Claims:We claim:

1. An arrangement of splined shaft and gear configured with tapered splines for reducing stresses, wherein the splined portion has a length (x) and the spline width reduces at a predetermined rate from the shaft end (a) towards the spline end (b) resulting in a taper (a-b).

2. Arrangement as claimed in claim 1, wherein the taper (y) is a function of the spline geometry (y/x).

3. Arrangement as claimed in claim 2, wherein the stress reduction obtained represented by the following equation:

% Stress Reduction = - 779325 (y/x)2 + 8557.1 (y/x) – 0.142.

4. Arrangement as claimed in claim 1, wherein the spline is configured on one involute face of the spline.

5. Arrangement as claimed in claim 1, wherein the spline is configured on both involute faces of the spline.

6. Arrangement as claimed in anyone of the claim 1, wherein the splined shaft is a solid shaft.

7. Arrangement as claimed in anyone of the claim 1, wherein the splined shaft is a hollow shaft.

8. Arrangement as claimed in anyone of the claim 1, wherein the spline is a shaft spline or external spline.

9. Arrangement as claimed in anyone of the claim 1, wherein the spline is a gear spline or internal spline.

10. Arrangement as claimed in anyone of the claim 1, wherein the spline taper is on one of the splines for reducing the stresses.

11. Arrangement as claimed in anyone of the claim 1, wherein the spline taper is on both splines for reducing the stresses.

12. Arrangement as claimed in anyone of the claim 1, wherein the arrangement is made of metallic, non-metallic or any other type of material processed with or without a heat treatment.

Dated: this day of 26th November, 2015. SANJAY KESHARWANI
APPLICANT’S PATENT AGENT , Description:FIELD OF INVENTION

The present invention relates to drive shafts in any power transmission system. In particular, the present invention relates to splined shafts which mesh with mating gear to transmit power to it. More particularly, the present invention relates to reducing the stresses at the spline end to avoid stress concentration in splined shafts configured with tapered splines.

BACKGROUND OF THE INVENTION

Splines are ridges or teeth on a drive shaft that mesh with a mating gear for transferring torque to it, while maintaining the angular relationship between the splined shaft and the mating gear and enabling both to rotate together at a ratio of 1:1. Generally, splined shafts are used for the applications, such as coupling shafts for transmitting relatively heavy torques without slippage; transmitting power to floating or permanently fixed gears, pulleys and other rotating members; and coupling parts requiring frequent removal for indexing or change of angular position.

In many of the conventional splined shaft and mating gear, it was observed that the spline end experienced very high stresses during torsional loading. So, for reducing such stresses, the following conventional methods are predominantly used for splined shafts improving their performance:

• Increase the diameter of shaft,
• Increase the surface hardness of splines, and
• Select high strength material.

However, the ductility of shaft material needs to be compromised for increasing the surface hardness, which is more prone to fatigue failure during operational life of splined shafts. The yield strength of such shaft material needs to be over 1500 MPa, which is not readily available raw materials in the market and also quite expensive.

PRIOR ART

US 20100303537 A1 discloses a connection between a shaft and a coupling that preferably involves involute shaped splines is designed to reduce stress from torque applied to the shaft by a drive motor. To avoid stress concentration at the mouth of the coupling on startup, the shaft splines are made to taper from the shaft end down to the spline end. As a result, the initial contact with the coupling splines occurs within the coupling and removed from its mouth. The shaft is allowed to elastically twist in response to the applied torque as the contact area increases with shaft twisting and the contact line moves toward the mouth of the coupling. Stress concentration that formerly occurred at the coupling mouth is alleviated as some shaft elastic twist occurs without adding stress to the shaft splines until coupling contact is made.

However, this US patent documents relates to the issue of splined shafts, without touching upon the issue of stress concentration at the spline end, as proposed in accordance with the present invention.

DISADVANTAGES WITH THE PRIOR ART

The limitation with the existing solutions to reduce spline end stresses discussed above are mainly by using a high-strength material, whereby shaft material strength requirements for high-torque applications exceeding about 1500 MPa are suitably met. However, as indicated above, such high-strength materials are not readily available off-the-shelves and are thus expensive. Therefore, this material selection limits the use of readily available raw materials in the market.

In addition, for obtaining such high-strength levels, the ductility has to be compromised. The selected raw materials are therefore more brittle and prone to fatigue failure in the spline end. Even by increasing the diameter of the splined shaft to reduce the spline end stresses, leads to substantial weight addition and cost is also increased, thereby impacting the cost of end product.

DESCRIPTION OF THE PRESENT INVENTION

Therefore, for avoiding stress-concentration or for reducing excessive stresses developed at the spline end during torsional loading of such splined shafts; it is proposed in accordance with the present invention to make the shaft splines tapering from the shaft end to the spline end. Therefore, the improved splined shaft has a gradual contact dis-engagement with the mating gear, which significantly reduces the stresses at the spline end.

This invention is not only limited to use in the tractor rear axle, but is also applicable to any power transmission shafts having splines. Therefore, it can be easily extended to any automobile and off-highway industrial use. Moreover, this stress reduction technique can be implemented for both internal and external tooth splines.

OBJECTS OF THE INVENTION

Some of the objects of the present invention - satisfied by at least one embodiment of the present invention - are as follows:

The object of this invention is to reduce the spline end stresses in splined shaft by providing slight taper at the spline end.

An object of the present invention is to make the contact dis-engagement with the mating spline gradual for reducing the stresses at the spline end.

Another object of the present invention is to reduce stresses at the spline end of a splined shaft for power transmission.

Still another object of the present invention is to provide a gradual contact disengagement of the splined shaft with the mating gear to reduce stresses.

Yet another object of the present invention is to provide a cost-effective solution for reducing stresses developed during torque loading of splined shafts.

These and other objects and advantages of the present invention will become more apparent from the following description when read with the accompanying figures of drawing, which are, however, not intended to limit the scope of the present invention in any way.

SUMMARY OF THE INVENTION

In accordance with the present invention, there is provided an arrangement of splined shaft and gear configured with tapered splines for reducing stresses, wherein the splined portion has a length (x) and the spline width reduces at a predetermined rate from the shaft end (a) towards the spline end (b) resulting in a taper (a-b).

Typically, the taper (y) is a function of the spline geometry (y/x).

Typically, the stress reduction obtained represented by the following equation:

% Stress Reduction = - 779325 (y/x)2 + 8557.1 (y/x) – 0.142.

Typically, the spline is configured on one involute face of the spline.

Typically, the spline is configured on both involute faces of the spline.

Typically, the shaft is a solid splined shaft.

Typically, the shaft is a hollow splined shaft.

Typically, the spline is a shaft spline or external spline.

Typically, the spline is a gear spline or internal spline.

Typically, the spline taper is on one of the splines for reducing the stresses.

Typically, the spline taper is on both splines for reducing the stresses.

Typically, the arrangement is made of metallic, non-metallic or any other type of material processed with or without a heat treatment.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS

The present invention will be briefly described with reference to the accompanying drawings, which include:

Figure 1 shows a perspective view of the conventional splined end of a splined shaft.

Figure 2 shows a perspective view of the conventional splined shaft and mating gear arrangement.

Figure 3 shows a perspective view of the conventional splined shaft and mating gear arrangement.

Figure 4 shows the detailed enlarged view of the splined end of the conventional splined shaft and mating gear arrangement shown in Figure 3.

Figure 5 shows a front view of the splined shaft and gear arrangement configured in accordance with the present invention.

Figure 6 shows a perspective enlarged view of the splines in accordance with the present invention in the arrangement of the splined rear-axle shaft and bull gear configured with a tapered spline for reducing stress concentration.

Figure 7 shows a graphical representation of the relationship between the percentage reduction in stress and the spline geometry.

DETAILED DESCRIPTION OF THE ACCOMPANYING DRAWINGS

In the following, different embodiments of the present invention will be described in more details with reference to the accompanying drawings without limiting the scope and ambit of the present invention in any way.

Figure 1 shows a perspective view of the conventional splined end of a splined shaft 10. The splines extend from the shaft end 12 to spline end 14.

Figure 2 shows a perspective view of the conventional arrangement of the splined rear-axle shaft 10 and mating bull gear 20. The splined axle shaft 10 is fixed on the wheel rim by means of a plurality of bolts (not shown) tightened through the holes 18 (six holes here) provided in the flange 22. The external splines 16 provided on the rear-axle shaft 10 mesh with the internal gear teeth on the bull gear 20 for power or torque transmission. Load ‘P’ tangentially acts on the bull gear 20 to induce the torque in the splined shaft 10. Normally, the spline end 14 experiences very high stresses during torsional loading. The only known solutions to reducing these high stresses during torsional loading are:

a) Increasing the diameter of the shaft, thereby increasing the weight of the overall power transmission system, and/or

b) Increasing the surface hardness of the splined portion of the shaft, and/or

c) Selecting a high strength material.

The ductility of the shaft material is to be compromised while increasing the surface hardness. This makes shaft to be more prone to fatigue failure during service life thereof. Moreover, using high strength materials, e.g. which have yield strength over 1500 MPa are not readily available in the market and thus they make the shaft substantially costlier.

Figure 3 shows a perspective view of the conventional arrangement of the rear-axle splined shaft 10 and mating bull gear 20 as a reference model, wherein high stress concentrations were noticed at the spline end 14 of the rear-axle splined shaft 10.

Figure 4 shows the detailed enlarged view of the spline end 14 of the conventional splined rear-axle shaft 10 and mating gear 20 shown in Figure 3.
The colored contour plot were drawn by using for von Mises Stress to observe stress concentration in different regions of the splined shaft shown in Figure 2. The maximum stress of 2285 MPa and minimum stress of 2044 MPa were observed. However, at splined end 14, the stress were of the order of about 1895 MPa (shown in Red color), which were substantially high and required one or more of the steps a) to c) as mentioned in respect of Figure 3.

Figure 5 shows a front view of the arrangement of improved splined rear-axle shaft 110 and bull gear 120 in accordance with the present invention, in which the splines 116 having contact length ‘x’ are configured tapering from shaft end 112 to spline end 114.

Figure 6 shows a perspective enlarged view of the splines 116 in accordance with the present invention in the arrangement of the splined rear-axle shaft and bull gear and configured with a tapered spline for reducing stress concentration accordance with the present invention. The contact face or spline dimension at shaft end 112 has a width ‘a’ (mm) and at the spline end 114, it has a width ‘b’ (mm). Therefore, taper ‘y’ is equal to ‘a – b’, and the spline geometry (y/x = 0.003) has a very small taper, which gives up to 18% stress reduction at the spline end 114. The stress analysis was also conducted for different trials to predict the empirical relationship between the conventional spline and tapered spline configured in accordance with the present invention as described above. This relationship is as under:

% Stress Reduction = - 779325 (y/x)2 + 8557.1 (y/x) – 0.142

The results are subsequently given in Table - 1. During this analysis the loads and boundary conditions remain the same as reference model

Figure 7 shows a graphical representation of the relationship between the percentage reduction in stress and the spline geometry. It can be seen from this graph that the percentage reduction in stress is linearly proportional to the Spline geometry (y/x) till y/x reaches a value of about 0.003. Thereafter, the effect of y/x is negligible on the stress reduction.

TABLE - 1
Trial No. y=a-b (mm) x (mm) y/x Maximum Stress at Spline end (MPa) Maximum Stress for Reference Model (MPa) Reduction in Stress (%)
0* 0 41 0 1895 1895 0
1 0.015 41 0.00037 1839 1895 2.96
2 0.03 41 0.00073 1792 1895 5.44
3 0.045 41 0.00110 1742 1895 8.07
4 0.06 41 0.00146 1692 1895 10.70
5 0.082 41 0.00200 1624 1895 14.30
6 0.123 41 0.00300 1547 1895 18.37
7 0.164 41 0.00400 1540 1895 18.73
8 0.205 41 0.00500 1540 1895 18.75
9 0.246 41 0.00600 1539 1895 18.78
10 0.2868 41 0.00700 1539 1895 18.80
11 0.328 41 0.00800 1538 1895 18.83
12 0.369 41 0.00900 1538 1895 18.84
13 0.411 41 0.01002 1538 1895 18.84
14 0.444 41 0.01083 1538 1895 18.84
15 0.453 41 0.01105 1538 1895 18.84
16 0.492 41 0.01200 1538 1895 18.84
* Reference Model

TECHNICAL ADVANTAGES AND ECONOMIC SIGNIFICANCE

The arrangement of the splined rear-axle shaft and bull gear configured with a tapered spline in accordance with the present invention for reducing stress concentration has the following advantages:

• Very small taper at spline end facilitates up to 18% stress reduction.

• Tapered spline can be implemented in any power transmission splined shafts.

• Invention can be applied not only to tractor rear-axle, but also to any automobile and off-highway industries.

• Stress reduction technique of the invention can be incorporated for both internal and external tooth splines.

• Splines are geometrically shaped in involute profiles.

• Both shaft spline and external splines can be provided.

• Gear spline or any internal spline for reducing stresses.

• Taper can be provided on both splines for reduction stresses.

• Taper can be provided both on internal as well as external splines.

• Taper can be provided on single involute face of spline or on both involute faces of spline.

• Splined can be provided on solid as well as hollow shafts.

• Tapered splines are applicable for metallic, non-metallic or any other type of material with or without heat treatment.

Throughout this specification the word “comprise”, or variations such as “comprises” or “comprising”, shall be understood to implies including a described element, integer or method step, or group of elements, integers or method steps, however, does not imply excluding any other element, integer or step, or group of elements, integers or method steps.

The use of the expression “a”, “at least” or “at least one” shall imply using one or more elements or ingredients or quantities, as used in the embodiment of the disclosure in order to achieve one or more of the intended objects or results of the present invention.

The exemplary embodiments described in this specification are intended merely to provide an understanding of various manners in which this embodiment may be used and to further enable the skilled person in the relevant art to practice this invention.

Although, only the preferred embodiments have been described herein, the skilled person in the art would readily recognize to apply these embodiments with any modification possible within the spirit and scope of the present invention as described in this specification.

Therefore, innumerable changes, variations, modifications, alterations may be made and/or integrations in terms of materials and method used may be devised to configure, manufacture and assemble various constituents, components, subassemblies and assemblies according to their size, shapes, orientations and interrelationships.

The description provided herein is purely by way of example and illustration. The various features and advantageous details are explained with reference to this non-limiting embodiment in the above description in accordance with the present invention. The descriptions of well-known components and manufacturing and processing techniques are consciously omitted in this specification, so as not to unnecessarily obscure the specification.

While considerable emphasis has been placed on the specific features of the preferred embodiment described here, it will be appreciated that many additional features can be added and that many changes can be made in the preferred embodiments without departing from the principles of the invention. These and other changes in the preferred embodiment of the invention will be apparent to those skilled in the art from the disclosure herein, whereby it is to be distinctly understood that the foregoing descriptive matter is to be interpreted merely as illustrative of the invention and not as a limitation.