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A novel coupling for two parallel shafts with non-collinear axes has been developed and used in a cycloidal transmission with magnetic gears. Such a coupling has been designed as an alternative to traditional couplings to transmit the rotation from the orbiting gear to the output shaft. The driving shaft transmits a couple consisting of two equal and opposite forces to a central element which, in turn, transmits the same couple, also consisting of two equal and opposite forces to the driven shaft. This novel coupling was successfully used instead of a traditional coupling resulting in, not only a smother operation, but also a more efficient power transmission.

Sometimes it is required to transmit rotary motion from one shaft to another that has a parallel offset and angular misalignment with respect to the first one. Although, misalignment is commonly observed in parallel coupling, such a phenomenon has been scarcely investigated. Some attempts are reported in the literature aiming to understand the effect of parallel offset and angular misalignment on power loss and vibrations [

There are two versions of the coupling, depending on a central element, which is either a cross or a grooved plate. This central element is flanked by two lateral flanges, each keyed to one of the two shafts to be coupled together. On each flange, a number of cantilevered ball bearings are mounted; four in the case of the cross type coupling and two in the case of the grooved plate.

As shown in

cross. No forces are being transmitted by bearings 3, 4, as indicated by exaggerated gaps shown where these bearings would contact the cross. For equilibrium of the cross, a counterclockwise moment of equal magnitude, M, must be transmitted to the cross from flange B by contact between bearings 5, 6 and the horizontal arms of the cross. No forces are being transmitted by bearings 7, 8, as indicated again by gaps where they would contact the cross. A patent covering the two versions of the coupling has been applied for [

As mentioned earlier, cycloidal speed reducers incorporate a coupling to transmit rotation between the orbiting gear and an output shaft. One such reducer has been equipped with a cross type of coupling previously described. This speed reducer has magnetic gears and is one of three that share a patented feature [

Because loads between moving parts are transferred in this coupling by rolling rather than by sliding action, the power loss is very small. Following is an analysis for the estimation of such loss.

Although the analysis is valid for either version of the coupling, for clarity in the argument the cross type of coupling will be assumed. Let M be the moment transmitted by the coupling and L the length of the longer side of the rectangle formed by the centers of the four ball bearings of a lateral flange. Then the normal force, P, being transmitted by the each of the two active bearings of a flange, is given by

P = M L , (1)

where the friction forces between the bearings and the surfaces on which they roll were considered negligible.

It is apparent that, if M is constant, P also remains constant as the shafts rotate. The diagram of _{1} and O_{2} represent the axes of the shafts. Let the eccentricity O 1 O 2 ¯ = e . Now, angle O_{1}AO_{2} is a right angle and remains so as the shafts rotate. This implies that the locus of A is a circle having a diameter e. Assuming that the shafts and cross have a clockwise rotation, as A advances from O_{1} to O_{2}, the cross will execute a 900 rotation and BAC will go from a horizontal to a vertical alignment, and the active bearings will have rolled a distance e. The power loss per revolution consists of the loss due to rotation of the bearings plus the loss due to their rolling along the arms of the cross. The first of these may be estimated by using a friction coefficient for ball bearings [

T 1 = 0.0015 P ⋅ ( d 2 ) , (2)

where d is the shaft diameter for the bearing. Then, to overcome this torque, a friction force T_{1}/(D/2), where D is the outside bearing diameter, is developed at the contact between the bearing and the cross surface. The rolling friction coefficient is assumed to be in the range 0.005 to 0.01 [

F = ( 0.0015 d D + 0.01 ) ⋅ P (3)

As explained before, each active bearing rolls a distance e each quarter of a revolution. Thus, the sum of the distances rolled by the four active bearings (two per flange) during one revolution, is 4 × 4e. Multiplying this displacement by the friction force given by Equation (1) yields the energy loss per revolution. Then, dividing by the transmitted energy per revolution, 2πPL, and multiplying by 100%, one obtains the percent power loss:

P . L . = 8 e π L ( 0.0015 d D + 0.01 ) × 100 % (4)

For the speed reducer and coupling mentioned in the previous paragraph:

e = 3 mm, L = 84 mm, d = 7 mm, D = 19 mm, resulting in a power loss, P.L. = 0.096% or, equivalently, an efficiency of 99.9%.

This is indeed an outstanding finding considering that, both misaligned shafts and parallel non-collinear shafts induce high radial forces resulting in less energy transferred from one shaft to the other one [

A novel coupling for two parallel shafts with non-collinear axes has been described. The driving shaft transmits a couple consisting of two equal and opposite forces to a central element which, in turn, transmits the same couple, also consisting of two equal and opposite forces to the driven shaft. The magnitudes of the forces only depend on the magnitude of the transmitted moment. There is no sliding between moving parts, so transmission of forces occurs only at rolling contacts with minimal power loss. This type of coupling was tried in a cycloidal transmission with magnetic gears, in substitution of a traditional coupling, to transmit the rotation from the orbiting gear to the output shaft. After the substitution, a smother operation was observed. Also, it is important to point out that radial forces induced by non-collinear shafts were reduced with the coupling proposed in this work, so that the efficiency was noticeably increased.

The financial support from DGAPA-UNAM through grant IT101117 is highly acknowledged. Authors thank to Mr. David Santoyo García and Luis E. Calderon for the technical support provided.

The authors declare no conflicts of interest regarding the publication of this paper.

Chicurel, R. and Ascanio, G. (2019) Coupling for Parallel Non-Collinear Shafts. Modern Mechanical Engineering, 9, 57-63. https://doi.org/10.4236/mme.2019.93006