WO2011154921A2

WO2011154921A2 - Discretely variable diameter planetary gear set

Info

Publication number: WO2011154921A2
Application number: PCT/IB2011/052534
Authority: WO
Inventors: Nimrod Eitan; Jonathan Brentnall
Original assignee: Iqwind Ltd.
Priority date: 2010-06-10
Filing date: 2011-06-10
Publication date: 2011-12-15
Also published as: WO2011154921A3

Abstract

A discretely variable diameter gear set having a planetary configuration. The gear set may vary a diameter of a gearwheel by whole numbers of gear teeth in response to changes in input speed of a rotor shaft. Typically, the diameter may be shifted in increments of one gear tooth at a time. A variable effective number of teeth in the sun gear of the gear set may be achieved. Four embodiments of the planetary gear set are outlined: (i) a gear set with a ring and two idler/pinion sets around the sun gear (ii) a gear set with a ring and three idler/pinion sets around the sun gear, (iii) a gear set with a secondary sun (and no ring) and two idler/pinion sets around the sun gear and (iv) a gear set with a secondary sun (and no ring) and three idler/pinion sets around the sun gear.

Description

APPLICATION FOR PATENT

Inventor(s): Nimrod Eitan; Jonathan Brentnall

Title: Discretely Variable Diameter Planetary Gear Set

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to apparatuses and methods for variable diameter gear sets and, more particularly to discretely variable diameter gear sets having a planetary configuration.

A transmission transfers rotational power between an input shaft and an output shaft, and defines a transmission ratio between a rate of rotation at the input shaft and the corresponding rate of rotation at the output shaft. This ratio may be less than one where output rotation is slower, but higher torque, than the input, may be equal to one where the input and output rotate at the same rate, or may be greater than one where the output rotates faster, but with lower torque, than the input. The transmission may be bidirectional, i.e., allowing an input in either a clockwise or an anticlockwise rotational direction, and may be reversible, i.e., where the "output" may be rotated to transfer power to the "input".

In many circumstances, it is desirable or necessary to provide a variable transmission, i.e., where the transmission ratio can be changed. Examples include vehicles, where a variable output speed is needed while maintaining the power source operating as near as possible to its optimal speed for the required power output, and power generators, where it may be preferably to maintain a constant output speed despite variations in the power of a source of mechanical power being harnessed.

In transmission systems based on gearwheels (either in direct engagement or via chain linkages), the transmission ratio between two gearwheels is defined by the ratio between the number of gear teeth in each. Thus, if an input shaft has a gearwheel with ni=60 teeth and drives, directly or via a chain, an output shaft gear with n₂=30 teeth, the transmission ratio TR will be ni/n₂ = 2, and the output shaft will turn 2 revolutions for each revolution of the input shaft. In order to vary the transmission ratio, a set of gearwheels with differing numbers of teeth are typically provided. However, switching engagement from one gearwheel to another is problematic. There is typically a momentary loss of driving relation between the input and the output, as in a traditional "manual" automobile transmission, and/or the shift may result in a sudden jolt or reduced reliability, such as in a derailer gear system common in bicycles. None of the available options for switching engagement between multiple gearwheels provides for a reliable and smooth transition between transmission ratios without momentary loss of driving engagement.

As an alternative to switching between gears, various transmissions have been proposed which employ variable diameter pulleys or conical drive elements with corresponding belts to achieve variable transmission ratios. However, gradual variations of diameter can typically only be achieved in toothless friction-based systems. Reliance on frictional transfer of torque introduces its own set of problems, including loss of torque through slippage, and mechanical wear and unreliability due to high tension required to maintain frictional engagement.

Various attempts have been made to design a gearwheel that would provide a variable diameter and variable effective number of teeth. For bicycles, for example, many designs have been proposed in which segments of a gearwheel can be moved radially outwards so that the segments approximate to rounded corners of a toothed polygon with variable spaces there between. These designs can engage a chain and have a variable effective number of teeth where the spaces correspond to "missing" teeth. Examples of such designs may be found in US Patent Nos. 2,782,649 and 4,634,406, and in PCT Patent Application Publication No. WO 83/02925. This approach generates a non-circular effective gear that has missing teeth between the gearwheel segments. As a result, it is incompatible with direct engagement between gearwheels. Even when used with a chain or belt, the rotating polygonal shape may be expected to cause instability and vibration if used at significant speeds, and does not provide uniform power transfer during rotation.

A device similar to the above examples, but implemented as a toothless continuously variable transmission, is disclosed in US 4,655,730. In this example, radial motion of segments of a ring is controlled by relative rotation of two slotted discs, one with radial slots and the other with a spiral slot.

A further variant of the aforementioned approach is presented in German Patent Application Publication No. DE 10016698 Al. In this case, sprocket teeth are provided as part of s flexible chain that is wrapped around a structure of radially displaceable segments. The chain is anchored to one of the displaceable segments and a variable excess length at the other end of the chain is spring-biased to a recoiled storage state within an inner volume of the device. This structure would appear to be an improvement over the aforementioned documents in the sense that sprocket teeth are provided spanning the gaps between the radially displaceable segments. However, since there is still a gap between the teeth where the chain enters the inner storage volume, and since the proposed structure still fails to maintain a circular profile, it still shares most if not all of the aforementioned disadvantages of the radially displaceable segment designs: it cannot be used in direct engagement with a gearwheel and does not provide uniform power transfer during rotation. There is therefore a need for a variable diameter gear device which would provide a variable effective number of teeth while maintaining circular form and symmetry and allowing continuous direct engagement with another gearwheel.

Applicant has filed pending U.S. patent applications and other patent applications for gear sets that that will improve the reliability and energy efficiency of wind turbines while providing wind turbines at the exact conditions demanded by electric grids and at reasonable cost. These gear sets are also useful in other settings. Reference is made to pending U.S. published patent application no. 12/204,027 by Applicant Nimrod Eitan published on May 7, 2009 under Publication No. US2009- 0118043- Al, which Applicant hereby incorporates by reference in its entirety. This application describes gears or gear sets having a discretely variable diameter changer but which are arranged in a co-axial configuration.

There is a compelling need to have a discretely variable diameter gear set that is compact. In the context of wind turbines, there is a compelling need to have a gear set that will improve the reliability and energy efficiency of wind turbines in a manner that allows retrofitting of the existing wind turbine within the pre-defined space limitations of the existing wind turbine's gear set.

SUMMARY OF THE PRESENT INVENTION

One aspect of the present invention is a discretely variable diameter gear set having a planetary configuration, comprising a ring; a sun gear having a tooth sequence, the sun gear capable of opening and closing radially to adjust a gap in the tooth sequence and a diameter of the sun gear by a discrete effective number of teeth; a first idler gear enmeshed with the sun gear; an output pinion enmeshed with the first idler gear and with the ring; a second idler gear enmeshed with the sun gear; and a second pinion enmeshed with the second idler gear and with the ring, the sun gear always enmeshed with at least one of the idler gears.

A further aspect of the present invention is a method of operating a discretely variable diameter gear set in which a tooth sequence of a sun gear is enmeshed with two or more of three idler gears, the three idler gears enmeshed with their respective pinions, the pinions enmeshed with a ring, comprising adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence; moving, during the adjusting of the diameter, a second pinion to adjust an angle ds_a between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation s_a=n-(360/(R+S)), where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that a gap is not situated along an arc subsumed by as_a; and moving, during the adjusting of the diameter, a third pinion to adjust an angle, ( st,, between the first radius and a third radius running between the center of the sun gear and a center of the third pinion, to maintain an equation s_b=n-(360/(R+S)) where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that the gap is not situated along an arc subsumed by as_a + 0.5b, where _5a and _5b are adjacent angles.

A further aspect of the present invention is directed to a method of operating a discretely variable diameter gear set having a sun gear having a tooth sequence, a first output pinion enmeshed with a ring, a second pinion enmeshed with a second idler gear and with the ring, the method comprising adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence; and moving, during the adjusting of the diameter, the second pinion to adjust an angle, a, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation a=n-(360/(R-S)), where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that the gap is not situated along an arc subsumed by a.

A still further aspect of the present invention is directed to a discretely variable diameter gear set having a planetary configuration, comprising a sun gear having a tooth sequence and capable of opening and closing radially to adjust a gap in the tooth sequence and a diameter of the sun gear by a discrete effective number of teeth; a secondary sun gear co-axial with the sun gear; a first idler gear enmeshed with the sun gear; a second idler gear enmeshed with the sun gear; a first output pinion enmeshed with the first idler gear and co-axial with a second output pinion, the second output pinion enmeshed with the secondary sun gear; and a third pinion enmeshed with the second idler gear and co-axial with a fourth pinion, the fourth pinion enmeshed with the secondary sun gear, the sun gear enmeshed with at least one of the idler gears.

A yet still further aspect of the present invention is a method of operating a discretely variable diameter gear set that includes a sun gear having a tooth sequence, a first output pinion enmeshed with a first idler gear and co-axial with a second output pinion, the second output pinion enmeshed with a secondary sun gear, a second idler gear enmeshed with a third pinion, the method comprising adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence; and moving, during the adjusting of the diameter, the third pinion to adjust an angle, a, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the third pinion, to maintain an equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun gear, in a manner that the gap is not situated along an arc subsumed by a.

A further aspect of the present invention is a discretely variable diameter gear set having a planetary configuration, comprising a sun gear having a tooth sequence and capable of opening and closing radially to adjust a gap in the tooth sequence and a diameter of the sun gear by a discrete effective number of teeth; a secondary sun gear co-axial with the sun gear and enmeshed with a fourth output pinion, a fifth pinion and a sixth pinion; a first idler gear enmeshed with the sun gear and enmeshed with a first output pinion, the first output pinion co-axial with the fourth output pinion; a second idler gear enmeshed with the sun gear and enmeshed with a second pinion, the second pinion co-axial with the fifth pinion; and a third idler gear enmeshed with the sun gear and enmeshed with a third pinion, the third pinion co-axial with the sixth pinion, the sun gear enmeshed with at least two of the idler gears.

A still further aspect of the present invention is directed to a method of operating a discretely variable diameter gear set in which a sun gear has a tooth sequence, the sun gear is co-axial with a secondary sun gear, a first idler gear is enmeshed with the sun gear and enmeshed with a first output pinion, a second idler gear is enmeshed with the sun gear and enmeshed with a second pinion, a third idler gear is enmeshed with the sun gear and enmeshed with a third pinion, the method comprising adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence; moving, during the adjusting of the diameter, the second pinion to adjust an angle, U\, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun, in a manner that the gap is not situated along an arc subsumed by a ; and moving, during the adjusting of the diameter, the third pinion to adjust an angle, ₂, between a first radius running between a center of the sun gear and a center of the first output pinion and a third radius running between the center of the sun gear and a center of the third pinion, to maintain an equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun, in a manner that the gap is not situated along an arc subsumed by ( i + ₂, where i and ₂ are adjacent angles.

These and other features, aspects and advantages of the present invention will become better understood with reference to the following drawings, descriptions and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments are herein described, by way of example only, with reference to the accompanying drawings, wherein: FIG. 1 is a front plan view of a gear set utilizing a ring in open position in accordance with one embodiment of the present invention;

FIG. 2 is a front plan view of a gear set similar to the gear set of FIG. 1 in closed position in accordance with one embodiment of the present invention;

FIG. 3A is a front plan view of the gear set of FIG. 1 with one idler gear enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 3B is a front plan view as in FIG. 3A with two idler gears enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 3C is a front plan view as in FIG. 3 A with one idler gear enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 3D is a front plan view as in FIG. 3A but with the gap in the tooth sequence between the two idler gears, a condition not occurring during diameter shifting, in accordance with one embodiment of the present invention;

FIG. 4 is an isometric view of the gear set of FIG. 1 , in accordance with one embodiment of the present invention;

FIG. 5 is a front plan view of a gear set utilizing a secondary sun and in open position in accordance with one embodiment of the present invention;

FIG. 6 is a front plan view of a gear set similar to the gear set of FIG. 5 in closed position in accordance with one embodiment of the present invention;

FIG. 7 is a front plan view, from the opposite side of that shown in FIG. 6 of the gear set of FIG. 5 in accordance with one embodiment of the present invention;

FIG. 8 is an isometric view of the gear set shown in FIG. 5, in accordance with one embodiment of the present invention; FIG. 8A is a front plan view of the gear set of FIG. 5 showing two idler gears enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 8B is a front plan view of the gear set shown in FIG. 5 showing one idler gear enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 8C is a front plan view of the gear set shown in FIG. 5 with the gap in the tooth sequence between two idler gears, a condition not occurring during diameter shifting, in accordance with one embodiment of the present invention;

FIG. 8D is a front plan view of the gear set shown in FIG. 5 showing one idler gear enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 9 is a front plan view of a gear set utilizing a ring in open position with three idlers in accordance with one embodiment of the present invention;

FIG. 10 is a front plan view of a gear set similar to the gear set of FIG. 9 in closed position in accordance with one embodiment of the present invention;

FIG. 11A is a front plan view of the gear set of FIG. 9 in a condition that may not occur during diameter shifting, in accordance with one embodiment of the present invention;

FIG. 11 B is a front plan view of the gear set of FIG. 9 in a condition that may not occur during diameter shifting, in accordance with one embodiment of the present invention;

FIG. l lC is a front plan view as in FIG. 9 in a condition that may not occur during diameter shifting, in accordance with one embodiment of the present invention; FIG. 12A is a front plan view as in FIG. 9 showing two idler gears enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 12B is a front plan view as in FIG. 9 showing three idler gears enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 12C is a front plan view as in FIG. 9 showing two idler gear enmeshed with the sun gear, in accordance with one embodiment of the present invention;

FIG. 13 is an isometric view of the gear set of FIG. 9 in accordance with one embodiment of the present invention;

FIG. 14 is a front plan view of a gear set utilizing a secondary sun and three idler gears in open position in accordance with one embodiment of the present invention;

FIG. 15 is a front plan view of a gear set similar to the gear set of FIG. 14 in closed position in accordance with one embodiment of the present invention;

FIG. 16 is a rear plan view, from the opposite side of that shown in FIG. 15, of the gear set of FIG. 14 in accordance with one embodiment of the present invention;

FIG. 17 is an isometric view of the gear set of FIG. 14 in accordance with one embodiment of the present invention;

FIG. 18 is a flow chart showing a method in accordance with one embodiment of the present invention;

FIG. 19 is a flow chart showing a further method in accordance with one embodiment of the present invention;

FIG. 20 is a flow chart showing a further method in accordance with one embodiment of the present invention;

FIG. 20A is a flow chart showing a further method in accordance with one embodiment of the present invention; FIG. 21 is a graph showing a geometric condition for an angle, ά, for a gear set similar to the gear set of FIG. 1 ;

FIG. 22 is a graph showing a geometric condition for an angle, ά, for a gear set similar to the gear set of FIG. 5;

FIG. 23 is an overall view of an embodiment of a variable diameter gear device, constructed and operative according to the teachings of the present invention, including two gear tooth sequences which provide a variable diameter effective cylindrical gear engaged with an idler gear arrangement as part of a variable ratio transmission system;

FIG. 24A is an isometric view of one gear tooth sequence and an associated disc with a spiral track, forming part of a diameter changer, from the gear device of FIG. 23;

FIG. 24B is an axial view of the gear tooth sequence and disc of FIG. 24A, shown in a maximum diameter state;

FIG. 24C is a cross-sectional view taken along line A-A in Figure 24B;

FIGS. 25A and 25B are views similar to Figures 24A and 24B, respectively, where the teeth not lying on the line of cross-section have been omitted for clarity;

FIGS. 26A-26E are a sequence of views similar to Figure 24A showing a range of positions of the disc relative to the tooth sequence, ranging from an open state to a fully closed state. In each case, alongside the figure is shown a circle corresponding to the pitch circle of the effective gear wheel superimposed on a dashed-line circle corresponding to the disc outline, thereby illustrating the range of variation of the effective diameter; FIG. 27 is a partial isometric view illustrating an adjustment mechanism for generating relative rotation between a disc of the diameter changer and the main axle of the gear device;

FIGS. 28 and 29 are schematic diagrams illustrating certain terminology which will be used in an analysis of the geometry of the present invention;

FIGS. 30A and 3 OB are schematic representations of two types of linkage suitable for use in implementing the variable gear device of FIG. 23;

FIGS. 31 and 32 are schematic diagrams illustrating certain terminology which will be used in an analysis of the geometry when implementing an embodiment of the invention with the linkage of FIG. 3 OB; and

FIG. 33 A is a front plan view of a gear set as in FIG. 14 during rotation, in accordance with one embodiment of the present invention;

FIG. 33B is a front plan view of a gear set as in FIG. 14 during rotation, in accordance with one embodiment of the present invention;

FIG. 33C is a front plan view of a gear set as in FIG. 14 during rotation, in accordance with one embodiment of the present invention;

FIG. 33D is a front plan view of a gear set as in FIG. 14 during rotation, in accordance with one embodiment of the present invention;

FIG. 33E is a front plan view of a gear set as in FIG. 14 during rotation, in accordance with one embodiment of the present invention; and

FIG. 33F is a front plan view of a gear set as in FIG. 14 during rotation, in accordance with one embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION The following detailed description is of the best currently contemplated modes of carrying out the invention. The description is not to be taken in a limiting sense, but is made merely for the purpose of illustrating the general principles of the invention, since the scope of the invention is best defined by the appended claims.

The present invention generally provides a discretely variable diameter gear set having a planetary configuration. The gear set may vary a diameter of a gearwheel by whole numbers of gear teeth in response to changes in input speed of a rotor shaft. Typically, the diameter may be shifted in increments of one gear tooth at a time. A variable effective number of teeth in the sun gear of the gear set may be achieved. Four embodiments of the planetary gear set are outlined: (i) a gear set with a ring and two idler/pinion sets around the sun gear (ii) a gear set with a ring and three idler/pinion sets around the sun gear, (iii) a gear set with a secondary sun (and no ring) and two idler/pinion sets around the sun gear and (iv) a gear set with a secondary sun (and no ring) and three idler/pinion sets around the sun gear.

In contrast to the prior art gear sets, which are of fixed diameter, the gear set of the present invention may have a discretely variable diameter. This may allow the gear set to be used in wind turbines and other environments in which the input speed is necessarily or may be variable, for example because of changes in wind speed. The discretely variable diameter gear set may receive varying rotational energy from a varying rotational speed of the rotor shaft and may output a fixed speed. In further contrast to prior art transmissions, in which either classical automotive gearboxes with gearwheels and teeth are not used or classical gears that are used cannot shift gears under full load without a clutch disengagement, the gear set of the present invention may use classical gears that can shift gears under full load without any clutch disenaggement. In still furrther contrast to the prior art, in which the gear set and gearbox, when used inside a wind turbine cannot optimize the efficiency of the wind turbine either because a fixed speed gearbox cannot handle the variability in the wind speed or because a variable ratio gearbox cannot avoid the use of power electronics, the gear set of the present invention when used in a gearbox inside a wind turbine may be able to maximize energy efficincy by having the benefits of variable diameter gearbox without the drawbacks. In still further contrast to the prior art gearboxes, the gear set of the present invention may provide, in its gearbox, a variable effective number of gear ratios while allowing toothed engagement around the entire periphery of the effective cylindrical gearwheel for any diameter that the gearwheel of the gearbox is in. This may allow the gearbox to transmit high torque at high efficiency. This may also provide greater power for the discrete variable ratio gearbox of the present invention over the continuous variable transmission (CVT) gearbox of the prior art. In further contrast to certain prior art gear sets, which may have a co-axial arrangement in which a variable diameter gear set is two or three times the length of a normal gear set since it has two gearwheels with overlapping sets of gear teeth, the gear set of the present invention may have a planetary configuration. Since the gear set is not co-axial, the gear set may employ a single variable-diameter gearwheel. This may avoid the necessity of having to double or triple the length of the gear set while still maintaining all of the advantages of a discretely variable diameter gear set. This may be particularly useful when retrofitting a wind turbine by replacing the original fixed-speed gearbox of the wind turbine with a discretely variable ratio gearbox containing a discretely variable diameter gear set where the space available for the gear set is pre-defined.

The principles and operation of a method and system for a discretely variable diameter gear set having a planetary configuration according to the present invention may be better understood with reference to the drawings and the accompanying description.

As seen in FIG. 1, a gear set 10 having a planetary configuration includes a sun gear 20 having a tooth sequence 21. Sun gear 20 may be situated on an input shaft 18. FIG. 1 shows the tooth sequence 21 having a gap 19 since in FIG. 1 sun gear 20 may already be in an open position. When sun gear 20 opens radially outwardly its diameter increases. In fact, FIG. 1 shows sun gear 20 in its most open position with its diameter at its maximum. During the short time span of the actual diameter shift, the effective number of teeth may change continuously until it reaches the next whole integer of effective number of teeth. For example, in FIG. 1, the effective number of teeth is 46. Although the number of actual teeth on tooth sequence 21 may be thirty- four, sun gear 20 may have the diameter of a sun gear having forty-six teeth if one includes gap 19. Accordingly, sun gear 20 shown in FIG. 1 may be said to have an effective number of teeth equal to thirty-four.

FIG. 2 shows sun gear 20 in a closed position without a gap in tooth sequence

21 and having its smallest possible diameter. In FIG.2, sun gear 20 may have thirty- four actual teeth in tooth sequence 21 and may also have an effective number of teeth that is equal to thirty-four. This means that sun gear 20 may have opened radially twelve increments, which may have occurred on twelve occasions, from its closed position shown in FIG. 1. This may have increased the diameter of sun gear 20 as measured by its effective number of teeth from thirty-four to forty-six. Each diameter shift may increase the effective number of teeth of sun gear 20 by a single integer. Similarly, to go from the fully open position in FIG. 1 to the closed position of sun gear 20 in FIG. 2, sun gear 20 may shift diameter twelve increments, which may occur over twelve occasions, so as to decrease its diameter by a single integer each time back down to thirty-four effective number of teeth.

In all, gear set 10 may have approximately thirteen to twenty- five gears, which means thirteen to twenty- five different diameter positions.

As seen in FIG. 1, first idler gear 32 and second idler gear 34 may be enmeshed with sun gear 20. The term "enmeshed" when used in connection with gears refers to the fact that the tooth sequence of a gear is operatively engaged with a tooth sequence of another gear. First idler gear 32 may further be enmeshed with an output pinion 22, sometimes called "first output pinion". Output pinion 22 may be considered fixed in that output pinion 22 may have a fixed rotational position along the rotational periphery of sun gear 20. Output pinion 22 may be operatively engaged to or may be a continuation of an output shaft 90 (see FIG. 4). Second idler gear 34 may be enmeshed with a seond pinion 24. Both output pinion 22 and second pinion 24 may be enmeshed to a ring 40. It may also be appreciated that neither pinion 22, 24 may be enmeshed with sun gear 20.

FIGS. 3 A through 3D show various positions of gap 19 as sun gear 20 rotates. As sun gear 20 rotates, first and second idler gears 32, 34 change from being enmeshed to being not enmeshed with sun gear 20. FIG. 3B depicts a situation in which the torque transmitted by sun gear 20 may be held equally by both idler gears 32, 34 since these idler gears 32, 34 are both enmeshed with sun gear 20. As shown in FIG. 3 A, however, sun gear 20 may rotate to a position wherein gap 19 is situated so that first idler gear 32 may be not enmeshed with sun gear 20 while second idler gear 34 may be enmeshed with sun gear 20 and may be enmeshed with second pinion 24. Since second pinion 24 may also be enmeshed with ring 40, ring 40 may transfer its torque to first output pinion 22 which may also be enmeshed with ring 40. For this very reason, each idler gear 32, 34 may be designed to carry the full load or torque transmitted by sun gear 20. Similarly, each pinion 22, 24 may be designed to carry the full load.

FIG. 3C shows the situation converse to that of FIG. 3A. In FIG. 3C, the gap 19 is such that second idler gear 34 may not be enmeshed with sun gear 20 and first idler gear 32 may be enmeshed with sun gear 20. First idler gear 32 may also be enmeshed with output pinion 22, which may be enmeshed with ring 40. Accordingly, ring 40 may not transfer any torque to second pinion 24. The path of the torque may in this case be from sun gear 29 to first idler gear 32 to output pinion 22.

FIG. 3D depicts a configuration that should not be allowed to occur during the actual shifting of the diameter of sun gear 20. Instead, one should start after and finish before the configuration shown in FIG. 3D. One should therefore finish shifting diameter before the first sun gear teeth re-engags with the idler. The configuration of FIG. 3D should not occur during diameter shofting because, as discussed below, in FIG. 3D gap 19 is on the same side as the arc subsumed by the angle, άι shown in FIG. 1 between the first radius running between a center of sun gear 20 and a center of the first output pinion 22 and the second radius running between the center of sun gear 20 and a center of the second pinion 24. The configuration of FIG. 3B may be the best position in which to start shifting diameter.

In order to adjust the gap 19 and control the extent to which sun gear 20 opens or closes radially, sun gear 20 may be operatively engaged to a motor (not shown). The sun gear motor (not shown) or shift motor may be controlled by a controller (not shown). This controller may be used to control the various motors connected to the various parts of gear set 10 in order to regulate when and how to shift the diameter of the gear set 10. For example, besides the shift motor (not shown), an idler motor (not shown) may be operatively engaged to the idler gears 32, 34 and the idler motor may be connected to and controlled by the controller (not shown).

One or more idler gear movers 99 (see FIG. 2), such as idler motors, may be capable of moving the one or more idler gears that are enmeshed with sun gear 20 away from sun gear 20 to compensate for an increase in diameter of sun gear 20 when sun gear 20 opens radially.

As a result of the novel diameter shifting implemented by the gear set 10 of the present invention, certain rules may need to be followed in order to ensure that the teeth of idler gears 32, 34 mesh smoothly and do not collide with tooth sequence 21 of sun gear 20 each time sun gear 20 rotates. In general, this may be accomplished by having second pinion 24 maintain a certain rotational distance from output pinion 22. This rotational distance may be a function of the effective number of teeth in the tooth sequence 21 of sun gear 20. The idler gear associated with a pinion may move when that pinion moves.

FIG. 2 shows an angle, ά₂, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion. FIG. 1 shows an angle, άι, between the first radius running between a center of the sun gear and a center of the first output pinion and the second radius running between the center of the sun gear and a center of the second pinion. It can be appreciated from viewing FIG. 1 and FIG. 2 that the angle, ( i in FIG. 1 wherein sun gear 20 is open is larger than the angle, ₂ in FIG. 2, which depicts sun gear 20 in closed position This is because during the adjusting of the diameter, the second pinion may be moved to adjust the angle, ά, to maintain the equation a=n-(360/(R-S)), where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring. Furthermore, this adjusting of angle ά may be implemented in a manner that the gap 19 is not situated along an arc subsumed by a. In general, it is noted that it is not intended regarding FIG. 1, FIG. 2, FIG. 5, FIG. 6, FIG. 9, FIG. 10 and FIG. 14, that these figures depict the angle, a, precisely to scale.

The equation a=n-(360/(R-S)) is a known equation for gears in planetary configuration. However, utilizing the gear set of the present invention, S, the effective number of teeth on sun gear 10 may vary while R, the number of teeth in the ring 40 is constant. If S increases, for example by one, due to radial opening of sun gear 20, the angle ά may also need to be increased. This is because as S increaaes "R- S" decreases and "360/(R-S)" increases so a, which is equal to "n-(360/(R-S))", must increases. As shown by Table 1, "Θ" is used to represent"360/(R-S)". In Table 1 , "IQ Sun T" represents "S", or sun gear 20, whose effective number of teeth vary.

Table 1 :

The angle ά may be increased by motors operative ly engaged to second pinion 24, which is the pinion that is not the output pinion 22, since output pinion 22 is rotationally fixed in relation to its position along the periphery of sun gear 20 and cannot be adjusted in position. Second pinion 24, in contrast, may be adjusted to comply with the equation a=n-(360/(R-S)). In doing so, however, another rule may need to be followed. When adjusting the position of second pinion 24 in order to maintain the equation a=n-(360/(R-S)) during diameter shofting, gap 19 may not be situated along the arc subsumed by a but rather should be located in the arc subsumed by the complementary angle (360- a).

As seen in FIG. 21 , during diameter shifting, gap 19 should be in the arc subsumed by the angle where the equation is not maintained. It should be understood that while it may be necessary to maintain the equation a=n-(360/(R-S)) ("the equation") for an angle a, that angle may be chosen to be the angle complementary to the angle a shown in FIG. 1. In that case, though, gap 19 should be along the arc subsumed by a. Wherever the equation is maintained, the gap 19 may be situated on the other side. For example, if I need to increase the diameter of sun gear 20 during a diameter shift, then the angle a may be increased by moving second pinion 24 counterclockwise as shown in FIG. 2 (in relation to FIG. 1) and by maintaining gap 19 in the arc subsumed by the angle complementary to a. If instead, one wished to rotate second pinion 24 clockwise, then the equation would only be maintained in the arc subsumed by the angle complementary to a. Consequently, the diameter shifting may then be timed so that second pinion 24 is rotated clockwise when the gap 19 is positioned in the arc subsumed by a (since gap 19 may be positioned on the opposite side of where the equation is maintained.

The pinions 22, 24 may be structured so that the angle, , is as small as possible provided that the angle, a, exceeds the arc subsumed by gap 19.

If one needs to shift the diameter of sun gear 20 downward, then to maintain the equation one may move second pinion 24 clockwise and maintain gap 19 in the arc subsumed by the complement to angle a. As seen in FIG. 18, the present invention may be described as a method 100 of operating a discretely variable diameter gear set in which a tooth sequence of a sun gear is enmeshed with first and second idler gears, a first output pinion is enmeshed with the first idler gear and with a ring, the second idler gear is enmeshed with the sun gear, a second pinion is enmeshed with the second idler gear and with the ring.

Mehtod 100 may comprise a first step 1 10 of adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence. Further, method 100 may also include a second step 120 of moving, during the adjusting of the diameter, the second pinion to adjust an angle, a, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation a=n-(360/(R-S)), where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that the gap is not situated along an arc subsumed by a.

As shown in FIG. 9, three idlers and three pinions may be used instead of two and two. With three idlers and three pinions, sun gear 60 may be enmeshed with at least two of three idler gears at any given time. Accordingly, in that case, with three pinions and at least two of three idlers enmeshed with the sun gear, the load may be shared between at least two pinions. This may be advantage over the embodiment of FIG. 1 utilizing two pinions and two idlers, in which at times the entire load may be borne by a single pinion (for example during the times when only one idler is enmeshed with sun gear 10).

In other respects, gear set 12 may include all of the elements discussed with respect to gear set 10. For example, as seen in FIG. 9 through FIG. 13, gear set 12 may include sun gear 60 that may have a tooth sequence 61 that may have a gap 59 when sun gear 60 is open. Gear set 12 may also include a ring 62, and may include first idler gear 66 that may be enmeshed with sun gear 67 and second idler gear 67 that may be enmeshed with sun gear 60, an output pinion 63 enmeshed with first idler gear 66 and a second pinion 64 enmeshed with second idler gear 67. Pinions 63, 64 may not be enmeshed with the sun gear 60. In this case, moreover, gear set 12 may further include a third idler gear 68 enmeshed with the sun gear 60 and a third pinion 65 that may be enmeshed both with the third idler gear 68 and with ring 62.

In regard to gear set 12, wherein at least two of three idler gears 65, 66, 67 may be enmeshed with sun gear 60, the equation =n-(360/(R-S)) may be maintained for each of two angles. FIG. 10 depicts sun gear 60 in closed position and showing a first angle, _6a, between a first radius running between a center of the sun gear 60 and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion 65. FIG. 10 also shows a second angle, a₆b, between a first radius running between a center of the sun gear 60 and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the third pinion 64. The first and second angles ₆b and ₆b need not be identical though they are shown as identical in FIG. 9. These angles may be identical when the value of N is kept constant.

The angles as_aand asb (see FIG. 9) may be increased by means of motors operatively engaged to second pinion 64 and third pinion 65. The positions of these pinions may be adjusted to comply with the equation =n-(360/(R-S)). As in the case with two pinions, another rule may have to be followed. When adjusting the position of second pinion 64 or third pinion 65 in order to maintain the equation =n-(360/(R- S)) during diameter shifting, gap 59 may not be situated along the arc subsumed by ( 5_a or as_h as the case may be but rather should be located in the arc subsumed by the complementary angle s_c having an arc of X degrees, where X = (360 - (as_a + ( sb)).

Just as with the embodiment shown in FIG. 1 , in the embodiment shown in FIGS. 9-13, when starting diameter shifting, gap 59 may be in the arc subsumed by the complementary angle where this equation is not maintained. When considering this rule for angle as_a angle asb is not considered in measuring the complementary arc/angle and when considering this rule for angle asb angle as_a is not considered when measuring the complementary arc/angle. For example, with respect to angle as_a gap 59 can be in the arc subsumed by angle s_c. Similarly, regarding angle asb gap 59 can be in the arc subsumed by angle s_c.

Generally, it is noted that FIGS. 1 1A, 1 IB, 11C depict configurations during operation of gear set 12 in which diameter shifting may not be initiated while FIGS. 12A, 12B, 12C depict configurations during operation of gear set 12 in which diameter shifting may be initiated. It is also noted that when rotating sun gear 60 clockwise, shifting can start in the configuration shown in FIG. 12A and end before the configuration shown in FIG. 1 1 A.

One aspect of the present invention is a discretely variable diameter gear set having a planetary configuration, comprising a ring; a sun gear having a tooth sequence, the sun gear capable of opening and closing radially to adjust a gap in the tooth sequence and a diameter of the sun gear by a discrete effective number of teeth; a first idler gear enmeshed with the sun gear, an output pinion enmeshed with the first idler gear and with the ring; a second idler gear enmeshed with the sun gear; a second pinion enmeshed with the second idler gear and with the ring, a third idler gear enmeshed with the sun gear and a third pinion enmeshed with the third idler gear and with the ring, the sun gear always enmeshed with at least two of the idler gears. The present invention may also be described as a method of operating a discretely variable diameter gear set in which a tooth sequence of a sun gear is enmeshed with two or more of first, second and third idler gears wherein the three idler gears may be enmeshed with their respective pinions, the pinions being enmeshed with a ring. Method 400 may comprise a first step 410 of adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence. Method 400 may also comprise a further step 420 of moving, during the adjusting of the diameter, a second pinion 64 to adjust an angle ds_a between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation

where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that a gap is not situated along an arc subsumed by s_a. In a further step 430, method 400 may also include moving, during the adjusting of the diameter, a third pinion 65 to adjust an angle, ( st,, between the first radius (running between a center of the sun gear and a center of the first output pinion) and a third radius running between the center of the sun gear and a center of the third pinion, to maintain an equation s_b=n-(360/(R+S)) where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that the gap is not situated along an arc subsumed by _5a + _5b, where _5a and _5b are adjacent angles. Method 400 may involve moving the second and third pinions 64, 65 simultaneously during the adjusting of the diameter.

As shown in FIG. 5 through FIG. 8, in order to make the gear set of the present invention even more compact, ring 40 (see FIG. 1) may be replaced by a secondary sun 52, sometimes called S₂. As best seen from FIG. 5 and FIG. 8, a discretely variable diameter gear set 11 having a planetary configuration may then comprise a sun gear 50 having a tooth sequence 51 and be capable of opening and closing radially to adjust a gap 19 in the tooth sequence 51 and a diameter of the sun gear 40 by a discrete effective number of teeth. Gear set 11 may further include a secondary sun gear 52 that may be co-axial with the sun gear 50.

As seen in FIG. 5, gear set 11 may include a first idler gear 54 enmeshed with the sun gear 50 (Si), a second idler gear 58 enmeshed with sun gear 50, a first output pinion 56A enmeshed with the first idler gear 54 and co-axial with a second output pinion 56B (seen in FIG. 7 and FIG. 8), the second output pinion 56B enmeshed with the secondary sun gear 52.

Gear set 11 may also include a third pinion 59A enmeshed with the second idler gear 58. Third pinion 59A may be co-axial with a fourth pinion 59B. Fourth pinion 59B may be enmeshed with secondary sun gear 52. In gear set 11, sun gear 50 may be enmeshed with at least one of the idler gears at any given time.

By comparing FIG. 5, wherein sun gear 50 may be in fully open position, to FIG. 6, in which sun gear 50 may be in a closed position, it can be appreciated that the tooth sequence 51 of sun gear 52 may have a variable effective number of teeth. Tooth sequence 51 may range from 34 to 46. Gear set 11 may include one or more idler gear movers (not shown) capable of moving the one or more idler gears 54, 58 enmeshed with sun gear 50 away from sun gear 50 to compensate for an increase in diameter of sun gear 50 when sun gear 50 opens radially. Sun gear 50 may not be enmeshed with third or fourth pinions 59A, 59B or with first or second output pinions 56A, 56B. FIG. 6 shows an angle, a₄, between a first radius running between a center of the sun gear 50 and a center of the first idler gear 54 and a second radius running between the center of sun gear 50 and a center of the second idler gear 58. A similar angle can be measured using the pinions instead o fthe idler gears. FIG. 5 shows an angle, a₃, between the first radius running between a center of sun gear 50 and a center of first idler gear 54 and the second radius running between the center of sun gear 50 and a center of second idler gear 58. It can be appreciated from viewing FIG. 1 and FIG. 2 that the angle, άι in FIG. 1 wherein sun gear 20 is open is larger than the angle, a₂ in FIG. 2, which depicts sun gear 20 in closed position. This is because during the adjusting of the diameter, the third pinion may be moved to adjust the angle, a, to maintain the equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun gear. Furthermore, this adjusting of angle a may be implemented in a manner that the gap 19 is not situated along an arc subsumed by a.

Since the denominator of the fraction in the equation has a plus operator rathern than a minus, if one needs to increase the diameter of sun gear 20 during a diameter shift, then the angle a may be increased by moving third pinion 59A clockwise as shown in FIG. 5 (relative to FIG. 6) and by maintaining gap 19 in the arc subsumed by the angle complementary to a. If instead, one wished to rotate third pinion 59A counterclockwise, then the equation would only be maintained in the arc subsumed by the angle complementary to a. Consequently, gap 19 would then be positioned in the arc subsumed by a (since gap 19 may be positioned on the opposite side of where the equation is maintained.

The equation

is a known equation for gears in planetary configuration. However, utilizing the gear set of the present invention, Si, the effective number of teeth on sun gear 50 may vary while S₂, the number of teeth in the secondary sun 52 is constant. If Si increases, for example by one, due to radial opening of sun gear 50, the angle a may also need to be decreased. This is because as Si increaaes "S1+S2" increases and "360/( S1+S2)" decreases so ά, which is equal to "η·(360/( Si+S₂))", must decrease. As shown by Table 2, "Θ" is used to

represent"360/( S1+S2)". In Table 2, "IQ Sun T" represents "Si", or sun gear 50, whose effective number of teeth vary.

Table 2:

Generally, it is noted that FIGS. 8A, 8B, 8D depict configurations during operation of gear set 1 1 in which diameter shifting may be initiated while FIG. 8C depicts configurations during operation of gear set 1 1 in which diameter shifting may not be initiated.

As shown in FIG. 19, the present invention may also be characterized as a method 200 of operating a discretely variable diameter gear set in which a sun gear has a tooth sequence, a first idler gear is enmeshed with the sun gear, a first output pinion is enmeshed with the first idler gear and co-axial with a second output pinion, the second output pinion is enmeshed with a secondary sun gear, a second idler gear is enmeshed with the sun gear; and a third pinion is enmeshed with the second idler gear and co-axial with a fourth pinion, the fourth pinion enmeshed with the secondary sun gear. A first step 210 of method 200 may involve adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence. Method 200 may include a further step 220 of moving, during the adjusting of the diameter, the third pinion to adjust an angle, ά, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the third pinion, to maintain an equation

The embodiment wherein the gear set utilizes a secondary sun may also be combined with the use of three instead of two pinion/idler gear sets. As shown in FIG. 14, a gear set 13 may comprise a sun gear 70 having a tooth sequence 72 and capable of opening and closing radially to adjust a gap 71 in the tooth sequence 72 and to adjust a diameter of the sun gear 70 by a discrete effective number of teeth.

As shown in FIG. 16, which depicts the rear view of gear set 13 from the opposite side to that of FIG. 14, gear set 13 may also include a secondary sun gear 82 co-axial with the sun gear 70. As best seen in FIG. 15, gear set 13 may also include a first idler gear 73 enmeshed with the sun gear 70. First idler gear 73 may be enmeshed with a first output pinion 76. First output pinion 76 may be co-axial with a fourth output pinion 79. A second idler gear 75 may be enmeshed with sun gear 70. Second idler gear 75 may be enmeshed with a second pinion 78. Second pinion 78 may be co-axial with a fifth pinion 81. Gear set 13 may also include a third idler gear 74 which may be enmeshed (see FIG. 15) with sun gear 70. Third idler gear 74 may be enmeshed with a third pinion 77. Third pinion 77 may be co-axial with the sixth pinion 80,. Sun gear may be enmeshed with at least two of the idler gears 73, 74, 75.

As seen from FIG. 16, secondary sun 82 may be enmeshed with three pinions, namely a fourth output pinion 79 (coaxial with first output pinion 76), a fifth pinion 81 (co-axial with second pinion 78) and a sixth pinion 80 (co-axial with third pinion 77).

As a result of the novel diameter shifting implemented by the gear set 13 of the present invention, certain rules may need to be followed in order to ensure that the teeth of idler gears 73, 74, 75 mesh smoothly and do not collide with tooth sequence 72 of sun gear 70 each time sun gear 70 rotates. In general, this may be accomplished by having pinions 81, 80 maintain a certain rotational distance from first output pinion 76. This rotational distance may be a function of the effective number of teeth in the tooth sequence 72 of sun gear 70. The idler gear associated with a pinion may move when that pinion moves.

FIG. 15 shows an angle, ds_a, between a first radius running between a center of the sun gear 70 and a center of the first output pinion 76 and a second radius running between the center of the sun gear 70 and a center of the third pinion 78. FIG. 14 shows an angle, άι , between the first radius running between a center of the sun gear and a center of the first output pinion and the second radius running between the center of the sun gear and a center of the second pinion. It can be appreciated from viewing FIG. 14 and FIG. 15 that the angle, as_a and the angle, as_b in FIG. 14 wherein sun gear 20 is open is smaller than the same angles in FIG. 15, which depicts sun gear 20 in closed position This is because during the adjusting of the diameter, the second and third pinions 77, 78 may be moved to adjust the angle, ά, to maintain the equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun gear.

Furthermore, this adjusting of angle ά may be implemented in a manner that the gap 19 is not situated along an arc subsumed by a.

As previously noted (for the embodiment with a ring and two idler gears), the equation

is a known equation for gears in planetary configuration where there is a secondary sun instead of a ring. However, utilizing the gear set of the present invention, Si, the effective number of teeth on sun gear 13 may vary while S₂, the number of teeth in the secondary sun gear 82 is constant. If Si increases, for example by one, due to radial opening of sun gear 70, the angle ds_a and the angle dsb may need to be decreased. This is because as Si increaaes "(S₁+S₂)" decreases and "360/(Si+S2)" decreases so a, which is equal to "n-(360/(Si+S2))", must also decrease. As shown by Table 2, "Θ" is used to represent"360/( S₁+S₂)". In Table 2, "IQ Sun T" represents "Si", or sun gear 50, whose effective number of teeth vary.

Table 2:

As seen in FIG. 21 , during diameter shifting, gap 71 should be in the arc subsumed by the angle where the equation is not maintained. It should be understood that while it may be necessary to maintain the equation

("the equation") for an angle a, that angle may be chosen to be the angle complementary to , where a may be the sum of the two angles, as_a and asb shown in FIG. 14. In that case, though, gap 71 should be along the arc subsumed by the sum of the two angles, asa and asb. The rule that may be maintained is that wherever (i.e. the arc subsumed by alpha or its complementary arc) the equation is maintained, the gap 71 may be situated on the other side. For example, if one needs to increase the diameter of sun gear 70 during a diameter shift, then the angle a may be decreased by moving third pinion 78 clockwise (and by moving second pinion 77 counter-clockwise) as shown in FIG. 15 (in relation to FIG. 14) and by maintaining gap 71 in the arc subsumed by the angle complementary to a. If instead, one wished to rotate third pinion 78 counterclockwise (and rotate second pinion 77 clockwise), then the equation would only be maintained in the arc subsumed by the angle complementary to a. Consequently, the diameter shifting may then be timed so that third pinion 78 is rotated counter- clockwise (and second pinion 77 is rotated clockwise) when the gap 71 is positioned in the arc subsumed by a (since gap 71 may be positioned on the opposite side of where the equation is maintained.

Generally, it is noted that FIG. 33B, FIG. 33C and FIG. 33D depict configurations during operation of gear set 13 which may be allowed during diameter shifting while FIG. 33A, FIG. 33E and FIG. 33F depict configurations during operation of gear set 13 which may not be allowed during diameter shifting. The pinions 77, 78 may be structured so that the angle, , is as small as possible provided that the angle, a, exceeds the arc subsumed by gap 71.

If one needed to shift the diameter of sun gear 70 downward, then to maintain the equation one may increase the angle a, for example by moving third pinion 78 counter-clockwise and moving second pinion 77 clockwise and maintain gap 71 in the arc subsumed by the complement to angle a where a may be the sum of the two angles, as_a and asb shown in FIG. 14.

In regard to gear set 13, wherein at least two of three idler gears 73, 74, 75 may be enmeshed with sun gear 70, the equation

may be maintained for each of two angles. FIG. 15 depicts sun gear 70 in closed position. FIG. 14 depicts sun gear 70 in open position and showing a first angle, as_a, between a first radius running between a center of the sun gear 70 and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion 77. FIG. 14 also shows a second angle, ₆b, between a first radius running between a center of the sun gear 70 and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the third pinion 78. The first and second angles asb and asb need not be identical though they are shown as identical in FIG. 14. These angles may be identical when the value of N is kept constant.

The angles s_aand as_b (see FIG. 14) may be increased by means of motors operatively engaged to second pinion 77 and third pinion 78. The positions of these pinions may be adjusted to comply with the equation

Si+S₂)). As in the case with three pinions and a ring (FIG. 9), another rule may have to be followed. When adjusting the position of second pinion 77 or third pinion 78 in order to maintain the equation =n-(360/(R-S)) during diameter shifting, gap 71 may not be situated along the arc subsumed by as_a or asb as the case may be but rather should be located in the arc subsumed by the complementary angle having an arc of X degrees, where X = (360 - ( s_a + asb)). Just as with the embodiment shown in FIGS. 9-13, during diameter shifting regarding the embodiment shown in FIGS. 14-17, gap 59 may be in the arc subsumed by the complementary angle where this equation is not maintained. When considering this rule for angle as_a, angle as_b is not considered in measuring the complementary arc/angle and when considering this rule for angle a_5b, angle s_ais not considered when measuring the complementary arc/angle. For example, with respect to angle as_a gap 71 can be in the arc subsumed by angle s_c. Similarly, regarding angle as_b gap 71 can be in the arc subsumed by angle s_c.

As shown in FIG. 20, the present invention may also be described as a method 300 of operating a discretely variable diameter gear set in which a sun gear has a tooth sequence, a secondary sun gear is co-axial with the sun gear and enmeshed with a fourth output pinion, a fifth pinion and a sixth pinion, a first idler gear is enmeshed with the sun gear and enmeshed with a first output pinion, the first output pinion is co-axial with the fourth output pinion, a second idler gear is enmeshed with the sun gear and enmeshed with a second pinion, the second pinion is co-axial with the fifth pinion, a third idler gear is enmeshed with the sun gear and enmeshed with a third pinion, the third pinion co-axial with the sixth pinion.

Method 300 may include a first step 310 of adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence. Further, method 300 may include a step 320 of moving, during the adjusting of the diameter, the second pinion 77 to adjust an angle, άι, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun, in a manner that the gap is not situated along an arc subsumed by a\. In FIG. 14, the angle ( i is labeled as s_a.

In a further step 330, method 300 may also include moving, during the adjusting of the diameter, the third pinion 78 to adjust an angle, ₂, between a first radius running between a center of the sun gear and a center of the first output pinion and a third radius running between the center of the sun gear and a center of the third pinion, to maintain an equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun, in a manner that the gap is not situated along an arc subsumed by U_\ + 2, where i and ₂ are adjacent angles. In FIG. 14, the angle ₂ is labeled as a₅b. Method 300 may involve moving the second and third pinions 77, 78 simultaneously during the adjusting of the diameter.

As a result of the fact that gear set 10, 11, 12, 13 may have a variable effective number of teeth while allowing toothed engagement around an entire periphery of sun gear 20 (which may have an effectively cylindrical shape) regardless of its diameter, gear set 10, 11, 12, 13 may be able to transmit high torque at high efficiency.

Moreover, discretely variable diameter gear set 10 may be capable of shifting gears under full load without a clutch disengagement or torque discontinuation.

A wind turbine having a gearbox that includes gear set 10, 11 , 12, 13 of the present invention may extract more energy from a fixed speed turbine by turning it into a variable speed turbine. The power extracted by the turbine from the wind may be calculated by the following formula:

P ——p _* V^s _* C

2 * where

p= Air density

A = Rotor's swept area V = wind speed

Cp = Power coefficient

In stall-controlled turbines, the Cp is at its maximum point only at one wind speed, and at other wind speeds Cp is reduced. The use of variable speed allows the turbine to improve the Cp. For every wind speed, there is one rotor speed that is a maximum point. The use of variable speed allows the turbine to reach these maximum points.

The gear set of the present invention is referred to herein as "discretely variable" in diameter since the diameter of the sun gear varies in diameter by discrete whole numbers of teeth of the tooth sequence around the periphery of the sun gear. In may be appreciated, however, that during the very small time span in which the actual shifting of diameter occurs, the change in diameter occurs continuously rather than discretely. Other than during the actual shifting, the magnitude of the diameter of the sun gear may be measured in discrete whole numbers measuring an effective number of gear teeth.

How the Sun Gear Opens

The following description and analysis is provided to illustrate and provide a particular example of how, in any of the configurations of the gear set of the present invention, the sun gear may open radially and expand the diameter of the sun gear and the radius of the gear teeth while still maintaining a circular shape that allows the sun gear to enmesh successfully and maintain toothed engagement with other circular gears such as the first, second and/or third idler gears (32, 34, 68) referred to in the four main embodiments herein. During the diameter shifting, moreover, the gear teeth of the sun gear may remain at a constant pitch. Figure 23 shows an embodiment of a variable gear device, constructed and operative according to an aspect of the teachings of the present invention, generally designated 110, which is shown engaged with an idler gear arrangement 1100, for use as part of a variable ratio transmission system.

Generally speaking, variable gear device 110 has an axle 120 defining an axis of rotation 122. A gear tooth set includes at least one, and in this case two, displaceable gear tooth sequences 1 11, each formed from a plurality of interconnected gear teeth 12 lying on a virtual cylinder coaxial with axle 120. Gear teeth 112 in each gear tooth sequence are spaced at a uniform pitch.

As best seen in FIG. 24A, a torque linkage is mechanically linked to axle 120 and to gear tooth sequence 111 so as to transfer a turning moment between the axle and the gear tooth set. In the preferred example illustrated here, the torque linkage is formed by a radially displaceable shaft 124, attached to or integrally formed with a given tooth 1 12, referred to as the "alpha" tooth. Shaft 124 passes through a corresponding slot in axle 120, typically via a linear bearing (not shown).

As best seen in FIGS. 24A-24E, variable gear device includes a diameter changer which includes at least one disc 1 14 having a spiral track 116. Each gear tooth 112 is mechanically linked to spiral track 116 such that rotation of disc 114 relative to axle 112 causes variation of an effective diameter of the virtual cylinder while maintaining the virtual cylinder centered on the axis of rotation and while the uniform pitch remains constant.

According to a preferred but non-limiting embodiment of the invention illustrated here, the diameter changer includes a pair of discs 1 14 deployed on opposite sides of each gear tooth sequence 111, and each gear tooth 112 is mechanically linked to the spiral track of both of the pair of discs. This provides stable and symmetrical support to define the radial position of each tooth. In the views of FIGS. 24A and 24B, the disc closer to the viewer has been removed for clarity of presentation.

According to a preferred but non-limiting embodiment of the invention illustrated here, the spiral track is implemented as a spiral slot 116, which may be a through-slot or may be formed on only one face of disc 114. When the track is implemented as a slot, each gear tooth 112 preferably has an associated projection, such as a pin 118, which engages and slides within spiral slot 116. Each pin 1 18 typically has a unique offset, i.e., radial position relative to the geometrical center of the corresponding tooth 112. Thus, for example, looking at FIG. 24A, pin 118 for the alpha tooth is at the maximum radially inward offset while the tooth at the other end of the tooth sequence has the maximum radially outward offset. This corresponds to the portion of the spiral slot with which each tooth is engaged in order to maintain the gear teeth on a virtual cylinder.

The overall effect of rotation of discs 114 relative to axle 120 is illustrated in

FIGS. 26A-26E. This sequence of views shows the change in effective diameter of a single tooth sequence while the axle and the alpha tooth are kept at a constant angular position (12 o'clock) while disc 114 is rotated anticlockwise as viewed here. The corresponding change in effective diameter of the pitch centers of the teeth, corresponding to the aforementioned "virtual cylinder", is shown as a solid circle next to each drawing. The dashed- line circle represents the outer boundary of disc 1 14 as a reference.

At this point, it will be helpful to define certain terminology as used herein in the description and claims. Reference is made to a "gear tooth sequence". This refers generically to any strip, chain or other support structure which maintains the required spacing between the teeth around the periphery of the gear device in its various different states. In certain particularly preferred implementations of the gear tooth sequences of the present invention discussed below, the gear tooth sequences are formed from sequences of gear teeth which have hinge joints between them.

Reference is made to gear teeth in each gear tooth sequence having a "uniform pitch". The "uniform pitch" here is defined functionally by the ability to mesh with a given idler gear arrangement 1100 or chain across the entire range of variable diameters of gear device 110. It will be noted that a full geometrical definition of the "pitch" is non-trivial since the radius of curvature of the tooth sequences varies between states, and thus the distance between the tips of adjacent teeth typically vary as the gear device is adjusted. Furthermore, the angular pitch between adjacent teeth necessarily varies as the radial position of the tooth sequences varies. As a non- limiting exemplary geometrical definition, in some cases, it may be advantageous to maintain a constant distance between the geometrical centers (defined as the intersection of the standard pitch circle and a center line of the tooth) of adjacent gear teeth during adjustment of the gear device. In other cases, it may be preferable to maintain the distance along the pitch circle between adjacent geometrical centers substantially constant. The differentials between these definitions are typically small, and they all fall within the aforementioned broad functional definition of enabling meshing with a given idler gear over the entire range of variable diameters. Nevertheless, these options may correspond, or approximate, to different structural implementations of the linkage between adjacent teeth, and this may have an impact on the analysis and solution of the form of spiral guide track required. These distinctions will be addressed further below. Reference is made to an "effective number of teeth" of gear device 1 10 in each state. The effective number of teeth in any given state is taken to be 2π divided by the angular pitch in radians between adjacent teeth about the axis of rotation. In intuitive terms, the effective number of teeth corresponds to the number of teeth that would be in a simple gear wheel which would function similarly to the current state of gear device 1 10. Where two or more tooth sequences are used with their gear teeth aligned in-phase with each other, the effective number of teeth is simply the number of teeth of the combined gear tooth set as projected along the axis.

Where two or more gear tooth sequences are used, reference is made to a "degree of peripheral coextension" between the gear tooth sequences. The degree of peripheral coextension corresponds to the angular extent of coextension of the gear tooth sequences around the periphery of the effective cylindrical gear, independent of the current diameter of the cylinder. When reference is made to a variable degree of peripheral coextension, this includes the possibility of the coextension being reduced to zero, i.e., where one tooth sequence provides one tooth and another provides the next tooth without any overlap therebetween. In certain particularly preferred embodiments, the maximum diameter state of each tooth sequence extends around more than half the periphery of the virtual cylinder. In this case, the peripheral coextension of the tooth sequences is preferably greater than zero.

Reference is made to an "effective cylindrical gear" to refer to a structure which is capable of providing continuous toothed engagement with a simple or compound cylindrical idler gear. The individual gear sequences of the present invention typically have spaces in them, as illustrated in FIGS. 24A and 24B. However, when used together, as illustrated in FIG. 23, they allow continuous engagement around the entire revolution of the gear device. It will be noted that the present invention may be used to advantage in transmissions based on directly engaged gear wheels and in chain-based transmissions. In all cases, it may be helpful to refer to an idler gear as a theoretical construct which may be used to define the geometrical properties of gear device 1 10.

An "idler gear arrangement" in this context is any gear configured for toothed engagement with gear device 110. The term "idler gear arrangement" is used to reflect a typical arrangement in which an idler gear arrangement is an intermediate component in a gear train, but without excluding the possibility of the "idler gear arrangement" being directly connected to a power input or power output axle. The idler gear arrangement is typically a compound idler gear in which two or more gear wheels are mounted so as to rotate together with a common idler axle, such as is illustrated in FIG. 23. The gear wheels making up a compound idler gear are typically identical and in-phase (i.e., with their teeth aligned), but may be implemented as out- of-phase (non-aligned teeth) gear wheels if a corresponding phase difference is implemented between the tooth sequences.

Turning now to the features of an embodiment of the invention in more details, as mentioned, the gear teeth in each gear tooth sequence are arranged so as to have a constant pitch in all states of the variable diameter gear wheel. Whatever the precise measure of pitch used, the property of maintaining constant pitch between teeth as the diameter changes necessarily results in a variable angular spacing of the teeth around the axis of the device as the diameter varies. This is clearly visible by comparing the positions of the first and last gear teeth in Figures 26A and 26E. As a result, a simple Archimedean spiral (radius increasing as a linear function of angle) cannot provide a true circular geometry throughout the range of diameters. A closer approximation is provided by a logarithmic spiral, which has the property of a constant increase in radius for a given length along the spiral. This too is not a theoretically perfect solution, since it is the pitch which is constant rather than the distance between pins of the offset brackets along the spiral slot. Nevertheless, particularly for a relatively shallow-angle spiral, a path corresponding to, or approximating to, a logarithmic spiral may be found, either by analytical numerical methods or empirically by trial and error, to maintain the circular profile of the gear teeth at each diameter to within an acceptable range of tolerances throughout the range of diameters covered by the device.

By way of non-limiting examples, the Theoretical Analysis section below sets out a theoretical analysis and a practical example of a solution for the shape of the spiral slot and the corresponding pin offsets. The particular values mentioned as an example in the example may be regarded as indicative of a particularly preferred example, but are also non-limiting with regard to the general scope of the present invention.

It will be appreciated that, during normal driving engagement with variable diameter gear 110 while no transmission ratio shift is being implemented, tooth sequences 11 1 and discs 114 rotate at the same speed. When a shift in transmission ratio is required, a predefined angular motion between discs 114 and tooth sequences 1 11 is performed. Various mechanisms may be used to ensure that the discs and tooth sequences normally turn together and can made to undergo relative rotation as required. One non-limiting example is illustrated herein with reference to FIG. 27.

Thus, according to an embodiment of the invention, the diameter changer has an adjustment mechanism in which a planetary gear assembly has a first input driven, directly or indirectly, by rotation of axle 120, an output directly or indirectly driving rotation of discs 114, and a diameter adjustment input. The planetary gear assembly is configured such that, when the adjustment input is maintained static, disc 114 is driven to rotate in constant angular alignment with axle 120, and when the adjustment input is rotated, disc 114 undergoes a corresponding rotation relative to axle 120.

Specifically, the non-limiting preferred example of FIG. 27 illustrates a gear wheel 126, which is fixed to rotate together with axle 20 (and hence also with the gear tooth sequences 1 11 which are omitted here for clarity). Gear 126 engages a gear 128 which turns the "planets" yoke of a planetary gear arrangement 130. The "sun" 132 of the planetary gear arrangement is fixed to an axle 134 which also rotates gear wheels 136 which engage a gear wheel 138 integrated with the discs 114. An actuator, such as a motor (not shown), is deployed for selectively driving an outer ring 140 of the planetary gear arrangement in order to effect the diameter change. The ratios of all of the gear wheels in this sequence are chosen such that, when outer ring 140 of the planetary gear arrangement is kept still, gears 126 and 138 turn at the same angular rate, thereby keeping gear tooth sequences 111 and discs 114 in constant angular relation as they rotate. Rotation of outer ring 140 of the planetary arrangement causes angular displacement between gear tooth sequence 11 1 and disc 114, thereby achieving diameter adjustment.

The embodiment of the adjustment mechanism described here is believed to provide various advantages, including allowing control of ratio shifting by operation of a single motor, and by avoiding structural complexity of the central axle of the device. Nevertheless, it should be noted that alternative implementations of an adjustment mechanism for controlling rotation of discs 114 relative to axle 120, for example, employing an on-axis mechanism for varying alignment of coaxial hollow shafts, also fall within the scope of the invention. Referring again briefly to FIG. 23, as mentioned above, an embodiment of variable gear device 110 employs a gear tooth set including two similar displaceable gear tooth sequences 111 which are displaced by the diameter changer so as to vary a degree of peripheral coextension between at least the first and the second gear tooth sequences. Gear device 1 10 is thereby transformed between a first state in which the gear tooth set is deployed to provide an effective cylindrical gear with a first effective number of teeth, and a second state in which the gear tooth set is deployed to provide an effective cylindrical gear with a second effective number of teeth greater than the first effective number of teeth.

Theoretical Analysis

Presentation of the Problem

Referring now to FIGS. 28-32, a theoretical analysis and practical example of a solution for the shape of a spiral slot and corresponding pin offsets for various cases will be addressed. It should be noted that this analysis is provided to facilitate understanding, but should not be considered to limit the scope of the present invention, which may be implemented in numerous alternative ways. Specifically, the approximation of the spiral as a logarithmic spiral, with or without further adjustments by calculation or by trial and error, is fully sufficient to allow implementation of the present invention as claimed, independent of the accuracy or otherwise of the theoretical analysis herein. The particular values mentioned as an example below may be regarded as indicative of a particularly preferred example, but are also non-limiting with regard to the general scope of the present invention.

The geometric analysis relates to a situation as described in which, by employing a rotating spiral groove, a gear can change its outer diameter between two given limits. In the process of diameter increase, the teeth are pushed out, keeping their outer ends on a common circle. In the increased circumference, additional effective teeth are introduced (for example, by overlap of two sequences), keeping the gear complete at all times.

In the process of diameter increase, the number of effective teeth changes from some Zmi_n to z_max. During this process, all teeth move outward in their radial direction, but only one tooth, named the "alpha tooth," remains in a constant angular direction, while all other teeth change their angular orientation in addition to their radial displacement. A schematic description of the rotation mechanism is shown in FIG. 28.

In FIG. 28, the gear wheel is shown in its closed state, with teeth numbered from 1 to Zmin, while the alpha tooth gets the number k. All teeth are attached to a spiral groove, etched in the rotating disc. The attachments are done via pins, with an offset length appropriate for each individual tooth. From the closed state (as shown in FIG. 6) the disc rotates counter-clockwise (CCW), while all teeth attachments slide in the groove in the clockwise (CW) direction - relative to the disc. During the disc rotation, the alpha tooth is kept in a fixed (x) direction, moving outward radially, according to the local slope of the spiral. At the same time all the other teeth also slide along the spiral, while increasing their pitch diameter. Since the teeth are linked to one another by a rigid link (see FIGS. 30A and 30B below), they are forced to decrease their angular pitch in accordance with the diameter increase. As a result, all teeth become closer to the alpha tooth in their angular position, which means that an angular gap is being created between tooth 1 and tooth z_min. This gap is assumed to be filled by additional effective teeth (e.g., from another gear tooth sequence not shown here), so that the total number of effective teeth increases to z_max. The angular position of the teeth along the spiral is measured by the angle φ, such that in a closed gear (with minimum number of teeth) the alpha tooth is at angle φ = 0. When the disc with the spiral groove is rotated CCW by a certain angle φ, the angular value of the alpha tooth increases by exactly the same amount φ, but the increase is in the CW direction relative to the disc (see FIG. 28). At the same time, because of the changing angular distance between adjacent teeth, all teeth except the alpha tooth change their angular position on the spiral by an angle slightly different from <p. For all teeth between 1 and k the angular change along the spiral becomes slightly greater than φ, while for all teeth above k the change is slightly less than <p. This variation of angular displacement is used for devising an approximate analytic solution of the spiral function, as shown below.

Approximate Analytic Solution

The analytic solution given in this section derives a differential equation of the spiral radius, which depends on the spiral angle φ (FIG. 28). For the definition of the differential equation we reduce the pitch length, p, to an infmitesimally small magnitude. A projection of p on the spiral, which will be called here the "spiral pitch," is approximately proportional to p. The spiral pitch will be named q. FIG. 29 shows two such infinitesimal spiral-pitch lengths on the assumed spiral curve.

If we imagine that the disc with its spiral groove is rotated CCW by a small angle, such that the tooth positioned at r\ moves to r₂, while the tooth at r₂ moves to r₃. The radius of the spiral grows from one step to the next (r₂>ri), while the spiral pitch, q, is assumed constant, which means that the consecutive angular steps must decrease. At the same time, in order to keep the pitch radius of the teeth unique, the radial increment, dr, must be kept constant. The derivative of the spiral radius at position r is dr/άψι. According to the

Y

explanation given in the preceding paragraph, the derivative at position ² must be modified to

dr _ dr r₂ _ dr r_x + dr

d<p d<p_x r_x d<p_x r_x _ ^i) The second derivative of the spiral radius is by definition given by

where άψ is an "average" angular step.

A substitution of Equation 2.1 in Equation 2.2 gives the following differential equation of the spiral radius:

The solution of Equation 2.3 is given by the following simple exponential function: r(_V) = r₀e^b (2.4)

where ro and b are parameters to be determined by additional conditions of the spiral. Here ro is the (yet unknown) spiral radius at φ = 0 (which is the position of the alpha tooth on the spiral in a closed gear), and b is the slope of the spiral. An optimal solution of these parameters is derived by an iterative calculation of curve fitting, shown in Chapter 5. For starting the iterations we need some initial values of the two parameters. For such initialization we assume that the spiral is rotated from φ = 0 to some maximum turn angle, φ^~ψπιαχ·, while the pitch radius grows from R_mm to R_max . For the initialization we only need very approximate parameter values, for which it can be assumed that the spiral radius (at the alpha tooth) is equal at all times to the current pitch radius, which means that r(0) = R_min and r(<p_max)=R_max. These two conditions result in the following initial parameter values:

ro = Rmin, (2.5) b =— ln^__

max ^min _ (2.6)

Side Hinge Links

FIGS. 30A and 30B illustrate two non-limiting geometrical arrangements for interlinking of adjacent teeth of the tooth sequences. In the option of FIG. 3 OA, each tooth corresponds to a pivot axis in the linkage. This arrangement typically maintains a substantially constant linear pitch between adjacent gear teeth.

An alternative linkage, referred to as a "side hinge link" or a "tooth centered link", is shown in FIG. 30B. This linkage may be preferred in certain cases, since it provides a better approximation to a constant pitch between teeth as measured along the pitch circle.

In a center hinge link such as in FIG. 3 OA, the chord, which is the linear distance between adjacent teeth, is constant, which means that in a variable-diameter gear the circular pitch varies as a result of the diameter change: the greater the diameter, the smaller becomes the circular pitch. In a side hinge link, in contrast, as a result of the diameter increase there is a slight increase of the linear distance between adjacent teeth, which to a large extent compensates for the circular-pitch variation which occurs in the center hinge geometry.

The exact geometry of a side-hinge link is determined for a gear wheel with a given number of teeth, zi, and a given module, giving a certain pitch radius, Ri. The characteristic geometric parameters of a side-hinge link are shown in FIG. 31. In this basic geometry, all the tooth centers and the hinging points are located on the same pitch circle of radius Rj. The hinging points are located at exactly a halfway between the angular teeth locations. The pitch angle, τ_?, is in this case given by

For the later calculations of variable diameter we shall need the values of the parameters u and v, shown in FIG. 31. These parameters are given by u = ( R, — h ) sin— , v = R, - (R, - h) cos—

' 2 > 2 , (3.2) where h is a given displacement of the hinge point from the pitch circle.

The pitch radius, Ri, is given by

where m is the module.

Suppose now that the number of teeth in the gear has been changed to z₂, with a new pitch radius R₂. In the new gear, the linear distance between adjacent teeth is determined by the geometry shown in FIG. 32.

In the new gear, the pitch angle is given by

And, according to the geometry in Figure 27, the linear distance between tooth centers is f τ τ ^Λ

s₂ = 2 ί/ cos— + vsin—

(3.5) where u and v are given by Equations 3.2.

It can be verified that in the original gear, with number of teeth equal to zj, Equation 3.4 reduces to si = 2u, as it should be (compare with FIG. 9). This result is obtained by substituting τ_? instead of τ₂ in Equation 3.5, in addition to the substitution of the explicit expressions of u and v from Equations 3.2. According to Figure 27, the pitch radius in the modified gear, R₂, is given by

and the circular pitch of the two gears is given by

and 2₈₁ ^η(τ₂/2) _ ^

Optimal Displacement Determination

An "optimal" value of the hinge displacement, h (FIG. 31), by our definition, is such which equates the circular pitches of the two gear sizes, z and z^. The equality requirement states that

pi = P2 , (4.1)

where pi and j¾ are the corresponding circular pitches in gears with zj and teeth, respectively.

By using the explicit Equations 3.7 and 3.8 for the two circular pitches, Equation 4.1 becomes

2sin (r₂/2) _^ ^ where ¾ is given by Equation 3.5.

Notice that ¾ depends on the displacement, h, via u and v, which are functions of h, as given by Equations 3.2. Hence, by substituting Equations 3.2 in Equation 3.5, and then substituting the resulting expression of _¾ in Equation 4.2, we get a single equation which is linearly dependent on h. This linear equation provides the following solution of the necessary displacement:

where Rj is the pitch radius of the first gear (Equation 3.3), and n and ¾ are the pitch angles of the two gears (Equations 3.1 and 3.4).

Since n and are very small angles, the sines in Equation 4.3 can be expanded into a power series, retaining only the first two terms of the series and ignoring the rest. As a result of such expansion, Equation 4.3 is reduced to the following simple approximation:

24 ^{2 U} . (4.4)

Equation 4.4 provides results practically identical to those of Equation 4.3.

Obviously, the displacement, h, can be determined by equating the circular pitches of any two selected gear sizes, z and z^. For other gear sizes, different from either z or z^, the resulting circular pitch (for the given h) will differ slightly from the original circular pitch, pj. For a given number of teeth, zj, the resulting circular pitch, p can be calculated by an equation similar to Equation 3.8:

where τ, is the pitch angle and Si is the corresponding distance between the tooth centers, both calculated by equations similar to Equations 3.4 and 3.5.

As said before, there will be a slight difference between the resulting circular pitch, pi, and the original pitch, p_t. This difference is given by

Api = Pi -pi. (4.6) As a numeric example for demonstrating the effect of the hinge-point displacement, the following parameters were used:

m = 5 mm Module

Z] = 36 Number of teeth in basic gear

Z2 = 48 Number of teeth in increased gear

Without displacement, i.e., when h = 0, the circular pitches of the two gears become:

pi= 15.7080 mm, j¾= 15.7105 mm,

which show a difference of 2.5 μ.

In order to reduce the magnitude of j¾ exactly to the length of pi, the "h" displacement, calculated by Equation 4.3 or 4.4, becomes

h = 57.1 μ.

With such hinge displacement, j¾ becomes exactly equal to pi, but at the other intermediate gear sizes, small deviations from pi still remain. These deviations, calculated by Equation 4.6, correspond to a maximum pitch difference of only about 0.6 micron.

Optimal Solution

By rotating the disc from its initial orientation (<p = 0) to final orientation (<p = the pitch radius of the gear increases from a given R_min (closed gear) to some Rmax (open gear), while the number of teeth increases from a given z_min to a given z_max. In one of these limits, say at the closed state, the pitch radius can be obtained exactly, such that all teeth can be positioned at the same identical R_mi„. This condition is achieved by choosing the appropriate exact bracket offsets which connect all teeth to the computed spiral in the closed state of the gear. However, by rotating the disc to the other limit, with the number of teeth increased to z_max, all teeth will not exactly match at a common pitch radius, but each tooth will deviate to a certain extent from some average pitch radius. The goal of the optimal solution, given in this chapter, is to find the best set of parameters ro and b (Equation 2.4) which will minimize, as much as possible, the radial differences of the individual teeth in all stages of the disc rotation.

The required data for the spiral design include the following input parameters: m - module

Zmin - minimum number of teeth

^m_ax - maximum number of teeth

k - sequential number of the alpha tooth

ψηιαχ - maximum turning angle

All the rest is calculated as will now be explained.

Rmin⁼ mz^m,nl2 Minimum pitch radius (5.1)

zi = 360/z_min Pitch angle in closed gear (5.2)

T2 = 360/z_maxPitc angle in open gear (5.3)

We assume at present that the side-hinge link is determined by the minimum number of teeth, z_m„, which means that for the calculation of the u and v parameters, z_min and Rmin have to be substituted for zi and Ri, respectively. In that case, the linear pitch distance, ¾ and the maximum pitch radius, R_max, are calculated by Equations 3.4 and 3.5, respectively, where ¾ is given by Equation 5.3. The u and v parameters, required for executing Equation 3.5, are calculated by Equations 3.2, using a hinge displacement, h, calculated by Equation 4.3 or 4.4. (Notice that the maximum radius is not exactly proportional to the number of teeth because of the constrained step ¾.)

In the closed gear, the alpha tooth is by definition positioned at the spiral angle φ = 0, with all the other teeth, at different angles, given by

, 2,..., z_max. (5.4)

Equation 5.4 is calculated for all teeth, even though in the closed state there are only z_m!-„ teeth in the gear. However, in this state the extra teeth (from z_mi_n + 1 to Zma ) are still attached to the spiral, with an overlapping of a corresponding portion of the other teeth (from 1 to z_max - z_min).

In the open gear the alpha tooth slides to φ =φ _ηαχ· In this state, the spiral angles of all teeth are calculated by

ψ2ί = ψηιαχ +(i-k)z₂; z = 1 , 2,..., Z_max. (5.5)

Now, for given (or guessed) values of the parameters r^and b the spiral radii of the closed and the open gears can be calculated by using Equation 2.4: 0 closed gear, (5.6) l^{i ~ r}°^e open gear. (5.7)

In the closed gear all teeth can be positioned on an exactly equal pitch radius by using appropriate bracket offsets which correspond to such condition:

where R_mj„ is the given minimum pitch radius.

The bracket offsets, calculated by Equation 5.8, remain constant at all turning angles of the disc, implying a certain maximum pitch radius of the individual teeth in the open gear:

Since the entire calculation is not completely accurate, the resulting maximum pitch radii, given by Equation 5.9, will not exactly match the requirement of the maximum pitch radius, ^{m x} , given by Equation 3.6. The following residuals will be created: ARi = R_2i - R_max. (5.10) The problem is now to find a best combination of the parameters TQ and b which would minimize, as much as possible, the ARi residuals. For the convenience of such minimization, Equation 5.10 is written in a more explicit form by a substitution of Equations 5.6 through 5.9 there:

AR_i = r₀ (e^ - e^ ) - (R_max -R_mm ) ^ ^ where ψη and ψ2 are the spiral angles in the closed and in the open gear, given by Equations 5.4 and 5.5.

Assume now that we wish to enforce a certain ARi to zero by varying the system parameters, TQ and b, by a small amount, Ar^and Ab. Since the variations involved are small numbers, the zeroing condition can be reduced to the following linear approximation: dAR_t dAR_t

Ar₀ H Ab = AR.

dr₀ db ' _{(5 n)}

The derivatives used in Equation 5.12 are directly obtained from Equation 5.1 1 :

db (5.14)

In reality, we have not just one equation of the type 5.12, but a list of such equations, in accordance with the list of ARi residuals. This system of equations can conveniently be written in the following matrix form: TAV = AR. (5.15) The variables contained in Equation 5.15 are arrays, defined as follows. T is an «x2 "transformation matrix," constructed of the derivatives given by Equations 5.13 and 5.14: dAR_l dAR_l

dr_n db dAR„ dAR

db

(5.16) a correction vector of the optimization parameters:

and AR is a vector of residuals:

The size of the system, n, can in principle be equal to the maximum number of teeth, z_max, or be some smaller number, as will be explained later.

Equation 5.15 is an over-determined system of equations because it has more constraints (number of residuals) than unknowns (the corrections Aro and Ab). Such system cannot in principle be solved completely, but it can be optimized by a minimization of the Root-Mean-Square (RMS) of the residuals: " -ⁱ , (5.19) where ARi is given by Equation 5.10 or 5.1 1.

The method of minimization (called the Least-Square or LS method) has a well known solution, according to its original definition by Newton and Gauss: AV=( ^rT)^{~1 r}AR. (5.20) In linear problems, a single execution of Equation 5.20 provides the final result of the LS solution. In nonlinear problems, such as the present spiral design, a single calculation of Equation 5.20 is not sufficient, and an iterative process becomes necessary. By this procedure, after every calculation of Equation 5.20 the system parameters are corrected by

r₀=r₀ - Ar₀ (5.21)

b = b - Ab, (5.22)

where Aro and Ab are the first and the second terms, respectively, of the correction vector computed by Equation 5.20 (see Equation 5.17).

Following the parameters' correction, the arrays T and AR are reconstructed (by recomputing all relevant parts from Equations 5.6 through 5.18), after which Equations 5.20 through 5.22 are executed again. The iterations continue until the RMS change (Equation 5.19) becomes small enough.

The bracket offsets, calculated by Equation 5.8, guarantee an accurate pitch radius in the closed gear, which matches all teeth, while in the open gear some radial residuals, AR_h still remain. These residuals, however, can be halved by means of decreasing all offsets, /,·, by one half of AR_t. The decreased offsets are computed by

where on the right hand side of Equation 5.23, /; is taken from the latest calculation of Equation 5.8. By this way, all the original residuals will be evenly divided between the closed and the open gears, at only one half of their original values.

The resulting offsets, are defined here as the distance between the spiral (at the center of the groove on the disc) and the pitch radius. However, in case the point of attachment of the bracket to the tooth is not exactly at the pitch radius, an appropriate correction of the bracket offset must be made.

We shall now define the desired size of the equation system, given by n in Equations 5.16 and 5.18. As illustrated by a numeric example below, the radial residuals, which result from the LS solution, display a parabolic function of the angular position, where the greatest residuals (in their absolute values) are at the two ends and in the middle of the teeth range. If we are interested in a minimax solution (which makes the maximum residual as small as possible), we should give in the process of the LS solution a maximal weight to those extreme points, and ignore all the other teeth. In order to make the solution symmetric, only four teeth have to be considered for the equation system, namely the first, the last, and two teeth in the middle. For example, if the number of teeth (z_max) is 48, the teeth selected for the optimization have to be

i = 1 , 24, 25, and 48, (5.24)

which makes n = 4, and retains only four rows in Equations 5.16 and 5.18.

The results shown in the next chapter confirm that such selection actually provides the desired minimax solution.

Another comment concerning a possible improvement of the LS calculation is given. As mentioned before, Equation 2.4 is a nonlinear function of b, which implies that the LS solution must be made with the aid of iterations, simultaneously for the two system parameters, rg and b. However, the rg parameter appears in Equation 2.4 in a linear form, which means that it can in principle be extracted from the calculations by expressing it as a function of the other parameter, which is b. By such procedure the LS solution can be reduced to a form of a single unknown, which requires a single solution of a nonlinear function of φ, and also rids us of the matrix arithmetic. Such improvement, however, requires a more complicated mathematical preparation, which could be done in a case of a necessity to reduce the computational load of the calculations.

Numerical Example

For the numeric example shown below the following input data has been used: m = 5 mm Module

= 36 Minimum number of teeth

= 48 Maximum number of teeth

k = 13 Sequential number of the alpha tooth

ψπιαχ = 500 dej I Maximum turning angle

According to Equations 4.1 through 4.3, the following geometric parameters have been computed:

Rmin ⁼ 90 mm Minimum pitch radius

Ti = 10 deg Pitch angle in closed gear

τ₂= 7.5 deg Pitch angle in open gear

In this example, the side-hinge link is determined by the minimum number of teeth, which is 36. Its characteristic dimensions, according to Equations 3.2, become u = 7.8390 mm, v = 0.3994 mm

with the optimal hinge displacement, h (Equation 4.4),

/z = 0.0571 mm.

Initial values of the estimated parameters, according to equations 2.5 and 2.6, are in this case

b = 5.743xl0^"4 1/deg. Next, the angular values of all teeth in the two extreme states of the gear, <pn and ψ2ί, are computed only once by using Equations 5.4 and 5.5. After that, the execution of Equations 5.6 through 5.22 is repeated until the change of RMS (Equation 5.19) becomes smaller than 0.01 mm. In this case, four iterations were required for convergence. The resulting optimization parameters were the following:

ro = 83.68 mm,

b = 6.137 X 10-⁴ _1/deg>

After convergence, a halving of the radial residuals was made by applying Equation 5.23.

The teeth numbers, selected for the residual minimization, were those given by Equation 5.24.

The residuals for three different rotation angles of the disc were calculated: no rotation (closed gear), full rotation (500 deg, open gear), and an intermediate rotation (250 deg). The maximum calculated residuals were 0.06 mm, and they appear in the extreme rotation states - no turn or maximum turn. At the intermediate rotation the maximum residual is one order of magnitude smaller than at the extreme states. These values are well within the manufacturing tolerances which are considered acceptable for implementation of a gear wheel.

The use of the hinge displacement, h, introduced for keeping the circular pitch nearly constant (see above), makes a change of about 0.1 mm in the spiral radius, but it does not have any detectable effect on the radial residuals.

In this example, the radius varies between 77.7 and 133.6 mm.

While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made. Therefore, the claimed invention as recited in the claims that follow is not limited to the embodiments described herein.

Claims

WHAT IS CLAIMED IS:

1. A discretely variable diameter gear set having a planetary configuration, comprising:

a ring;

a sun gear having a tooth sequence, the sun gear capable of opening and closing radially to adjust a gap in the tooth sequence and a diameter of the sun gear by a discrete effective number of teeth;

a first idler gear enmeshed with the sun gear;

an output pinion enmeshed with the first idler gear and with the ring;

a second idler gear enmeshed with the sun gear; and

a second pinion enmeshed with the second idler gear and with the ring, the sun gear always enmeshed with at least one of the idler gears.

2. The gear set of claim 1, wherein the sun gear tooth sequence has a variable effective number of teeth ranging from 34 to 46.

3. The gear set of claim 1, further including one or more idler gear movers capable of moving the one or more idler gears enmeshed with the sun gear away from the sun gear to compensate for an increase in diameter of the sun gear when the sun gear opens radially.

4. The gear set of claim 1 , wherein the second pinion maintains a rotational distance from the output pinion, the rotational distance being a function of an effective number of teeth in the tooth sequence of the sun gear.

5. The gear set of claim 1, wherein the sun gear is not enmeshed with a pinion.

6. The gear set of claim 1, further including a third idler gear enmeshed with the sun gear and further including a third pinion enmeshed with the third idler gear and with the ring.

7. The gear set of claim 6, wherein the the sun gear is always enmeshed with at least two of three idler gears.

8. A method of operating a discretely variable diameter gear set in which a tooth sequence of a sun gear is enmeshed with two or more of three idler gears, the three idler gears enmeshed with their respective pinions, the pinions enmeshed with a ring, comprising

adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence;

moving, during the adjusting of the diameter, a second pinion to adjust an angle ds_a between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation s_a=n-(360/(R+S)), where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that a gap is not situated along an arc subsumed by as_a; and

moving, during the adjusting of the diameter, a third pinion to adjust an angle, asb, between the first radius and a third radius running between the center of the sun gear and a center of the third pinion, to maintain an equation (X5b=n-(360/(R+S)) where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that the gap is not situated along an arc subsumed by as_a + (X51,, where as_a and asb are adjacent angles.

9. A method of operating a discretely variable diameter gear set having a sun gear having a tooth sequence, a first output pinion enmeshed with a ring, a second pinion enmeshed with a second idler gear and with the ring, the method comprising: adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence; and moving, during the adjusting of the diameter, the second pinion to adjust an angle, a, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation a=n-(360/(R-S)), where n is a constant integer, S is the effective number of teeth on the sun gear and R is the number of teeth in the ring, in a manner that the gap is not situated along an arc subsumed by a.

10. A discretely variable diameter gear set having a planetary configuration, comprising:

a sun gear having a tooth sequence and capable of opening and closing radially to adjust a gap in the tooth sequence and a diameter of the sun gear by a discrete effective number of teeth;

a secondary sun gear co-axial with the sun gear;

a first idler gear enmeshed with the sun gear; a second idler gear enmeshed with the sun gear;

a first output pinion enmeshed with the first idler gear and co-axial with a second output pinion, the second output pinion enmeshed with the secondary sun gear; and

a third pinion enmeshed with the second idler gear and co-axial with a fourth pinion, the fourth pinion enmeshed with the secondary sun gear, the sun gear enmeshed with at least one of the idler gears.

11. The gear set of claim 10, wherein the sun gear tooth sequence has a variable effective number of teeth ranging from 34 to 46.

12. The gear set of claim 10, further including one or more idler gear movers capable of moving the one or more idler gears enmeshed with the sun gear away from the sun gear to compensate for an increase in diameter of the sun gear when the sun gear opens radially.

13. The gear set of claim 10, wherein the sun gear is not enmeshed with a firth or fourth pinion or with a first or second output pinion.

14. A method of operating a discretely variable diameter gear set that includes a sun gear having a tooth sequence, a first output pinion enmeshed with a first idler gear and co-axial with a second output pinion, the second output pinion enmeshed with a secondary sun gear, a second idler gear enmeshed with a third pinion, the method comprising: adjusting a diameter of the sun gear by a discrete effective number of teeth by having the sun gear open or close radially to adjust a gap in the tooth sequence; and moving, during the adjusting of the diameter, the third pinion to adjust an angle, a, between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the third pinion, to maintain an equation

15. A discretely variable diameter gear set having a planetary configuration, comprising:

a secondary sun gear co-axial with the sun gear and enmeshed with a fourth output pinion, a fifth pinion and a sixth pinion;

a first idler gear enmeshed with the sun gear and enmeshed with a first output pinion, the first output pinion co-axial with the fourth output pinion;

a second idler gear enmeshed with the sun gear and enmeshed with a second pinion, the second pinion co-axial with the fifth pinion; and

a third idler gear enmeshed with the sun gear and enmeshed with a third pinion, the third pinion co-axial with the sixth pinion, the sun gear enmeshed with at least two of the idler gears.

16. The gear set of claim 15, wherein the sun gear tooth sequence has a variable effective number of teeth ranging from 34 to 46.

17. The gear set of claim 15, further including one or more idler gear movers capable of moving the two or more idler gears enmeshed with the sun gear away from the sun gear to compensate for an increase in diameter of the sun gear when the sun gear opens radially.

18. A method of operating a discretely variable diameter gear set in which a sun gear has a tooth sequence, the sun gear is co-axial with a secondary sun gear, a first idler gear is enmeshed with the sun gear and enmeshed with a first output pinion, a second idler gear is enmeshed with the sun gear and enmeshed with a second pinion, a third idler gear is enmeshed with the sun gear and enmeshed with a third pinion, the method comprising:

moving, during the adjusting of the diameter, the second pinion to adjust an angle, U\ , between a first radius running between a center of the sun gear and a center of the first output pinion and a second radius running between the center of the sun gear and a center of the second pinion, to maintain an equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun, in a manner that the gap is not situated along an arc subsumed by άι; and

moving, during the adjusting of the diameter, the third pinion to adjust an angle, ₂, between a first radius running between a center of the sun gear and a center of the first output pinion and a third radius running between the center of the sun gear and a center of the third pinion, to maintain an equation

where n is a constant integer, Si is the effective number of teeth on the sun gear and S₂ is the number of teeth in the secondary sun, in a manner that the gap is not situated along an arc subsumed by i + ο¾, where i and ο¾ are adjacent angles.

19. The method of claim 18, further including moving the second and third pinions simultaneously during the adjusting of the diameter.