Patent Publication Number: US-2017370359-A1

Title: Gear pump and manufacturing method of the same

Description:
This is a national phase application of PCT/JP2015/086533 filed 28 Dec. 2015, claiming priority to Japanese Patent Application No. JP2015-17762 filed 30 Jan. 2015, the contents of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a gear pump including an inner rotor configured to have a plurality of external teeth and an outer rotor configured to have a plurality of internal teeth and arranged to be eccentric with respect to the inner rotor, and to a manufacturing method of the same. 
     BACKGROUND 
     A known configuration of a gear pump includes one intake port arranged to communicate with pump chambers (inter-teeth chambers) of which volumes increase by rotations of an external gear and an internal gear and two discharge ports arranged to communicate with pump chambers of which volumes decrease by rotations of the external gear and the internal gear among pump chambers defined by external teeth of the external gear and internal teeth of the internal gear (as described in, for example, Patent Literature 1). This gear pump is designed such that a minimum clearance between an external tooth and an internal tooth located on a partition wall arranged to separate the two discharge ports from each other is not less than 0.020 mm and not greater than 0.110 mm in the state that the external gear and the internal gear are pressed in opposite directions along a radial direction. 
     CITATION LIST 
     Patent Literature 
     PTL1: JP No. 5469875 
     SUMMARY 
     Setting the minimum clearance between the external tooth and the internal tooth located on the partition wall arranged to separate the two discharge ports from each other like the above prior art gear pump is expected to reduce leakage of a hydraulic operating fluid from the pump chamber which communicates with one discharge port on the higher pressure side to the pump chamber which communicates with the other discharge port on the lower pressure side and thereby enhance the volume efficiency of the pump. Decreasing the minimum clearance between the external tooth and the internal tooth located on the partition wall is, however, likely to cause cavitation during the inflow of the fluid into the pump chamber communicating with the intake port. The occurrence of cavitation is likely to decrease the volume efficiency and cause the noise and the vibration. 
     A subject matter of the present disclosure is accordingly to provide a gear pump configured to suppress the occurrence of cavitation while enhancing the volume efficiency, and a manufacturing method of the same. 
     The present disclosure is directed to a gear pump. The gear pump includes an inner rotor configured to have a plurality of external teeth, an outer rotor configured to have a greater number of internal teeth than number of the external teeth of the inner rotor and arranged to be eccentric with respect to the inner rotor, and a plurality of inter-teeth chambers, each being defined by two adjacent external teeth and two adjacent internal teeth. The gear pump further includes one intake port configured to communicate with the inter-teeth chamber of which volume increases with rotations of the inner rotor and the outer rotor, and a first discharge port and a second discharge port separated from each other by a partition wall to be independent of each other, each of the discharge ports being configured to communicate with the inter-teeth chamber of which volume decreases with the rotations of the inner rotor and the outer rotor. An intake-side clearance is larger than a discharge-side clearance, where the intake-side clearance denotes a minimum value of a clearance between the external tooth and the internal tooth defining the inter-teeth chamber which communicates with the intake port and in which an amount of change in volume during rotation of the inner rotor by a unit angle is maximized, and the discharge-side clearance denotes a minimum value of a clearance between the external tooth and the internal tooth defining the inter-teeth chamber which at least partially overlaps with the partition wall between the first discharge port and the second discharge port when the amount of change in volume per unit angle is maximized. 
     In the gear pump of this aspect, the inner rotor is formed such that the minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which communicates with the intake port and in which the amount of change in volume during rotation of the inner rotor by the unit angle is maximized is larger than the minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which at least partially overlaps with the partition wall when the amount of change in volume per unit angle is maximized. As described above, the inner rotor is configured by taking into account the change in volume of the inter-teeth chamber which communicates with the intake port, such as to increase the minimum value of the clearance in the inter-teeth chamber in which the amount of change in volume is maximized, based on the minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which at least partially overlaps with the partition wall. This configuration suppresses the occurrence of cavitation in the inter-teeth chamber communicating with the intake port, while controlling circulation of a fluid between the first and the second discharge ports such as to enhance the volume efficiency. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic configuration diagram illustrating a gear pump according to one embodiment of the present disclosure; 
         FIG. 2  is a schematic diagram illustrating a procedure of creating the internal teeth of the outer rotor included in the gear pump of the present disclosure; 
         FIG. 3  is a schematic configuration diagram illustrating the external teeth of the inner rotor included in the gear pump of the present disclosure; 
         FIG. 4  is a schematic diagram illustrating a procedure of creating the external teeth of the inner rotor included in the gear pump of the present disclosure; 
         FIG. 5  illustrates a relationship between rotational angle of the inner rotor about the center of rotation and minimum value of a clearance between the external tooth and the internal tooth; 
         FIG. 6  illustrates relationships between rotational angle of the inner rotor about the center of rotation, and volume and a volume change rate of one inter-teeth chamber; and 
         FIG. 7  is a schematic configuration diagram illustrating a minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber in which the volume change rate is maximized and a minimum value of the clearance between the external tooth and the internal tooth overlapping with a partition wall. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The following describes some embodiments of the present disclosure with reference to drawings. 
       FIG. 1  is a schematic configuration diagram illustrating a gear pump  1  according to one embodiment of the present disclosure. The gear pump illustrated in  FIG. 1  may be configured, for example, as an oil pump mounted on a non-illustrated vehicle to suck a hydraulic operating fluid (ATF) accumulated in an oil pan and press-feed the sucked hydraulic operating fluid to a hydraulic pressure control device (none of them shown). The gear pump  1  includes a pump housing comprised of, for example, a pump body fixed to a transmission casing of an automatic transmission and a pump cover fastened to the pump body (none of them shown), and an inner rotor (drive gear)  2  and an outer rotor (driven gear)  3  that are respectively placed in a rotatable manner in a non-illustrated gear chamber defined by the pump housing. The gear pump  1  may be configured as an on-vehicle pump (for example, engine oil pump) other than the oil pump configured to pressure-feed the hydraulic operating fluid for the transmission or may be employed for an application other than the on-vehicle pump. 
     The inner rotor  2  is fixed to a rotating shaft  4  that is linked with a crankshaft of an engine mounted on the vehicle (none of them shown) and is driven and rotated by the power applied to the rotating shaft  4 . A plurality of external teeth  20  (for example, eleven teeth according to the embodiment) are formed on an outer circumference of the inner rotor  2 . A larger number of internal teeth  30  that is larger by one than the total number of the external teeth  20  of the inner rotor (for example, twelve teeth according to the embodiment) are, on the other hand, formed on an inner circumference of the outer rotor  3 . The outer rotor  3  is arranged eccentric with respect to the inner rotor  2  and is placed in a rotatable manner in the gear chamber described above, such that the plurality of internal teeth  30  located on the lower side in  FIG. 1  are engaged with the corresponding external teeth  20  of the inner rotor  2 . Additionally, a plurality of inter-teeth chambers (pump chambers)  5  are formed by two adjacent external teeth  20  and two adjacent internal teeth  30  between the inner rotor  2  and the outer rotor  3 . 
     When the inner rotor  2  is rotated in a direction of thick arrow in  FIG. 1  by the power applied from the rotating shaft  4 , part of the plurality of internal teeth  30  is engaged with part of the plurality of external teeth  20 . The outer rotor  3  is accordingly rotated along with the inner rotor  2  in the same direction about a center of rotation  3   c  that is away from a center of rotation  2   c  of the inner rotor  2  by an eccentric amount e. When the inner rotor  2  and the outer rotor  3  are rotated, volumes of the respective inter-teeth chambers  5  are increased (the inter-teeth chambers  5  are expanded) accompanied with the rotations of the inner rotor  2  and the like in a rear side area in their rotating direction (as shown by the thick arrow in  FIG. 1 ), i.e., mainly in a right half area of  FIG. 1 . When the inner rotor  2  and the outer rotor  3  are rotated, the volumes of the respective inter-teeth chambers  5  are decreased (the inter-teeth chambers  5  are contracted) accompanied with the rotations of the inner rotor  2  and the like in a front side area in the rotating direction of the inner rotor  2  and the like, i.e., mainly in a left half area of  FIG. 1 . 
     An intake port  6  extending in an approximately arc shape such as to communicate with (such as to be opposed to) the inter-teeth chambers  5  of which volumes increase with the rotations of the inner rotor  2  and the outer rotor  3  among the plurality of inter-teeth chambers  5  defined by the external teeth  20  and the internal teeth  30 , and a first discharge port  7  and a second discharge port  8  respectively extending in approximately arc shapes such as to communicate with (such as to be opposed to) the inter-teeth chambers  5  of which volumes decrease with the rotations of the inner rotor  2  and the outer rotor  3  among the plurality of inter-teeth chambers  5  are formed in the non-illustrated pump housing of the gear pump  1 . The first and the second discharge ports  7  and  8  are separated from each other by a partition wall  9  to be independent of each other as illustrated. According to this embodiment, the first discharge port  7  located on a rear side in the rotating direction of the inner rotor  2  and the like serves as a low pressure port, and the second discharge port  8  located on a front side in the rotating direction serves as a high pressure port. 
     The first and the second discharge ports  7  and  8  may be connected with different hydraulic pathways or may be connected with a common hydraulic pathway. The intake port  6  and the first and the second discharge ports  7  and  8  may be formed on both sides in an axial direction of the inner rotor  2  and the outer rotor  3  (in both the pump body and the pump cover) or may be formed on one side in the axial direction of the inner rotor  2  and the outer rotor  3  (in either one of the pump body and the pump cover). For example, the intake port  6  may be formed on one side in the axial direction of the inner rotor  2  and the like, while the first and the second discharge ports  7  and  8  may be formed on the other side in the axial direction of the inner rotor  2  and the like. Additionally, the first discharge port  7  may be formed on one side in the axial direction of the inner rotor  2  and the like, while the second discharge port  8  may be formed on the other side in the axial direction of the inner rotor  2  and the like. 
       FIG. 2  is a schematic diagram illustrating a procedure of creating the internal teeth  30  of the outer rotor  3  included in the gear pump  1 . As illustrated, a teeth profile (outer shape) of the outer rotor  3  defined by the plurality of internal teeth  30  is determined, based on an envelope line drawn with respect to a multiple-teeth profile (outer shape of the inner rotor  2 , as shown by a two-dot chain line in  FIG. 2 ) obtained by revolving the center of rotation  2   c  of the inner rotor  2  by a predetermined angle δ on a circle of 2·e+t in diameter about the center of rotation  3   c  of the outer rotor  3  and rotating the inner rotor  2  by a rotational angle δ/N during revolution of the center of rotation  2   c  by the predetermined angle δ. Herein “t” denotes a clearance (tip clearance) between a top  21   t  of a tooth crest  21  of an external tooth  20  and a top of a tooth crest of an internal tooth  30  when the center of rotation  2   c  of the inner rotor  2 , the center of rotation  3   c  of the outer rotor  3 , the top  21   t  and the top of the internal tooth  30  are aligned and may be, for example, a value of approximately 0.03 to 0.07 mm. This configuration readily provides the outer rotor  3  that is appropriately engageable with the inner rotor  2 . The teeth profile (outer shape) of the outer rotor  3  may be equal to the above envelope line itself or may be determined to be located on an outer side of this envelope line. The internal teeth of the outer rotor  3  may be created by a gear cutting tool having an approximately identical shape with that of the inner rotor  2 . 
       FIG. 3  is a schematic configuration diagram illustrating the external teeth  20  of the inner rotor  2 .  FIG. 4  is a schematic diagram illustrating a procedure of creating the external teeth  20 . As illustrated in these drawings, each external tooth  20  of the inner rotor  2  includes a tooth crest  21  in a convex curved shape, a tooth root  22  in a concave curved shape, a first middle portion  23  that is located on a front side of the tooth crest  21  in a rotating direction of the inner rotor  2  (shown by a thick arrow in  FIG. 3 ) and is placed between the tooth crest  21  and the tooth root  22 , and a second middle portion  24  that is located on a rear side of the tooth crest  21  in the rotating direction of the inner rotor  2  and placed between the tooth crest  21  and the tooth root  22 . As illustrated, the external tooth  20  is formed asymmetrical with respect to a tooth profile centerline Lc that passes through the top  21   t  located on the outermost side in a radial direction of the tooth crest  21  and the center of rotation  2   c  of the inner rotor  2 . 
     As shown in  FIG. 4 , the tooth crest  21  is formed in a convex curved shape by an epitrochoid curve having a trochoid coefficient of greater than 1 (for example, a value of approximately 1.2), which is obtained by dividing a radius rde of a first drawing point by a radius re of an externally rolling circle Co. The epitrochoid curve forming the tooth crest  21  is obtained by keeping the radius rde of the first drawing point at a first value Rde (fixed value) and rolling the externally rolling circle Co having the smaller radius re than the first value Rde without sliding while circumscribing the externally rolling circle Co about a base circle BCt having a common center O with the center of rotation  2   c  of the inner rotor  2 . 
     The tooth root  22  is formed in a concave curved shape by a hypotrochoid curve having the trochoid coefficient of greater than 1, which is obtained by dividing a radius rdh of a second drawing point by a radius rh of an internally rolling circle Ci. The hypotrochoid curve forming the tooth root  22  shares the base circle BCt with the epitrochoid curve forming the tooth crest  21  and is obtained by keeping the radius rdh of the second drawing point at a second value Rdh (fixed value) and rolling the internally rolling curve Ci having the smaller radius rh than the second value Rdh without sliding while inscribing the internally rolling circle Ci with the above base circle BCt as shown in  FIG. 4 . 
     The tooth root  22  is divided into a first tooth root portion  22   a  that is located on the front side of the tooth crest  21  in the rotating direction of the inner rotor  2  and a second tooth root portion  22   b  that is located on the rear side of the tooth crest  21  in the rotating direction of the inner rotor  2  across a boundary that is an intersection  22   x  of the tooth root  22  and a line segment Le that is rotated forward or rearward in the above rotating direction from the tooth profile centerline Lc by ½(φ/2) of an angle φ corresponding to one tooth of the external teeth  20  (360 degrees/number of external teeth  20 ). As shown in  FIGS. 3 and 4 , with respect to the inner rotor  2 , a range between two intersections  22   x  arranged across the tooth profile centerline Lc denotes a range of one tooth of the external teeth  20 . The second tooth root portion  22   b  is arranged to be continuous with the first tooth root portion  22   a  on the rear side in the rotating direction of the inner rotor  2 , as shown in  FIGS. 3 and 4 . 
     According to this embodiment, the radius rde of the first drawing point for drawing the epitrochoid curve forming the tooth crest  21 , i.e., the first value Rde and the radius rdh of the second drawing point for drawing the hypotrochoid curve forming the tooth root  22 , i.e., the second value Rdh are determined to be an identical value Rd. Similarly the radius re of the externally rolling circle Co and the radius rh of the internally rolling circle Ci are determined to be an identical value R. Accordingly the inner rotor  2  is configured to satisfy relationships of Rde=Rdh=Rd, re=rh=R and tooth height=Rde+re+Rdh+rh=2·e. 
     As shown in  FIGS. 3 and 4 , the first middle portion  23  is formed between the tooth crest  21  and the first tooth root portion  22   a  of the tooth root  22  and is configured to include an outer middle portion  23   o  located on the tooth crest  21 -side and an inner middle portion  23   i  located on the first tooth root portion  22   a -side. According to this embodiment, the outer middle portion  230  is formed by an involute curve determined such that a tangent line at a front end  21   f  of the tooth crest  21  in the rotating direction of the inner rotor  2  is common with a tangent line of the above epitrochoid curve at the end  21   f . This configuration enables the tooth crest  21  and the outer middle portion  23   o  to be smoothly continuous with each other at the end  21   f . The inner middle portion  23   i  is formed by a smooth curve (for example, an arc) that is smoothly continuous with the first tooth root portion  22   a  at a rear end  22   r  of the first tooth root portion  22   a  in the rotating direction of the inner rotor  2  and is smoothly continuous with the outer middle portion  230  at a boundary  23   x  with the outer middle portion  230 . The curve forming the inner middle portion  23   i  is preferably selected to be as short as possible compared with the involute curve forming the outer middle portion  23   o  as illustrated. 
     The first middle portion  23  may be formed by an involute curve obtained using a base circle that has a common center O with the base circle BCt of the epitrochoid curve and the hypotrochoid curve described above (as shown in JP 2014-181620A). In this case, it may be preferable that diameters Rbt and Rbi satisfy a relationship of Rbi≦Rbt, where “Rbi” denotes a diameter of the base circle of the involute curve forming the first middle portion  23  and “Rbt” denotes a diameter of the base circle BCt of the epitrochoid curve forming the tooth crest  21  and the hypotrochoid curve forming the tooth root  22 . In this case, it may also be preferable that the first middle portion  23  includes linkage surfaces formed by smooth curves (for example, arcs) on an inner side (front side) and an outer side (rear side) of a portion formed by the involute curve described above. 
     As shown in  FIGS. 3 and 4 , the second middle portion  24  is formed between the tooth crest  21  and the second tooth root portion  22   b  of the tooth root  22  and is configured to include an outer middle portion  24   o  located on the tooth crest  21 -side of an intersection  24   x  with the above base circle BCt and an inner middle portion  24   i  located on the second tooth root  22   b -side of the intersection  24   x . According to this embodiment, a range of the outer middle portion  24   o  or more specifically a range from the intersection  24   x  to a rear end (boundary)  21   r  of the tooth crest  21  in the rotating direction of the inner rotor  2  is formed by a first curve obtained by rolling the externally rolling circle Co that is circumscribed about the base circle BCt without sliding while changing the radius of the above first drawing point (as shown by a dotted line in the drawing) as shown in  FIG. 4 . A range of the inner middle portion  24   i  or more specifically a range from the intersection  24   x  to a front end (boundary)  22   f  of the second tooth root portion  22   b  in the rotating direction of the inner rotor  2  is formed by a second curve obtained by rolling the internally rolling circle Ci that is inscribed with the base circle BCt without sliding while changing the radius of the above second drawing point (as shown by a two-dot chain line in the drawing). A procedure of changing the radius of the first drawing point or the second drawing point of the externally rolling circle Co or the internally rolling circle Ci is described in JP 2014-181619A. 
     In the gear pump  1  having the first and the second discharge ports  7  and  8 , there is a need to minimize the minimum value of the clearance between the external tooth  20  and the internal tooth  30  overlapping with the partition wall  9  viewed from the axial direction of the gear pump  1 , in order to control the circulation of the hydraulic operating fluid between the first and the second discharge ports  7  and  8  and improve the volume efficiency. With respect to the inter-teeth chamber  5  communicating with the intake port  6 , on the other hand, there is a need to increase the minimum value of the clearance between the external tooth  20  and the internal tooth  30 , such as to allow for circulation of the hydraulic operating fluid between adjacent inter-teeth chambers  5  and thereby decrease the flow rate of the hydraulic operating fluid flowing in from the intake port  6 , in terms of suppressing the occurrence of cavitation accompanied with the inflow (intake) of the hydraulic operating fluid from the intake port  6 . The inventors have intensively studied to optimize the minimum value of the clearance between the external tooth  20  and the internal tooth  30  at a position between the first discharge port  7  and the second discharge port  8  and optimize the minimum value of the clearance between the external tooth  20  and the internal tooth  30  on the intake port  6 -side. As a result, the inventors have noted an amount of change in volume V of the inter-teeth chamber  5  which communicates with the intake port  6  during rotation of the inner rotor  2  by a unit angle (amount of change in volume per unit angle, hereinafter referred to as “volume change rate ΔV”). 
     In the inter-teeth chamber  5  which communicates with the intake port  6  and in which the volume change rate ΔV is maximized, the internal pressure is significantly decreased at the maximum volume change rate ΔV, and the decrease of the internal pressure causes the hydraulic operating fluid to be flowed in at a high flow rate from the intake port  6 . This increases the possibility of cavitation. The smaller minimum value of the clearance between the external tooth  20  and the internal tooth  30  defining the inter-teeth chamber  5  which communicates with the intake port  6  and in which the volume change rate ΔV (hereinafter may be called “intake-side clearance”) becomes a maximum value provides a larger reduction (larger negative pressure) in the internal pressure of the inter-teeth chamber  5  at the maximum volume change rate ΔV. 
     By taking into account the foregoing, each of the plurality of external teeth  20  of the inner rotor  2  is formed asymmetrical with respect to the tooth profile centerline Lc such that the intake-side clearance is larger than the minimum value of the clearance between the external tooth  20  and the internal tooth  30  overlapping with the partition wall  9  at the maximum volume change rate ΔV (hereinafter may be called “discharge-side clearance”) in an ideal center state. The “ideal center state” herein means a state that the center of rotation  2   c  of the inner rotor  2  is identical with the center of rotation of the rotating shaft  4  fixed to the inner rotor  2  and that the center of rotation  3   c  of the outer rotor  3  is identical with the center of the gear chamber in which the outer rotor  3  is placed. 
     In order to make the intake-side clearance larger than the discharge-side clearance, the length of the curve forming the first middle portion  23  or more specifically the length from the end  21   f  of the tooth crest  21  to the end  22   r  of the first tooth root portion  22   a  is determined to be longer than the length of the curve forming the second middle portion  24  or more specifically the length from the end  21   r  of the tooth crest  21  to the end  22   f  of the second tooth root portion  22   b . Additionally, the length of the hypotrochoid curve forming the first tooth root portion  22   a  or more specifically the length from the end  22   r  of the first tooth root portion  22   a  to the intersection  22   x  is determined to be shorter than the length of the hypotrochoid curve forming the second tooth root portion  22   b  or more specifically the length from the end  22   f  of the second tooth root portion  22   b  to the intersection  22   x . Such configuration of setting the length of the curve forming the first middle portion  23  to be longer than the length of the curve forming the second middle portion  24  and setting the length of the hypotrochoid curve forming the first tooth root portion  22   a  to be shorter than the length of the hypotrochoid curve forming the second tooth root portion  22   b  makes the rear end  21   r  in the rotating direction of the epitrochoid curve forming the tooth crest  21  closer to the second tooth root portion  22   b  and shifts the front end  21   f  in the rotating direction of the epitrochoid curve to the outer side in the radial direction of the inner rotor  2  as shown in  FIG. 3 . 
     The configuration that the rear end  21   r  in the rotating direction of the epitrochoid curve forming the tooth crest  21  is made closer to the second tooth root portion  22   b  totally decreases the minimum value of the clearance between the external tooth  20  and the internal tooth  30  defining the inter-teeth chamber  5  which communicates with the first and the second discharge ports  7  and  8 . The configuration that the front end  21   f  in the rotating direction of the epitrochoid curve forming the tooth crest  21  is shifted to the outer side in the radial direction of the inner rotor  2  totally increases the minimum value of the clearance between the external tooth  20  and the internal tooth  30  defining the inter-teeth chamber  5  which communicates with the intake port  6 . As a result, these configurations further decrease the minimum value of the clearance between the external tooth  20  and the internal tooth  30  overlapping with the partition wall  9  (discharge-side clearance) and sufficiently increase the minimum value of the clearance in the inter-teeth chamber  5  in which the volume change rate ΔV (intake-side clearance) is maximized, such as to effectively suppress the occurrence of cavitation in the inter-teeth chamber  5 , while enhancing the degree of freedom in determining the position of the partition wall  9  that separates the first and the second discharge ports  7  and  8  from each other, i.e., in determining the distribution ratio of the discharge flow rates from the first and the second discharge ports  7  and  8 . 
     In the gear pump  1 , the plurality of external teeth  20  of the inner rotor  2  are formed such that while any one external tooth  20  located on the rear side of the inter-teeth chamber  5  reaching a top dead center in the rotating direction of the inner rotor  2  is in contact with a corresponding internal tooth  30 , an adjacent external tooth  20  located on the rear side of the any one external tooth  20  in the rotating direction of the inner rotor  2  is in contact with a corresponding internal tooth  30  during rotations of the inner rotor  2  and the outer rotor  3  in the state eccentric from the ideal center state. More specifically, while any one external tooth  20  that passes through a top dead center and comes closest to a position where the top  21   t  of the tooth crest  21  of the external tooth  20  and the top  21   t  of the tooth crest  21  of the internal tooth  30  are aligned with and opposed to each other (shown as a position between the intake port  6  and the first discharge port  7  in  FIG. 7 ) is in contact with a corresponding internal tooth  30 , an adjacent external tooth  20  located on the rear side of the any one external tooth  20  in the rotating direction of the inner rotor  2  is in contact with a corresponding internal tooth  30 . The specifications of the tooth crest  21 , the first and the second tooth root portions  22   a  and  22   b  and the first and the second middle portions  23  and  24  are determined such as to satisfy this condition. This configuration stabilizes the behaviors of the inner rotor  2  and the outer rotor  3  during operation of the gear pump  1  and reduces the vibration and the noise. The “top dead center” herein denotes a position where the volume of the inter-teeth chamber  5  increased with rotation of the inner rotor  2  and the like is maximized (i.e., the position between the intake port  6  and the first discharge port  7  in  FIG. 1 ). The “state eccentric from the ideal center state” herein denotes a state that at least one of a deviation between the center of rotation  2   c  of the inner rotor  2  and the center of rotation of the rotating shaft  4  and a deviation between the center of rotation  3   c  of the outer rotor  3  and the center of the gear chamber occurs. 
       FIG. 5  illustrates a relationship between rotational angle θ of the inner rotor  2  about the center of rotation  2   c  and minimum value of the clearance between the external tooth  20  and the internal tooth  30  in the gear pump  1 .  FIG. 6  illustrates relationships between rotational angle θ of the inner rotor  2  about the center of rotation  2   c , and volume V and volume change rate ΔV of one inter-teeth chamber  5 . 
       FIGS. 5 and 6  show the results of analysis with respect to the gear pump  1  configured to respectively select the diameter of a tooth root circle of the inner rotor  2  in a range of, for example, 20 to 80 mm, the diameter of a tooth root circle of the outer rotor in a range of, for example, 25 to 110 mm, the eccentric amount e in a range of, for example, 1.05 to 5.00 mm, Rde=Rdh=Rd in a range of, for example, 0.55 to 3.00 mm, and re=rh=R in a range of, for example, 0.5 to 2.0 mm. The minimum value of the clearance between the external tooth  20  and the internal tooth  30  denotes an interval measured in the direction of a normal line relative to tooth surfaces of the external tooth  20  and the internal tooth  30  located closest to each other in the ideal center state as shown in  FIG. 7 . The rotational angle θ about the center of rotation  2   c  of the inner rotor  2  denotes a rotational angle about the center of rotation  2   c  of a line section connecting a bottommost portion (deepest portion) of the tooth root  22  of a certain external tooth  20  with the center of rotation  2   c  and is measured counterclockwise in  FIG. 7  with respect to the state of 0 degree that the bottommost portion of the tooth root  22  of the external tooth  20  is located immediately below the center of rotation  2   c  of the inner rotor  2  in  FIG. 7 . Additionally, a range A shown in  FIG. 5  indicates a range where the bottommost portion of the tooth root  22  of the external tooth  20  described above overlaps with the partition wall  9 . The volume V shown in  FIG. 6  indicates the volume of the inter-teeth chamber  5  defined by two adjacent external teeth  20  across the tooth root  22  as a measurement object of the rotational angle θ and two adjacent internal teeth  30  corresponding to the external teeth  20 . Additionally, the volume change rate ΔV shown in  FIG. 6  indicates the amount of change in the volume V when the rotational angle θ is changed (increased) by, for example, 5 degrees. 
     The results of analysis shown in  FIG. 5  show that the gear pump  1  is configured to totally minimize the minimum value of the clearance between the external tooth  20  and the internal tooth  30  defining the inter-teeth chambers  5  which communicate with the first and the second discharge ports  7  and  8  and to totally increase the minimum value of the clearance between the external tooth  20  and the internal tooth  30  defining the inter-teeth chambers  5  which communicate with the intake port  6 . In the gear pump  1  having the specifications described above, as shown in  FIG. 6 , when the rotational angle θ of the inner rotor  2  is changed from 90 degrees to 95 degrees, the volume change rate ΔV of an inter-teeth chamber  5   m  shown in  FIG. 7  is maximized and the smaller of clearances CLi and CLi′ between the external tooth  20  and the internal tooth  30  defining the inter-teeth chamber  5   m , i.e., a minimum value CLi of a clearance between an external tooth  20   i  and an internal tooth  30   i  shown in  FIG. 7  is specified as the intake-side clearance described above. Additionally, when the volume change rate ΔV of the inter-teeth chamber  5   m  is maximized, a minimum value CLd of a clearance between an external tooth  20   d  and an internal tooth  30   d  overlapping with the partition wall  9  is specified as the discharge-side clearance described above. As shown in  FIG. 5 , the minimum value CLi of the clearance between the external tooth  20   i  and the internal tooth  30   i  (intake-side clearance) is approximately nine to ten times larger than the minimum value CLd of the clearance between the external tooth  20   d  and the internal tooth  30   d  overlapping with the partition wall  9  (value in the range A shown in  FIG. 5 ). These results of analysis indicate that the configuration of the gear pump  1  to further decrease the minimum value of the clearance between the external tooth  20  and the internal tooth  30  overlapping with the partition wall  9  (discharge-side clearance) and sufficiently increase the minimum value of the clearance in the inter-teeth chamber  5  in which the volume change rate ΔV (intake-side clearance) is maximized, thereby effectively suppressing the occurrence of cavitation in the inter-teeth chamber  5 . 
     The minimum value of the clearance shown in  FIG. 5  is a design value (analytical value) in the ideal center state. The minimum value of the clearance between the external tooth  20  and the internal tooth  30  in the gear pump  1  as a product is varied due to a manufacturing tolerance or the like. By the experiments and their analyses, the inventors have confirmed that setting the intake-side clearance (CLi) of a product to be at least three or more times larger than the discharge-side clearance (CLd) practically sufficiently decreases the minimum value of the clearance between the external tooth  20  and the internal tooth  30  overlapping with the partition wall  9  and practically sufficiently increases the minimum value of the clearance in the inter-teeth chamber  5  in which the volume change rate ΔV is maximized. The gear pump  1  is configured such that while any one external tooth  20  coming closest to the top dead center is in contact with a corresponding internal tooth  30 , an adjacent external tooth  20  located on the rear side of the any one external tooth  20  in the rotating direction is in contact with a corresponding internal tooth  30 . Designing the plurality of external teeth  20  of the inner rotor  2  to satisfy this condition determines the upper limit of the intake-side clearance (CLi). 
     The gear pump  1  is configured such that one set of the external tooth  20   d  and the internal tooth  30   d  overlaps with the partition wall  9  when the volume change rate ΔV of the inter-teeth chamber  5   m  shown in  FIG. 7  is maximized. The minimum value CLd of the clearance between the eternal tooth  20   d  and the internal tooth  30   d  is accordingly specified as the discharge-side clearance described above. This configuration is, however, not necessarily restricted. According to a modification, the gear pump  1  may be configured such that two sets of external teeth  20  and internal teeth  30  overlap with the partition wall  9  when the volume change rate ΔV of the inter-teeth chamber  5   m  is maximized. In this modification, the smaller minimum value of the clearances between the two sets of external teeth  20  and the internal teeth  30  may be specified as the discharge-side clearance described above. In other words, the discharge-side clearance may be the minimum value of the clearance between the external tooth  20  and the internal tooth  30  defining the inter-teeth chamber  5  that at least partially overlaps with the partition wall at a position between the first and the second discharge ports  7  and  8  when the volume change rate ΔV is maximized. 
     Furthermore, in order to achieve the condition that any one external tooth  20  coming closest to the top dead center is in contact with a corresponding internal tooth  30 , an adjacent external tooth  20  located on the rear side of the any one external tooth  20  in the rotating direction is in contact with a corresponding internal tooth  30  during rotations of the inner rotor  2  and the outer rotor  3  in the state eccentric from the ideal center state, a tip clearance CLx (shown in  FIG. 7 ) between the external tooth  20  and the internal tooth  30  at the top dead center in the ideal center state may be equal to or greater than a minimum value CLy (shown in  FIG. 7 ) of a clearance between a driving tooth surface of an adjacent external tooth  20  located on the rear side in the rotating direction of the external tooth  20  at the top dead center and a driven tooth surface of a corresponding internal tooth  30  in the ideal center state. The tip clearance CLx between the external tooth  20  and the internal tooth  30  at the top dead center in the ideal center state may be not greater than 200 μm. This configuration suppresses an increase of the discharge-side clearance and controls leakage of the hydraulic operating fluid from the first discharge port  7  toward the second discharge port  8  such as to enhance the volume efficiency. The lower limit value of the tip clearance CLx in the ideal center state may be not less than 5 μm by taking into account the manufacturing tolerance. 
     As described above, the gear pump  1  is configured by taking into account the change in volume of the inter-teeth chamber  5  which communicates with the intake port  6 , such that each of the external teeth  20  of the inner rotor  2  is formed asymmetrical such as to increase the minimum value of the clearance in the inter-teeth chamber  5  in which the volume change rate ΔV is maximized, based on the minimum value of the clearance between the external tooth  20  and the internal tooth  30  overlapping with the partition wall  9 . This configuration suppresses the occurrence of cavitation in the inter-teeth chambers  5  which communicates with the intake port  6 , while controlling circulation of the hydraulic operating fluid between the first and the second discharge ports  7  and  8  such as to enhance the volume efficiency. 
     In the gear pump  1 , the tooth crest  21  of each of the external teeth  20  of the inner rotor  2  is formed by a portion other than a loop portion of the epitrochoid curve that has the trochoid coefficient of greater than 1, and the tooth root  22  is formed by a portion other than a loop portion of the hypotrochoid curve that shares the base circle BCt with the epitrochoid curve and has the trochoid coefficient of greater than 1. This configuration increases the radius rde of the first drawing point and the radius rdh of the second drawing point, i.e., the first value Rde and the second value Rdh, while keeping small the radius re of the externally rolling circle Co and the radius rh of the internally rolling circle Ci (cc radius of the base circle BCt/number of teeth). This configuration accordingly determines the profiles of the tooth crest  21  and the tooth root  22  using one base circle BCt and readily increases the tooth height while keeping small the outer diameter of the base circle BCt, i.e., the outer diameter of the inner rotor  2 . 
     Additionally, in the gear pump  1 , the first middle portion  23  located on the front side of the tooth crest  21  in the rotating direction of the inner rotor  2  is formed by the involute curve. This configuration enables the external teeth  20  of the inner rotor  2  and the internal teeth  30  of the outer rotor  3  to be more smoothly engaged with each other and provides the constant rotation speed ratio of the inner rotor  2  to the outer rotor  3 . The first middle portion  23  may, however, be formed by a curve other than the involute curve, for example, an n-dimensional function (where “n” is an integral number of not less than 1), an arc, any polynomial expression, a trigonometric function, a relaxation curve or any combination thereof. 
     Furthermore, in the gear pump  1 , the range of the second middle portion  24  from the intersection  24   x  with the base circle BCt to the end  21   r  of the tooth crest  21  is formed by the first curve obtained by rolling the externally rolling circle Co that is circumscribed about the base circle BCt without sliding while changing the radius of the drawing point of the externally rolling circle Co. Additionally, the range of the second middle portion  24  from the intersection  24   x  with the base circle BCt to the end  22   f  of the second tooth root portion  22   b  is formed by the second curve obtained by rolling the internally rolling circle Ci that is inscribed with the base circle BCt without sliding while changing the radius of the drawing point of the internally rolling Ci. The second middle portion  24  may thus be configured to smoothly connect the tooth crest  21  with the second tooth root portion  22   b , while making the rear end  21   r  of the tooth crest  21  in the rotating direction of the inner rotor closest possible to the second tooth root portion  22   b . The second middle portion  24  may also be formed by a curve other than the involute curve, for example, an n-dimensional function (where “n” is an integral number of not less than 1), an arc, any polynomial expression, a trigonometric function, a relaxation curve or any combination thereof. 
     As described above, the gear pump of the present disclosure includes an inner rotor configured to have a plurality of external teeth, an outer rotor configured to have a greater number of internal teeth than number of the external teeth of the inner rotor and arranged to be eccentric with respect to the inner rotor, and a plurality of inter-teeth chambers, each being defined by two adjacent external teeth and two adjacent internal teeth. The gear pump further includes one intake port configured to communicate with the inter-teeth chamber of which volume increases with rotations of the inner rotor and the outer rotor, and a first discharge port and a second discharge port separated from each other by a partition wall to be independent of each other, each of the discharge ports being configured to communicate with the inter-teeth chamber of which volume decreases with the rotations of the inner rotor and the outer rotor. An intake-side clearance is larger than a discharge-side clearance, where the intake-side clearance denotes a minimum value of a clearance between the external tooth and the internal tooth defining the inter-teeth chamber which communicates with the intake port and in which an amount of change in volume during rotation of the inner rotor by a unit angle is maximized, and the discharge-side clearance denotes a minimum value of a clearance between the external tooth and the internal tooth defining the inter-teeth chamber which at least partially overlaps with the partition wall between the first discharge port and the second discharge port when the amount of change in volume per unit angle is maximized. 
     The gear pump of this aspect includes one intake port and the first and the second discharge ports that are separated from each other by the partition wall to be independent of each other. In the gear pump of this aspect, the configuration of further decreasing the minimum value of the clearance between the external tooth and the internal tooth overlapping with the partition wall between the first discharge port and the second discharge port controls circulation of a fluid between the first discharge port and the second discharge port and thereby enhances the volume efficiency. With respect to the inter-teeth chamber communicating with the intake port, on the other hand, in terms of suppressing the occurrence of cavitation accompanied with the inflow (intake) of the fluid from the intake port, there is a need to increase the minimum value of the clearance between the external tooth and the internal tooth. Especially in the inter-teeth chamber which communicates with the intake port and in which the amount of change in volume during rotation of the inner rotor by the unit angle is maximized, the internal pressure is significantly decreased at the maximum amount of change in volume per unit angle, and the decrease of the internal pressure causes the fluid to be flowed in at a high flow rate from the intake port. This increases the possibility of cavitation. The smaller minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which communicates with the intake port and in which the amount of change in volume during rotation of the inner rotor by the unit angle is maximized, i.e., the smaller intake-side clearance provides a larger reduction (larger negative pressure) in the internal pressure of the inter-teeth chamber at the maximum amount of change in volume per unit angle. By taking into account the foregoing, the inner rotor of this gear pump is configured such that the intake-side clearance is larger than the minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which at least partially overlaps with the partition wall at the maximum amount of change in volume per unit angle, i.e., larger than the discharge-side clearance. As described above, the inner rotor is configured by taking into account the change in volume of the inter-teeth chamber communicating with the intake port, such as to increase the minimum value of the clearance in the inter-teeth chamber in which the amount of change in volume is maximized, based on the minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which at least partially overlaps with the partition wall. This configuration suppresses the occurrence of cavitation in the inter-teeth chamber communicating with the intake port, while controlling circulation of a fluid between the first and the second discharge ports such as to enhance the volume efficiency. 
     In the gear pump of the above aspect, each of the external teeth may be formed asymmetrical with respect to a tooth profile centerline. This configuration enables the intake-side clearance to be larger than the discharge-side clearance. The tooth profile centerline may be a straight line connecting a top of a tooth crest with a center of rotation of the inner rotor. 
     Further, in the gear pump of the above aspect, the intake-side clearance may be at least three or more times larger than the discharge-side clearance. Each of the plurality of external teeth is formed asymmetrical with respect to a tooth profile centerline, such that the intake-side clearance is three or more times larger than the discharge-side clearance. This configuration practically and sufficiently decreases the minimum value of the clearance between the external tooth and the internal tooth overlapping with the partition wall and practically and sufficiently increases the minimum value of the clearance in the inter-teeth chamber in which the amount of change in volume is maximized. This configuration effectively suppresses the occurrence of cavitation in the inter-teeth chamber communicating with the intake port, while further enhancing the volume efficiency. 
     Moreover, in the gear pump of the above aspect, while any one external tooth coming closest to a position where a top of a tooth crest of the external tooth and a top of a tooth crest of the internal tooth are aligned with and opposed to each other is in contact with a corresponding internal tooth, an adjacent external tooth located on a rear side of the any one external tooth in a rotating direction of the inner rotor may be contact with a corresponding internal tooth, during the rotations of the inner rotor and the outer rotor. This configuration stabilizes the behaviors of the inner rotor and the outer rotor during operation of the gear pump and reduces the vibration and the noise. 
     In the gear pump of the above aspect, a tip clearance between any one external tooth and a corresponding internal tooth when a top of a tooth crest of the any one external tooth and a top of a tooth crest of the corresponding internal tooth are aligned may be equal to or greater than a minimum value of a clearance between a driving tooth surface of an adjacent external tooth located on a rear side of the any one external tooth in a rotating direction of the inner rotor and a driven tooth surface of a corresponding internal tooth. This configuration enables the adjacent external tooth located on the rear side of the any one external tooth in the rotating direction to be in contact with the corresponding internal tooth, while any one external tooth coming closest to the position where the top of the tooth crest of the external tooth and the top of the tooth crest of the internal tooth are aligned with and opposed to each other is in contact with the corresponding internal tooth during rotations of the inner rotor and the outer rotor. 
     In the gear pump of the above aspect, the tip clearance between the any one external tooth and the corresponding internal tooth may be not greater than 200 μm. This configuration restricts an increase in the discharge-side clearance and controls circulation of the fluid between the first and the second discharge ports, such as to enhance the volume efficiency. 
     Further, in the gear pump of the above aspect, each of the external teeth of the inner rotor may be configured to include a tooth crest formed by an epitrochoid curve obtained by rolling an externally rolling circle having a smaller radius than a radius of a drawing point without sliding while circumscribing the externally rolling circle about a base circle, a first tooth root portion formed by a hypotrochoid curve obtained by rolling an internally rolling circle having a smaller radius than a radius of a drawing point without sliding while inscribing the internally rolling circle with the base circle that is shared by the epitrochoid curve, the first tooth root located on a front side of the tooth crest in a rotating direction of the inner rotor, a second tooth root portion formed by a hypotrochoid curve obtained by rolling the internally rolling circle without sliding while inscribing the internally rolling circle with the base circle, the second tooth root arranged to be continuous with the first tooth root portion on a rear side in the rotating direction, a first middle portion formed by any curve and located between the tooth crest and the first tooth root portion, and a second middle portion formed by any curve and located between the tooth crest and the second tooth root portion. A length of the curve forming the first middle portion may be longer than a length of the curve forming the second middle portion. 
     Such configuration of the external teeth of the inner rotor further increases the minimum value of the clearance in the inter-teeth chamber in which the amount of change in volume is maximized, while further decreasing the minimum value of the clearance between the external tooth and the internal tooth overlapping with the partition wall. More specifically, setting the length of the curve forming the first middle portion to be longer than the length of the curve forming the second middle portion makes the rear end in the rotating direction of the epitrochoid curve forming the tooth crest closer to the second tooth root portion and shifts the front end in the rotating direction of the epitrochoid curve to the outer side in the radial direction of the inner rotor. The configuration that the rear end in the rotating direction of the epitrochoid curve forming the tooth crest is made closer to the second tooth root portion totally decreases the minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which communicates with the first and the second discharge ports. The configuration that the front end in the rotating direction of the epitrochoid curve forming the tooth crest is shifted to the outer side in the radial direction of the inner rotor totally increases the minimum value of the clearance between the external tooth and the internal tooth defining the inter-teeth chamber which communicates with the intake port. As a result, these configurations further decrease the minimum value of the clearance between the external tooth and the internal tooth overlapping with the partition wall and sufficiently increase the minimum value of the clearance in the inter-teeth chamber in which the amount of change in volume is maximized, such as to effectively suppress the occurrence of cavitation in the inter-teeth chamber, while enhancing the degree of freedom in determining the position of the partition wall that separates the first and the second discharge ports from each other, i.e., in determining the distribution ratio of the discharge flow rates from the first and the second discharge ports. Additionally, the configuration of increasing the radius of the drawing point of the epitrochoid curve or the hypotrochoid curve while keeping small the radius of the externally rolling circle or the internally rolling circle (∝ radius of the base circle/number of teeth) determines the profiles of the tooth crest and the tooth root using one base circle and readily increases the tooth height of the external tooth while keeping small the outer diameter of the base circle, i.e., the outer diameter of the inner rotor. 
     In the gear pump of the above aspect, the first middle portion may be formed by at least an involute curve. This configuration enables the external teeth and the internal teeth to be more smoothly engaged with each other and provides the constant rotation speed ratio of the inner rotor to the outer rotor. 
     Further, in the gear pump of the above aspect, a range of the second middle portion from an intersection with the base circle to a boundary with the tooth crest may be formed by a first curve obtained by rolling the externally rolling circle that is circumscribed about the base circle without sliding while changing the radius of the drawing point of the externally rolling circle, and a range of the second middle portion from the intersection with the base circle to a boundary with the second tooth root portion may be formed by a second curve obtained by rolling the internally rolling circle that is inscribed with the base circle without sliding while changing the radius of the drawing point of the internally rolling circle. The second middle portion may thus be configured to smoothly connect the tooth crest with the second tooth root portion, while making the rear end of the tooth crest in the rotating direction of the inner rotor closest possible to the second tooth root portion. 
     Moreover, in the gear pump of the above aspect, a teeth profile of the outer rotor defined by the plurality of internal teeth may be determined, based on an envelope line drawn with respect to a multiple-teeth profile obtained by revolving a center of rotation of the inner rotor by a predetermined angle on a circle of 2·e+t in diameter about a center of rotation of the outer rotor and rotating the inner rotor by a rotational angle according to the predetermined angle and a number of teeth of the inner rotor during revolution of the center of rotation of the inner rotor by the predetermined angle, where “e” denotes an eccentric amount of the center of rotation of the outer rotor with respect to the center of rotation of the inner rotor, and “t” denotes a clearance between a tooth crest of the external tooth and a tooth crest of the internal tooth when the center of rotation of the inner rotor, the center of rotation of the outer rotor, a top of the tooth crest of the external tooth and a top of the tooth crest of the internal tooth are aligned. This configuration readily provides the outer rotor that is appropriately engageable with the inner rotor as described above. 
     The present disclosure is also directed to a manufacturing method of a gear pump including an inner rotor configured to have a plurality of external teeth, an outer rotor configured to have a greater number of internal teeth than number of the external teeth of the inner rotor and arranged to be eccentric with respect to the inner rotor, a plurality of inter-teeth chambers, each being defined by two adjacent external teeth and two adjacent internal teeth, one intake port configured to communicate with the inter-teeth chamber of which volume increases with rotations of the inner rotor and the outer rotor, and a first discharge port and a second discharge port separated from each other by a partition wall to be independent of each other, each of the discharge ports being configured to communicate with the inter-teeth chamber of which volume decreases with the rotations of the inner rotor and the outer rotor. The manufacturing method of the gear pump includes forming the inner rotor such that an intake-side clearance is larger than a discharge-side clearance, where the intake-side clearance denotes a minimum value of a clearance between the external tooth and the internal tooth defining the inter-teeth chamber which communicates with the intake port and in which an amount of change in volume during rotation of the inner rotor by a unit angle is maximized, and the discharge-side clearance denotes a minimum value of a clearance between the external tooth and the internal tooth defining the inter-teeth chamber which at least partially overlaps with the partition wall between the first discharge port and the second discharge port when the amount of change in volume per unit angle is maximized. 
     The gear pump manufactured by this method suppresses the occurrence of cavitation in the inter-teeth chamber communicating with the intake port, while controlling circulation of a fluid between the first and the second discharge ports such as to enhance the volume efficiency. 
     The disclosure is not limited to the above embodiments in any sense but may be changed, altered or modified in various ways within the scope of extension of the disclosure. Additionally, the embodiments described above are only concrete examples of some aspect of the disclosure described in Summary and are not intended to limit the elements of the disclosure described in Summary. 
     INDUSTRIAL APPLICABILITY 
     The present disclosure is applicable to, for example, the field of manufacture of the gear pump.