⋅n+23n (b2−e2)=C / 2ρmin=K and satisfying K < 1, the radius (C / 2) of the locus circle C is permanently smaller than the radius of curvature ρ of the trochoidal curve T in Fig. 8, so that peaks s are prevented from forming at the opposite corners of each protrusion 2a in the tooth profile of the inner rotor, thereby achieving the aforementioned first objective.

[0031] Next, to obtain a product (i.e., (mechanical efficiency) x (Hertz load safety factor)) of 75% or higher, as mentioned above, the value of K is set to 0.2 ≤ K ≤ 0.97 based on the following experimental result. If K1 = 2ρ min - C, 0.3 ≤ K1 ≤ 9.8 is satisfied.

[0032] Furthermore, assuming that K2=K1B2+e2 (B=A / n) 0.06 ≤ K2 ≤ 1.8 is satisfied.

[0033] To achieve a mechanical efficiency of 50% or higher and a Hertz load safety factor of 1.5 times or more, it is desirable that 0.7 ≤ K ≤ 0.96, 0.5 ≤ K1 ≤ 2, and 0.1 ≤ K2 ≤ 0.7 are met.

[0034] By obtaining a dental profile that meets these conditions, the aforementioned second goal is achieved.

[0035] In this case, K specifies a "rate", K1 denotes a "quantity", and K2 expresses K1 in rates. Advantageous effects of the invention

[0036] The present invention has the configuration described above, such that both the formation of loops R or points s at the opposite corners of each bulge of a tooth profile formed by applying a trochoidal curve is prevented, as well as a reduction in mechanical efficiency and an increase in Hertz load is suppressed. Brief description of the illustrations [ Fig.1] Fig. Figure 1 is an end surface diagram of an internal gear pump according to an embodiment of the present invention, showing a state in which a cover is removed from a housing. [ Fig. 2] Fig. Figure 2 is an enlarged view of a tooth of an inner rotor according to the embodiment. [ Fig. 3] Fig. Figure 3 represents the relationship between “mechanical efficiency x Hertz load safety factor” and K in the embodiment. [ Fig. 4] Fig. Figure 4 represents the relationship between “mechanical efficiency x Hertz load safety factor” and K1 in the embodiment. [ Fig. 5] Fig. Figure 5 represents the relationship between “mechanical efficiency x Hertz load safety factor” and K2 in the embodiment. [ Fig. 6(a)] Fig.6(a) represents an envelope of a circle C obtained when the center of the circle C moves along a locus curve T, and shows a case where a diameter r of an arc segment is smaller than a radius c of the circle C. [ Fig. 6(b)] Fig. 6(b) represents an envelope of the circle C obtained when the center of the circle C moves along the locus line T, and shows a case where r equals c. [ Fig. 6(c)] Fig. 6(c) represents an envelope of a circle C obtained when the center of the circle C moves along the locus line T, and shows a case where r is greater than c. [ Fig. 7(a)] Fig. Figure 7(a) shows how a minimum radius of curvature ρ min a trochoidal curve T is calculated. [ Fig. 7(b)] Fig. 7(b) shows how the minimum curve radius ρ minthe trochoidal curve T is calculated. [ Fig. 8] Fig. Figure 8 represents a construction of an inner rotor using a trochoidal curve. [ Fig. 9(a)] Fig. Figure 9(a) is an enlarged view showing a tooth profile shape of an internal rotor in the related technique. [ Fig. 9(b)] Fig. 9(b) is an enlarged representation showing the tooth profile shape of the inner rotor in the related technique. Description of embodiments

[0037] Fig. 1 and Fig. Figure 2 represents an embodiment of the present invention. In this embodiment, the tooth profile of an inner rotor 2 is formed based on the tooth profile formation method in Fig.8, and the tooth profile of an outer rotor is formed based on the method discussed in Patent Specification 1 and Patent Specification 2. Then, the inner rotor 2, consisting of an iron-based sintered alloy and having six teeth, and the outer rotor 3, consisting of an iron-based sintered alloy and having seven teeth, are manufactured and combined together, forming an internal gear oil pump rotor 1. The internal gear oil pump rotor 1 is contained in a rotor chamber 6 of a pump housing 5, which has an intake port 7 and a discharge port 8, thereby forming an internal gear pump 9.

[0038] When the tooth profile of the inner rotor is constructed, the condition K < 1 in the above expression (1) is satisfied, whereby loops R or peaks s are not formed at the opposite ends of each bulge 2a of an inner rotor curve (tooth profile) TC, as in Fig. 2 shown.

[0039] In particular, the number n of teeth of the inner rotor is six, the diameter of the rolling circle B is 5 mm (the same applies below), the base circle diameter A is 30 (n x B), the magnitude of a displacement e is 2, the outer diameter of the outer rotor is a larger diameter + 6 (wall thickness of 3), and the theoretical exhaust rate is 3.25 cm 3 / rev, a tip spacing t is 0.08 mm, a side spacing is 0.03 mm, a body spacing is 0.13 mm, an oil type / oil temperature is ATF 80 °C, an outlet pressure is 0.3 MPa, a rotational speed is 3000 rpm, and a material contact fatigue strength is 600 MPa. The material contact fatigue strength is a representative value for a sintered material, and the material is selected approximately in accordance with the intended use of the rotor (i.e., an increase in Hertz load due to an increase in outlet pressure).

[0040] The relationship between "mechanical efficiency x Hertz load safety factor (hereinafter referred to simply as "Hertz safety factor" or "safety factor")" and "C / 2ρ min (= K)“ is in Fig. Figure 3 is shown. Table I below shows the “mechanical efficiency”, the “Hertz load”, the “Hertz safety factor”, and “mechanical efficiency x safety factor” with respect to each K (C / 2ρ min ). Furthermore, it states Fig. 4 the relationship between “mechanical efficiency x Hertz load safety factor” and “(2ρ min - C) = K1" and Table II below shows the "mechanical efficiency", the "Hertz load", the "Hertz safety factor", and "mechanical efficiency x safety factor" with respect to each K1 (2ρ min - C). Furthermore, it states Fig.5. The relationship between “mechanical efficiency x Hertz load safety factor” and the aforementioned K2 is shown. Table III below shows the “mechanical efficiency”, the “Hertz load”, the “Hertz safety factor”, and “mechanical efficiency x safety factor” with respect to each K2. Table I C / 2 p min =K mechanical efficiency (%) Hertz load (kgf / mm²) 2 ) Hertz safety factor (%) mechanical efficiency x safety factor (%) 0.1 35.3 372 161 57.0 0.2 37.6 266 226 84.9 0.3 40.0 221 271 108.5 0.4 42.5 197 304 129.3 0.5 45.0 184 326 146.8 0.6 47.7 179 335 159.7 0.7 50.4 182 329 165.7 0.8 53.2 199 301 160.0 0.9 56.0 253 237 132.5 0.92 56.5 277 216 122.2 0.94 57.1 314 191 109.1 0.96 57.7 377 159 91.8 0.97 57.9 431 139 80.7 0.98 58.2 523 115 66.9 0.99 58,5 732 82 48.0 Table II 2 p min - C= K1 mechanical efficiency (%) Hertz load (kgf / mm²) 2 ) Hertz safety factor (%) mechanical efficiency x safety factor (%) 0.1 58.6 794 76 44.2 0.2 58.3 566 106 61.8 0.3 58.1 466 126 75.0 0.4 57.8 407 147 85.2 0.5 57.6 367 163 94.1 0.6 57.4 338 177 101.8 0.7 57.1 316 190 108.5 0.8 56.9 298 201 114.6 0.9 56.6 283 212 120.0 1 56.4 271 221 124.8 2 54.0 209 286 154.7 5 47.0 180 334 157.2 8 40.5 214 280 113.5 9 38.5 245 245 94.3 10 36.5 302 199 72.7 Table III (2 ρ min - C) / (B 2 + e 2 ) 1 / 2 = K3 mechanical efficiency (%) Hertz load (kgf / mm²) 2 ) Hertz safety factor (%) mechanical efficiency x safety factor (%) 58.5 766 78 45.9 K2 58.0 450 133 77.3 0.1 57.5 355 169 97.2 0.2 56.2 263 228 128.3 0.3 54.9 225 267 146.4 0.5 52.4 193 312 163.2 0.7 50.0 181 331 165.3 0.8 48.6 179 335 162.8 0.9 47.4 179 335 158.7 1 46.2 181 332 153.2 1.2 43.8 189 317 139.0 1.5 40.4 216 278 112.1 1.8 37.1 280 214 79.6 2 35.1 395 152 53.2

[0041] For "mechanical efficiency x safety factor" to be greater than or equal to 75%, it is obviously necessary to... Fig. 3 and Table I, that 0.2 ≤ K ≤ 0.97 is satisfied, from Fig. 4 and Table II, that 0.3 ≤ K1 ≤ 9.8 is satisfied, and from Fig. 5 and Table III, that 0.06 ≤ K2 ≤ 1.8 is satisfied.

[0042] To continue to achieve a mechanical efficiency of 50% or higher and a Hertz load safety factor of 1.5 times (150%) or more, it is obviously necessary to Fig.3 and Table I, that 0.7 ≤ K ≤ 0.96 is satisfied, from Fig. 4 and Table II, that 0.5 ≤ K1 ≤ 2 is satisfied, and from Fig. 5 and Table III, that 0.1 ≤ K2 ≤ 0.7 is satisfied.

[0043] The tooth profile of the outer rotor 3 is not limited to an envelope of a group of tooth profile curves formed by the revolution and rotation of the inner rotor 2 as described above. Alternatively, the tooth profile of the outer rotor 3 can be obtained based on any method, provided that the envelope is, for example, the minimum tooth profile line of the outer rotor 3 to allow rotation without causing mutual obstruction of the inner rotor 2 and the outer rotor 3, and the tooth profile is drawn on the outer side of the envelope.

[0044] Furthermore, the number of teeth of the inner rotor 2 is not limited to six and can be any freely chosen number.

[0045] Accordingly, the disclosed embodiment is only an example in all aspects and should not be considered limiting. The scope of the invention is defined by the claims and is intended to encompass interpretations equivalent to the scope of the claims and to include all modifications within that scope. List of reference symbols 1 internal transmission oil pump rotor 2 inner rotor 2a Deregistration of the inner rotor 3 outer rotor 4 pump chambers 5 Pump housings 6 rotor chamber 7 Intake opening 8 Outlet opening 9 internal gear pump A Base circle diameter B Rolling circle diameter C locus circle diameter T trochoidal curve TC tooth profile (inner rotor curve)

Claims

[1] An internal gear pump wherein a diameter of a base circle is specified at A mm, a diameter of a rolling circle is specified at B mm, a radius of the rolling circle is specified at b mm, a diameter of a locus circle is specified at C mm, and an amount of a displacement is specified at e mm, wherein a trochoidal curve (T) is drawn by rolling the rolling circle along the base circle without slippage and by applying a locus of a fixed point that is e away from a center of the rolling circle, wherein a tooth profile of an inner rotor (2) having n teeth is formed based on an envelope of a group of locus circles, each of which has a center on the trochoidal curve (T), wherein a pump rotor (1) is formed by combining the inner rotor (2) with an outer rotor (3) having (n+1) teeth, and where a tooth profile curve of the inner rotor (2) satisfies expression (1): K=C6⋅n+2n+1⋅n+23n(b2−e2)<1 where, if a minimum radius of curvature ρ min the trochoidal curve (T) is determined by expression (2) and K1 = (2ρ min - C), 0.5 ≤ K1 ≤ 2 is satisfied: ρmin=3⋅n+1n+2⋅3n(b2−e2)n+2 [2] The internal gear pump according to claim 1, wherein 0.2 ≤ K ≤ 0.97 is satisfied. [3] The internal gear pump according to claim 2, wherein 0.7 ≤ K ≤ 0.96 is satisfied. [4] The internal gear pump according to claim 1, wherein, if K2 is defined by expression (3), 0.06 ≤ K2 ≤ 1.8 is satisfied: K2=K1B2+e2(B=A / n) [5] The internal gear pump according to claim 4, wherein 0.1 ≤ K2 ≤ 0.7 is satisfied. [6] A method for forming a tooth profile of an internal rotor of an internal gear pump (9), comprising: Setting a diameter of a base circle to A mm, a diameter of a rolling circle to B mm, a radius of the rolling circle to b mm, a diameter of a locus circle to C mm, and an amount of a displacement to e mm; Drawing a trochoidal curve (T) by rolling the rolling circle along the base circle without slippage and by applying a locus curve from a fixed point that is e away from a center of the rolling circle; Forming a tooth profile of an inner rotor (2) having n teeth, based on an envelope of a group of locus circles, each of which has a center on the trochoidal curve (T); and Forming a pump rotor (1) by combining the inner rotor (2) with an outer rotor having (n+1) teeth, where a tooth profile curve of the inner rotor satisfies condition (1): K=C6⋅n+2n+1⋅n+23n(b2−e2)<1 where, if a minimum radius of curvature ρ min the trochoidal curve (T) is defined by expression (2) and K1 = (2ρ min - C), 0.5 ≤ K1 ≤ 2 is satisfied: ρmin=3⋅n+1n+2⋅3n(b2−e2)n+2 [7] The method for forming a tooth profile of an inner rotor of an internal gear pump according to claim 6, wherein 0.2 ≤ K ≤ 0.97 is satisfied. [8] The method for forming a tooth profile of an inner rotor of an internal gear pump according to claim 7, wherein 0.7 ≤ K ≤ 0.96 is satisfied. [9] The method for forming a tooth profile of an inner rotor of an internal gear pump according to claim 6, wherein, if K2 is defined by expression (3), 0.06 ≤ K2 ≤ 1.8 is fulfilled: K2=⋅K1B2+e2(B=A / n) [10] The method for forming a tooth profile of an inner rotor of an internal gear pump according to claim 9, wherein 0.1 ≤ K2 ≤ 0.7 is satisfied.

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