WO2010052574A1

WO2010052574A1 - Modification to the novolute profile for power gears, and method to calculate the proposed profiles and their optimization

Info

Publication number: WO2010052574A1
Application number: PCT/IB2009/007487
Authority: WO
Inventors: Alejandro Pardo
Original assignee: Alejandro Pardo
Priority date: 2008-11-10
Filing date: 2009-11-10
Publication date: 2010-05-14
Also published as: CO6050063A1

Abstract

The invention is a transmission power system that contains a pair of mating screws, each screw having an upper axial end and a lower axial end, wherein the axial thread profile of the first screw is defined: on its upper edge, by a counternovolute located inside of the pitch diameter of the first screw, and a novolute contiguously located outside of said pitch diameter; and, on its lower edge, another counternovolute, located inside of the pitch diameter of the first screw, and another novolute contiguously located outside of said pitch diameter. All the contacting surfaces are defined as to produce a path of contact between the matting members which is located close to the line of centers in the proximity of the pitch circles, and then evolves when farther from the pitch point, going farther from the line of centers, into a more tangential position.

Description

MODIFICATION TO THE NOVOLUTE PROFILE FOR POWER

GEARS, AND METHOD TO CALCULATE THE PROPOSED

PROFILES AND THEIR OPTIMIZATION

FIELD OF THE INVENTION

The present invention belongs to the field of mechanics, more specifically to the toothed wheels used to transmit power and movement.

The power gears must satisfy two main conditions: they must have enough load carrying capacity for contact and for bending for the use they are intended for.

PREVIOUS ART

To evaluate the contact capacity of conventional gears, the Hertz theory about the contact of two parallel cylinder is applied. The curvature radii are measured in a plane perpendicular to the geometrical axis of the cylinders and of the path of contact, which is located on one generatrix of each cylinder.

To evaluate them for bending, the cantilever beam formula is used. The capacity is proportional to the length, to the square of the thickness of the base, and inversely proportional to the height.

In conventional gear design, both factor are evaluated, generally are very different from one another, and the capacity of the gear is specified as the smaller one. Very frequently there is a waste of material and size, as the factor with the excess capacity can not be used to its full potential, but neither is it possible to decrease the size of the part reducing the excess capacity. It is said that the design is not balanced when its two capacities are different.

DESCRIPTION OF THE INVENTION The present invention is an improvement of the Colombian patent application No. 02-076.759 filed on 29 August, 2002. That patent is priority to the International Application PCT/IB2003/03832, published as WO2004/020135, and entitled "NON INVOLUTE PROFILE FOR POWER GEARS".

DESCRPTION OF THE IMPROVED PROFILE

The following description is about novolute gears with parallel shafts, for simplicity, but applies in similar manner for those with shafts located in any angle.

The shape of the generating profile of a novolute gear, determines the shape and other features of the contact path, within them its load capacity to bending and to contact. For instance, the use of short profiles close to the pitch point, either curved or straight, concave or convex, generate contact paths with very long novolutes, extending from the pitch point until theirs end, in locations very far of the line of centers. This path give very wide contact angles, measured in the rotation plane, as is indicated by the first patent. This is one of the strength of the novolute geometry, as it makes a long portion of the thread working all the time, and consequently the bending capacity is increased.

That path of contact of those novolutes has the limiting factor in respect to contact capacity, as the curvatures of the contact path change a lot, being very small close to the pith point, and grow while getting away from it. Also the direction of them changes constantly, keeping perpendicular to the path of contact. As the radiuses of curvature vary continuously, their contact load carrying capacity varies also in every point.

The external points have better load capacity, because of two reasons: 1) The curvatures of the novolutes grow while they are farther from the pitch point; and,

2) The curvatures in tangential planes of the two parts, generator and novolute, are much bigger than the curvatures of the same parts, measured in the radial direction. Long concave profiles with pronounced curvatures, generate paths of contact going from the pitch point to the external edge of the novolute, ending close to the line of centers. Those contact paths make contact on very small angles measured on the plane of rotation, limiting their bending load capacity. Those gears have very good contact load capacity, given the fact that the contact path is located in the radial direction, and the curvatures which define their contact load capacity, being perpendicular to the path of contact, go in an almost tangential direction. In the pitch point and in the nearby zone, the contact load capacity is extraordinary, as there the surfaces are very close to a straight line on top of another one, as the tangents to both surfaces coincide.

The firstly describe profiles have very good bending capacity from the generous length of the cantilever beam supporting the load, but they have a limited contact capacity, limited by the capacity of the points close to the pitch point. In the second type of contact path described, the situation is opposite: has great contact capacity, but very limited for bending, as the working beam is short, and has all of the contact path concentrated there, not distributed along the beam. In both instances, the design is not balanced, and thus the material is not used in optimum conditions.

A possible solution is to use only one fraction of the novolute surface, away from the pitch diameter. There, good contact and bending capacities are obtained, even the length of the contact path seen in the plane of rotation, is only, in the best of cases close to half of the interference zone between the two bodies of the two parts of the engagement. Additionally it happens that, while getting away from the pitch circle, the pressure angle tends to grow, and this might come to be a severe limiting factor in some cases.

Another possible solution is to build two contact zones making double novolute engagements, but without contact in the zone nearby the line of centers when seen on the plane of rotation, but the lack of contact in the intermediate zone make it necessary that conjugate action be kept with axial overlap, which leads to require engagements too long at least, in some cases.

This factor will consume the advantage obtained in size by the good contact load capacity given by the novolute in the zone where it is being used.

The most efficient solution is to obtain a path of contact which gives unity to the advantages of the two described paths: in the pitch point zone, must be approximately radial in order to give it good contact capacity. While getting away from there, going to the edge of the novolute, it should become torn smoothly in order to give more length to the cantilever beam that supports the bending load. Such contact path has a very constant contact load capacity, and thus it is optimum: the contact load capacity of an engagement is given by the least capable point. Such path is also the most capable for bending, because it is the longest that can be accommodated within the bodies of the two parts of the engagement. Al of the above can by built within a double novolute engagement. The thickness of the thread or cantilever beam can be selected following the contact load capacity obtained, in order to get a balanced design. The use of the smallest thickness minimum required, will optimize the face width of the gear, and thus, its size.

The present in invention then is the optimum shape of the modified novolute, generated from an optimum contact path, to get the most capable engagements and the smallest ones. The description above gives the basic concepts which influence the definition of an optimum contact path.

OTHER DISPOSITIONS OF THE PARTS

The same calculation processes already described for parallel shaft engagements, can be used for other dispositions of the engagements. One of them is the placement of two gears with perpendicular shafts or in other angle between them, another is the construction of engagements with gears still with parallel shafts, but internals where one of them has the threads worked on an inner part of a ring where the other threaded part is lodged. Another is the construction of engagements with more than two parts, transmitting motion and force in cascade. A special arrangement of this is the planetary engagement.

In the design of engagements in cascade, firstly one pair of gears is calculated, with its double novolutes and generating profiles . Then, the third member of the engagement is calculated, engaged with the one that corresponds of the other two. In this stage, novolutes and generating profile are produced in the new part, without modifying the other two. With the three designed, its load capacity is evaluated, for bending and contact for each step of engagement , and modifications are carried in order to improve the global capacity of the set, until optimum values are obtained. The capacity of the set will be limited by the capacity of the weakest pair within the set, for either one of the design factors. The most important variation produced with the improvements here published, is the se of helix angles similar to those used in common practice for helical involute gears, where novolute designs have been design with extraordinary load capacity.

As the novolute is a geometry has its origin in the used of engaged screws, it is a valuable achievement the fact that novolutes can be applied in such field, where so many gears are produced and used and the for load capacity is so earnestly searched for.

DESCRIPTION OF THE POINT BY POINT METHOD

Just as it is described in the International Patent Application PCT/IB2003/03832, published with the number WO/2004/020135 and entitled '¹NON INVOLUTE PROFILE FOR POWER GEARS." A modified novolute is generated when the novolute surface is defined by a series of simple novolutes with diameters varying in succession in abundant and small increments, growing towards the exterior from the pith circle. The first novolute generated from the pitch circle of the generated part, defines a novolute surface. Is defined by a generating helical located on the pitch diameter of the generator part. If the generator part has another helical concentric with the first with a slightly smaller diameter, it will modify the first surface in more, less or nothing, depending on the position along the shaft. If it is located in far away it will not produce any effect. While getting closer in the appropriate direction, it will modify the first surface beginning in the external edge and then more towards the inner portion getting closer to the line of centers, while displacing axially. The modification is produced only along the generating helical, and within the external edge and the line of centers.

There are several ways to define how to do that process for successive points.

WITH DEFINED INCREMENTS OF PROFILE AND NOVOLUTE RADIUS

Firstly, the increments of radiuses for novolute and generating profile which will be used in the generation. The generator point will have defined its position on the plane of by those two values. The next step is to place the generating helical on the point, following some of the following criteria:

A) Generation taking away the minimum amount of material when modifying the novolute. B) Generation taking away a determined amount of material.

The generating helical is placed on the given point, in such a way as for to make it take the given amount of material. Here again, several options exist:

1) Taking a constant amount on every point.

2) Taking away a variable amount in order to produce diverse effects on the profiles , in example obtaining a concave generator profile, in those designs where this would produce a concave generator surface, and because of it an improvement in contact load capacity is obtained.

WITH CONTACT PATH DEFINED Again, beginning with the generation of a simple novolute from the pitch point of a gear, the generating process of a modified novolute is continued with generating helical with radiuses each time smaller than the former, which go generating the modified point by point. As the following contact point can be chosen by the designer if it is within the intersection zone of the generating helical and the line of centers.

It is the same as saying that can chose the position of the contact path within those limits. At the beginning of contact, and being the novolute surface modified, a portion of the contact path has been defined, going from the point where the first simple novolute begins, until the beginning of the second one. If the designer chooses the place where such contact should take place, defining its coordinates in the transversal plane, then the point of the generator profile is defined from the point of the path. With the two specified coordinates for the path in the transversal plane, the third coordinate is found by placing the generating helical in contact with the novolute surface. With that coordinate, the point of the generating profile can be found in the transversal and axial planes. Successive repetitions of the same procedure complete the generation of modified novolute surfaces and the generator profile which make contact over the path of contact initially defined. This process serves always that the point of the path defined by the designer remains within the zone of the former generating helical. If the point is outside of such zone, the generation should continue with the point by point process described above which will give the widest possible path of contact. So, the use of more than one generating process within a gear is not only possible, but very helpful while optimizing designs.

Once a design has been done, its load contact capacity can be evaluated along the path of contact. Its bending capacity can also be evaluated. With that information it is possible to optimize its capacity correcting the path of contact in order to improve the capacity of the weakest portions. In like a manner, the bending capacity can be made more suitable in order to get the smallest possible parts keeping the needed load capacity. The coordinated modification of capacities, contact and bending allows the balancing of the design. This statement applies for all of the design processes here described.

DESCRIPTION OF THE FIGURES

FIGURE 1 : Is a transversal view of a double novolute engagement following the present invention.

The path of contact (1) can be seen, which simultaneously comprises the widest possible angle on the transversal plane, and has, close to the pitch point zone, portions above and below the pitch point where the direction of the contact path very vertical, aligned with the line of centers. On the pitch diameters the path of contact becomes very wide, showing a very comfortable contact because the curvatures of the surfaces are very wide.

FIGURE 2: Containing the transversal view of a novolute engagement designed following the first patent from the same inventor, with similar general dimensions to those of the Figure 1, but different from that in the way the path of contact (1) is close to the pitch point. In Figure 2 the path almost coincides with the pitch circles of each part. FIGURE 3: Contains the tangential cut of the engagements of Figures 1 and 2.

Only one drawing is included, because the sections for both designs are very similar. The drawing shows the curvature radiuses (15 and 16) of both threads in contact measured on the plane of section, it is the one of the drawing. There it is shown, for comparison, the dimension of the pinion pitch radius, with the line number 17. It can be easily seen that the radiuses of curvature in this plane are several times bigger than the pitch radius of the pinion. These big radiuses produce a very wide contact band as the Figure 1 shows. As the gear of Figure 1 has the path of contact almost normal to the one shown in Figure 3, these values of curvature are the ones which should be used when calculating the contact load capacity. As the gear of Figure 2 has the path of contact along the plane of Figure 3, in the proximity of the pitch point, the radiuses that should be used when evaluating its contact capacity are those perpendicular to the path, located in the transversal view, and shown by Figure 4.

FIGURE 4: Contains the transversal cut of the gear of Figure 2.

Shows the curvature radiuses (18 and 19) of the two surfaces in the contact point close to the pitch point. Even with the advantage given a concave profile in the wheel (18) making the contact easier, this gear has very low contact load capacity. The difference in magnitude in the two radiuses of curvature is a clear symptom showing that the path of contact is not in the plane of section. Also it is easy to see that the curvature radiuses are several times smaller than the pitch radius of the pinion, and thus, much smaller than those of the gear following the present invention shown in Figure 3.

FIGURE 5: Contains the transversal section of the engagement of Figure 1, in the plane containing the zone where the path of contact crosses the pitch point the curvature radiuses (18 and 19) of the two contacting surfaces are, besides very small, almost coincident: in the drawing it is hard to differentiate them. This shows that the direction of the contact path almost coincides with the direction of the contact path, and consequently the curvatures defining the contact capacity are those of the plane of Figure 3 and other close to it, for other nearby points of the contact path.

Claims

1. A transmission power system that contains a pair of mating screws, each screw having an upper axial end and a lower axial end, wherein:

i) the axial thread profile of the first screw is defined:

on its upper edge, by a counternovolute located inside of the pitch diameter of the first screw, and a novolute contiguously located outside of said pitch diameter; and,

on its lower edge, another counternovolute, located inside of the pitch diameter of the first screw, and another novolute contiguously located outside of said pitch diameter.

All the contacting surfaces are defined as to produce a path of contact between the matting members which is located close to the line of centers in the proximity of the pitch circles, and then evolves when farther from the pitch point, going farther from the line of centers , into a more tangential position.

ii) the axial thread profile of the second screw is defined:

on its upper edge, by a counternovolute located inside of the pitch diameter of the second screw, and a novolute contiguously located outside of said pitch diameter; and,

on its lower edge, another counternovolute, located inside of the pitch diameter of the second screw, and another novolute contiguously located outside of said pitch diameter.

All the contacting surfaces are defined as to produce a path of contact between the matting members which is located close to the line of centers in the proximity of the pitch circles, and evolves smoothly when farther from the pitch point, going farther from the line of centers , into a more tangential position.

2. A process to design the shapes of the no volute and counterno volute consisting of:

build a novolute surface using the pitch point as generator;

- select a subsequent point of the path near by, such that the coordinates of such point on the plane of rotation, are defined by variable increments in radius and/or angle in the path of contact;

The coordinate of the subsequent generating points in the direction of the axis of the engagement, is defined as that point of the novolute surface with the said coordinates in the plane of rotation;

With this new point serving as generator, the novolute surface already built is modified towards the exterior edge of the novolute; and

carry on this process with small increments, until the shape of a novolute is obtained in one part, and the corresponding counternovolute is obtained in the other part.

3. The process of Claim 2, wherein the procedure described in Claim 2 applies when the generating and the generated parts are inverted.

4. The process to design the shapes of the novolute and counternovolute surfaces of Claim 2, wherein the coordinate of the subsequent generating point in the direction of the axis of the engagement, is defined as that point of the novolute surface with the said coordinates in the plane of rotation, further displaced within the novolute surface by a given amount.

5. The process to design the shapes of the novolute and counternovolute surfaces of Claim 2, wherein the coordinates of subsequent points on the plane of rotation, are defined by variable increments either in radius and angle or in radius or angle.

6. The process to design the shapes of the novolute and counternovolute surfaces of Claim 2, wherein the path of contact in the rotation plane is first defined, then both profiles are built defining the increments of generator angle and radius, defining the contact path.