Patent Publication Number: US-7588429-B2

Title: Oil pump rotor assembly

Description:
CROSS-REFERENCE TO PRIOR APPLICATION 
     This is a U.S. national phase application under 35 U.S.C. §371 of International Patent Application No. PCT/JP2004/012170 filed Aug. 25, 2004 and claims the benefit of Japanese Patent Application No. 2003-309348 filed Sep. 1, 2003, both of which are incorporated by reference herein. The International Application was published in Japanese on Mar. 10, 2005 as WO 2004/021969 A1 under PCT Article 21(2). 
     TECHNICAL FIELD 
     This invention relates to an oil pump rotor assembly used in an oil pump which draws and discharges fluid by volume change of cells formed between an inner rotor and an outer rotor. 
     BACKGROUND ART 
     A conventional oil pump comprises an inner rotor formed with “n” external teeth (“n” is a natural number), an outer rotor formed with “n+1” internal teeth which are engageable with the external teeth, and a casing in which a suction port for drawing fluid and a discharge port for discharging fluid are formed. The inner rotor is rotated to rotate the outer rotor by the engagement of the external teeth with the internal teeth, so that fluid is drawn and is discharged by changes in the volumes of plural cells formed between the inner and outer rotors. 
     Each of the cells is delimited at a front portion and at a rear portion as viewed in the direction of rotation of the inner rotor and outer rotor by contact between the external teeth of the inner rotor and the internal teeth of the outer rotor, and is also delimited at either side portions by the casing, so that an independent fluid conveying chamber is formed. While the external teeth and the internal teeth engage with each other, the cell becomes the smallest in volume. Then, when the cell moves along the inlet port, it increases in volume to draw fluid, and thereby it has the largest volume. Then, when the cell moves along the discharge port, it decreases in volume to discharge fluid. 
     Since such oil pumps having the above construction are compact and simply constructed, it is widely used as pumps for lubrication oil in automobiles and as oil pumps for automatic transmissions, etc. When an oil pump is mounted on an automobile, means for driving the oil pump includes a crankshaft directly-connected and driven method in which an inner rotor is directly connected to a crankshaft of an engine and the inner rotor is driven by the rotation of the engine. 
     With regard to the oil pump as described above, in order to reduce noise emitted from an oil pump and to improve mechanical efficiency accompanied therewith, an appropriate size of clearance is set between a tooth tip of the inner rotor and a tooth tip of the outer rotor in a rotational phase advancing by 180° from a rotational phase in which the inner and outer rotors engage with each other in their combined state. 
     Meanwhile, the conditions that are required to determine the tooth profile of an inner rotor ri and the tooth profile of an outer rotor ro will be described. First, with regard to the inner rotor ri, the rolling distance of a first circumscribed-rolling circle Di′ (the diameter thereof is φDi′) and the rolling distance of a first inscribed-rolling circle di′ (the diameter thereof is φdi′) must be completed in one cycle. That is, since the rolling distance of the first circumscribed-rolling circle Di′ and the rolling distance of the first inscribed-rolling circle di′ must be equal to the length of circumference of a base circle bi′ (the diameter thereof is φbi′) of the inner rotor ri, the following equation is satisfied:
 
φ bi′=n ·(φ Di′+φdi ′)
 
     Similarly, with regard to the outer rotor ro, since the rolling distance of a second circumscribed-rolling circle Do′ (the diameter thereof is φDo′) and the rolling distance of a second inscribed-rolling circle do′ (the diameter thereof is φdo′) must be equal to the length of circumference of a base circle bo′ (the diameter thereof is φbo′) of the outer rotor ro,
 
φ bo ′=( n+ 1)·(φ Do′+φdo ′)
 
     Next, since the inner rotor ri engages with the outer rotor ro, the eccentric distance e′ between the inner and outer rotors ri and ro satisfies the following equations:
 
φ Di′+φdi′=φDo′+φdo′= 2 e  
 
     Based on the respective equations, the following equation is obtained:
 
 n·φbo ′=( n+ 1)·φ bi′ 
 
The tooth profile of the inner rotor ri and the tooth profile of the outer rotor ro are constructed to satisfy the above conditions.
 
     Here, in order to divide the clearance t into a tip clearance between a tooth space and a tooth tip in a rotational phase in which the inner and outer rotors engage with each other, and a tip clearance between tooth tips in a rotational phase advanced by 180° from the rotational phase in which the inner and outer rotors engage with each other, the circumscribed-rolling circle and the inscribed-rolling circle are respectively constructed to satisfy the following equations:
 
φ Do′=φDi′+t/ 2, and
 
φ do′=φdi′−t/ 2
 
     That is, the circumscribed-rolling circle of the outer rotor is made larger than that of the inner rotor (φDo′&gt;φDi). As a result, as shown in  FIG. 6 , a clearance 2/t is formed between a tooth space of the outer rotor ro and a tooth tip of the inner rotor ri in the rotational phase in which the inner and outer rotors engage with each other. On the other hand, the inscribed-rolling circle of the inner rotor is made larger than that of outer rotor (φdi′&gt;φdo′). As a result, as shown in  FIG. 7 , a clearance t/2 is formed between a tooth tip of the outer rotor ro and a tooth space of the inner rotor ri in a rotational phase in which the inner and outer rotors engage with each other (For example, see Patent Document 1). Moreover, as shown in  FIGS. 6 and 7 , not only a tip clearance tt is formed between tip portions of the external and internal teeth of the inner and outer rotors, but also a side clearance ts is formed between the tooth surfaces of the external and internal teeth of the inner and outer rotors. 
     An oil pump rotor assembly constructed to satisfy the above relations is shown  FIGS. 5 to 7 . In the inner rotor ri, φbi′=52.00 mm; φDi′=2.50 mm; and φdi′=2.70 mm; and n=10, where φbi′ is the diameter of the base circle bi′, φDi′ is the diameter of the first circumscribed-rolling circle Di′, φdi′ is the diameter of the first inscribed-rolling circle di′, and n is the number of the external teeth, and in the outer rotor ro, φ=70 mm; φbo′=57.20 mm; φDo′=2.56 mm; φdo′=2.64 mm; n+1=11; and e′=2.6 mm, where φ is the external diameter of the outer rotor, φbo′ is the diameter of the base circle bo′, φDo′ is the diameter of the second circumscribed-rolling circle Do′, and φdo′ is the diameter of the second inscribed-rolling circle do′, n+1 is the number of the internal teeth, and n+1 is the eccentric distance. 
     In the oil pump rotor assembly have the above construction, the inner and outer rotors are formed such that the profile of a tooth tip of the inner rotor is smaller than the profile of a tooth space of the outer rotor and the profile of a tooth space of the inner rotor is larger than the profile of a tooth tip of the outer rotor. Thus, the backlash is set to an appropriate size and the tip clearance tt is set to an appropriate size. As a result, a large backlash can be surely obtained while the tip clearance tt is kept small. Thus, in particular, in a state where the pressure of oil supplied to the oil pump rotor assembly and the torque that drives the oil pump rotor assembly are stable, noise caused by collision between the external teeth of the inner rotor and the internal teeth of the outer rotor can be prevented from being generated. 
     [Patent Document 1] 
     Japanese Unexamined Patent Application Publication No. 11-264381 
     DISCLOSURE OF THE INVENTION 
     However, when the diameter of the second circumscribed-rolling circle Do′ and the diameter of the second inscribed-rolling circle do′ are adjusted to obtain the tip clearance tt=2/t, as shown in  FIGS. 6 and 7 , the side clearance ts may become large inevitably. Accordingly, with regard to the silence property of the oil pump rotor assembly, the following problems are left unsolved. That is, in a case that the hydraulic pressure generated in the oil pump rotor assembly is extremely small, and the torque that drives the oil pump rotor assembly changes, the internal teeth of the outer rotor and the external teeth of the inner rotor collide with each other. The collision energy at this time is transformed into sound. The sound may reach the level of audible sound, which is turned into noise. 
     The present invention has been made in consideration of the above circumstances. It is therefore an object of the present invention to appropriately set the tooth profile of an inner rotor and the tooth profile of an outer rotor, and appropriately set clearances between the inner and outer rotors, so that, even when the hydraulic pressure generated in the oil pump rotor assembly is extremely small and the torque that drives the oil pump rotor assembly changes, noise can be surely prevented from being generated. 
     In order to solve the above problems and accomplish the above object, the present invention proposes the following means. 
     According to the first aspect of the present invention, there is provided an oil pump rotor assembly comprising: an inner rotor formed with “n” external teeth (“n” is a natural number); and an outer rotor formed with (n+1) internal teeth which are engageable with the external teeth, and a casing having a suction port for drawing fluid and a discharge port for discharging fluid, wherein the fluid is conveyed by drawing and discharging the fluid by volume change of cells formed between tooth surfaces of the inner and outer rotors during relative rotation between the inner and outer rotors engaging each other. Each of the tooth profiles of the inner rotor is formed such that the profile of a tooth tip thereof is formed using an epicycloid curve which is generated by rolling a first circumscribed-rolling circle Di along a base circle bi without slippage, and the profile of a tooth space thereof is formed using a hypocycloid curve which is generated by rolling an inscribed-rolling circle di along the base circle bi without slippage. Each of the tooth profiles of the outer rotor is formed such that the profile of a tooth space thereof is formed using an epicycloid curve which is generated by rolling a second circumscribed-rolling circle Do along a base circle bo without slippage, and the profile of a tooth tip thereof is formed using a hypocycloid curve which is generated by rolling a second inscribed-rolling circle do along the base circle bo without slippage. The inner and outer rotors are constructed to satisfy the following relations:
 
φ bi=n ·(φ Di+φdi ),
 
φ bo =( n+ 1)·(φ Do+φdo ),
 
φ Di+φdi= 2 e , or φ Do+φdo= 2 e  
 
φDo&gt;φDi,
 
φdi&gt;φdo, and
 
(φ Di+φdi )&lt;(φ Do+φdo ),
 
where φbi is the diameter of the base circle bi of the inner rotor, φDi is the diameter of the first circumscribed-rolling circle Di of the inner rotor, φdi is the diameter of the first inscribed-rolling circle di of the inner rotor, φbo is the diameter of the base circle bo of the outer rotor, φDo is the diameter of the second circumscribed-rolling circle Do of the outer rotor, φdo is the diameter of the second inscribed-rolling circle do of the outer rotor, and e is the eccentric distance between the inner and outer rotors.
 
     That is, in order to determine the tooth profiles of the inner and outer rotors, first, since the rolling distance of the circumscribed-rolling circle of the inner rotor and the rolling distance of the inscribed-rolling circle of the outer rotor must be completed in one cycle, the following equations are satisfied:
 
φ bi=n ·( φDi+φdi ), and
 
φ bo =( n+ 1)·(φ Do+φdo )
 
     In order to obtain a large backlash between the tooth surfaces of the inner and outer rotors while they engages with each other, the profile of a tooth tip of the inner rotor formed by the first circumscribed-rolling circle Di with respect to the profile of a tooth space of the outer rotor formed by the second circumscribed-rolling circle Do and the profile of a tooth tip of the outer rotor formed by the second inscribed-rolling circle do with respect to the profile of a tooth space of the inner rotor formed by the first inscribed-rolling circle di must satisfy the following inequalities:
 
φDo&gt;φDi, and
 
φdi&gt;φdo
 
Here, the backlash means a clearance that may be created between the tooth surface of the outer rotor and the tooth surface of the inner rotor opposite to the tooth surface thereof to which load is applied when the inner and outer rotors engage with each other.
 
     Further, since the inner rotor engages with the outer rotor, any one of the following equations must be satisfied:
 
φ Di+φdi= 2 e , and
 
φDo+φdo=2 e  
 
     Moreover, in the present invention, in order to rotate the inner rotor inside the outer rotor well, to adequately maintain the size of backlash while the tip clearance is surely obtained, and to reduce the engaging resistance, the diameter of the base circle of the outer rotor is made large compared with the conventional oil pump rotor assembly such that the base circle of the inner rotor does not comes in contact with the base circle of the outer rotor in a rotational phase in which the inner and outer rotors engage with each other. That is, the following inequality is satisfied:
 
( n+ 1)·φ bi&lt;n·φbo  
 
     As a result, the following inequality is derived:
 
(φ Di+φdi )&lt;(φ Do+φdo )
 
     According to this invention, the side clearance between the tooth surfaces of the inner and outer rotors is made small compared with the conventional oil pump rotor assembly while the tip clearance between the external teeth of the inner rotor and the internal teeth of the outer rotor is surely obtained. Thus, it is possible to realize an oil pump rotor assembly with a small play between the inner and outer rotors and an excellent silence property. Particularly, even if the hydraulic pressure generated in the oil pump rotor assembly is extremely small, and the torque that drives the oil pump rotor assembly changes, the internal teeth of the outer rotor can be prevented from colliding with the external teeth of the inner rotor. Thus, the silence property of the oil pump rotor assembly can be surely improved. 
     According to a second aspect of the present invention, there is provided the oil pump rotor assembly according to the first aspect in which the inner and outer rotors are constructed to satisfy the following inequality:
 
0.005 mm≦(φ Do+φdo )−(φ Di+φdi )≦0.070 mm (mm: millimeters)
 
     According to this invention, the inner and outer rotors are constructed to satisfy the following inequality:
 
0.005 mm≦(φDo+φdo)−(φ Di+φdi )
 
As a result, the size of backlash can be adequately maintained while the tip clearance can be surely obtained, and noise due to the engagement between the inner and outer rotors can be reduced. Further, the inner and outer rotors are constructed to satisfy the following inequality:
 
(φ Do+φdo )−(φ Di+φdi )≦0.070 mm
 
As a result, the mechanical efficiency can be prevented from being reduced and noise can be prevented from being generated.
 
     According to the oil pump rotor related to the present invention, clearances between the external teeth of the inner rotor and the internal teeth of the outer rotor are surely obtained and the side clearance between tooth surfaces of the inner and outer rotors is made small compared with the conventional oil pump rotor assembly. Thus, it is possible to realize an oil pump rotor assembly with a small play between the inner and outer rotors and an excellent silence property. Particularly, even when the hydraulic pressure generated in the oil pump rotor assembly is extremely small and the torque that drives the oil pump rotor assembly changes, noise can be surely prevented from being generated. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a plan view illustrating an oil pump according to one embodiment of the present invention; 
         FIG. 2  is an enlarged view taken along the line II, which illustrates engaging portions of the oil pump in  FIG. 1 ; 
         FIG. 3  is a graph that compares backlashes of the oil pump shown in  FIG. 1  with backlashes of a conventional oil pump. 
         FIG. 4  is a graph that compares noise caused by the oil pump in  FIG. 1  with noise caused by the conventional oil pump; 
         FIG. 5  is a plan view illustrating the conventional oil pump in which inner and outer rotors are constructed to satisfy the following relations:
 φ bi=n ·(φ Di+φdi ), φ bo =( n+ 1)·(φ Do+φdo ) φ Di+φdi= 2 e , or φ Do+φdo= 2 e    φDo&gt;φDi, and φdi&gt;φdo 
and (φDo+φdo)−(φDi+φdi) is set to 0.009 mm;
 
         FIG. 6  is an enlarged view taken along the line V, which illustrates engaging portions of the oil pump shown in  FIG. 5 ; and 
         FIG. 7  is an enlarged view illustrating the engaging portions of the oil pump shown in  FIG. 5  in a state where a tooth tip of the outer rotor and a tooth space of the inner rotor engages with each other. 
     
    
    
     REFERENCE NUMERALS 
     
         
           10  inner rotor 
           11  external teeth 
           20  outer rotor 
           21  internal teeth 
           50  casing 
         Di circumscribed-rolling circle of inner rotor (first circumscribed-rolling circle) 
         Do circumscribed-rolling circle of outer rotor (second circumscribed-rolling circle) 
         di inscribed-rolling circle of inner rotor (first inscribed-rolling circle) 
         do inscribed-rolling circle of outer rotor (second inscribed-rolling circle) 
         C cell 
         bi base circle of inner rotor 
         bo base circle of outer rotor 
         Oi axis of inner rotor 
         Oo axis of outer rotor 
       
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     One embodiment of an oil pump rotor assembly according to the present invention will now be described with reference to  FIGS. 1 through 4 . 
     The oil pump shown in  FIG. 1  comprises an inner rotor  10  formed with “n” external teeth (“n” is a natural number, and n=10 in this embodiment), an outer rotor  20  formed with “n+1” internal teeth (n+1=11 in this embodiment) which are engageable with the external teeth, and a casing  50  which accommodates the inner rotor  10  and the outer rotor  20 . 
     Between the tooth surfaces of the inner and outer rotors  10  and  20 , there are formed plural cells C in the direction of rotation of the inner and outer rotors  10  and  20 . Each of the cells C is delimited at a front portion and at a rear portion as viewed in the direction of rotation of the inner and outer rotors  10  and  20  by contact between the external teeth  11  of the inner rotor  10  and the internal teeth  21  of the outer rotor  20 , and is also delimited at either side portions by the casing  50 , so that an independent fluid conveying chamber is formed. Each of the cells C moves while the inner and outer rotors  10  and  20  rotate, and the volume of each of the cells C cyclically increases and decreases so as to complete one cycle in a rotation. 
     The inner rotor  10  is mounted on a rotational axis so as to be rotatable about the axis Oi. The profile of a tooth tip of the inner rotor  10  is formed using an epicycloid curve, which is generated by rolling a first circumscribed-rolling circle Di along the base circle bi of the inner rotor  10  without slippage, and the profile of a tooth space of the inner rotor  10  is formed using a hypocycloid curve, which is generated by rolling a first inscribed-rolling circle di along the base circle bi without slippage. 
     The outer rotor  20  is supported so as to be rotatable about the axis Oo in the casing  50 , and the axis Oo thereof is positioned so as to have an offset (the eccentric distance is “e”) from the axis Oi of the inner rotor  10 . The profile of a tooth space of the outer rotor  20  is formed using an epicycloid curve which is generated by rolling a second circumscribed-rolling circle Do along a base circle bo without slippage, and the profile of a tooth tip thereof is formed using a hypocycloid curve which is generated by rolling a second inscribed-rolling circle do along the base circle bo without slippage. 
     When φbi is the diameter of the base circle bi of the inner rotor  10 , φDi is the diameter of the first circumscribed-rolling circle Di thereof, φdi is the diameter of the first inscribed-rolling circle di thereof, φbo is the diameter of the base circle bo of the outer rotor  20 , φDo is the diameter of the second circumscribed-rolling circle Do thereof, and φdo is the diameter of the second inscribed-rolling circle do thereof, the following relations are to be satisfied between the inner and outer rotors  10  and  20 . Note that dimensions will be expressed in millimeters. 
     First, with regard to the inner rotor  10 , the rolling distance of the first circumscribed-rolling circle Di and the rolling distance of the first inscribed-rolling circle di must be completed in one cycle. That is, since the rolling distance of the first circumscribed-rolling circle Di and the rolling distance of the first inscribed-rolling circle di must be equal to the length of circumference of the base circle bi,
 
·φ bi=n ··(φ Di+φdi ), i.e.,
 
φ bi=n ·(φ Di+φdi )  (Ia)
 
     Similarly, with regard to the outer rotor  20 , since the rolling distance of the second circumscribed-rolling circle Do and the rolling distance of the second inscribed-rolling circle do must be equal to the length of circumference of the base circle bo,
 
·φ bo =( n+ 1)··(φ Do+φdo ), i.e.,
 
φ bo =( n+ 1)·(φ Do+φdo )  (Ib)
 
     In order to obtain a large backlash between the tooth surfaces of the inner and outer rotors while they engage with each other, the profile of a tooth tip of the inner rotor formed by the first circumscribed-rolling circle Di with respect to the profile of a tooth space of the outer rotor formed by the second circumscribed-rolling circle Do and the profile of a tooth tip of the outer rotor formed by the second inscribed-rolling circle do with respect to the profile of a tooth space of the inner rotor formed by the first inscribed-rolling circle di must satisfy the following inequalities:
 
φDo&gt;φDi, and
 
φdi&gt;φdo
 
Here, the backlash means a clearance that may be created between the tooth surface of the outer rotor and the tooth surface of the inner rotor opposite to the tooth surface thereof to which load is applied while the inner and outer rotors engage with each other.
 
     Further, since the inner rotor engages with the outer rotor, any one of the following equations must be satisfied:
 
φ Di+φdi= 2 e , and
 
φ Do+φdo= 2 e  
 
     Moreover, in the present invention, in order to rotate the inner rotor  10  inside the outer rotor  20  well, to adequately maintain the size of backlash while the tip clearance is surely obtained, and to reduce the engaging resistance, the diameter of the base circle bo of the outer rotor  20  is made large such that the base circle bi of the inner rotor  10  does not comes in contact with the base circle bo of the outer rotor  20  in a rotational phase in which the inner and outer rotors  10  and  20  engages with each other. That is, the following inequality is satisfied:
 
( n+ 1)·φ bi&lt;n·φbo  
 
     Based on the above inequality and the equations (Ia) and (Ib), the following inequality is obtained:
 
(φ Di+φdi )&lt;(φ Do+φdo )
 
     Furthermore, the rotational phase in which the inner and outer rotors engage with each other means a rotational phase in which a tooth tip of each of the internal teeth  21  of the outer rotor directly faces a tooth space of each of the external teeth  11  of the inner rotor  10 , as shown in  FIG. 2 . 
     Here, the inner and outer rotors  10  and  20  are constructed such that the following inequality is satisfied:
 
0.005 mm≦(φ Do+φdo )−(φ Di+φdi )≦0.070 mm (mm: millimeters)  (Ic)
 
     Hereinafter, “(φDo+φdo)−(φDi+φdi)” is simply referred to as “A”. 
     Moreover, in the present embodiment, the inner rotor  10  (φbi=65.00 mm; φDi=3.90 mm; φdi=2.60 mm; and n=10, where φbi is the diameter of the base circle bi, φDi is the diameter of the first circumscribed-rolling circle Di, φdi is the diameter of the first inscribed-rolling circle di, and n is the number of teeth) and the outer rotor  20  (φ=87.0 mm; φbo=71.599 mm; φDo=3.9135 mm; φdo=2.5955 mm, where φ is the external diameter of the outer rotor, φbo is the diameter of the base circle bo, φDo is the diameter of the second circumscribed-rolling circle Do, and φdo is the diameter of the second inscribed-rolling circle do), which satisfy the above relations, are combined with each other with the eccentric distance of e=3.25 mm, to construct an oil pump rotor assembly. Moreover, in the present embodiment, the tooth width of the inner and outer rotors (the size of teeth in the direction of the rotational axis of each rotor) is set to 10 mm. Further, the diameter φDi of the first circumscribed-rolling circle Di is set to 3.90 mm, the diameter φdi of the first inscribed-rolling circle di is set to 2.60 mm, the diameter φDo of the second circumscribed-rolling circle Do is set to 3.9135 mm, and the diameter φdo of the second inscribed rolling circle do is set to 2.5955 mm. As a result, “A” is set to 0.009 (See  FIG. 2 ). 
     The casing  50  is formed with a circular-arc-shaped inlet port (not shown) along a cell C whose volume is being increasing, among cells C formed between the tooth surfaces of the inner and outer rotors  10  and  20 , and the casing is also formed with a circular-arc-shaped discharge port (not shown) along a cell C whose volume is being decreasing. 
     While the external teeth  11  and the internal teeth  21  engage with each other, the cell C becomes the smallest in volume. Then, when the cell moves along the inlet port, it increases in volume to draw fluid, and thereby it has the largest volume. Then, when the cell moves along the discharge port, it decreases in volume to discharge fluid. 
     When “A” is too small, the tip clearance and the size of backlash cannot be adequately maintained, and the noise generated when the external teeth  11  of the inner rotor and the internal teeth  21  of the outer rotor engages with each other cannot be reduced. 
     On the other hand, when “A” is too large, the difference between the tooth height (the size of teeth in the direction normal to the base circle) of the external teeth  11  of the inner rotor and the tooth height of the internal teeth  21  of the outer rotor, and the difference between the thickness (the size of teeth in the circumferential direction of the base circle) of the external teeth  11  and the thickness of the internal teeth  21  cannot be adequately maintained, so that a portion with no backlash may be created during the rotation of an oil pump rotor assembly. In this case, the oil pump rotor assembly cannot rotate well, so that the mechanical efficiency may be reduced and different noises may be generated due to the collision between the external teeth  11  and the internal teeth  21 . 
     Therefore, it is preferable that “A” be set to a range that satisfies the following inequality:
 
0.005 mm≦A≦0.070 mm
 
In the present embodiment, it is most preferable that “A” be set to 0.009 mm.
 
     In the oil pump rotor assembly having the above construction, the profile of tooth tips of the outer rotor  20  is substantially equal to the profile of tooth spaces of the inner rotor  10 . As a result, as shown in  FIG. 2 , since the side clearance ts becomes small while the tip clearance tt is surely obtained similar to the related art, the impact applied to the inner and outer rotors  10  and  20  during rotation thereof becomes small. Accordingly, even if the hydraulic pressure generated in the oil pump rotor assembly is extremely small, and the torque that drives the oil pump rotor assembly changes, the internal teeth  21  of the outer rotor can be prevented from colliding with the external teeth  11  of the inner rotor. Thus, the silence property of the oil pump rotor assembly can be surely improved. Further, since the direction of pressure when the inner and outer rotors engage with each other is perpendicular to the tooth surfaces, the torque transmission between the inner and outer rotors  10  and  20  can be performed with high efficiency without slippage, and heat and noise caused by sliding resistance can be reduced. 
       FIG. 3  is a graph that compares backlashes (a broken line in  FIG. 3 ) for every rotational angle of an inner rotor in an oil pump rotor assembly of the related art with backlashes (a solid line in  FIG. 3 ) for every rotational angle of the inner rotor in the oil pump rotor assembly according to the present invention. It can be understood from the graph that the backlash in the oil pump rotor assembly according to the present embodiment can be made smaller than that in the conventional oil pump rotor assembly in the rotational phase in which the inner and outer rotors engage with each other and while the volume of the cell C increases or decreases, and the backlash in the oil pump rotor assembly according to the present embodiment can be equal to that in the conventional oil pump rotor assembly in a rotational phase in which the volume of the cell C becomes the largest. Accordingly, it can be understood that, in the latter case, the liquid-tightness of the cell C when the volume of the cell C becomes the largest can be surely obtained, and the conveying efficiency can be maintained at the same level as the conventional oil pump rotor assembly. Moreover, only the backlashes for the rotational angle of the inner rotor ranging from 0° to 180° are shown in  FIG. 3 , and the other backlashes are omitted. This is because a change in backlashes for the rotational angle of the inner rotor ranging from 180° to 360° (0°) is equal to that in backlashes for the rotational angle of the inner rotor from 180° to 0°. 
     Further,  FIG. 4  is a graph that compares the noise generated when the oil pump rotor assembly of the related art is used with the noise generated when the oil pump rotor assembly generated when the oil pump rotor assembly according to the present embodiment is used. It can be understood from the graph that the backlashes in the oil pump rotor assembly according to the present embodiment, as shown in  FIG. 3 , becomes smaller than those in the conventional oil pump rotor assembly in the rotational phase in which the inner and outer rotors engage with each other and while the volume of the cell C increases or decreases, so that noise can be decreased compared with the conventional oil pump rotor assembly and the silence property can be improved. 
     The technical scope of the present invention is not limited to the aforementioned embodiment, but various modifications can be made without departing from the spirit of the present invention. 
     INDUSTRIAL APPLICABILITY 
     The tooth profile of the inner rotor and the tooth profile of the outer rotor are appropriately set, and the clearance between the inner and outer rotors is appropriately set. As a result, even when the hydraulic pressure generated in the oil pump rotor assembly is extremely small and the torque that drives the oil pump rotor assembly changes, noise generation can be surely suppressed.