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### OPERATION

QUICK FACTS

• Gear Ratios of 3:1, 6:1, 18:1 & 36:1
• Output speed range from 21 RPM to 1,440 RPM (at supplied voltage of 1.5v)
• Max and Min output torque of 5,580 and 71 g-mm respectively (at supplied voltage of 1.5v)
• Two shaft configurations (“low speed” and “high speed”)

HOW IT WORKS

There are only two major 3D Printed components of GBOX: the motor plate (01-GBOX) and the cap plate (02-GBOX). The intention of these is to provide bearing support to the shafts at exactly the required distance from each other or from the motor. They also constrain the axial movement of the shafts permitting only their rotation. Each shaft is supported at each end through a hole in the corresponding plate. The hole size is just slightly bigger than the shaft so that it can freely rotate but with minimum radial displacement within the hole. The vertical distance between each hole inside the plate sets the distance between parallel shafts and is chosen so that the teeth of the gear inside one can mesh with those at the other. The same goes for the location of the motor within the casing. The shaft’s axial position is constrained by the location of the gears within the shaft and in some cases by the use of spacers (03-GBOX, 04-GBOX). The gears assemble on to the shafts by a pressure or “interference” fit (gear bore slightly undersized compared to shaft) to guarantee that the shaft does not slide inside the gears and can therefore transmit torque. In the drawing, the figure shows the adequate axial position of the gears within the shafts.

Both K1-M1 and K1-M2 motors can be used. In both cases, the motor always carries the smallest gear K1-G10 (red-pinion). Motor K1-M2 has a pressure fit with the casing but motor K1-M1 has a looser one. The holes on either side of the motor casing can be used to place screws and help secure K1-M1 somewhat better.

The low speed (high torque) configuration of the GBOX connects the first shaft to the motor with a gear ratio of 6:1 (refer to the drawing) and with the shaft protruding in the motor direction. In this orientation the shaft cannot be used because it is difficult to attach to anything externally, however, it can easily be made to protrude in the opposite direction if a gear ratio of 6 is desired. The second (or output) shaft then connects to the first through the meshing of gears K1-G30—and K1-G60 or a gear ratio of 6:1. The total gear ratio or speed reduction is 36:1 (6×6). The output portion of the shaft has an axial length of 16mm and any load can be connected here (a pulley, a wheel, etc…see the drawing). Also a portion of the teeth on the output gear is exposed in order to be able to be meshed with external toothed parts.

The high speed (low torque) configuration has two output shafts protruding in the opposite direction to the motor. The first shaft has a gear ratio of 3 and the second with a gear ratio of 18 (3×6. Under this configuration, the axial movement of the first shaft needs to be constrained quite accurately by using shaft spacer 03-GBOX or else the shaft can fall off the support.

During assembly, the DBS (Distance Between Shafts) must be ensured so that the gear teeth remain meshed at all times and under minimum vibration. The bearings where the shaft rotate must not be too small because this would produce excessive rotational friction (seizing all motion), nor too big because this would result in shaft eccentricity and potential gear uncoupling or unreasonable vibration. Also, the bearing holes must be perfectly aligned to their counterpart in the opposing plate so the shafts can freely rotate and remain parallel to each other. To guarantee this, place the shafts into position after the gears have been assembled and test manually for rotation. If too tight, open the holes slightly with a metal file and test again. You must repeat in small steps so that the bearing holes never become too loose. Also, when screwing the plates together, use only two bolts in cross pillars and do not screw too tight. If the GBOX has trouble rotating when applying 1.5v to the motor, try opening the holes somewhat more. If on the other hand, you think the plates are deflecting too much, use all screws in all four pillars. A well-tuned gearbox should make almost no noise. Knowing how to tune gear-boxes is actually a real profession!

At LAYKANICS, we’ll be touching on the topic of gear theory on repeated occasions, but for the moment we’ll start with some basics. The first condition for meshing two gears of any given diameter is that they must share the same “module” (or “pitch” in the imperial system).  The module is an indirect measure of the tooth thickness and is obtained by dividing the number of teeth of a gear (N) by its pitch diameter (d) (…two gears meshing must share the same teeth thickness) The pitch diameter is that diameter at which a tooth of a gear contacts that of the other.

$m = \dfrac{d}{N}$
m = module [mm], d = pitch diameter [mm], N= number of theeth

To compute the reduction (or increase) of rotational speed happening in a gear mesh, we must realize that at the point of contact both gears have the same tangential velocity hence:

$V = r_1\omega_1 = r_2 \omega_2$
V = tangential velocity [mm/s], r1=pitch radius of input gear [mm], r2=pitch radius of output gear [mm], ω1,2 = angular velocity of input,output gear respectively [rad/s or RPM when multiplied by 30/Π]

Or expressed in module terms:

$V = 2mN_1\omega_1 = 2mN_2\omega_2 \rightarrow GR=\dfrac{RPM_1}{RPM_2}=\dfrac{N2}{N1}$
GR = gear ratio, expressed as GR:1

With these formulas, we immediately realize that the speed reduction (or increase) depends directly on the ratio of gear diameter, or the ratio of the number of teeth. This is what is known as the gear ratio (input velocity / output velocity, typically expresses as ratio:1). Under its different configurations, GBOX has gear ratios of 3:1 ,6:1 ,18:1 and 36:1.

The crucial point is to understand how a transformation of speed leads to a transformation of torque in the opposite direction (ie: reduced speed means increased torque and increased speed means reduced torque).  It’s all in the conservation of energy! Mechanical energy is transmitted from the motor rotor on to the first shaft and from the first shaft on to the output shaft (hence the name given to mechanical transmissions). At the output shaft we’ll be connecting a “load” which will be the end receiver of the energy supplied from the motor (Question: do you think all the energy from the motor reaches the load? Could some be lost to friction at the shaft bearings and/or the teeth contact?). The amount of mechanical energy per time unit (Power) transferred from the motor on to the shafts is computed as the product of the rotational speed and the torque. Supposing all energy from the motor reaches the output shaft (no losses) we can see that:

$P = T\omega = constant \rightarrow T_1\omega_1 = T_2\omega_2$
P = power [W], T1,2 = torque of input/output gear [Nm, gf.mm]

From above is easy to spot that if the velocity of the shaft is lower than that of the motor, the torque of the shaft must then be larger. Power will be preserved! Best of all, torque is also directly proportional to the gear ratio:

$GR=\dfrac{RPM_1}{RPM_2}=\dfrac{N_2}{N_1} =\dfrac{T_2}{T_1}$

So now we understand completely, that the intention of GBOX is to reduce the rotational speed and to increase the torque delivered to our load. Test this is really happening by stopping the motor rotor with your fingers. Then try to stop the output shaft. You probably won’t be able to do it under a gear ratio of 36 (torque is increased 36 times!). To put some numbers to what’s happening, we’ve taken the formulas above and the torque and speed values of K1-M1 and K1-M2 at 1.5v and transformed them in the following table. The minimum value of output torque is that corresponding to K1-M1, GR=3:1. The maximum is 5,580 g.mm corresponding to K1-M2, at GR=36:1. With these in mind, we can now start thinking about all the things we can move with GBOX. Expect tons of projects ahead!

OUTPUT TORQUE & SPEED AS A FUNCTION OF GEAR RATIO
K1-M1K1-M2
ω (RPM)T (g.mm)ω (RPM)T(g.mm)
INPUT 1,40071744155
OUTPUT, GR= 3:1480212248465
OUTPUT, GR=6:1240423124930
OUTPUT, GR=18:1801,269412,790
OUTPUT, GR=36:1402,538215,580

### VIDEO

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