Before deciding to regear, a thorough understanding of the functions of RPM and torque conversion is recommended, if results are to be more than speculation. Once you understand the principles, determine what you have at the start and where you would like to go. Careful analysis and planning will save wasted time, effort and expenses. Selecting the right gears, materials and installation can reduce wear, damage and future replacement.
First look for examples. Next look for the easy way, using ready made parts that may be modified to fit. Then thoroughly examine the more difficult methods to determine if your ability and funds can handle them. Search for sources in magazines and catalogues. Find out what tools are needed and how to use them. Some caveats concerning tools and methods should be recognized to avoid damaging mistakes. When you are sure, go to it. The results are very rewarding, especially when you show the operation of your new gem to the other guys.
NOTE: Rigidly mounted gear trains or boxes can not be used with sprung drivers, if the springs are to function. In the former, the driver gear mesh would change. While boxes with axle bearings will prevent spring travel.
Gears are used to change motor RPM, torque or direction to those of the drivers.
Torque 'T' is equal to a force 'F' multiplied by its radial distance 'R' from the center of the shaft. For a shaft and all gears fixed to it, torque is constant. Here it is measured in ounce-inches, newton-centimeters or gram (force)-centimeters.
Gear ratio for two gears is normally stated as output to input tooth count. A ratio of 2:1 or 2/1 doubles the torque and halves the RPM. Conversely if the large gear is the driver, (ratio = 1:2) all relationships still hold except the torque halves and the RPM doubles.
Note: Some prototype railroads (PRR) listed ratios as input to output.
Multiple gears may or may not effect the final ratio. Idler gears do not and the overall ratio is that of the final output to the input gear.. However, in compound gears the ultimate gear ratio is determined by the step gears. In either case, the the final ratio is the product of the individual gear pair ratios.
Since output power is
It appears that power remains constant, since if torque doubles and RPM halves, the result is the same. But friction, which is an opposing force, adds torque all along the way, which the motor must supply. This is evident in the rise in the pitch of the motor when a loco is first lubricated, reducing the losses. The resulting loss of efficiency here has a far greater impact than any gain in motor efficiency .
In a practical case, an HO loco with 62" drivers and 29:1 gear ratio hauls 30 freight cars at a drawbar pull of 3 oz.
Driver radius is:
axle torque = 3 * 0.356 = 1.07 oz-in.
motor torque = 1.07 / 29 = 0.037 oz-in.
This is the motor torque required to move the train. But measuring the current and referring to the motor graph reveals the motor torque should be 0.2 oz-in. A torque of 0.2 - 0.037 = 0.163 oz-in is required to move the loco and tender. Checking the deadhead current would reveal this to be very close to the truth.
Torque is lost through friction in motor brushes, bearings, gear mesh, axle bearings, rods and truck journals. Simple tests comparing deadhead and various train length currents will verify that current does not appreciably increase from the deadhead value with the addition of cars. Adding gears increases the losses slightly, if done correctly. But any good powerpack and motor should handle this. The importance of proper lubrication can not be over stressed in reducing these frictions.
SEE PICTURES
For our purposes, gear usage is divided into two groups with either parallel or perpendicular shafts. Although possible, other angles are not often designed. Probably most common are spur gears with parallel shafts, straight teeth perpendicular to side faces and no side thrust. Often teeth are skewed at an angle to reduce effective tooth spacing for smoother mesh, introducing side thrust. Two oppositely skewed gears are often placed together on a shaft, forming a herring bone, improving mesh without thrust.
Bevel gears , often used on Shays, are similar, but have teeth at other angles to the face to permit shaft orientation changes with accompanying side thrust. Most often the face angle is 45 degrees, the teeth are on radii and the shafts are perpendicular. The teeth may be skewed from the radii to reduce effective tooth spacing.
Crown gears , having teeth perpendicular to the face and perpendicular shafts and little side thrust, are often cheap stampings used in inexpensive toys.
Although not normally considered gears, chains and sprockets provide a very useful alternative when large center distances are to be bridged. A bicycle is a good example. Ratios are obtained by counting teeth as with spur gears. Without the teeth, belts and pulleys perform the same function with possible slippage. To reduce this, springs are occasionally used. The ratios are found from the measured diameters of the pulleys. All have been used in models over the years. Athearn produced several HI-F drives with twisted belt, using the shaft and enlarged axles as pulleys.
The remaining useful types are derived from a screw or helix, developed by Archimedes, based on an inclined plane. Many machine tools use this type of gearing and are commonly referred to as screw machines. Since it is impractical to design a pinion (small driving gear) with fewer than eight teeth, helix types are used to produce one to four or more tooth equivalents.
Worm and wheel (worm gear) are the most common with perpendicular shafts and high side thrust. Since the worm threads spiral at a skewed angle, the gear teeth must be skewed, resembling a skewed spur gear. However the helical geometry of the teeth is quite different in higher precision gears, since the contact surfaces are sliding in addition to just pushing and rolling as in the ideal spur. Due to the force angles and ratios involved the gear can not normally drive the worm, accounting for many screeching halts when power is removed at speed.
With possibly a slight compromise in geometry, another type was developed from a less common left-hand wheel used with left-hand worms, for use in idler worm gear boxes and later offered for general use. The reverse worm gear is essentially a worm gear with opposite skew, which meshes well with the former permitting the two to perform as skewed spur gears or even to form herring bones.
Usually worms are designed with from one to four thread starts or leads, countable by examining the end. More starts produce smoother operations and higher strength at the expense of lower gear ratio. A single start advances one thread per revolution, rotating the wheel by one tooth, producing a 36:1 ratio with a 36 tooth gear. While a three lead, often used by Rivarossi, advances three threads per revolution rotating the driven gear by three teeth to reduce the speed ratio to 12:1.
Advantageously, designed worm diameter can vary over a fair range with little compromise, permitting several sizes to mesh with the same gear. Penn-Line did this to enable either flat or angle mounted motors to be used with the same driver gears.
Of similar design, helical gears with much larger pitch angles are more often used to change shaft orientation. Ratios are normally below 3:1 and more often 1:1 using identical gears. Size and reversibility are their biggest advantage.
Often overlooked, the rack and pinion is a spur gear used with an unrolled gear having matching teeth, more often a straight bar. With the pinion held stationary, the bar provides linear motion as in the Sensipress and Panapress. The cog railway is an example of a stationary, slightly curved rack and a locomotive propelled by a pinion driver. Unfortunately, as normally used in industry, most racks are rigid. As a possibility, a 72 teeth per inch, band saw blade might be used with a 72 DP spur gear for a cog railway. Frogs could be a problem. Some of the turntables and transfertables on the market use this principle.
Materials for hobby gears are widely varied and cost dependent. Particularly with worm gears, they should be dissimilar with the harder material used for the driver to reduce wear. The ratio, of driver to driven tooth contacts and thus wear potential, is the gear ratio. In single lead worm gears with some end play, only a little over one thread ever contacts the wheel.
Steel is often used for worms with excellent life but greater friction. Hard bronze worms have a little less life and friction at higher cost. Frequently used in most other gears under medium loading, brass provides an excellent compromise between wear and friction. Common nylons have a tendency to be abrasive, so should be avoided. This was exemplified a few years ago, when one brand of RTR locos used nylon for both worm and wheel, resulting in an extremely high replacement rate due to concaved gear teeth with no mesh. For lighter loading delrin (acetal) has excellent life and very low friction, but does not glue very well, if required. Avoid cheap cast styrene and stamped gears at all cost.
Gears are rated by precision of mesh. The high cost of precision rated gears can not usually be justified in locomotive work. Another parameter, pressure angle, is important here only because teeth of different angles will not mesh well. This may prevent equal pitch gears, of different sources, from working well together.
Of far greater importance to us is PITCH, which is commonly measured in one of two ways. Gear pitch diameters are always measured across points at about half tooth depth on the pitch circle.
>Note: Adjust brightness and contrast for optimum viewing.
American standard.
Diametric pitch (DP) = number of teeth (N) / diameter (PDi) inches
DP = 36 teeth / .75 in = 48
The metric rating:
Module (mod) = diameter (PDm) millimeters / number of teeth (N)
MOD = 18 mm / 36 teeth = .5
Using the first DP example above:
Since 25.4 mm = 1 in or 1mm = 1 / 25.4 in = .3937 in
Using the first MOD example above:
To convert:
Practically, higher DP or smaller M permits more compact gear trains but requires lighter loading because of smaller teeth. Usable pitches range from 32 dp or (25.4/32=) .794 mod to .2 mod or (25.4/.2 =) 127 dp.
The outside diameter (OD), required for clearance, is based on the addendum (AD) which is outside radius minus pitch radius. The latter is the radius we use for torque measurement and meshing. Usually by design
OD = PD + 2 * AD = N/DP + 2/DP = (N+2) / DP
OD = (N+2) / DP = (48 +2) / 48 = 50 / 48 = 1.042 in
OD = (N+2) * M = 50 * 0.5 = 25 mm
Better, if you count teeth add two and divide by the measured OD (easier), you have the pitch. This does not hold true for N less than about 12, since tooth geometry must be altered to maintain good mesh.
With a little detective work you can probably find an unknown pitch.
DP = (24+2) / 0.307 in = 84.69-- probably module
Convert
Or remeasure in mm.
It might be obvious with a little examination that module and addendum are equivalent dimensions for metric gears.
Worm pitch is usually determined with gauges similar to screw pitch gauges or from a matching gear, since the lead (L) or thread distance is difficult to measure accurately enough to differentiate. For two common sizes DP = 48 and MOD = .5, L is within four thousandths of an inch. Knowing the source may be helpful, American are probably DP while others are probably MOD. Using the 48 DP above:
The lead is very close to the tooth spacing on the mating wheel.
L =¶ * M = ¶ * .5 = 1.57 mm = .0618 in
Worm pitch diameter does not always have a direct relationship to pitch and is even more difficult to determine by direct measurement , due to the angles involved. It should be approximately
NWSL's 72 DP worm is listed as OD = 3/16 = .1875 in and PD = .16 in.
Rely on suppliers' data, if possible, for optimum mesh.
mesh is determined by center distance (CD)+ clearance (K). NWSL recommends k = 0.004 in on their 72 DP gears. This is about the thickness of single ply toilet paper placed between the gear mesh and pressed lightly but firmly.
CD = PD1 / 2 + PD2 / 2 + K
CD = (PD1 + PD2) / 2 + K
If you can't find the PD's.
CD = (N1 + N2) / 2 / DP + K
For N1 = 20, N2 = 36 and DP = 72
Module is done the same way.
(N1 + N2) /2 * M + K mm
For N1 = 15, N2 = 40 and M = .3
Now that you understand what to look for, check the market for ready made gear boxes and any other work savers.
Choices are very limited and although these may be very convenient, they may not fit very well without frame surgery. Some may require requartering, when replacing the driver gear. The bottom of the housing or cover plate may not clear coupler magnets on smaller drivers. Even though they are enclosed and keep most lube in and dirt out, they are not hermetically sealed and require some cleaning.
NWSL offers a series of delrin 0.3 module WORM GEAR BOXES with 15:1 ratio and 1 axle to drive shaft distance; 28:1 and 3 distances; 36:1 and 2 distances. Separate gears are available for other applications.
They also offer spur gear TRANSFER BOXES in various sizes.
PRECISION SCALE offers several gear boxes. A 37:1 brass 80 pitch WORM GEAR BOX and separate gears, similar to those used by KTM and others on brass locos. Two idler boxes at 27:1 and 37:1 ratio. A coasting box at 27:1. And a triple reduction box at 136:1.
There are also some gear box parts from loco kits that may be modified for idler and step gear usage with universal joints and shafts.
Over thr years, MANTUA has offered several types of WORM GEAR BOXES. The newer have been used in both retrofit and new applications. Parts and rollingstock will be available from new owner, MODEL POWER.
BOWSER has pedestal type worm shaft mounts.
Although some conversions may be accomplished with only a screw driver, most require more specialized tools. A soft hammer and drift pin or a puller and press will often suffice to remove and install worms and gears.
MDC (Roundhouse) has two types of double reduction gear mounts that are easily adapted. The one used on larger locos was the basis for many of the more sophistcated examples shown.
Now before giving up or running down to the hobby to buy all the fancy tools, look around a bit. There are several regear jobs that can be done inexpensively and with few tools.
If you have any ATHEARN diesels, ERNST offers a line of regear kits to cut their speeds to one third to about 35 to 50. The only tradeoffs are more noise and a little less efficiency? The only warnings are: read and understand the instructions very thoroughly before starting, keep the parts straight during disassembly and reassembly and work under a bright light on a light surface, since all parts are black. The aid of a cohort is invaluable here to check the drawings while you do the labor. Even my American-GK E-60's got the treatment.
Check NWSL to see if any of their many regear kits fit your locos. Their catalog gives full descriptions.
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If none of these work, check examples here or in magazines for ideas then tools and methods for how to do it.
SEE SELECTING GEARS
Again I repeat , know what you have at the start, decide what you want and determine how to get there, before jumping in.
Good Luck!
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