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There are many uses of gearwheels in every form of engineering and the methods of cutting the various kinds of gears are remarkable for their ingenuity and precision


MACHINE-CUT STRAIGHT TOOTH GEARS awaiting assembly in machines. Towards the back of the group are spur wheels of the ordinary and of the bevel types ; at the front are ordinary and bevel pinions. In front of the bevel pinions are three worms, which are used to drive the curved-face worm wheels seen on the right.

AS the anchor is the accepted symbol of seafaring life, so to the artist and the architect the symbol of engineering is generally a cogwheel — to use a term which, though not uncommon colloquially, has long since disappeared from the vocabulary of the engineer. He calls this basic unit for transmitting power a gearwheel, or, more correctly — as one is of no use by itself — gears.

With the coming of the motor car the term “gears” and a compound of it, “gear changing”, have become more frequently heard and the keen motorist is, moreover, familiar with the appearance of the gears in his car. Further, any one who has a watch or a clock can see gearwheels by opening the cover, though these are necessarily on a small scale.

The term “cogwheel” goes back to the days of the old millwrights who, before the days of the steam engine, had to transmit the power of the waterwheel or of the windmill sails to the machinery they wished to drive. The wheels in those days were “fashioned” with “cogs” of hardwood at regular separate intervals all round the circumference of a circular disk. Though effective for slow-moving machinery transmitting little power, the wooden cog was too weak for heavy loads and, though an occasional example or two of the cogwheel survives, it ceased to be generally used about the end of the eighteenth century.

The wooden toothed wheel was displaced by wheels made wholly of cast iron. The pattern for one of the first of this kind of wheel, if not the first, was made by William Murdock, the father of James Watt’s right-hand man of the same name, and castings were made from it in 1766. The wheel with cast teeth, sometimes chipped and filed to give them a smoother surface, survives for certain purposes, but no engineer to-day would dream of using gears thus made in, say, a lathe, a motor car or a turbine drive. Nearly all gearwheels to-day have their teeth carefully cut from the solid metal, whether that metal is cast or forged, or whether it is of bronze, iron or alloy steel.

The object of using gearwheels is to transmit power, and this involves motion. With ordinary gears mounted on parallel shafts the speed of rotation of the driven shaft is the same as that of the driving shaft if both wheels have the same diameter.

If the driven shaft has to go faster than the driving shDOUBLE HELICAL PINIONS cut out of solid high-tensile steel forgingsaft the wheel on the former is smaller than that on the latter. The reverse is true if the speed of the driven shaft is to be decreased. With two differently sized wheels, the larger is generally of such a diameter that the rim on which the teeth are cut is carried on arms radiating from the boss, and is known as a spur wheel. The smaller wheel may have the teeth cut almost on the boss and is known as a pinion. A drive showing spur wheels and pinions is illustrated below. This photograph shows what is known as a double reduction gear. The pinion in the foreground is driven by a motor which, to be efficient, must be run at a high speed. It meshes with a spur wheel on whose shaft is a second pinion, which, in turn, meshes with a second spur wheel. This is mounted on the shaft of the drum that is required to rotate at a comparatively slow speed. The speed is reduced in two steps: hence the phrase “double reduction”.

DOUBLE HELICAL PINIONS cut out of solid high-tensile steel forgings are used for actuating the rolls of steel-rolling mills. The power is supplied to one of the shafts by an engine or electric motor and is transmitted to the other by the pinions working in mesh as shown. Extremely heavy loads are carried by the teeth.

This illustration shows also two different forms of tooth. The first reduction gears have double helical teeth, a form also called herring-bone teeth. The second reduction gears are cut parallel to the shaft. The driven shaft and the driving shaft are parallel, but a drive between shafts at right angles is often required and sometimes at other angles. In this instance the wheels are made with a conical surface, and are known as bevel gears. A pile of bevel gears is seen to the left of the illustration at the top of this page and towards the centre is a number of bevel pinions. Bevel gears are sometimes made with helical teeth. On the right of the illustration are seen several wheels with a curved periphery. These are worm wheels and mesh with the worms (really forms of screws) in front of the bevel pinions. Worm gear is an alternative form of right-angle drive. All the wheels in both illustrations have machine-cut teeth.

DOUBLE REDUCTION GEAR for transmitting the drive of a fast-running electric motor to a slow-running ball mill for grinding ore

DOUBLE REDUCTION GEAR (right) for transmitting the drive of a fast-running electric motor to a slow-running ball mill for grinding ore. The pair of wheels in the foreground have double helical teeth as they run at a faster speed than the pair in the background with straight teeth, which are satisfactory at comparatively low speeds and are more readily cut.

Cycloidal and Involute Teeth

None of the teeth of the wheels and pinions is rectangular, but all have curved surfaces. This is necessary so that the surfaces of the teeth of wheels in mesh shall remain in contact until the following pair come into engagement. There are two main forms of tooth profile, the “cycloidal” and the “involute”, though the cycloidal form is little used nowadays. The involute system will transmit the motion from one shaft to the other with uniformity, provided the teeth are accurately formed, an operation by no means simple. Gear-cutting methods, of which there are a number, can be classed either as “forming” or as “generation”. A forming process consists of cutting the teeth by a tool which is shaped to the curve of the finished tooth. It is a comparatively simple method, but it can be understood only by reference to an illustration of the tool and tooth. Such a tool is shown in the lower inset of the photograph reproduced below. The tool is the conical object seen between two finished teeth. It is formed with cutting edges, one of which is visible at the top, and rotates at a high speed.

The wheel shown in the photograph has double helical teeth, but to understand the action of the cutter a plain spur gear with teeth parallel to the axis of the shaft should be considered. The uncut wheel, or blank, as it is called, is mounted on a shaft and prevented from turning. The cutter is then fed to the required depth just clear of one side of the blank and is started up. It is then traversed slowly, while rotating, across the face of the blank and cuts a groove of the required shape across that face.

STRAIGHT TOOTH PINION in a rack planing machine

STRAIGHT TOOTH PINION in a rack planing machine (left). The tool reciprocates horizontally as the pinion blank is rotated. The large wheel at the left regulates the motion of the blank in keeping with the motion of the teeth. The bar in front of the machine is removed when a spur wheel has to be cut. The seated man gives a good idea of the size of modern machine parts.

The cutter is then run back to the starting point and when it is out of the groove the blank is turned on its axis through an angle, which will give the required thickness of the tooth. A second cut is then made and one perfect tooth is thus formed. The process is repeated round the blank until all the teeth are cut, the machine being set to produce an exact number, an operation so accurately performed that, when the wheel is finished, it is impossible to tell where the original cut was made.

When double helical teeth are to be cut, however, the operation is more complicated. The cutter rotates and is traversed in a straight line as before, but the blank is not stationary. Instead it is slowly rotated on its axis so that the groove is cut at an angle to that axis. When the centre is reached the blank is rotated in the opposite direction so that the slope of the second half of the groove is opposed to that of the first half.

Although a plain parallel gear is so much simpler to cut, a double helical gear is used, because with a parallel tooth the whole surface makes contact and breaks contact at the same moment, and if the machining is not exact there is a tendency for a little jerk to occur at each tooth.

CAST-STEEL SPUR WHEEL with 203 double helical teeth. This wheel is fitted to the driving shaft of a rolling mill and is cast in one piece. It has a diameter of 13 ft. 71 in. and is 3 ft. 4 in. wide. The inset photograph on the left shows a pinion with triple helical teeth; the inset on the right shows a rotary cutting tool in position between two teeth.

With a sloped or helical tooth there are always several teeth in engagement, on different parts of the face, and thus the motion is smoother. But if a single helix is used the driving force has a tendency not only to turn the driven wheel but also to slide both wheels along their shafts — and so an expensive form of bearing is necessary to take this sideways thrust. By using a double helical tooth the sideways thrust cancels out, so that not only are no special bearings required, but also the advantages of constant mesh are secured. The upper inset photograph shown above shows a triple helical tooth. The portions of the tooth at either side which slope in the same direction are together equal in length to the central portion, which slopes in the opposite direction, so that the cancellation of the sideways thrust is still obtained. Some engineers prefer the triple helical tooth, but it is difficult to see that it has any advantage over the double helical tooth, and it takes longer to cut.

Largest Wheel of Its Kind

The wheel illustrated above is for the main drive of a steel-rolling mill and is made of cast steel. Of a diameter of 13 ft. 7½ in., having 203 teeth with a face width of 3 ft. 4 in. and weighing 24 tons, it is probably the largest wheel of its kind that has ever been cast in one piece. It forms an excellent example of modern gear cutting, but should be contrasted with the excellent example of double helical pinions shown above. These are also for a rolling mill, but they are not cast, as is the wheel. Being solid, they are high-tensile steel forgings. Before cutting they resemble cylindrical rolls, the teeth being formed by the end-mill cutters similar to those just described. The cutters are made of high-speed steel containing 18 per cent of tungsten and are ground to the correct profile. Each pinion of this type may weigh as much as 40 tons and may have teeth of 8 in. pitch. This means that the distance from the centre of one tooth to the next, looked at from the side, may be 8 in.

The types of gear-cutting machine used on these two examples are entirely automatic in action. The reversal at the centre and the traverse of the cutter, as well as the rotation of the blank, need no adjustment once the machine has been set up. The same machine, with a different tool, is used also to round off slightly the sharp edges at the top of the tooth.

The end-milling process, although eminently suitable for cutting gears of large pitch which have to run at low or moderate speeds, is not adapted for cutting the teeth of such wheels as are used in high-speed drives of the type used for turbine reduction gears. These gears may have to run at the rate of from 3,000 to 5,000 revolutions a minute, or even more, and the pitch of the teeth is generally comparatively fine. Thus, it may be anything between 0.4 in. and 1.0 in. Moreover, the teeth have to be made with an extremely high degree of precision so that the load is uniformly distributed over the maximum number of teeth.

For this class of work the end-mill, as used in the gear-cutting machines, gives place to a different type of cutter, though still a rotating one, known as a “hob”. The process of hobbing belongs to the generating class of gear cutting. A hob is shown in the inset of the photograph on this page. It is, in essence, a large screw or worm with a spiral thread. This thread is, however, notched at intervals to form a continuous series of cutting edges which are sloped away, or “relieved”, at the back in the same way as are all cutting tools for metal. The hob is mounted with its spindle inclined to match the slope, or helix of the helical tooth, and the blank is mounted on a vertical work spindle. It is rotated in a certain relation to the rotation of the hob.

CUTTING THE TEETH of a large double helical wheel used for turbine reduction gear in a doubleheaded hobbing machine. One of the cutting tools, or hobs, is shown in the inset photograph. The hob is formed with a number of cutting edges arranged helically, and is rotated on its axis at a high speed as the wheel blank is rotated slowly past it.

This photograph shows a large double helical gearwheel being cut in a double-headed hobbing machine in the works of David Brown & Sons (Hudd.) Ltd.. Huddersfield. At first sight it would appear that there are two single helical wheels placed one on top of the other, but this is not so. The central groove has to be turned in the blank before the gear cutting is started, as the hobs, of which there are two, cannot cut continuous double helical teeth. The hobs are carried one on either of the two columns, one hob cutting the upper half of the gear and the other cutting the lower half. This saves time. When a finishing cut is being made on a large gear, the machine must work without a moment’s pause for four or five days, so that the saving is important.

The teeth of the two parts of the wheel are not opposite to one another but are “staggered”, that is, the tooth of one part is opposite the space between two teeth of the other part. This arrangement reduces the gap between the two parts and thus reduces the width of the wheel. The arrangement is, moreover, believed by some engineers to give better running results than with the two parts in line, as they are in end-mill finished gears.

Rack Planing

The hobs, after they have been hardened, are ground in such a way that even after they have been resharpened they will cut the teeth of the same contour as before. This is a valuable feature, as the degree of accuracy required for high-speed gears is exceedingly great. The mean “cumulative error”, that is, the departure of each tooth from the position it ought to occupy, is generally not more than 0.0002 in., and the “adjacent error”, that is, the departure from the theoretical distance between the same faces of each pair of teeth, is not more than 0.0003 in. Considering the size of the gears often produced, this is a remarkable degree of manufacturing refinement. The double reduction gears, for example, made for the turbines driving the compressors of the coal hydrogenation plant at Billingham (see the chapter “Petrol from Coal”) weigh 53 tons a unit, and each gear transmits 3,250 horse-power.

Another method of gear cutting is the rack planing method. As the name implies, the cutting tool makes a reciprocating stroke and does not rotate as do the end-mill and the hob. The term “rack” simply denotes a flat toothed bar of metal which is used in mesh with a pinion when a rotary motion is to be transformed into a linear one, or vice versa. This mechanism is to be found on some machine tools and has a number of other uses. A rack is much the same as the rim of a spur wheel cut at one point and straightened out.

The rack planing machine makes use of a tool resembling a short rack in shape, except that the teeth have straight faces and not curved ones. The tool is, therefore, easily made and can be ground accurately after it has been hardened. By a somewhat complicated motion of the tool and the blank a tooth of correct involute profile can be cut. A rack planing machine for double helical teeth is shown at the bottom of this page. The two tools, one for either half of the wheel face, are seen in the centre and are set at the slope of the tooth. The spindle at the left hand carries a large disk or face plate to which the blank to be cut is attached. The blank is rotated during part of the cutting strokes.

The tools cut alternately and stop at the centre of the wheel face, this motion giving a perfectly sharp finish at the apex of each tooth so that full contact is ensured right across the face of the wheel. The photograph below shows a double helical spur wheel for a mine winder in a rack planing machine. This wheel is 15 feet in diameter and forms a striking contrast to the small pinion

shown in the inset. The cutters can be seen in position in the teeth in the inset. A rack planing machine with a straight tooth pinion in position is shown in the photograph above. The seated man gives a good idea of the size of modern machine parts.

Small, straight tooth gears are often cut by side-mills, that is, by rotating tools resembling little circular saws but having the periphery ground to the profile of the tooth to be cut. The blank is traversed in the direction of the length of the tooth across the sidemill so that, although the cutting edge of the tool is curved, the finished cut is straight. Only one space is cut at a time, the blank being rotated, or indexed as it is called, through an angle equal to another pitch for the next tooth.

AN IMMENSE DOUBLE HELICAL WHEEL in process of being cut in a rack planing machine. The rack-shaped tools, which reciprocate and do not rotate, are shown in the inset. The rack planing method enables the tooth to be cut with a sharp apex. With the hobbing process a gap has to be left between the halves of the teeth.

Many other kinds of machines are used in gear cutting but, for most part, they are all variations of the types described. The method of cutting the teeth of that important gear — the worm wheel — is of special interest. The worm-and-wheel combination is used in a number of ways in engineering and it can transmit efficiently large amounts of power. It is, however, not as a rule used where high speeds are necessary.

The worm which meshes with the wheel is simply a short length of screw, but it differs from an ordinary screw in having coarsely pitched threads with a considerably greater helix angle. The teeth of the wheel fit in these threads and are curved, to embrace as much of them as possible.

A large worm wheel of phosphor bronze, for the steering gear of a liner, is shown below, after having been cut. The cutting tool is really a hob, but whereas the hob for cutting straight or helical teeth has not the same profile as the tooth it cuts, the worm hob must be exactly the same as the worm which has eventually to mesh with the wheel. Thus each design of worm must have its own special hob.

PHOSPHOR-BRONZE WORM WHEEL for the steering gear of a large liner. The teeth have been cut by a hob of the same size and shape as the worm which will mesh with the wheel, though the hob has numerous cutting edges. The hob, while rotating, is traversed across the edge of the wheel, which is rotated round a vertical axis.

The hob differs from the worm, however, in that its “thread” is notched so as to form a series of cutting edges. The wheel blank is mounted so that it can be rotated round its axis, and the hob is both rotated and traversed tangentially to the wheel. The processes are quite simple, but the setting up of a machine is a task requiring considerable skill and the designing and building of the machines call for even more skill. The devices needed to produce the requisite movements are complicated and all the working parts of the machines have to be made with a great degree of accuracy.

To realize fully the marvels of gear development in the comparatively brief period which has elapsed since the days of cast gears, it is necessary to see and study the intricate motions needed to produce worm, helical, straight tooth, spiral or bevel gears. Even in the motor car, an everyday product, the spiral bevels used in many rear axles are a wonder in themselves. The spiral

form, although approximating to the Archimedean spiral, is produced by three independent rolling motions in one operation, giving perfect generation from a theoretical basic rack.

The precision of construction of modern gears is a thing to marvel at, and special devices are in common use for checking it. The teeth are generally tested for errors in pitch, “cumulative” and “adjacent”, and are also examined for errors in profile. Mechanical methods are often used for this test, but a common method is an optical one.

The correct theoretical form of the tooth is carefully drawn to a scale a great many times larger than the actual size. This drawing is then pinned to a screen in a dark room, and the wheel whose teeth are to be examined is placed before a special form of optical lantern. The teeth in silhouette are projected as a dark shadow on the screen.

If the outline of the shadow coincides approximately with the drawn outline, the work is sufficiently good, but, as any error is magnified enormously, even negligible defects show up in a startling way. This method cannot be applied to a double helical wheel, as the “bend” in the teeth interrupts the passage of the rays of light.

TOOL SLIDES of a rack planing machine for cutting double helical teeth. The rack-shaped cutting tools are seen in the centre. They are reciprocated alternately in directions corresponding to the slope or helix of the halves of the tooth. The wheel blank is carried on a face plate mounted on the shaft at the left.

You can read more on “Machine Tool Development”, “Romance of Motor Car Making” and “Windmills and Their Story” on this website.

Gears and Gear Cutting