Abstract:
A method of designing a gear in which a tooth trace of the tooth flank, which is to be engaged with another mating tooth flank, is curved with respect to an axial direction of the body of the gear. The mating tooth flank of the mating gear is designed in such a manner that a desired tooth contact can be achieved. Accordingly, sufficient design precision can be attained. Furthermore, stress at the tooth flanks can be controlled when the gears are engaged with each other, thereby leading to high durability of the gears.

Description:
FIELD OF THE INVENTION 
     This invention relates to a method of designing a gear to be used in a power transmission part of an automobile, for example. In particular, this invention relates to a method of designing a gear wherein a tooth trace of a tooth flank, which is to be engaged with another mating tooth flank, is curved with respect to an axial direction of the body of the gear. 
     BACKGROUND ART 
     In general, in a power transmission part. of an automobile or the like, gears may be used for transmitting a driving force between two shafts. As the gears, there are known a helical gear whose tooth trace is helical, and a circular arc gear whose tooth trace is circular arc. As a prior art document, there is known JP-A-59-137661. 
     In the gear, a tooth contact thereof is one of important matters. If a desired tooth contact is achieved, generation of contact noise can be inhibited when gears are engaged with each other. In addition, if a desired tooth contact is achieved, stress at tooth flanks of gears can be controlled when the gears are engaged with each other, which improves durability of the gears. 
     However, in such a gear that a tooth trace of a tooth flank, which is to be engaged with another mating tooth flank, is curved with respect to an axial direction of the body of the gear, it has been difficult to achieve a desired tooth contact, because conventionally the tooth trace is continuously formed into a circular arc from a tooth root of the gear to a tooth tip thereof. 
     SUMMARY OF THE INVENTION 
     The inventor has studied hard for achievement of a desired tooth contact, for a gear wherein a tooth trace of a tooth flank to be engaged with another mating tooth flank is curved with respect to an axial direction of the body of the gear. That is, the object of this invention is to provide a gear wherein a tooth trace of a tooth flank to be engaged with another mating tooth flank is curved with respect to an axial direction of the body of the gear, the gear being capable of achieving a desired tooth contact, inhibiting generation of contact noise at engagement, and achieving high durability, and also to provide a method of designing such a gear. 
     In order to achieve the above object, the present invention is a method of designing a gear, the method comprising: a first modeling step of modeling one tooth flank ( 4   a ) of one gear (W 1   a ) in a CAD system, in such a manner that the one tooth flank ( 4   a ) is formed by continuously transitioning a tooth trace consisting of a circular arc (R 1 ), from a tooth root of the gear to a tooth tip thereof; a first designing step of generating a tooth contact curve (R 3 ) as a desired tooth contact position, on the one tooth flank ( 4   a ), in the CAD system; a second modeling step of modeling a hypothetical mating tooth flank ( 51 ) capable of coming in contact with the one tooth flank ( 4   a ) in the CAD system, in such a manner that the hypothetical mating tooth flank ( 51 ) is formed by continuously transitioning a hypothetical tooth trace consisting of a circular arc, from a tooth root of a gear to a tooth tip thereof; a second designing step of generating a mating tooth contact curve (R 4 ) on the hypothetical mating tooth flank ( 51 ), so as to correspond to the tooth contact curve (R 3 ) on the tooth flank ( 4   a ), in the CAD system; a contact-point calculating step of: extracting a plurality of hypothetical tooth traces ( 54 ) from the continuously transitioning hypothetical tooth trace from the tooth root to the tooth tip; and obtaining a plurality of contact points ( 55 ) of the plurality of hypothetical tooth traces ( 54 ) and the mating tooth contact curve (R 4 ), in the CAD system; a third designing step of: judging whether or not each of the plurality of hypothetical tooth traces ( 54 ) has two contact points with the mating tooth contact curve (R 4 ); if yes, generating a circle ( 62 ,  64 ) for each of the contact points ( 55   a ,  55   b ) in such a manner that the circle ( 62 ,  64 ) comes in contact with a circular arc being the corresponding hypothetical tooth trace ( 54 ) and has a diameter smaller than that of the circular arc being the corresponding hypothetical tooth trace ( 54 ); determining a circular arc ( 61 ,  63 ) formed by the circle ( 62 ,  64 ) as a tooth trace curve outside each of the contact points ( 55   a ,  55   b ); generating an ellipse ( 66 ) for the contact points ( 55   a ,  55   b ) in such a manner that the ellipse ( 66 ) comes in contact with the circular arc being the corresponding hypothetical tooth trace ( 54 ) at both the contact points ( 55   a ,  55   b ) and forms a predetermined gap (t) with the circular arc being the corresponding hypothetical tooth trace ( 54 ); and determining an elliptical arc ( 65 ) formed by the ellipse ( 66 ) as a tooth trace curve (R 2 ) between the contact points ( 55   a ,  55   b ); in the CAD system; and a third modeling step of modeling a mating tooth flank ( 3   b ) of a mating gear (W 1   b ) in the CAD system so as to come in contact with the one tooth flank ( 4   a ) of the one gear (W 1   a ), in such a manner that the mating tooth flank ( 3   b ) is formed by connecting the tooth trace curves determined in the third designing step, from a tooth root ( 52 ) of the mating gear to a tooth tip ( 53 ) thereof. 
     According to the above invention, it is possible to design the mating tooth flank ( 3   b ) of the mating gear (W 1   b ) in such a manner that a desired tooth contact is surely achieved. 
     Alternatively, the present invention is a method of designing a gear, the method comprising: a first modeling step of modeling one tooth flank ( 4   a ) of one gear (W 1   a ) in a CAD system, in such a manner that the one tooth flank ( 4   a ) is formed by continuously transitioning a tooth trace consisting of a circular arc (RI), from a tooth root of the gear to a tooth tip thereof; a first designing step of generating a tooth contact curve (R 3 ) as a desired tooth contact position, on the one tooth flank ( 4   a ), in the CAD system; a second modeling step of modeling a hypothetical mating tooth flank ( 51 ) capable of coming in contact with the one tooth flank ( 4   a ) in the CAD system, in such a manner that the hypothetical mating tooth flank ( 51 ) is formed by continuously transitioning a hypothetical tooth trace consisting of a circular arc, from a tooth root of a gear to a tooth tip thereof; a second designing step of generating a mating tooth contact curve (R 4 ) on the hypothetical mating tooth flank ( 51 ), so as to correspond to the tooth contact curve (R 3 ) on the tooth flank ( 4   a ), in the CAD system; a contact-point calculating step of: extracting a plurality of hypothetical tooth traces ( 54 ) from the continuously transitioning hypothetical tooth trace from the tooth root to the tooth tip; and obtaining a plurality of contact points ( 55 ) of the plurality of hypothetical tooth traces ( 54 ) and the mating tooth contact curve (R 4 ), in the CAD system; a third designing step of: judging whether or not each of the plurality of hypothetical tooth traces ( 54 ) has two contact points with the mating tooth contact curve (R 4 ); if yes, generating a circle ( 62 ,  64 ) for each of the contact points ( 55   a ,  55   b ) in such a manner that the circle ( 62 ,  64 ) comes in contact with a circular arc being the corresponding hypothetical tooth trace ( 54 ) and has a diameter smaller than that of the circular arc being the corresponding hypothetical tooth trace ( 54 ); determining a circular arc ( 61 ,  63 ) formed by the circle ( 62 ,  64 ) as a tooth trace curve outside each of the contact points ( 55   a ,  55   b ); generating a curve for the contact points ( 55   a ,  55   b ) in such a manner that the curve comes in contact with the corresponding circular arc ( 61 ,  63 ) at each of the contact points ( 55   a ,  55   b ) and forms a predetermined gap (t) with the circular arc being the corresponding hypothetical tooth trace ( 54 ); and determining the curve as a tooth trace curve (R 2 ) between the contact points ( 55   a ,  55   b ); in the CAD system; and a third modeling step of modeling a mating tooth flank ( 3   b ) of a mating gear (W 1   b ) in the CAD system so as to come in contact with the one tooth flank ( 4   a ) of the one gear (W 1   a ), in such a manner that the mating tooth flank ( 3   b ) is formed by connecting the tooth trace curves determined in the third designing step, from a tooth root ( 52 ) of the mating gear to a tooth tip ( 53 ) thereof. 
     According to the above invention as well, it is possible to design the mating tooth flank ( 3   b ) of the mating gear (W 1   b ) in such a manner that a desired tooth contact is surely achieved. 
     It is preferable that: in the first modeling step, the one tooth flank ( 4   a ) of the one gear (W 1   a ) is modeled in such a manner that the one tooth flank ( 4   a ) is formed by continuously transitioning a tooth trace consisting of a circular arc (R 1 ), from the tooth root to the tooth tip, along an involute curve (L); in the second modeling step, the hypothetical mating tooth flank ( 51 ) is modeled in such a manner that the hypothetical mating tooth flank ( 51 ) is capable of coming in contact with the one tooth flank ( 4   a ) and is formed by continuously transitioning a hypothetical tooth trace consisting of a circular arc, from the tooth root to the tooth tip, along the involute curve (L); and in the third modeling step, the mating tooth flank ( 3   b ) of the mating gear (W 1   b ), which is to come in contact with the one tooth flank ( 4   a ) of the one gear (W 1   a ), is modeled in the CAD system in such a manner that the mating tooth flank ( 3   b ) is formed by transitionally connecting the tooth trace curves determined in the third designing step, from the tooth root ( 52 ) of the mating gear to the tooth tip ( 53 ) thereof, along the involute curve (L). 
     In addition, preferably, fifteen or more hypothetical tooth traces ( 54 ) are extracted in the contact-point calculating step. In that case, sufficient design precision can be guaranteed. 
     In addition, the present invention is a pair of gears, each of which has a tooth to be engaged with another mating tooth, wherein one tooth flank ( 4   a ) of one gear (W 1   a ) is formed by continuously transitioning a tooth trace consisting of a circular arc (R 1 ), from a tooth root of the gear to a tooth tip thereof; and wherein a mating tooth flank ( 3   b ) of a mating gear (W 1   b ), which is to come in contact with the one tooth flank ( 4   a ), is formed by continuously transitioning a tooth trace curve (R 2 ) consisting of two circular arcs ( 61 ,  63 ) and of a connecting curve ( 65 ) connecting the two circular arcs ( 61 ,  63 ), from a tooth root of the mating gear to a tooth tip thereof. 
     In the above gear, it is easy to obtain a desired tooth contact. Thus, contact noise can be inhibited. In addition, stress at the tooth flanks can be controlled when the gears are engaged with each other. Thus, the gears can have high durability. 
     Preferably, the connecting curve ( 65 ) is formed by an. ellipse that comes in contact with the two circular arcs ( 61 ,  63 ) at connecting points of each other. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a front view of an embodiment of a gear according to the present invention; 
         FIG. 2  is a front view showing an engagement state of the embodiment of a gear according to the present invention; 
         FIG. 3A  is an explanatory view of a first modeling step in an embodiment of a method of designing a gear according to the present invention; 
         FIG. 3B  is an explanatory view of a first designing step in the embodiment of a method of designing a gear according to the present invention; 
         FIG. 4  is an explanatory view of a contact-point calculating step in the embodiment of a method of designing a gear according to the present invention; 
         FIGS. 5A and 5B  are explanatory views of a third designing step in the embodiment of a method of designing a gear according to the present invention; 
         FIG. 6  is also an explanatory view of the third designing step in the embodiment of a method of designing a gear according to the present invention; and 
         FIG. 7  is a flowchart of a method of designing a gear according to the present invention. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Hereinafter, the present invention is described in details based on an embodiment thereof. 
       FIG. 1  is a front view of an embodiment of a gear according to the present invention.  FIG. 2  is a front view showing an engagement state of the embodiment of a gear according to the present invention.  FIG. 3A  is an explanatory view of a first modeling step in an embodiment of a method of designing a gear according to the present invention.  FIG. 3B  is an explanatory view of a first designing step in the embodiment of a method of designing a gear according to the present invention.  FIG. 4  is an explanatory view of a contact-point calculating step in the embodiment of a method of designing a gear according to the present invention.  FIGS. 5A ,  5 A and  6  are explanatory views of a third designing step in the embodiment of a method of designing a gear according to the present invention.  FIG. 7  is a flowchart of a method of designing a gear according to the present invention. 
     At first, with reference to  FIG. 1 , one gear W 1   a  in a pair of gears W 1  is explained. 
     The one gear W 1   a  includes a cylindrical body  9 , and a plurality of teeth  2  provided on an outer periphery of the body  9 . The teeth  2  consist of convex tooth flanks  3   a , each of which extends in a convex arc manner in a tooth trace direction, and concave tooth flanks  4   a , each of which extends in a concave arc manner in the tooth trace direction. The position of a starting end portion (one end portion)  5  and the position of a terminating end portion (the other end portion)  6  of each convex tooth flank  3   a  are the same in a circumferential direction in the lateral view of the one gear W 1   a . In the same manner, the position of a starting end portion (one end portion)  7  and the position of a terminating end portion (the other end portion)  8  of each concave tooth flank  4   a  are the same in the circumferential direction in the lateral view of the one gear W 1   a.    
     Each of the concave tooth flanks  4   a  of the one gear W 1   a  is formed by continuously transitioning a tooth trace consisting of a circular arc, from a tooth root of the gear to a tooth tip thereof, the circular arc being curved with respect to the axial direction of the cylindrical body  9 . On the other hand, each of the convex tooth flanks  3   a  of the one gear W 1   a  is formed by continuously transitioning a tooth trace curve (described below in details) consisting of circular arcs and of a connecting curve connecting the circular arcs, from a tooth root of the gear to a tooth tip thereof. 
     A mating gear W 1   b , which is to be engaged with the one gear W 1   a , has the same shape as the one gear W 1   a.    
     With reference to  FIG. 2 , an engagement state of the pair of gears W 1  is explained. When the one gear W 1   a  on a driving side rotates around a shaft center thereof, the mating gear W 1   b  on a driven side also rotates around a shaft center thereof, via the engaged (mating) teeth  2   a ,  2   b , synchronously. At that time, the convex tooth flanks  3   a  of the one gear W 1   a  on the driving side come in contact with the concave tooth flanks  4   b  of the mating gear W 1   b  on the driven side, and the concave tooth flanks  4   a  of the one gear W 1   a  on the driving side come in contact with the convex tooth flanks  3   b  of the mating gear W 1   b  on the driven side, so that a driving force is transmitted therebetween. 
     Next, a designing method by means of a three-dimension CAD system, for designing the above pair of gears, is explained. 
     At first, as a first modeling step, as shown in  FIG. 3A , one concave tooth flank  4   a  of the one gear W 1   a  is modeled in the three-dimension CAD system (P 1 : see  FIG. 7 ). In the one concave tooth flank  4   a , a tooth trace consisting of a circular arc R 1  is continuous (continuously transitioned) from a tooth root  12  of the gear W 1   a  to a tooth tip  13  thereof. 
     Then, as shown in  FIG. 3B , a tooth contact curve R 3  consisting of desired tooth-contact-points of the mating convex tooth flank  3   b  is generated on the one concave tooth flank  4   a  (P 2 : first designing step). The tooth contact curve R 3  is a curve connecting tooth contact points each of which achieves a large mating rate. Specifically, the tooth contact curve R 3  is a curve of substantially a semicircle which extends from the tooth root(s)  12  near both ends of the concave tooth flank  4   a  in the tooth trace direction to the tooth tip  13  located centrally in the tooth trace direction. 
     Next, as a second modeling step, as shown in  FIG. 4 , a three-dimensional model of a hypothetical mating convex tooth flank  51  is formed in the CAD system in such a manner that the hypothetical mating convex tooth flank  51  has a hypothetical tooth trace consisting of the same circular arc as that in the one concave tooth flank  4   a  (P 3 ). In the hypothetical mating convex tooth flank  51 , the hypothetical tooth trace consisting of the same circular arc is continuous (continuously transitioned) from a tooth root to a tooth tip. 
     Then, a mating tooth contact curve R 4  corresponding to the tooth contact curve R 3  of the concave tooth flank  4   a  of the one gear W 1   a  is generated on the hypothetical mating convex tooth flank  51  (P 4 : second designing step). 
     Then, a plurality of hypothetical tooth traces  54  is extracted from the continuously transitioning hypothetical tooth trace from the tooth root to the tooth tip, and a plurality of contact points  55  by the plurality of hypothetical tooth traces  54  and the mating tooth contact curve R 4  is obtained (P 5 : contact-point calculating step). In the present embodiment, about twenty hypothetical tooth traces  54  are extracted (some of them are omitted in the drawing). If fifteen or more hypothetical tooth traces  54  are extracted, sufficient design precision can be guaranteed. In addition, the contact points  55  in the present embodiment are symmetrical in the tooth trace direction with respect to a central involute curve L, which extends from a tooth root  52  to a tooth tip  53  through center(s) of the tooth trace(s). 
     Next, for each of the extracted hypothetical tooth traces  54 , it is judged whether the number of obtained contact points is two or not. If the number is two, as shown in  FIG. 5A , a first circular arc  61  is generated in such a manner that the first circular arc  61  comes in contact with the corresponding hypothetical tooth trace  54  at the first contact point  55   a , which is one of the contact points (P 6 : third designing step). The first circular arc  61  is a circular arc formed by a first circle  62  whose diameter is smaller than that of a circle forming the corresponding hypothetical tooth trace  54 . 
     Then, at the second contact point  55   b , in the same way as the first contact point  55   a , a second circular arc  63  is generated in such a manner that the second circular arc  63  comes in contact with the corresponding hypothetical tooth trace  54  at the second contact point  55   b  and that the second circular arc  63  is formed by a second circle  64  whose diameter is smaller than that of the circle forming the corresponding hypothetical tooth trace  54  (P 6 : third designing step). Herein, the second contact point  55   b  and the first contact point  55   a  are on the common corresponding hypothetical tooth trace  54 , and are symmetrical with respect to the central involute curve L extending from the tooth root  52  to the tooth tip  53  through the center(s) of the tooth trace(s). 
     Next, a connecting curve  65  connecting with the first circular arc  61  at the first contact point  55   a  and connecting with the second circular arc  63  at the second contact point  55   b  is generated (P 6 : third designing step). As shown in  FIG. 5B , the connecting curve  65  is a curve formed by an ellipse  66 , which forms a gap t with the hypothetical tooth trace  54  of the hypothetical mating convex tooth flank  51 . Herein, the ellipse  66  is in contact with the hypothetical tooth trace  54  of the hypothetical mating convex tooth flank  51  both at the first contact point  55   a  and at the second contact point  55   b.    
     Next, the two circular arcs  61 ,  63  and the connecting curve  65 , which are in contact with the hypothetical tooth trace  54  at the first contact point  55   a  and at the second contact point  55   b , are connected so as to generate a tooth trace curve R 2  (P 6 : third designing step). 
     Regarding the other contact points, for each of the extracted hypothetical tooth traces  54 , a tooth trace curve R 2  is generated. That is, the same number of tooth trace curves R 2 , each of which consists of two circular arcs and a connecting curve, is generated as the number of the extracted hypothetical tooth traces. By connecting (continuously transitioning) these tooth trace curves, a model of a mating convex tooth flank  3   b  can be generated (P 7 : third modeling step). 
     In the above pair of gears W 1 , the one gear W 1   a  and the mating gear W 1   b  have the same shape. That is, the mating convex tooth flanks  3   b  of the mating gear W 1   b  so as to come in contact with the concave tooth flanks  4   a  of the one gear W 1   a  are the same as the one convex tooth flanks  3   a  of the one gear W 1   a . Therefore, the model of a mating convex tooth flank  3   b  that has been designed according to the above procedures is used as the one convex tooth flank  3   a . That is, the one gear W 1   a  is modeled in the CAD system in such a manner that the one gear W 1   a  has: one concave tooth flanks  4   a  formed by transitioning the tooth trace R 1  consisting of the circular arc continuously from the tooth root to the tooth tip, and one convex tooth flanks  3   a  formed by connecting the tooth trace curves R 2 , each of which consists of two circular arcs and a connecting curve, continuously from the tooth root to the tooth tip. 
     As described above, according to the present embodiment, the mating convex tooth flanks  3   b  of the mating gear W 1   b  can be designed in such a manner that the mating convex tooth flanks  3   b  of the mating gear W 1   b  achieve a desired tooth contact with the concave tooth flanks  4   a  of the one gear W 1   a.    
     In the above embodiment, the mating convex tooth flank  3   b  is designed based on the concave tooth flank  4   a  of the one gear W 1   a . However, the reverse designing is also possible. That is, after the one convex tooth flank  3   a  of the one gear W 1  is modeled, based on a desired tooth contact with the modeled one convex tooth flank  3   a , the mating concave tooth flank  4   b  of the mating gear W 1   b  may be modeled according to the above procedures. 
     In addition, in the above embodiment, a desired tooth contact is defined as the tooth contact curve which extends from the tooth roots near both ends in the tooth trace direction to the tooth tip located centrally in the tooth trace direction. However, this invention is not limited thereto. The tooth contact positions may be changed in dependence on purpose or the like. 
     Furthermore, in the above embodiment, module 2.0 is assumed, so that about twenty hypothetical tooth traces  54  are extracted in the contact-point calculating step. However, this invention is not limited thereto. In order to obtain sufficient modeling precision, an appropriate number of hypothetical tooth traces  54  may be extracted. In general, if fifteen or more hypothetical tooth traces are extracted, sufficient design precision will be guaranteed. Herein, it is preferable that the hypothetical tooth traces are extracted at regular intervals. 
     In addition, in the above embodiment, as shown in  FIG. 5B , the connecting curve  65  is formed by the ellipse  66  which forms the gap t from the hypothetical tooth trace  54  and which is in contact with the hypothetical tooth trace  54  both at the first contact point  55   a  and at the second contact point  55   b . However, other manners may be adopted. That is, specifically, the connecting curve  65  may be any curve as long as the curve forms the gap t from the hypothetical tooth trace  54  and comes in contact with the first circular arc  61  at the first contact point  55   a  and with the second circular arc  63  at the second contact point  55   b.