Flexible coupling

Abstract: A flexible coupling comprises a sleeve (13) with inner gear teeth (13a) at each end engaged with the outer teeth (12a) of a pinion (12), for mounting on a shaft (11), the outer teeth (12a) being crowned, so that a tooth section along a pitch circle cylinder defines a convex curve, having a radius of curvature which increases from the centre of the tooth to the tooth end.

Description: This invention relates to a flexible coupling for freely rockably coupling a rotary shaft of an electric motor of an electric locomotive and a driven shaft of a gear unit incorporated into wheels on the bogie. The bogie of an electric locomotive comprises a spring between the wheels and the bogie frame for a comfortable ride. The electric motor is mounted to the bogie frame and the gear unit for driving the axle is incorporated into the wheel shaft. Therefore, a flexible coupling is provided between the sprung electric motor and the unsprung gear unit in order that the shake, vibrations and noise may not directly be transmitted to the motor side. An example of the structure of the conventional flexible coupling is disclosed in Japanese Utility Model Publication No. 47-14804. Fig. 7 is a sectional view of this flexible coupling. In the figure, 1 and 11 are rotary shafts, 2 and 12 are pinions secured to the rotary shafts 1 and 11 and each has formed thereon a crowned outer teeth gear 2a or 12a. 3 and 13 are sleeves fastened together by bolts and have formed inside an inner teeth gears 3a and 13a which are in mesh with the outer teeth gears 2a and 12a of the pinions 2 and 12. 4 and 14 are end covers secured to the sleeves 3 and 13 at one end and extend at the other ends into an annular groove formed in the securing portion of the pinions 2 and 12. 5 is a partition plate inserted between the joining surfaces of the sleeves 3 and 13 for partitioning the sleeves 3 and 13 from each other. 6, 16 are shaft end nuts for securing the pinions 2 and 12 onto the rotary shafts 1 and 11, and 7 and 17 are cushions secured to the end shaft nuts 6 and 16 for positioning the shaft end nuts 6 and 16 relative to the partition plate 5 for establishing a proper engagement between the inner teeth gears of the sleeves 3 and 13 and the outer teeth gears of the pinions 2 and 12. The flexible coupling of the above structure is connected to a motor rotary shaft at one of the rotary shaft 1 or 11 and to the gear unit combined with the wheel shaft of the bogie. In the conventional flexible coupling of the above construction, when the axes of the rotary shaft of the electric motor and the gear unit incorporated into the axle come out of alignment when the bogie shakes during the travel of the electric locomotive, the axes of the rotary shafts 1 and 11 at the opposite ends of the coupling displace as shown in Fig. 8. Even when such the displacement occurs the crowned outer teeth gears 2a and 12a of the pinions 2 and 12 always engage the inner teeth gears 3a and 13a of the sleeves 3 and 13, thereby to achieve smooth transmission of the driving power. In recent years, the speed of the electric locomotive has been significantly increased by increasing the rotational speed of the electric motor and by decreasing the size of the motor to make the overall vehicle weight small. While the increase of the motor speed significantly contributes to the decrease in weight, it also causes vibrations and noise to increase, whereby the comfort of ride is degraded. When the motor speed increases and the flexible coupling is being driven at a high speed, precession vibration or torsional vibration may occur because the sleeves are rockable due to the backlash between the meshing portions of the gears of the pinions 2 and the sleeves 3 and because of the possible unbalance as a rotating body. The conventional crowning of the gears of the flexible coupling is as shown in Fig. 9. Fig. 10 is a side view of the outer teeth gear of the pinion 2. In Fig. 9, 3a is an inner teeth gear of the sleeve 3 and 2a is an outer teeth gear of the pinion 2. As shown in Fig. 10(a), the outer teeth gears 2a of the pinion 2 are rounded by machining so that they smoothly mesh with the inner teeth gears on the sleeves even when the pair of the rotary shafts come out of alignment relative to each other. Also, they are crowned in the tooth thickness direction as shown in Fig. 9 showing the cross section along the pitch circle cylinder. In these figures, S is the pitch circle diameter, T is the tooth thickness at the pitch circle diameter S of the outer tooth gear 2a of the pinion 2, H is the inner tooth clearance at the pitch circle diameter S of the inner tooth gear 3a of the sleeve 3, G is the backlash, R c is the radius of the crowning of the outer tooth gear 2a, β w is the allowable displacement angle between the center lines of the sleeve 3 and the pinions 2, and β is the displacement angle. The backlash G at the pitch circle diameter S is expressed by the equation 8 given below and the dimensional relationship between the outer tooth gear 2a and the inner tooth gear 3a at the pitch circle diameter S is expressed by the equation 9 given below. G = ( 2 · R c - T) · (1 - cosβ w ) R c = (1/2) · {[G/(1-cosβ w )] + T)} where, R c : radius of crowning curve G : backlash β w : allowable displacement angle T : tooth thickness In the flexible coupling of this construction, in order to give a necessary allowable displacement angle β w the angle of the tangent line at the tooth width end of the crowned surface at the pitch circle S of the outer tooth gear of the pinion 2 relative to the axis of the pinion 2 should be equal to the allowable displacement angle β w , and the gap between the outer tooth gear and the inner tooth gear at the pitch circle diameter S when the displacement angle β should be equal to the backlash G, and it was necessary that G = 0.8 - 1.2 mm in order that the allowable displacement angle β w be 0.1 (β w = about 6 degrees), for example. Fig. 11 shows the state of engagement when the allowable displacement angle is β w . Thus, the engagement in the direction perpendicular to the direction of displacement is in the state in which the backlash G generates, and the center of rotation of the sleeve 3 displaces within the range of the backlash G, thereby generating an unbalance as a rotating body which may cause the precession vibration and the torsional vibration due to the play in the direction of rotation. Also, in the typical crowned gear flexible coupling, the number of teeth of the sleeve 3 or pinion 2 which are in simultaneous contact with each other decreases as the displacement angle β increases when the flexible coupling transmitting a constant force rotates. One example of this phenomenon is illustrated in Fig. 12. In the conventional flexible coupling, the gear teeth are crowned at a constant radius of curvature R c , so that, as the number of the simultaneously contacting teeth decreases, the contacting stress at the tooth surface inverse proportionally increases, increasing the possibility of roughening and damaging the tooth surface. As described above, the tooth surface is crowned at a constant radius of curvature in the conventional flexible coupling and the backlash defined between the meshing portions of the outer tooth gear of the pinion and the inner tooth gear of the sleeve is made large in order to establish a necessary allowable displacement angle, so that the precession vibration and the torsional vibration appear as the rotational speed increases to degrade the comfort of ride of the electric locomotive, making it impossible to increase the rotational speed. Also, since the conventional flexible coupling in which the gear is crowned at a constant radius of curvature has a large backlash, the number of the simultaneously meshing teeth decreases as the displacement increases, so that the stress at the contacting portions of the tooth surface increases substantially in inverse proportion to the displacement angle, posing the problem that roughening and damaging of the tooth surface easily occur. Accordingly, it would be desirableto be able to provide a flexible coupling free from the above-discussed problems of the conventional flexible coupling. It would also be desirable to be able to provide a flexible coupling in which the precession vibration and the torsional vibration are small even at a high speed rotation and the increase in the stress at the contacting portions is suppressed even when the number of the simultaneous contacting teeth decreased upon the displacement. GB-A-1 095 discloses a flexible coupling according to the pre-characterising part of claim 1. The present invention provides flexible coupling between a pair of rotary shafts which are arranged end to end and which are capable of limited relative transverse displacement, comprising a pair of pinions adapted to be mounted to the respective rotary shafts and each having an outer tooth gear thereon, and a sleeve having a pair of inner tooth gears engaged with the respective outer tooth gears for transmitting power between the rotary shafts, there being a given backlash (G) between the teeth of the inner and outer tooth gears when the rotary shafts are in axial alignment, an allowable displacement angle (β w ) being defined as the angle between the axes of the pitch circle cylinders of the inner and outer tooth gears at the maximum of the limited relative transverse displacement of the rotary shafts, wherein each flank of each tooth of the outer tooth gears is crowned in the axial direction in such a manner that, at a section along the pitch circle cylinder, the flank follows an outwardly convex curve having its apex at the center of its axial width, the said outwardly convex curve having a radius of curvature that becomes larger as the point on the curve approaches the tooth end; characterised in that: at a position at which the flank is contacted with the inner tooth gear when the angle between the axes of the pitch circle cylinders of the inner and outer tooth gears is the allowable displacement angle (β w ), a tangent line to the outwardly convex curve in a plane containing the axis of the pitch circle cylinder of the outer tooth gear at the allowable displacement angle (β w ) with respect to the direction of the axis of the pitch circle cylinder of the inner tooth gear extends through a point separated from the said apex of the curve by an amount equal to one half of the backlash (G). Preferably, the said outwardly convex curve is an exponential curve expressed by the equation given below: Y = m · X n where Y: crowning curve having an origin (O) at the center of the axial width of the tooth flank, X: axial distance from the origin (O), m: factor, and n: exponential number. Preferably, the origin of the curve falls on an apex of an imaginary reference hexagon (ABCDEF) within an imaginary outer hexagonal (abcdef) in which no backlash is provided at the center of the tooth width and in which the displacement angle of the sides (ab, bc, de, ef) in the axial direction is the allowable displacement angle (β w ), the said sides (ab, bc, de, ef) of the outer hexagon being positioned outside the corresponding sides (AB, CD, DE, EF) of the reference hexagon by an amount equal to 1/2 of the backlash (G), and the said position at which the flank is contacted with the inner tooth gear at the allowable displacement angle (β w ) lies on one of the said sides of the outer hexagon (abcdef). In one embodiment: n= ln[Y2/Y1] ln[X2/X1| m = Y1/X1 n (X1,Y1) and (X2,Y2) are the coordinates of two points (P1, P2) in the vicinity of the said position on the said one side of the outer hexagon (abcdef). In another embodiment: yw = tan βw · xw - (G/2) n = tan βw · xw / yw m = yw / xw n βw: the allowable displacement angle, G: backlash, and (xw,yw): the coordinates of the said position on the said one side of the outer hexagon (abcdef). The present invention will become more readily apparent from the following detailed description of the preferred embodiments of the present invention taken in conjunction with the accompanying drawings, in which: Fig. 1 is a tooth shape sectional view to be used as a base for the pitch circle diameter section of the outer tooth gear of the pinion of a flexible coupling in accordance with the present invention; Fig. 2 is a tooth shape sectional view at the pitch circle diameter of the outer tooth gear of the pinion of the flexible coupling in accordance with the present invention; Fig. 3 is a tooth shape sectional view for determining the tooth shape curve; Fig. 4a is a side view of the tooth shape shown in Fig. 3, in an axial plane; Fig. 4b is an end view of the tooth shape; Fig. 5 is an explanatory view for showing the manner in which the factor and the exponential of the exponential function representing the tooth shape are obtained; Fig. 6 is a view showing the relationship between the displacement angle of the engagement portion and the simultaneous contacting tooth number and the radius of curvature, in accordance with the present invention; Fig. 7 is a sectional view showing the structure of a conventional flexible coupling; Fig. 8 is an explanatory view for explaining the displacement of the rotary shafts of the flexible coupling; Fig. 9 is an explanatory view of the shape of a conventional flexible coupling; Figs. 10a and 10b are side and end views of a tooth shown in Fig. 9; Fig. 11 is an explanatory view for explaining how the outer tooth gear of the pinion and the inner tooth gear of the sleeve of the conventional flexible coupling are engaged; and Fig. 12 is a view showing the relationship between the displacement angle of the engagement portion and the simultaneous contacting tooth number and the radius of curvature of the conventional flexible coupling. DETAILED DESCRIPTION In order to reduce the precession vibration and torsional vibration of the flexible coupling rotating at a high speed, it is important to make the backlash at the meshing portion of the gears small. Figs. 1 and 2 are views for explaining how the crowning curve of the tooth surface of the outer tooth gear of the pinion of the flexible coupling is determined. The general structure of the flexible coupling may be identical to that of the flexible coupling illustrated in Fig. 7 except for the tooth shape. Fig. 1 illustrates an ideal tooth shape for allowing the flexure of the flexible coupling at the allowable displacement angle with no backlash, the polygon ABCDEF in Fig. 1 being an ideal tooth shape which realizes no backlash at the pitch circle diameter S and βw being an allowable displacement angle or inclination angle. With such a tooth shape, the gear teeth of the outer and inner tooth gears in the plane perpendicular to the direction of displacement of the gears mesh with each other with no backlash therebetween. However, the gear teeth are in contact with each other only at the apex at the center of the tooth width, generating a very large local stress at this contacting apex portion, so that, although this contacting portion may be quickly worn and rounded to slightly moderate the stress during operation, the contacting portion does not shift from the above contacting portion, resulting in a large stress fatigue which makes the performance of the flexible coupling not practical. According to the flexible coupling the present invention shown in Fig. 2, a backlash is provided in the meshing portion of the gear teeth of the outer tooth gear of the pinion and the inner tooth gear of the sleeve and the arrangement is such that, when the axes of the sleeve and the pinion are angularly displaced relative to each other, the point of contact between the tooth surfaces shifts toward the tooth end as the displacement angle increases and that the radius of curvature of the tooth surface becomes larger in the direction toward the tooth end, i.e., the larger the distance from the center of the tooth width, the larger the radius of curvature of the tooth surface. Fig. 2 is also a tooth shape explanation diagram for explaining how the backlash of the outer tooth gear of the pinion in which the central portion of the tooth surface is rounded for suppressing the contacting portion stress within an allowable limit is determined. According to this method, a polygon identical to the polygon shown in Fig. 1 is used as the reference polygon ABCDEF, each of the sides AB, BC, DE, EF of the reference polygon ABCDEF being added with 1/2 of the backlash G to imaginarily make an outer-contacting polygon abcdef of which sides are parallel to the sides AB, BC, DE, EF, respectively, of the reference polygon ABCDEF. The curve along which the gear teeth are to be crowned is a function curve which is within the range of 1/2 of the added backlash G, passes through the points of origin of the apex E or B of the reference polygon ABCDEF at the central portion of the tooth width, causes the gear tooth to contact at the allowable displacement angle βw and at the tooth ends in the sides ab and de or be and ef of the outer polygon abcdef, convex in the direction of thickness of the gear tooth and which has a radius of curvature that becomes larger as the point on the curve approaches to the gear end. Thus, the tooth shape of the outer gear of the pinion is defined according to the curve that is limited within the small backlash, convex in the direction of tooth width and that has a larger radius of curvature at the tooth end. Accordingly, even when the flexible coupling is rotating at a high speed, the precession vibration and the torsional vibration can be suppressed to be small. Also, since the radius of curvature is proportionally larger as the point approaches to the gear end and the point of contact shifts in the direction of the gear width as the displacement angle increases, even when the contacting gear number decreases when displaced, the increase in the contacting stress is suppressed and a larger power can be transmitted as compared to the conventional design. Embodiment 2. In the second embodiment of the flexible coupling of the present invention shown in Fig. 3, the backlash at the meshing portion between the outer tooth gear of the pinion and the inner tooth gear of the sleeve is made small and the crowning curve at the cylindrical section taken along the pitch circle cylinder of the outer tooth gear of the pinion is made as an exponential curve. The other structure of the flexible coupling may be identical to the conventional design shown in Fig. 7. As in the first embodiment and as shown in Fig. 2, a polygon identical to the polygon shown in Fig. 1 is used as the reference polygon ABCDEF, each of the sides AB, BC, DE, EF of the reference polygon ABCDEF being added with 1/2 of the backlash G to imaginarily make an outer polygon abcdef of which sides are parallel to the sides AB, BC, DE, EF, respectively, of the reference polygon ABCDEF. The curve along which the gear teeth are to be crowned is a function curve which is within the range of 1/2 of the added backlash G, has the points of origin of the apex E or B of the reference polygon ABCDEF at the central portion of the tooth width, causes the gear tooth to contact at the allowable displacement angle βw and at the tooth ends in the sides ab and de or be and ef of the outer polygon abcdef, convex in the direction of thickness of the gear tooth and which can be expressed by the equation 1 given below. The displacement angle at each point on the curve of the equation 1 is given by equation 2 which is a differential of the equation 1. Y = m · X n dY/dX= m · n · X (n-1) The factor m and exponential n of the equation 1 are values for satisfying the condition in which the curve of the exponential function 1 contacts the side de of the outer contacting polygon abcdef when the curve passes through the apex E of the reference polygon ABCDEF and at the allowable displacement angle βw. In order to determine the factor m and the exponential n , as shown in Fig. 3, a reference polygon ABCDEF and an outer-contacting polygon abcdef having sides parallel to the side DE of the reference polygon ABCDEF similar to those shown in Fig. 2 are assumed, the position of the side de at which it is brought into contact at the allowable displacement angle βw is selected on the side de of the outer-contacting polygon 1, and two points P1 (X1, Y1) and P2 (X2, Y2) are selected in the vicinity of that point on that side de. The respective positions of the points of coordinates P1 and P2 are substituted for in the equations 1 and 2, and the X value and Y value of the points of coordinates at P1 and P2 is substituted for in the equations 3 and 4 which are obtained from the equations of two points and calculated to obtain the exponential n , which is substituted for into equation 4 obtained by modifying the equation 1 to obtain the factor m , whereby the crowning curve can be determined. n = ln(Y2/Y1) ln(X2/X1) m = Y1/X1 n The exponential function curve of equation 1 of the factor m and the exponential n obtained from equations 3 and 4 has an allowable displacement angle βw slightly smaller than the theoretical value but in practice this value can be treated as an allowable displacement angle βw because the points P1 and P2 are on the substantially straight line region of the function. The exponential function curve shown in equation 1 of the factor m and the exponential n has a varying radius of curvature that becomes greater as the point on the curve approaches the tooth ends. Thus, since the crowning curve of the tooth shape of the outer tooth gear is an exponential function curve that is within a small backlash and passing through the tooth surface of the central region of the tooth width, even when the flexible coupling is rotating at a high speed, the precession vibration and the torsional vibration can be suppressed to be small, and the factor m and the exponential n of the curve can be easily obtained from two points on the side of the outer-contacting polygon. Also, as for the engagement state, the radius of curvature is larger as the point on the curve approaches to the gear end, and the point of contact shifts in the direction of the gear width as the displacement angle increases, even when the contacting gear number decreases when displaced, the increase in the contacting stress is suppressed and a larger power can be transmitted as compared to the conventional design. Embodiment 3. In this embodiment, the factor m and the exponential n of the exponential function of the crowning curve are obtained by another process. According to this process, similarly to the first and the second embodiments, as shown in Fig. 2, a polygon identical to the ideal polygon ABCDEF shown in Fig. 1 is used as the reference polygon ABCDEF, each of the sides AB, BC, DE, EF of the reference polygon ABCDEF being added with 112 of the backlash G to imaginarily make an outer polygon abcdef of which sides are parallel to the sides AB, BC, DE, EF, respectively, of the reference polygon ABCDEF. The curve along which the gear teeth are to be crowned is a function curve which is within the range of 1/2 of the added backlash G, has the points of origin of the apex E or B of the reference polygon ABCDEF at the central portion of the tooth width, causes the gear tooth to contact at the allowable displacement angle βw and at the tooth ends in the sides ab and de or bc and ef of the outer polygon abcdef, convex in the direction of thickness of the gear tooth and which has the exponential function of equation 1 given below and the same as that of the first embodiment. In the third embodiment, the exponential n and the factor m of the exponential function of equation 1 are obtained by the following process. Firstly, the position of contact at the allowable displacement angle βw is set on a point W in the vicinity of the tooth end on the side de of the outer contacting polygon abcdef and the exponential n and the factor m are obtained from the point of coordinate of this set position. The crowning curve is an exponential function of the equation 1 given below, and the displacement angle of the tangent line at the respective points is expressed by equation 2, and the coordinates of the contacting position upon the allowable displacement angle βw in the direction of tooth thickness when it is assumed that the distance between the contacting point and the center of tooth width is xw can be obtained by the equation 5, and the exponential n and the factor m can be obtained from the equation 6 and the equation 7, respectively, by substituting xw and yw for X and Y, respectively, of the equations 1 and 2. Y = m · X n dY/dX= m · n · X (n-1) yw = tan βw · xw - (G/2) n = tan β w · xw/yw m = yw/xw n Thus, since the crowning curve of the tooth shape of the outer tooth gear is an exponential function curve that is within a small backlash and passing through the central region of the tooth width, even when the flexible coupling is rotating at a high speed, the precession vibration and the torsional vibration can be suppressed to be small, and the factor m and the exponential n of the curve can be easily and precisely obtained from the coordinates of a contacting point set on a side of an outer contacting polygon. Also, as for the engagement state, the radius of curvature is larger as the point on the curve approaches to the gear end, and the point of contact shifts in the direction of the gear end as the displacement angle increases, so that even when the contacting gear number decreases when displaced, the increase in the contacting stress is suppressed and a larger power can be transmitted as compared to the conventional design. Even when the flexible coupling is rotating at a high speed, the precession vibration and the torsional vibration can be suppressed to be small. Also, as for the engagement state, the radius of curvature is larger as the point on the curve approaches to the gear end, and the point of contact shifts in the direction of the gear end as the displacement angle increases, so that even when the contacting gear number decreases when displaced, the increase in the contacting stress is suppressed and a larger power can be transmitted as compared to the conventional design.

Claims: A flexible coupling between a pair of rotary shafts (1,11) which are arranged end to end and which are capable of limited relative transverse displacement, comprising a pair of pinions (2,12) adapted to be mounted to the respective rotary shafts (1,11) and each having an outer tooth gear (2a,12a) thereon, and a sleeve (3,13) having a pair of inner tooth gears (3a,13a) engaged with the respective outer tooth gears (2a,12a) for transmitting power between the rotary shafts (1,11), there being a given backlash (G) between the teeth of the inner and outer tooth gears when the rotary shafts (1,11) are in axial alignment, an allowable displacement angle (β w ) being defined as the angle between the axes of the pitch circle cylinders of the inner and outer tooth gears at the maximum of the limited relative transverse displacement of the rotary shafts (1,11), wherein each flank of each tooth of the outer tooth gears (2a,12a) is crowned in the axial direction in such a manner that, at a section along the pitch circle cylinder, the flank follows an outwardly convex curve having its apex at the center of its axial width, the said outwardly convex curve having a radius of curvature that becomes larger as the point on the curve approaches the tooth end; characterised in that: at a position at which the flank is contacted with the inner tooth gear when the angle between the axes of the pitch circle cylinders of the inner and outer tooth gears is the allowable displacement angle (β w ), a tangent line to the outwardly convex curve in a plane containing the axis of the pitch circle cylinder of the outer tooth gear at the allowable displacement angle (β w ) with respect to the direction of the axis of the pitch circle cylinder of the inner tooth gear extends through a point separated from the said apex of the curve by an amount equal to one half of the backlash (G). A flexible coupling as claimed in claim 1, wherein the said outwardly convex curve is an exponential curve expressed by the equation given below: Y = m · X n where Y: crowning curve having an origin (O) at the center of the axial width of the tooth flank, X: axial distance from the origin (O), m: factor, and n: exponential number. A flexible coupling as claimed in claim 2, wherein the origin of the curve falls on an apex of an imaginary reference hexagon (ABCDEF) within an imaginary outer hexagonal (abcdef) in which no backlash is provided at the center of the tooth width and in which the displacement angle of the sides (ab, bc, de, ef) in the axial direction is the allowable displacement angle (β w ), the said sides (ab, bc, de, ef) of the outer hexagon being positioned outside the corresponding sides (AB, CD, DE, EF) of the reference hexagon by an amount equal to 1/2 of the backlash (G), and the said position at which the flank is contacted with the inner tooth gear at the allowable displacement angle (β w ) lies on one of the said sides of the outer hexagon (abcdef).

Inventors: SHIGEURA JUNICHI, SHIGEURA, JUNICHI
Applicants: MITSUBISHI ELECTRIC CORP, MITSUBISHI DENKI KABUSHIKI KAISHA
Application year: 1997
Main classification: F16D3
IPC codes: F16D3