Abstract:
A harmonic drive includes a rigid internal gear, a flexible external gear meshed with the rigid internal gear, and a wave generator abutted against the flexible external gear. Through a special parameter setting to design the outer peripheral edge of the wave generator in a surface of variable curvature, the contact area between the wave generator and the flexible external gear is increased to improve fretting wear, thereby enhancing transmission accuracy and reducing hysteresis error.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to speed reducing gear technology, and more particularly, to a harmonic drive that improves transmission accuracy. 
     2. Description of the Related Art 
     Harmonic drive is a high ratio of gear reducer. A conventional harmonic drive generally comprises a rigid internal gear, a flexible external gear rotatably mounted within the rigid internal gear, and a wave generator rotatably mounted within the flexible external gear. After installation of the wave generator in the flexible external gear, the flexible external gear is pushed by the outer perimeter of the wave generator and elastically deformed to provide an elliptical shape. Thus, when the wave generator is driven to rotate by a power source, the rigid internal gear and the flexible external gear are forced to mesh with each other in the major axis of the wave generator and to disengage from each other in the minor axis of the wave generator. Due to a difference in the number of teeth between the rigid internal gear and the flexible external gear, a high speed reduction ratio will be achieved to provide a high torque output when the wave generator is been continuously rotated. 
     However, because the flexible external gear will become oval in shape after it is inserted into the wave generator, a fretting wear problem will occur during power transmission through the inner perimeter of the flexible external gear, and the transmission accuracy will be affected after a long use. In order to eliminate this problem, Japan Utility Model Pub. No. 6-19872 teaches a measure of processing a recessed portion out of the outer peripheral edge of the axle bearing of the wave generator, wherein the recessed portion and a width of the flexible external gear exhibit a predetermined ratio so that the thrust force produced during installation of the flexible external gear can be reduced, thereby reducing fretting wear. However, in actual application, the effect of improvement of this measure is limited. 
     SUMMARY OF THE INVENTION 
     The present invention has been accomplished under the circumstances in view. It is the main object of the present invention to provide a harmonic drive, which effectively improves fretting wear resistance and transmission accuracy. 
     To achieve this and other objects of the present invention, a harmonic drive comprises a rigid internal gear, a flexible external gear rotatably mounted within the rigid internal gear, and a wave generator rotatably mounted within the flexible external gear. The wave generator comprises an axle bearing and an elliptic wheel mounted in the axle bearing. The axle bearing comprises an outer peripheral edge abutted against an inner perimeter of the flexible external gear. The radius of curvature of the outer peripheral edge in the YZ plane is defined as R GX , R GX =√{square root over (y x   2 +z x   2 )}. The relationship between y x  and z x  satisfies the ellipse parametric equation of:
 
 y   x   ={a   x   +ca   x ×(sin(4θ−(π/2))+1)}×sin θ,0≦θ≦2π
 
 z   x   ={b   x   +cb   x ×(sin(4θ−(π/2))+1)}×cos θ,0≦θ≦2π
 
     wherein a x  is the semi-major axis of the outer peripheral edge of the axle bearing of the wave generator in the YZ plane before insertion of the elliptic wheel; ca x  is the semi-major axis correction factor; b x  is the semi-minor axis of the outer peripheral edge of the axle bearing of the wave generator in the YZ plane before insertion of the elliptic wheel; cb x  is the semi-minor axis correction factor; θ is a centrifugal angle of the outer peripheral edge of the wave generator in the YZ plane. 
     Preferably, the radius of curvature of the outer peripheral edge of the wave generator in a XY plane is defined as R GZ , R GZ =√{square root over (x z   2 +y z   2 )}, wherein the relationship between x z  and y z  satisfies the following ellipse parametric equation of:
 
 x   z   ={a   z   +ca   z ×(sin(4Ψ−(π/2))+1)}×sin Ψ,0≦Ψ≦2π
 
 y   z   ={b   z   +cb   z ×(sin(4Ψ−(π/2))+1)}×cos Ψ,0≦Ψ≦2π
 
     in which, a z  is the semi-major axis of the outer peripheral edge of the axle bearing of the wave generator in the XY plane; ca z  is the semi-major axis correction factor; b z  is the semi-minor axis of the outer peripheral edge of the axle bearing of the wave generator in the XY plane; cb z  is the semi-minor axis correction factor; ψ is a centrifugal angle of the outer peripheral edge of the wave generator. 
     Thus, after correction through the aforesaid parametric equation, the curvature of the outer peripheral edge of the wave generator of the harmonic drive will be changed into an arc shape, so that the contact area between the wave generator and the flexible external gear can be increased to improve fretting wear resistance and transmission accuracy. 
     Other advantages and features of the present invention will be fully understood by reference to the following specification in conjunction with the accompanying drawings, in which like reference signs denote like components of structure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic structural view of a harmonic drive in accordance with the present invention. 
         FIG. 2  is a schematic drawing illustrating correction of the curvature of the wave generator in the YZ plane. 
         FIG. 3  is a schematic drawing of the present invention, illustrating correction of the curvature of the wave generator in the XY plane. 
         FIG. 4  is a transmission error curve obtained before and after adjustment of the curvature in accordance with the present invention. 
         FIG. 5  is a hysteresis error curve obtained before and after adjustment of the curvature in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , a harmonic drive  10  in accordance with the present invention comprises a rigid internal gear  20 , a flexible external gear  30 , and a wave generator  40 . 
     The rigid internal gear  20  comprises an inner annular toothed portion  22 . The flexible external gear  30  is mounted within the rigid internal gear  20 , comprising an outer annular toothed portion  32  facing toward the inner annular toothed portion  22  of the rigid internal gear  20 . It is to be noted that the number of teeth of the inner annular toothed portion  22  of the rigid internal gear  20  is 2 more than the number of teeth of the outer annular toothed portion  32  of the flexible external gear  30 . Further, the rigid internal gear  20  and the flexible external gear  30  have a same modulus therebetween. The modulus referred to therein is the quotient obtained by dividing the gear pitch diameter by the number of teeth. 
     The wave generator  40  is mounted within the flexible external gear  30 , comprising an axle bearing  42  and an elliptic wheel  44 . The axle bearing  42  has the outer peripheral edge  46  thereof abutted against the inner perimeter  34  of the flexible external gear  30 . The elliptic wheel  44  is mounted in the axle bearing  42 . When the elliptic wheel  44  is driven to rotate by a power source (not shown), the axle bearing  42  is synchronously rotated, causing the outer peripheral edge  46  of the axle bearing  42  to push the inner perimeter  34  of the flexible external gear  30  and to further elastically deform the flexible external gear  30 , causing the inner annular toothed portion  22  of the rigid internal gear  20  to be completely meshed with the outer annular toothed portion  32  of the flexible external gear  30  in the major axis direction of the wave generator  40  and completely disengaged from the outer annular toothed portion  32  of the flexible external gear  30  in the minor axis direction of the wave generator  40 . Thus, the rigid internal gear  20  can be rotated by the flexible external gear  30  to achieve the effect of torque output. 
     In order to increase the contact area between the outer peripheral edge  46  of the axle bearing  42  of the wave generator  40  and the inner perimeter  34  of the flexible external gear  30 , the invention makes a correction of the curvature of the outer peripheral edge  46  of the wave generator  40 . Referring to  FIG. 2 , define the radius of curvature of the outer peripheral edge  46  of the wave generator  40  in a YZ plane to be R GX , R GX =√{square root over (y x   2 +z x   2 )}, wherein the relationship between y x  and z x  satisfies the following ellipse parametric equation (1):
 
 y   x   ={a   x   +ca   x ×(sin(4θ−(π/2))+1)}×sin θ,0≦θ≦2π
 
 z   x   ={b   x   +cb   x ×(sin(4θ−(π/2))+1)}×cos θ,0≦θ≦2π
 
     In the aforesaid ellipse parametric equation (I), a x  is the semi-major axis of the outer peripheral edge  46  of the axle bearing  42  of the wave generator  40  in the YZ plane before insertion of the elliptic wheel  44 ; ca x  is a semi-major axis correction factor; b x  is the semi-minor axis of the outer peripheral edge  46  of the axle bearing  42  of the wave generator  40  in the YZ plane before insertion of the elliptic wheel  44 ; cb x  is the semi-minor axis correction factor; θ is a centrifugal angle of the outer peripheral edge  46  of the wave generator  40 . 
     Thereafter, referring also to  FIG. 3 , define the radius of curvature of the outer peripheral edge  46  of the wave generator  40  in a XY plane as R GZ , R GZ =√{square root over (x z   2 +y z   2 )}, wherein the relationship between x z  and y z  satisfies the following ellipse parametric equation (II):
 
 x   z   ={a   z   +ca   z ×(sin(4Ψ−(π/2))+1)}×sin Ψ,0≦Ψ≦2π
 
 y   z   ={b   z   +cb   z ×(sin(4Ψ−(π/2))+1)}×cos Ψ,0≦Ψ≦2π
 
     In the aforesaid ellipse parametric equation (II), a z  is the semi-major axis of the outer peripheral edge  46  of the axle bearing  42  of the wave generator  40  in the XY plane; ca z  is the semi-major axis correction factor; b z  is the semi-minor axis of the outer peripheral edge  46  of the axle bearing  42  of the wave generator  40  in the XY plane; cb z  is the semi-minor axis correction factor; ψ is a centrifugal angle of the outer peripheral edge  46  of the wave generator  40 . In addition to the ellipse parametric equation (II), the radius of curvature R GX  of the outer peripheral edge  46  of the wave generator  40  in the YZ plane also needs to satisfy the following conditions: after mounting of the elliptic wheel  44  in the axle bearing  42 , the outer peripheral edge  46  of the wave generator  40  exhibits an elliptical shape, and therefore R GX  must satisfy the ellipse parametric equation (III): 
     
       
         
           
             
               
                 R 
                 GX 
               
               ⁢ 
               sin 
               ⁢ 
               
                   
               
               ⁢ 
               θ 
             
             = 
             
               W 
               2 
             
           
         
       
       
         
           
             
               
                 R 
                 GX 
               
               ⁢ 
               cos 
               ⁢ 
               
                   
               
               ⁢ 
               θ 
             
             = 
             
               
                 
                   D 
                   FX 
                 
                 2 
               
               - 
               e 
             
           
         
       
       
         
           
             e 
             = 
             
               0.001 
               × 
               
                 
                   D 
                   FX 
                 
                 ~ 
                 0.05 
               
               × 
               
                 D 
                 FX 
               
             
           
         
       
     
     In the aforesaid ellipse parametric equation (III), R GX  is the radius of curvature of the outer peripheral edge  46  of the wave generator  40  in the YZ plane; W is the width of the axle bearing  42  of the wave generator  40 ; D FX  is the inner diameter of the flexible external gear  30  before deformation; e is the arc correction factor. 
     Further, after installation of the elliptic wheel  44  in the axle bearing  42  and before insertion of the wave generator  40  into the elliptic wheel  44 , the semi-major axis a x  of the outer peripheral edge  46  in the YZ plane needs to satisfy the equation (II) 
               a   x     =         D   FX     2     ⁢     :             
and the equation (III) a x =A+T, in which: D FX  is the inner diameter of the flexible external gear  30  before deformation; A is the semi-major axis of the elliptic wheel  4 ; T is the thickness of the axle bearing  42 .
 
     Thus, through the ellipse parametric equations (I)˜(III) and equations (I)˜(III), we can obtain the radius of curvature of the wave generator  40  in the YZ plane and the XY plane to be R GX  and R GZ . Through the relationship between R GX  and R GZ , the outer peripheral edge  42  of the wave generator  40  can be adjusted to optimize the elliptic curve. After adjustment, the contact area between the wave generator  40  and the flexible external gear  30  is greatly increased, improving the problem of fretting wear produced during power transmission through the wave generator  40 . Further, as illustrated in  FIG. 4 , under the same experimental conditions, the transmission error after adjustment is lowered by 43.61% when compared to that before adjustment; in hysteresis, it shows a reduction by 62.67% when compared to that before adjustment (see  FIG. 5  and Table II). Therefore, the invention greatly improves transmission accuracy and reduces hysteresis error after curvature adjustment. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                 Transmission 
                 Maximum 
                 Minimum 
                 Range 
                 Reduce 
               
               
                 error 
                 (degree) 
                 (degree) 
                 (degree) 
                 (%) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Curvature before 
                 0.276591 
                 0.271301 
                 0.005289 
                   
               
               
                 adjustment 
               
               
                 Curvature after 
                 0.266773 
                 0.26379 
                 0.002983 
                 43.61 
               
               
                 adjustment 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
           
               
                 TABLE II 
               
               
                   
               
               
                   
                 Maximum 
                 Minimum 
                 Range 
                 Reduce 
               
               
                 Hysteresis 
                 (degree) 
                 (degree) 
                 (degree) 
                 (%) 
               
               
                   
               
             
             
               
                 Curvature before 
                 0.0049495 
                 −0.003408 
                 0.008357 
                   
               
               
                 adjustment 
               
               
                 Curvature after 
                 0.0014981 
                 −0.001621 
                 0.003119 
                 62.67% 
               
               
                 adjustment 
               
               
                   
               
             
          
         
       
     
     On the other hand, the contact pressure between flexible external gear  30  and the wave generator  40  can be figured out based on the radius of curvature R GX  and the R GZ . At first, obtain R X  and R Z  respectively from equation (IV)): 
               1     R   x       =         1     R   Gx       +     1     R   Fx         =         1     R   Gx       +     1   ∞       =     1     R   Gx                 
and equation (V):
 
                 1     R   Z       =       1     R   GZ       +     1     R   FZ           ,         
in which R X  is the radius of curvature of the outer peripheral edge  46  of the wave generator  40  in the YZ plane before insertion of the elliptic wheel  44 ; R FX  is the radius of curvature of the flexile external gear  30  in the YZ plan; R Z  is the radius of curvature of the outer peripheral edge  46  of the wave generator  40  in the XY plan; R FZ  is the radius of curvature of the flexile external gear  30  in the XY plan. Thereafter, obtain the equivalent radius of curvature
 
             R   =         R   x     ×     R   Z           R   x     +     R   Z               
by means of the equation (VI):
 
               1   R     =       1     R   x       +       1     R   Z       .             
Thereafter, use the equivalent Young&#39;s modulus E, the approximate complete elliptic integral g, and the ellipse parameter k e  to figure out the major axis of the elliptical contact area to
 
               bea   e     =       (       6   ⁢     k   e   2     ⁢   ⁢           ⁢     W   Z     ⁢   R       π   ⁢           ⁢   E       )       1   ⁢     /     ⁢   3             
and the manor axis of the elliptical contact area to
 
               beb   e     =       (       6   ⁢   ⁢           ⁢     W   Z     ⁢   R       π   ⁢           ⁢     k   e     ⁢   E       )       1   ⁢     /     ⁢   3             
in which the equivalent Young&#39;s modulus
 
               E   =     2         (     1   -     V   a   2       )       E   a       +       (     1   -     V   b   2       )       E   b             ;         
the approximate complete elliptic integral
 
               =     1.0003   +       0.5968   ⁢     R   x         R   z           ;         
the ellipse parameter
 
                 k   e     =     1.0339   ×       (       R   z       R   x       )     0.636         ;     W   Z           
is the contact stress acted upon the outer perimeter edge  46  of the wave generator  40  upon engagement between the rigid internal gear  20  and the flexible external gear  30 ; V a  and E a  are the Poisson&#39;s ratio and Young&#39;s modulus of the flexible external gear  30 ; V b  and E b  are the Poisson&#39;s ratio and Young&#39;s modulus of the wave generator  40 . At final, the contact pressure is obtained through the equation (VII):
 
     
       
         
           
             P 
             = 
             
               
                 
                   3 
                   ⁢ 
                   
                     W 
                     Z 
                   
                 
                 
                   2 
                   ⁢ 
                   π 
                   × 
                   
                     a 
                     e 
                   
                   × 
                   
                     b 
                     e 
                   
                 
               
               .