First off, let me explain that
gear reduction in the context of this help section refers to speed
reduction in general whether it be by traditional gear, chain
and sprocket, or belts. The goal of this section is to give anyone
a basic understanding of what gear reduction is and how it can
be used to help give an idea on how to implement it in a robot.
Because there are different areas in a robot that could benefit
from gear reduction we will focus on the most important one, the
drive train. And, we will talk only about DC electric motors but
the fundamental can be applied to other motors as well.
The reason that we need to know
about gear reduction is because the output speed of a motor is
usually too fast for normal use. Most DC motors at normal operating
voltages spin at well over 1,000 rpm (revolutions per minute)
and some even as high at 50,000 rpm for brushless DC motors. If
we had a motor than spun at say, 3,000 rpm, and we attached a
6 inch wheel to it then the wheel would theoretically be able
to move the bot at almost 54 miles per hour! That is way too fast
to control in an arena due to other considerations that wouldn't
happen but we'll get into that later. So we need to reduce the
rate at which the wheel spins so that we get a robot that we can
at least control. Hint, the quick way of determining the speed
of a wheel is to multiply the diameter (in inches) of the wheel
by the rpm and divide the result by 336 (or for a really close
figure use 336.13523981).
What is it and why does it work?
Quite simply, gear reduction involves
using gears/sprockets/pulleys of two different sizes to work together.
Because they are of differing sizes they will have different circumferences
(distance around the outer edge) and we can use this to our advantage.
Let's take a look at what this circumference thing really
means. To the left is a representation of a 4 inch diameter wheel.
Click on the wheel to watch it as it moves through one complete
revolution. You will see that the distance covered in one revolution
is equal to the circumference of the wheel.
Now, let's take a look
at a wheel that is twice the size. Click on the 8 inch wheel to
watch it as it goes through one complete revolution. What you
will notice is that notice is that not only does the wheel have
twice the diameter but it travels twice the distance in one revolution.
Therefore the circumference is twice that of the 4 inch wheel.
So, if the 4 inch wheel were to cover the same distance as the
8 inch wheel then it has to complete 2 full revolutions.
So, is there a way to figure out
the circumference of a wheel? You bet! Remember the magical number
Pi? Pi is roughly equivalent to 3.14. So, to determine
the circumference of the wheel we multiply 2 times Pi times the
radius of the wheel (radius = half the wheel diameter). So, for
our four inch wheel we have 2 x 3.14 x 2 = 12.5663706144... inches.
(remember to keep your units of measure the same throughout your
calculations).
Okay, now that we know that they
have different circumferences how do we apply it? Well, this time
instead of rolling each along the ground we are going to roll
them against each other. What you will notice is that the smaller
wheel has to spin twice so that the arrows line back up whereas
the big wheel only has to spin once. In other words the input
has to spin 2 times to get the output to spin 1 time. Thus we
get a 2 to 1 ratio more commonly written as 2:1. A configuration
like this is referred to as a single stage reduction because there
is only a single interaction between wheels.
Now that we have the basic understanding, lets take it
one step further, or one stage further as the case may be. In
the example to the right we have added a second wheel/gear in
between the two that we already had. It actually is two gears
in one. The large gear interacts with the first input gear. It
is physically attached to a smaller third gear so that the smaller
one revolves at the same rate as the larger one. This smaller
gear is then in turn interacting with the fourth output gear.
Two keep things simple the second gear is twice the diameter of
the first gear. The third gear is the same diameter as the first
and the fourth is the same size as the second so that we have
a 2:1 reduction between the first and second and a 2:1 between
the third and fourth.
So, with all that laid out we can begin.
As we saw in the single stage reduction the small gear had to
spin twice to get the larger gear to spin once. Well, the same
holds true here but since the second gear is attached to the third
gear the third gear also only spun once which means that the fourth
gear only got turned half way. To spin the last gear the rest
of the way the first gear needs to spin two more times for a total
of four times. Therefore, when it is all said and done the input
gear had to spin 4 times to get the output gear to spin 1 time,
or 4 to 1, or 4:1. This example is known as a two stage reduction
because there are two places where the gears interact (mesh).
Remember that the second and third gear are the same piece of
material and do not move independently of each other.
Note: Reduction annotation is usually
written with how many input rotations it takes to get one output
rotation. Ex. 3.5 (input) : 1 (output)
There are also multistaged reductions
which involve many gears which can reductions of over 1000:1!
It just depends upon the required output speed and torque (we'll
get to that later). So, how can you determine what the gearing
is of a set of gears/sprockets/pulleys? Well, gears, timing belts,
and sprockets are easy because they are labeled according to how
many teeth they have. If you have an input gear with 10 teeth
on it and an output gear with 40 teeth then the 10 tooth gear
will have to rotate 4 times (40/10) to get the 40 tooth gear to
spin once. Therefore we have a 4:1 single stage reduction. V-Belt
pulleys, on the other hand are based upon pulley diameter.
Well, how do we determine the final
reduction of a multistaged gearbox? It's really pretty easy. Multiply
the reduction of the first set of gear times the reduction of
the next set times the reduction of the next set and so on until
you have included them all. That will give you the total gear
reduction. So, if we had a three stage gearbox where the first
gear set was reduced 4:1, the second set reduced 5:1, and the
third set 6:1 then we would multiply 4 x 5 x 6 to get 120:1. (Or
you could just look at the motor specs :-p) Now, let's use the
motor that we talked about at the beginning and put this gearbox
on it and then attach a wheel to the output shaft. Input rpm is
3000. With a 120:1 reduction we divide 3000 by 120 to get 125
rpm. If we attach a 6 inch wheel to that then our bot would move
at 2.32 miles per hour. Hmmmmm.... That's a little slow for our
taste so we'll have to come up with a gear box that gives us what
we are looking for. So, let's determine what type of reduction
we would need to achieve a target speed of 15 miles per hour for
our bot (that is a quick bot!) First, we know that we are using
6 inch wheels and our motor spins at 3000 rpm and are target speed
is 15 mph and our constant is 336. Plug them into this formula
((wheel size) x (motor rpm))/((target speed) x 336). If we plug
in our numbers we would get (6 x 3000)/(15 x 336) = 3.57:1. It
would be pretty hard to get that exact reduction but we can get
close using a 10 tooth input sprocket or gear and a 35 or 36 tooth
output sprocket or gear. But, also remember that the 3000 rpm
is for an unloaded motor. Loaded motors will spin at a slower
speed but determining that speed is beyond the scope of this help
section.
Now, there are those in the builders
community who say that your reduction should be the same as your
wheel size. i.e. If you are using a 6 inch wheel then you need
6:1 reduction or if you are using a 10 inch wheel then you need
10:1 reduction. I personally think that is over generalizing since
different motor spin at different rates.
What are the advantages and disadvantages
of gear reduction?
Well, the two main disadvantages
are #1 you lose speed and #2 you have added weight for the gear
box. But, on the other hand, there are some great advantages to
using gear reduction. First, you bring the bot down to a manageable
speed. Second, the motor doesn't have to work as hard to spin
the wheel which means it won't draw as much current from your
batteries. And third, along those lines, the torque produced by
the output is inversely proportional to the amount of reduction
in the gear box. Say what? Basically, if you have a 4:1 gear box
then the bot moves 1/4 as fast but has 4 times the torque! So
you can have a 120 pound robot with the right gearing that will
push a 400 pound load across the floor!
The optimum configuration will
give you greatest speed but still have enough torque to cause
the wheels to break traction (peel out) before the motor stalls.
That optimum configuration varies from bot to bot and is up to
you to figure out how to best implement it with your own robot.
