GB2199633A - Toothed gears and sprockets - Google Patents

Abstract

A toothed gear element in which the tooth profile arcs are generated from two separate circles equidistant from the pitch circle. The toothed gear element may be in the form of a rack (Fig 3), a worm and wheel (Fig 4), or a chain drive sprocket (Fig 6). <IMAGE>

Description

ELEMENTS OF CONVOLUTED ARCUATE GEARS AND SPROCKETS This invention relates to the structure of arcuate gears and chain sprockets, and, to a specific method of generating the gear tooth form, or profile, geometrically.

The shape or form of an involute gear tooth is inherently weak, and the need for an improved gear tooth is evident in constant machinery breakdown.

One alternative is an improved arcuate gear tooth form.

The sharp pointed teeth of chain sprockets are a weakness and a compromise. A correctly proportioned arcuate gear tooth will also be suitable for a chain sprocket.

Former attempts at designing an arcuate gear have resulted in teeth being too long and narrow, narrower in the dedendum part, or having flats or curves other than circular arcs in at least a part of the tooth profile.

The Convoluted Arcuate gears described in the following text, with diagrams, should be adequate for heavy duty, where strain or impact is a serious problem.

To avoid tedious repetition of the phj - Convoluted Arcuate gears whereby the profile arcs are generated from two separate circles apart from the pitch circle and whereby the tooth profile arcs inflect at a point of tangency only the gears will be referred to as Convoluted, or Convoluted Arcuate.

The tangency point is a third tangency point in gear terms, the other two being the pitch points common to involute gears.

The shortened tooth form of Convoluted gears is achieved by generating the tooth profile arcs from a major generating circle in the addendum part of the gear, and a minor generating circle in the dedendum part of the gear.

Convoluted gears have no interference, and have no cLearance other than the minute amount needed for temperature change, and a film of lubricant.

Examples of the tooth form, and method of construction, will be explained with reference to the following briefly tabulated diagrams.

Figures 1 and 2 show the method by which a Convoluted Arcuate gear tooth is constructed.

Figure 3 shows a Convoluted Arcuate rack.

~ . . . ~ ~. , . ~ ,~ Figure 4 shows awormwheel templet and a worm in which the thread profile ia, identical to the profile of a Convoluted Arcuate rack.

Figure 5 illustrates a chain drive in which the sprockets constructed are in exactly the same manner as equivalent diameter Convoluted Arcuate gears, and with a chain whereby the pitch of the link, and chain rollers, is equal to the distance between two adjacent tooth arc vertices on the major generation circle.

Figure 6 shows a Convoluted Arcuate gear, pinion and rack, in mesh.

For an example, a spur gear and pinion are required and the only known factors are the gear ratio and the distance between shaft or pin axes. The ratio is 2:1.

Therefore, the distance between the axes is divided by 3 to give the gear and pinion pitch circle radii,Gear 2/3, pinion 1/3.

The selected number of teeth for that ratio are 36 and 18.

Then, as shown in Figure 1, an arc is drawn of the pitch circle radius for the 18 teeth pinion.

A sector of the pitch circle is drawn whereby the angle at the pitch circle centre equals 3600 divided by the number of teeth.

A chord is drawn, to the pitch circle, which connects the points where the sector lines, or radii, intersect the pitch circle. The chord is bisected and a normal is drawn. The normal and sector lines are produced beyond the pitch circle.

To determine the diameters of the tooth arc generation circles, the chord is divided by ten and the resultant length is added to the pitch circle diameter to give the major tooth generation circle, and is subtracted from the pitch circle diameter, to give the minor circle.

This one tenth of a chord length is a mean of the arbitrary limits of the tooth depth. Having drawn the major and minor tooth generation circle arcs, as in Figure 1, a line is now drawn connecting the point where a sector line intersects the minor generating circle, to a point where the normal intersects the major generating circle. This line, when bisected, gives the radius of a tooth arc. If this measurement does not equal a standard measurement, whether metric or english, then the radius of the tooth arc is increased to the nearest standard increment, and the diameters of the generating circles adjusted accordingly.

This adjustment of tooth arc radius enables prototype gears or maintenance replacements to be cut with standard size milling cutters or hobs, and is imperative in the manufacture of Convoluted worms. Now that the tooth dimensions have been established, the point of inflection and tangency remains at the same distance from the pitch circle vertex, and the line, of revised length, is rotated in an anti-clockwise direction until it intersects the sector line and the normal, at it's full length only.

Having calculated the new radius of the major generating circle by trigonometric function, the sector can be drawn again, as in Figure 2 and the full tooth profile drawn. This shows the tooth arc vertices on the generating circles.

The distance between two adjacent vertices on the major generating circle, measured in a straight line, is the pitch of a Convoluted Arcuate gear or sprocket. It is the pitch of a chain link, as indicated by the letter P in Figure 5.

It is also the pitch of a Convoluted Arcuate rack as shown in Figure 3, and the pitch of a Convoluted Arcuate worm, a cross section of which, appears in Figure 4.

Figures 1 and 2 have been shown as separate drawings for clarity only. If they had been represented by one drawing, that drawing would show four separate generating cir-cles.

The two circles in Figure 1 are necessary for the location of the point of tangency and inflection. When that point has been located and the distance from the pitch circle vertex calculated, then the final diameters of the generating circles can be determined and drawn, as in Figure 2.

A rack, or worm, dimensions must be taken from a Convoluted Arcuate gear, as the distances of the arc vertices from the pitch-line and the tooth pitch cannot be calculated in any other way, with accuracy.

A Convoluted Arcuate gear sector has been superimposed on the rack drawing, Figure 3, to show how a rack drawing is developed and to give the geometrical proof of the rack pitch. It also indicates the relative positions of the point of tangency and inflection, which moves closer tothe pitch circle when there are greater numbers of teeth in the gear.

This movement may be imperceptible but is nevertheless of extreme importance for accuracy and as a limit to the arc lengths of cutters and grindstones.

The tooth arcs of a Convoluted Arcuate wormwheel must be adjusted to a standard size to enable the worm developed from it to conform to a standard screw thread pitch, or a thread that can be cut with standard equipment.

Claims (6)

1. A Convoluted Arcuate gear whereby the tooth form arcs are generated from specific points on two distinct and separate circles equidistant from the pitch circle.

2. A Convoluted Arcuate gear, as in Claim 1, in which the point of inflection of the tooth profile arcs is also a point of tangency which remains exactly midway, centre, of a straight line connecting two adjacent tooth arc vertices where one vertex is on the major generating circle and the other is on the minor gener ating circle.

3. A Convoluted Arcuate gear,as in Claims 1 and 2, where by any adjustment to the tooth arc radii has been de termined from the position of the point of tangency and inflection.

4. A Convoluted Arcuate rack developed from dimensions obtained from a Convoluted Arcuate gear as described in Claims 1, 2 and 3.

5. A chain drive sprocket identical in profile dimensions and contours to a Convoluted Arcuate gear as described in Claims 1, 2 and 3.

6. A worm, as shown in Figure 4, in which the thread con tours, pitch and depth have been determined by data obtained from a Convoluted Arcuate gear, as identi fied in Claims 1, 2 and 3.