# Gear ratio - Does it matter how you achieve it?

Autorama
Hi all,

I always wondered if the combination of gears used to achieve a specific gear ratio mattered. Assuming the desired gear ratio is 3:1, would it matter if the gears used were 10x30 or 9X27?

Homework Helper
If the gears are too small, friction can be an issue. If the gears are too large, momentum can be an issue. For the two examples you gave, they're so close it probably doesn't matter.

Gold Member
Also, the actual size of gears will depend on the load they will need to handle - particularly the impulsive loads.

It is best to use pairs of gears that share no common factor in the number of teeth. That implies that every tooth on one will meet every tooth on the other so wear is even and the gears remain quiet, even after disassembly and reassembly. That is called a hunting tooth system because each tooth hunts out all others.
With integer ratios such as 2:1 and 3:1, that can be achieved by using a roller chain or stepped belt. If the number of links in the chain, or steps in the belt, has no shared common factors with the gears then the system will wear evenly and remain quiet after reassembly. So, avoid integer ratios when possible. Spur gears with less than 12 teeth must be undercut and so are weaker than gears with more teeth.

Homework Helper
Gold Member
Gold Member
It is best to use pairs of gears that share no common factor in the number of teeth. That implies that every tooth on one will meet every tooth on the other so wear is even and the gears remain quiet, even after disassembly and reassembly. That is called a hunting tooth system because each tooth hunts out all others.
With integer ratios such as 2:1 and 3:1, that can be achieved by using a roller chain or stepped belt. If the number of links in the chain, or steps in the belt, has no shared common factors with the gears then the system will wear evenly and remain quiet after reassembly. So, avoid integer ratios when possible. Spur gears with less than 12 teeth must be undercut and so are weaker than gears with more teeth.

Sounds a bit like the Enigma Machine!
Smart idea, though and something that you wouldn't necessarily consider if you were starting from cold in the design business.

@ CWatters. I would not put too much value on that table except in heavy industry.
The geometrical limit of any gear pair is determined by the minimum number of teeth on the smaller gear, called the pinion. Beyond that limit the size of a gear tooth is decided by the torque it must handle. So a 100:1 reduction could be done by a single worm gear or an epicyclic, but the lightest and most economic system to manufacture is probably three stages of reduction, say 5:1, 5:1 then 4:1. Why? because the gear train is transmitting power, and power = torque * RPM. The first reduction pair can be small because it is rotating fast, the middle set is middle sized and the final pinion drives the big “bull gear” on the output shaft. The bull-gear must have the heaviest teeth to transmit all the power so slowly.

Imagine the minimum input pinion, a 12 tooth spur gear driving an impossible 1200 big toothed bull gear. Then imagine a 5, 5, 4 train. It has a small pair 12:60 followed by the medium 12:60 and finally the heavy 12:48 bull gear. The ratios are then dithered to eliminate common factors between gear pairs, so we end up with 12:61 x 12:61 x 12:47 = 101.2 ratio. This is a realistic engineering solution.
If the final stage had been a hypoid gear like the differential in a car then it could have had maybe only 7 teeth (determined by the tooth interference geometry) on the pinion and 29 only on the crown wheel. It does however cost more to make hypoid gears, also it puts a bend in the drive train which is exactly what is needed (about 90 deg) in a car differential.

Homework Helper
Gold Member
Thanks.

Pkruse
An engineer starting a clean sheet design has a great many factors to consider before deciding how he/she wishes to configure the overall system.

We already have much good information in this thread. I see nothing to argue with. So I’ll add a few thoughts based upon my experience.

Heat dissipation is sometimes a major concern. If the overall efficiency is 97% on a system transmitting 1000 hp, for example; then you have to figure out how to either increase the efficiency or else dissipate 30 hp worth of heat. If speeds are slow, then perhaps a generously flowing oil bath will do the trick. But if speeds are fast, then the oil bath will decrease the efficiency and generate more heat. You still have to get lubrication to the bearings, but you have to keep the oil to a minimum.

Space and weight become major factors for any mobile application, and greatly more so for an airborne application. So packaging becomes a major driver in the design.

Already mentioned is the staging of gears. That helps a lot for keeping things small and compact, because later stages can be much smaller. One application I worked required a reduction of about 10,000. Loads were low, but the torque was very high on the output shaft. Three planetary stages to a pinion that drove a huge bull gear on the fourth stage worked out very well. The three planetary stages packed into a space about the size of a starter motor for a full sized car. Using a very high speed input shaft enabled me to use a hydraulic motor about the size of a motorcycle starter motor. All of this for a truck mounted device in which space and weight had to be minimized at all reasonable costs.

I once parked three mobile cranes next to each other. They were all of the same physical dimensions and the same weight. They were rated at 140, 250, and 400 tons. (They all used the same Rockwell suspension system.) They were built in 1957, 1980, and 1990. Today, a crane of the same size and weight would be rated at about 800 tons. The main reason for these huge improvements is that the engineers learned to more efficiently transfer the power from the engine to the hoist. How you configure your gears and other power transmission devices is hugely important. A simple question of how many teeth to put on the gears is a very tiny part of this.

inspiredape
Hi I am building an electric bicycle and I want to use a high rpm(6-8000 rpm) brushless motor. the gear reducers I've found have not been able to hande more than about 4000rpm. I was wondering if anyone has heard of using a tesla turbine as a sort of reduction/torque convertor. My idea is to make something that looks like a clutch with input and output disks stacked and sandwiched with low tolerance in some sort of viscous oil and use the surface cohesion to transfer torque. In my mind the molecules of oil would roll against each other and create a kind of planetary like reduction. Is that completely ridiculous?

Mentor
I'm not sure how that should look like, but fluids as part of the device will always give significant loss.

Gold Member
Hi I am building an electric bicycle and I want to use a high rpm(6-8000 rpm) brushless motor. the gear reducers I've found have not been able to hande more than about 4000rpm. I was wondering if anyone has heard of using a tesla turbine as a sort of reduction/torque convertor. My idea is to make something that looks like a clutch with input and output disks stacked and sandwiched with low tolerance in some sort of viscous oil and use the surface cohesion to transfer torque. In my mind the molecules of oil would roll against each other and create a kind of planetary like reduction. Is that completely ridiculous?

How about another 2:1 gear before the reducer?
Using fluids to transmit power is potentially lossy. In vehicle torque converters, a fluid is used as a 'clutch' mechanism ('fluid flywheel') but afaik, they operate without slipping (reduction) for most of the time.

A Tesla turbine requires a fluid supply. A fluid coupling or torque converter will over-heat unless you use a circulation pump and radiator. No fluid solution will be efficient where 8000 RPM are involved. Cavitation, overheating and the entrainment of gas bubbles into the fluid will cause corrosion and inefficiency.

If you must use a high speed motor then an alternative possibility is a direct driven roller resting on the periphery of the bicycle wheel. The roller diameter to wheel diameter sets the gear ratio. Heat generated at the roller - tyre contact will be radiated from the tyre, convected away by the airflow or lost by conduction into the road. You could use a tapered roller to get a continuously variable ratio.

This is really an engineering problem. Selection of a sub-optimal motor greatly increases drive-line cost. Consider selection of a motor that has twice the diameter and half the length of the one being considered. It will have the same power, half the speed and twice the torque. Repeat that doubling several times until the motor approaches the size of the bicycle's wheel, they can then be integrated to become one component without gearing.

In effect you are trying to match the speed/torque ratio of the motor to the wheel. The gearbox is just a mechanical transformer. Selection of the optimum motor obviates need for an expensive mechanical power transformer. Motors cost less and are more reliable than gearboxes.

When you find the optimum motor, you will not have to buy an unnecessary gearbox, a gearbox that must be raised up every hill you will ever climb.

inspiredape
Yea this is a tough one. I can't have the motor on the wheel or the swingarm because it becomes sprung weight which is terrible for off road riding