Levers
The oldest and simplest converter is the lever. You can classify levers into three types. A first class lever is a crowbar with its business end under a rock, a stone a foot away serving as a pivot or fulcrum, and a man pushing down on the handle end three feet from the fulcrum. The man is three times as far from the fulcrum as the rock is. So if he pushes the bar down three inches, the end under the rock will rise only one inch. That loss of distance—and distance is a function of speed—is balanced by an increase in force. The 100 pounds of pressure he puts on the bar becomes a lift of 300 pounds under the rock.
Now move the fulcrum to a spot six inches from the rock, and you change the mechanical advantage. The fulcrum-to-handle distance is now three and a half feet, or 42 inches, while the working end remains six inches long. The handle end of the lever is therefore seven times as long as the working end. You’d have to push the handle down seven inches to raise the rock one inch, but the upward force against the rock increases to 700 pounds.
Here’s an interesting thing that can happen. If the rock is too heavy to be lifted and the fulcrum stone gets pushed down into the ground by the force you apply, the bar becomes a second class lever. The end under the rock becomes the fulcrum, and the lower stone becomes the load. The same distance and force ratios apply. So the difference between a first and second class lever may just be which of the two points is weaker.
A third class lever has the force applied between the fulcrum and the work. This type can only be used to increase speed or distance at the expense of force. You’ll find this type of leverage used in most front end loaders.
All parts of a lever move in curves rather than straight lines. Those curves are arcs of circles centering at the fulcrum. And a lever must be rigid for the distance-force ratios to apply accurately. These ratios are always figured in straight lines from the point where force is applied to the fulcrum, and from the fulcrum to the work-point. The lever itself may be straight, angled, curved, or offset.
If a lever has a sharp angle at the fulcrum, it’s called a bell crank. The space between the arms may be braced for greater rigidity, which produces a triangular bell crank.
When you turn a nut or a bolt with a wrench, you’re using a second class lever. The fulcrum is the center of the bolt, since that’s the hinge the wrench turns on. The resistance is at the threads, and the power is at the spot where your hand grips the wrench.
This brings up another fine point. The mechanical advantage of a lever is determined by the distances from the fulcrum to the power and to the load, not by the total length of the lever. If you grip a two foot wrench one foot from the end, you’re getting only one foot of leverage. If you hold it at the end, you get more leverage if you apply pressure through the outer part of your hand instead of evenly throughout your grip.
Local Shop Note:
You know, this takes me back to a conversation I had with a mechanic over in Wallkill, N.Y., who showed me why you never assume the first thing you find is the actual problem. I met him at an Albany, N.Y., heavy equipment seminar. He had a backhoe loader where the crowd function would slow down and stall under load, but only after the machine warmed up.
He pulled the crowd cylinder and found the rod seal weeping. Easy call—reseal the cylinder. But the linkage felt sloppy, so he measured it. The bell crank at the frame pivot had worn bushings, and the rod was slightly bent. That changed the effective lever arm. The crowd lever was no longer giving full travel to the valve spool, so the circuit was never fully open. The cylinder was fine; the mechanical advantage in the linkage had gone away. He replaced the bell crank bushings and pivot pin, straightened and adjusted the linkage, and resealed the cylinder. Crowd speed and force came back to spec.
Years later, I still remember that one because it showed me that on any lever-operated circuit, check the fulcrum and linkage geometry first. Worn bushings or a bent rod change your distance ratios, and that costs you force and travel at the work end—just like the lever theory says.
Wheel and Axle
A wheel and an axle or shaft is a specialized type of lever. Say this wheel were three feet in diameter and were rigidly fastened to a six inch axle revolving at ten revolutions per minute, or rpm. Any point on it will describe a circle every six seconds. The further the point is from the center, the larger the circle will be, and the faster that point must move to get around it in six seconds. A point on the axle surface moves nineteen inches with each turn. A point on the outer edge of the wheel moves 113 inches. As with all mechanical devices with a fixed amount of power, greater speed means less force. You can think of this wheel as a number of third class levers, with the center of rotation as the fulcrum, and the axle surface and the wheel perimeter as the work and power points.
If power is applied to the axle and work is done at the outer edge of the wheel, the result is an increase of speed and a decrease of force in a six to one ratio. If the power is applied to the wheel rim, the wheel acts as a number of second class levers, with the fulcrum again at the center of rotation but the work at the axle surface. In that case, power is multiplied by six and speed, or distance, is cut by the same amount.
If an axle is locked to two wheels of different size, it will deliver or receive different proportions of power to or from their circumferences because of the different leverage ratios.
Power may be applied to the rim of a wheel through gear teeth, or by friction with a belt or a lined band. Shafts may be turned by engines, motors, wheels, vanes, or gears.
Gears
A gear is a wheel with its rim notched into teeth that can be meshed with other gears or with chain links. Gears have almost unlimited capacity for changing power-speed relationships between input and output shafts.
Gear teeth are often not flat on their contact surfaces. They have a definite bulge or crown that reduces friction and counteracts any tendency of the metal to bend or cave in under heavy pressure.
Wheel-type gears are usually mounted on shafts. A gear may turn on a shaft or be locked to turn with it.
A gear that turns freely on its shaft usually has a soft metal bushing or a bearing in its hub to minimize friction and prevent hub wear on the gear itself. That kind of gear is usually an intermediate or idler gear, placed between a driving gear and a driven gear to change the direction of rotation or the gear ratio. The same result is frequently obtained by keying or splining the gear to a short shaft that is supported in bearings, and that does no work except to support the gear.
When it’s important that gears be quiet, they should be matched. That means they’re ground or run together by the manufacturer so the teeth match each other perfectly. This reduces noise, friction, and wear.
If a gear set of any type is taken apart, the gears should be marked so they can be meshed together exactly as before. That way, the advantages of their wearing in won’t be lost, and you’ll avoid new noise from different amounts of wear.
A spur gear has a rim notched so that the teeth are nearly the same size as the space between them, and the tooth edges are parallel to the axle. This is a simple, rugged type of gear. It tends to develop noise and backlash more readily than the next two types I’ll describe.
Spur gears transmit power between parallel shafts. They’re very widely used because they’re simple and economical to manufacture, they don’t cause end thrust—that is, they don’t set up a force that tends to slide the gear or shaft sideward—and they can be put in and out of mesh with each other by sliding one along a shaft. However, they tend to be noisy and they may develop annoying backlash.
These gears can be made in very large sizes. You may be thankful you won’t have to handle them that big. At least, you won’t unless you start servicing the largest stripping shovels.
A helical gear is wider than a spur gear. Its teeth are set diagonally, are generally comparatively small in cross-section, and may be curved. It’s usually quieter and smoother in operation than the spur, but it exerts considerable side thrust.
A herringbone gear is double helical, with teeth on the two sides sloping oppositely to each other. It has the advantages of the single helical and has no side thrust. It’s more expensive, however.
Helical gears are mated in opposite pairs. That is, a gear with a right hand slope will mesh with one with a left hand slope.
A rack or straight gear is a bar with teeth cut in one side. It’s used where the forces are too heavy to depend on friction between a wheel and a track, or where an exact relationship between turning and moving must be preserved. A very large circular gear may also be called a rack.
A worm is a cylinder with spiral teeth cut in it, and it resembles a coarsely threaded bolt. It turns a worm gear, or wheel gear, which is a type of spur gear with teeth cut in a curve to mesh with the worm.
Worm gears can be made to have a very high mechanical advantage. One worm and matching wheel gear can reduce speed much more than a bevel or spur gear set of anywhere near the same size. The worm and wheel usually rotate at right angles to each other.
Worms heat up when they operate under load, unless special cooling and oil circulation systems are provided. If you have any worm and gear units in the fleet you service, look up their instruction books and see how much steady operation they can take. If their time is limited, see to it that the operators and foremen are warned not to run them too long.
Bevel gears are truncated, or cut off, cones with teeth on their slopes. Standard bevels mesh when their shafts are at right angles to each other in the same plane.
Bevel gears have a variety of tooth types, being narrow or wide and straight or curved. The design problems behind these differences are complicated, but fortunately you don’t have to worry about them, since you have no option but to replace worn or broken gears with the same type.
The small drive gear is usually called the pinion, and the larger driven gear is called the ring or bevel gear. They’re often supplied in matched sets that have been run in together. When such sets are available, use them. They save a lot of noise.
Bevel gears require careful adjustment, as they are not automatically aligned by their shafts and bearings.
Hypoid gears are bevels with curved teeth, and they fall between worm and bevel gears in use. The shafts may not be in the same plane. For example, in a hypoid rear end, the drive shaft pinion is lower than the axles. Hypoids need excellent lubricant because the teeth tend to wipe themselves dry.
A sprocket gear usually has tapered or pointed teeth with rounded hollows between them. It’s used in connection with roller chain and must be carefully matched with it for tooth spacing and hollow shape.
Gear Ratios
When two gears meshed together are of very different sizes, the smaller may be called a pinion and the larger a bull, ring, or rack gear. A gear that is meshed with others but performs no function except change of direction or adjustment is called an idler gear.
In simple meshed gears, any two that are meshed with each other turn in opposite directions. If they’re the same size, they’ll turn at the same speed. If they’re of unequal diameters, the smaller will turn faster than the larger. Its rim speed in feet per minute must be the same because of the interlocking of the teeth, but it must turn more revolutions per minute for its teeth to keep up with those of the larger gear. A gear with 20 teeth, for example, must revolve twice in order to turn a 40 tooth gear once.
In a simple set, the speed ratio of any two gears is proportional to the number of their teeth, regardless of whether they may be connected through larger or smaller gears.
A compound gear set, in which two gears of different sizes are made in one piece or are locked on the same axle, permits great changes in ratio in a comparatively small space. Three gears together are called a cluster.
The rotation of a gear is described as clockwise if, from the point of view of the observer, its teeth turn in the same direction as a clock’s hands. Counterclockwise is opposite rotation.
Clockwise rotation viewed from the front would be counterclockwise from the rear, so direction of view must be made clear.