Abstract:
A worm reduction gear satisfies following relational Formula (1) and Formula (2): 
       3≧ D 2/ D 1≧1.7  (1)
 
       0.1°≦α−β≦0.5°  (2)
 
     where D1 is an outside diameter of a worm, D2 is an outside diameter of a hob for cutting a worm wheel to form tooth spaces, and α is a pressure angle of the worm wheel and β is a pressure angle of the worm at an intermeshing pitch circle of the worm and the worm wheel.

Description:
INCORPORATION BY REFERENCE 
       [0001]    The disclosure of Japanese Patent Application No. 2015-103717 filed on May 21, 2015 including the specification, drawings and abstract, is incorporated herein by reference in its entirety. 
       BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to a worm reduction gear and a steering system including this worm reduction gear. 
         [0004]    2. Description of Related Art 
         [0005]    In an electric power steering system disclosed in Japanese Patent Application Publication No. 2003-334724 (JP 2003-334724 A), the rotation of a motor for generating steering assist force is transmitted to wheels through a worm and a worm wheel that meshes with this worm so as to change the steering angle. The worm wheel is formed by hobbing. 
         [0006]    When the outside diameter of a hob used for hobbing a worm wheel is made closer to the outside diameter of a worm, the shape of each tooth space of the worm wheel after being bobbed more closely resembles the shape of a tooth of the worm. This configuration can theoretically reduce errors in torque transmission between the worm and the worm wheel (what is called “torque fluctuations”), However, in this case, there is no margin to allow assembling errors or machining errors of the worm wheel. Thus, when such errors occur, the positions where the tooth of the worm and the teeth of the worm wheel come into contact with each other may change from the appropriate positions. 
       SUMMARY OF THE INVENTION 
       [0007]    An object of the present invention is to provide a worm reduction gear that can reduce torque fluctuations while allowing assembling errors and machining errors, and a steering system including the worm reduction gear. 
         [0008]    A worm reduction gear according to one aspect of the present invention includes: a worm; and a worm wheel including tooth spaces that mesh with the worm, in which following relational Formula (1) and Formula (2) are satisfied: 
         [0000]      3≧ D 2/ D 1≧1.7  (1)
 
         [0000]      0.1°≦α−β≦0.5°  (2)
 
         [0000]    where D1 is an outside diameter of the worm, D2 is an outside diameter of a hob for cutting the worm wheel to form the tooth spaces, and α is a pressure angle of the worm wheel and β is a pressure angle of the worm at an intermeshing pitch circle of the worm and the worm wheel. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    The foregoing and further features and advantages of the invention will become apparent from the following description of example embodiments with reference to the accompanying drawings, wherein like numerals are used to represent like elements and wherein: 
           [0010]      FIG. 1  is a schematic diagram of a steering system according to one embodiment of the present invention; 
           [0011]      FIG. 2  is a side view of a main part in a worm reduction gear included in the steering system; 
           [0012]      FIG. 3  is a schematic diagram illustrating how a worm wheel of the worm reduction gear is formed by hobbing; 
           [0013]      FIG. 4  is a schematic diagram illustrating a part intermeshing between a worm and the worm wheel in the worm reduction gear; 
           [0014]      FIG. 5  is a perspective view of the worm wheel; 
           [0015]      FIG. 6  is a graph illustrating relations between the rotation angle of the worm and the applied load acting on tooth flanks of the worm wheel; 
           [0016]      FIG. 7  is a graph illustrating a relation between meshing deviation and difference between the pressure angle of the worm and the pressure angle of the worm wheel; and 
           [0017]      FIG. 8  is a graph illustrating relations between the rotation angle of the worm and torque. 
       
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       [0018]    Embodiments of the present invention will now be described in detail with reference to the accompanying drawings.  FIG. 1  is a schematic diagram of a steering system  1  according to one embodiment of the present invention. As depicted in  FIG. 1 , the steering system  1  is an electric power steering system, including a steering mechanism  2  and a steering operation mechanism  3 . The steering system  1  steers steered wheels  5  in response to steering (steering operation) of a steering wheel  4  (steering member) performed by a driver. The steering mechanism  2  includes an assist mechanism  6  that assists the driver in performing steering operation. 
         [0019]    The steering mechanism  2  includes an input shaft  7 , an output shaft  8 , an intermediate shaft  9 , and a pinion shaft  10 . The input shaft  7  is coupled to the steering wheel  4 . One end of the output shaft  8  is coupled to the input shaft  7  through a torsion bar  11 , and the other end thereof is coupled to the intermediate shaft  9  through a universal joint  12 . The intermediate shaft  9  is coupled to a pinion shaft  10  including a pinion  10 A through a universal joint  13 . 
         [0020]    The steering operation mechanism  3  includes a rack shaft  14  and tie rods  15 . The rack shaft  14  includes a rack  14 A that meshes with the pinion  10 A. One end of each tie rod  15  is coupled to the rack shaft  14 , and the other end thereof is coupled to the corresponding steered wheel  5 . When the driver is operating the steering wheel  4 , the rotation of the steering wheel  4  rotates the pinion shaft  10  through the input shaft  7 , the output shaft  8 , and the intermediate shaft  9 . The rotation of the pinion shaft  10  is converted into reciprocating motion of the rack shaft  14  in the axial direction thereof by the steering operation mechanism  3 . In response to the reciprocating motion of the rack shaft  14  in the axial direction, the steered angle of the steered wheels  5  changes. 
         [0021]    The assist mechanism  6  includes a torque sensor  16 , an electronic control unit (ECU)  17 , an electric motor  18  for auxiliary steering, and a worm reduction gear  19 . The worm reduction gear  19  includes a worm  20 , a worm wheel  21 , and a housing  22 . The worm wheel  21  is a reduction gear that meshes with the worm  20 . The housing  22  accommodates the worm  20  and the worm wheel  21 . The worm  20  is coupled to a rotary shaft (not depicted) of the electric motor  18 . The worm wheel  21  is coupled to the output shaft  8  in an integrally rotatable manner. 
         [0022]    When the steering wheel  4  is rotated by steering performed by the driver, the torque sensor  16  detects the amount of torsion between the input shaft  7  and the output shaft  8 . The ECU  17  determines an assist torque based on steering torque T and vehicle speed V, for example, The steering torque T is obtained based on the amount of torsion detected by the torque sensor  16 . The vehicle speed V is detected by a vehicle speed sensor  23 . The ECU  17  controls driving of the electric motor  18 . The electric motor  18  thus driven in response to steering of the steering wheel  4  transmits output rotation to the worm  20  to rotate the worm  20 . The worm wheel  21  meshing with the worm  20  rotates at a speed lower than that of the worm  20 , and the worm wheel  21  and the output shaft  8  integrally rotate. In this manner, the worm reduction gear  19  reduces the speed of the output rotation of the electric motor  18  with the worm wheel  21 , and transmits the resulting rotation as assist torque to the output shaft  8  of the steering mechanism  2 . Consequently, steering operation of the steering wheel  4  performed by the driver is assisted. 
         [0023]    The following describes the worm reduction gear  19  in detail.  FIG. 2  is a side view of a main part in the worm reduction gear  19 . In  FIG. 2 , illustration of the housing  22  described above is omitted. As depicted in  FIG. 2 , the worm  20  includes a shaft portion  30  having a cylindrical shape and a tooth  31  that is integrally formed on an outer peripheral surface  30 A of the shaft portion  30 . The direction in which the central axis J of the shaft portion  30  extends is called herein “axial direction X”. The tooth  31  is formed on the outer peripheral surface  30 A in a region inside both ends in the axial direction X so as to form a helix centered around the central axis J. The tooth  31  when viewed from the axial direction X has a circular profile having the central axis J as a center of the circle. The diameter of this profile is an outside diameter D1 of the worm  20 . 
         [0024]    The cross-section of the tooth  31  when sectioned in a virtual plane including the central axis J and extending in the axial direction X is formed in a substantially isosceles trapezoidal shape having a width that narrows toward a direction away from the central axis J (see  FIG. 4  described later). Both side surfaces of the tooth  31  in the axial direction X are called herein “tooth flanks  32 ”. To both ends of the shaft portion  30  in the axial direction X, bearings  33  are attached one by one. The worm  20  is rotatably supported by the housing  22  via these bearings  33 . At one end (right end in  FIG. 2 ) of the shaft portion  30  in the axial direction X, a joint  34  is attached to a portion protruding from the corresponding bearing  33 . The joint  34  is coupled to the rotary shaft (not depicted) of the electric motor  18 . Thus, as described above, when the electric motor  18  is driven, the worm  20  is rotated about the central axis J. 
         [0025]    The worm wheel  21  is disk-shaped. The central axis K of the worm wheel  21  extends in an axial direction Y that corresponds to the width direction of the worm wheel  21 . Hereinafter, the circumferential direction of the worm wheel  21  is called “circumferential direction S”, and the radial direction of the worm wheel  21  is called “radial direction R”, In the radial direction R, the direction toward the central axis K is referred to as “radially inward R1” and the direction away from the central axis K is referred to as “radially outward R2”. The circumferential direction S is a rotational direction of the worm wheel  21 . 
         [0026]    The worm wheel  21  includes a disk-shaped sleeve  40  and an annular tooth portion  41 . The sleeve  40  is positioned on the central axis K side. The tooth portion  41  surrounds the sleeve  40  in an outer periphery that is separated radially outward R2 from the central axis K. The sleeve  40  and the tooth portion  41  may be integrally formed of the same material (e.g., metal). Alternatively, by insert molding, the tooth portion  41  made of resin may be integrated with the sleeve  40  made of metal. At the circle center of the sleeve  40 , an insertion hole  40 A into which the output shaft  8  is fitted is formed. 
         [0027]    On the outer peripheral surface of the tooth portion  41 , a plurality of tooth spaces  42  that mesh with the worm  20  are formed at regular intervals in the circumferential direction S. The respective tooth spaces  42  cut out the outer periphery of the tooth portion  41  in the axial direction Y, and each have a shape recessed radially inward R1. When viewed from the axial direction Y, each tooth space  42  is formed in a substantially isosceles trapezoidal shape having a width that narrows radially inward R1. In the tooth portion  41 , each projecting portion between the tooth spaces  42  neighboring in the circumferential direction S is a tooth  43  in the worm wheel  21 . The cross-section of the tooth  43  when sectioned in a virtual plane orthogonal to the central axis K is formed in a substantially isosceles trapezoidal shape having a width that narrows radially outward R2 (see also  FIG. 4 ). Both side surfaces of each tooth  43  in the circumferential direction S are called herein “tooth flanks  44 ”. The tooth flanks  44  are two-dimensionally illustrated in  FIG. 2 , but specifically each have a curved shape. The space between each pair of tooth flanks  44  that are opposed with the corresponding tooth space  42  interposed between the teeth  43  neighboring in the circumferential direction S narrows radially inward R1. The pair of tooth flanks  44  defines one tooth space  42 . A space bottom  42 A of each tooth space  42  is formed as a bottom land between radially inward R1-side ends of the pair of tooth flanks  44 . 
         [0028]    By rotating the hob  50  depicted in  FIG. 3  to perform cutting (hobbing) on the worm wheel  21 , the tooth spaces  42  are formed. The hob  50  is a cylindrical body having an outer peripheral surface on which a plurality of cutting teeth  51  for cutting the worm wheel  21  are formed in a helically aligned manner. When viewed from the axial direction L of the hob  50 , edges of the cutting teeth  51  are arranged on a virtual circle. The diameter of this circle is an outside diameter D2 of the hob  50 . This circle is also a rotational path of the edges of the cutting teeth  51  when the hob  50  rotates. The relation between the outside diameter D1 (see  FIG. 2 ) of the worm  20  and the outside diameter D2 of the hob  50  is set so that Formula (1): 
         [0000]      3≧ D 2/ D 1≧1.7  (1)
 
         [0000]    is satisfied. 
         [0029]    In order to satisfy Formula (1), the outside diameter D2 of the hob  50  is set larger than the outside diameter D1 of the worm  20 . Accordingly, the tooth spaces  42  of the worm wheel  21  after being hobbed can receive the tooth  31  of the worm  20  with allowance to some extent, and thus each have a shape that can tolerate assembling errors and machining errors. In other words, properties of being insensitive to assembling errors and machining errors can be imparted to the worm wheel  21 . 
         [0030]    For reference, if a hob  50  is used that includes a large outside diameter D2 in which the value of D2/D1 is larger than three, the tooth flank  44  of each tooth  43  of the worm wheel  21  after being hobbed has a planar shape. Consequently, the tooth spaces  42  of the worm wheel  21  each have a shape that is significantly different from the shape of the tooth  31  of the worm  20 . Thus, intermeshing between the worm  20  and the worm wheel  21  becomes poor, which may cause large torque fluctuations. 
         [0031]      FIG. 4  is a schematic diagram illustrating a part intermeshing between the worm  20  and the worm wheel  21 . The long dashed short dashed line in  FIG. 4  indicates part of a path of an intermeshing pitch circle P of the worm  20  and the worm wheel  21  in a state in which a tooth flank  32  of a tooth  31  of the worm  20  comes into contact with a tooth flank  44  of a tooth  43  of the worm wheel  21 , and the worm  20  accordingly meshes with the worm wheel  21 . In  FIG. 4 , a pressure angle α of the worm wheel  21  and a pressure angle  3  of the worm  20  in the intermeshing pitch circle P are illustrated. The pressure angle α is an acute angle formed by a reference line Q extending along the radial direction R with the tooth flank  44  (specifically, a tangent to the outline of the tooth flank  44  when viewed from the axial direction Y) at an intersection point U of the reference line Q and the intermeshing pitch circle P. The pressure angle β is an acute angle formed by the reference line Q with the tooth flank  32  (specifically, a tangent to the outline of the tooth flank  32  when viewed from the axial direction Y) at the intersection point U. The relation between the pressure angle α and the pressure angle β is set so that Formula (2): 
         [0000]      0.1°≦α−β≦0.5°  (2)
 
         [0000]    is satisfied. 
         [0032]    In order to satisfy Formula (2), the pressure angle α of the worm wheel  21  at the intermeshing pitch circle P is set larger than the pressure angle β of the worm  20 . This makes it possible to reduce torque fluctuations between the worm  20  and the worm wheel  21 . The details will be described below.  FIG. 5  is a perspective view of the worm wheel  21 . With reference to  FIG. 5 , randomly chosen three teeth  43  that are continuously aligned on the worm wheel  21  in the circumferential direction S are focused on. These three teeth  43  are distinguished as a tooth  43 A, a tooth  43 B, and a tooth  43 C in order from one side S 1  in the circumferential direction S. When the worm wheel  21 , being driven by the rotation of the worm  20 , rotates toward the other side S 2  that is opposite to the one side Si in the circumferential direction S, the tooth flank  32  of the worm  20  comes into contact with the tooth flank  44  on the one side S 1  in each of the tooth  43 A, the tooth  43 B, and the tooth  43 C. An area in the tooth flank  44  with which the tooth flank  32  comes into contact is called herein “contact area”. A certain timing during rotation of the worm wheel  21  is now focused on, and when an contact area A between a portion of the tooth  31  of the worm  20  and the tooth  43 A that are in a beginning stage of intermeshing exists on the tooth tip side, a contact area B between another portion of the tooth  31  and the tooth  43 B that are in an intermediate stage of intermeshing exists between the tooth tip and the tooth root. A contact area C between still another portion of the tooth  31  and the tooth  43 C that are in a final stage of intermeshing exists on the tooth root side. 
         [0033]      FIG. 6  is a graph illustrating relations between the rotation angle of the worm  20  and the applied load acting on the tooth flanks  44  of the worm wheel  21  when the worm  20  rotates. The applied load herein corresponds to a force of the tooth flank  32  of the worm  20  pressing on each tooth flank  44  of the worm wheel  21 . As depicted in  FIG. 6 , for each of the tooth  43 A in the beginning stage of intermeshing and the tooth  43 B in the intermediate stage of intermeshing, the applied load increases as the rotation angle of the worm  20  increases. By contrast, for the tooth  43 C in the final stage of intermeshing, the applied load decreases as the rotation angle of the worm  20  increases. In  FIG. 6 , the curves in continuous line indicate changes in applied load in the present embodiment in which the pressure angle α and the pressure angle β are set so as to satisfy Formula (2). The curves in broken line, long dashed short dashed line, and long dashed double-short dashed line indicate changes in applied load in a comparative example in which the pressure angle α and the pressure angle β are the same. 
         [0034]    In the present embodiment, reducing the pressure angle β increases intermeshing (in other words, the contact area described above) between the tooth root of each tooth  43  of the worm wheel  21  and the worm  20 . This makes the slope of change in applied load less steep. In particular, for the tooth  43 C in the final stage of intermeshing, the slope of change in applied load is much less steep than that of the comparative example (see the curve in broken line). The applied load is smaller in the present embodiment than in the comparative example for each of the tooth  43 A in the beginning stage of intermeshing and the tooth  43 B in the intermediate stage of intermeshing. By contrast, the applied load is much larger for the tooth  43 C in the final stage of intermeshing. Consequently, for the entire worm wheel  21 , the average applied load is larger. Thus, efficiency of torque transmission from the worm  20  to the worm wheel  21  can be improved. 
         [0035]      FIG. 7  is a graph illustrating a relation between meshing deviation and difference between the pressure angle β of the worm  20  and the pressure angle α of the worm wheel  21 . The meshing deviation is an index representing difference between an actual value and a target value of torque transmitted from the worm  20  to each tooth  43  of the worm wheel  21 . As depicted in  FIG. 7 , the value of α−β increases when the pressure angle β decreases as described above. When the value of α−β exceeds 0°, the meshing deviation becomes smaller. In particular, when the value of α−β falls within the range of from 0.1° to 0.5° so as to satisfy Formula (2), the meshing deviation becomes significantly smaller, and the meshing deviation becomes smallest at 0.3°. However, when the value of α−β falls outside this range, the meshing deviation increases. In particular, when the pressure angle β is excessively reduced and the value of α−β exceeds 0.5°, tooth contact between the tooth tip of the tooth  43 A in the beginning stage of intermeshing in the worm wheel  21  and the worm  20  (in other words, the contact area A described above) decreases, and the contact ratio between the worm  20  and the worm wheel  21  accordingly decreases. This may increase the meshing deviation in torque borne by one tooth  43 . Thus, in the present embodiment, the value of α−β is set within the optimal range between  0 . 1 ° and  0 . 5 ° inclusive as represented by Formula ( 2 ) (range within ± 0 . 2 ° with respect to  0 . 3 °). 
         [0036]      FIG. 8  is a graph illustrating relations between the rotation angle of the worm  20  and torque transmitted from the worm  20  to the worm wheel  21 . The torque herein is not torque borne by each tooth  43  of the worm wheel  21 , but is torque transmitted to the entire worm wheel  21 . In  FIG. 8 , the curve in continuous line indicates changes in torque in the present embodiment in which the pressure angle α and the pressure angle β are set so as to satisfy Formula (2). The curve in broken line indicates changes in torque in the comparative example in which the pressure angle α and the pressure angle β are the same. 
         [0037]    Setting the pressure angle α and the pressure angle β so that the value of α−β falls within the optimal range described above reduces the meshing deviation (see  FIG. 7 ). Furthermore, this setting suppresses reduction in torque transmitted when the tooth root of the tooth  43 C in the final stage of intermeshing in the worm wheel  21  meshes with the tooth tip of the tooth  31  of the worm  20 . Consequently, as depicted in  FIG. 8 , in the present embodiment, torque fluctuations can be reduced in comparison with the comparative example. This causes torque to converge toward a reference value (e.g., around 40.4 N·m in  FIG. 8 ). 
         [0038]    The value of α−β is preferably equal to or larger than 0.2° and equal to or smaller than 0.4°, which can further reduce torque fluctuations. The present invention is not limited to the embodiments described above, and various modifications can be made within the scope of the claims. For example, in a state in which the worm  20  meshes with the worm wheel  21 , when viewed from the radially outward R2 side, the central axis J of the worm  20  and the central axis K of the worm wheel  21  may be orthogonal to each other as in the present embodiment (see  FIG. 2 ), or may extend obliquely to each other. 
         [0039]    Specific values for the applied load illustrated in  FIG. 6 , specific values for the meshing deviation illustrated in  FIG. 7 , and specific values for the torque illustrated in  FIG. 8  are merely examples, and vary depending on sizes of the worm  20  and the worm wheel  21 .