Gear ratio

1. Objective:

The main objective we set for ourselves when calculating the transmission ratio is that the electric kart is capable of reaching 50 km / h.

As no type of gear change system is planned a priori, the relationship will be based solely on the transmission ratio between the motor drive pinion and the crown that will be mounted on the rear axle of the kart, although other data Important to take into account will be the circumference length of the wheel that we mount.

2. Calculation of wheel revolutions:

As the objective is to reach 50 km / h, the first calculation that we will carry out will be the number of revolutions required in the wheels to reach that speed. Taking into account that the calculations are projected empty, ignoring data of vital importance such as rolling resistance (not negligible with the sum of the weight of the electric motor, batteries, chassis, wheels and weight of the pilot, among others) and other resistance produced by inertia, slope, air or mechanical friction, we will start from a calculation greater than the 50 km / h necessary and we will place it at 60 km / h.

Through the following formula it will allow us to know the necessary speed for a given wheel diameter:

Knowing both the input rpm of the engine, as well as those necessary at the output to the wheels to reach the desired speed of 60 km / h, we will calculate the transmission ratio through the following formula:

Being the input rpm of the motor 2070 and 1224.49 the necessary output we obtain a transmission ratio of 1.69 to 1.

4. Calculation of the crown:

Once the transmission ratio has been found, it is necessary to transfer it to the diameter and number of teeth necessary in the crown for that relationship to be effective, maintaining, in principle, the motor drive pinion that has 11 teeth and an outside diameter of 48 mm. as the image shows.The following table shows some crowns that we can find from 63 to 97 and that maintaining the necessary transmission ratio of 1.69 to 1 would result in drive pinions with certain teeth

KnFitting the smaller 63 tooth ring gear would break the desired gear ratio since, if the motor drive pinion is maintained, it would result in a gear ratio of 5.72 to 1 and the number of rpm in the The output would be reduced to 361'88, which would increase the output torque (we improved acceleration with respect to the previous transmission ratio from 1.69 to 1) at the cost of losing top speed, clearly putting at risk reaching the desired goal 60 km / h.

- Although the assembly of an 18 tooth crown is not an impossible task, we can modify the drive pinion and crown assembly in such a way that the coupling ends up being more feasible.

The following table shows some crowns that we can find from 63 to 97 and that maintaining the necessary transmission ratio of 1.69 to 1 would result in drive pinions with certain teethowing both the input rpm of the engine, as well as those necessin this way, knowing the gear ratio to apply and keeping the drive pinion of the 11-tooth motor, we proceed to calculate the necessary teeth on the crown through from the following foput we obtain a transmission ratio of 1.69 to 1.

4. Calculation of the crown:

Once the transmission ratio has been found, it is necessary to transfer it to the diameter and number of teeth necessary in the crown for that relationship to be effective, maintaining, in principle, the motor drive pinion that has 11 teeth and an outside diameter of 48 mm. as the image shows.

While it is true that the drive pinion has an internal conical shape (the internal diameter varies along its height to settle on the motor shaft which is also conical and secured with a key, as can be seen in the image below ) that might not fit with another straight internal cut pinion, a solution could be to internally turn the new pinion or proceed to join both pinions by welding and crown assembly in such a way that the coupling ends up being more feasible.

The following table shows some crowns that we can find from 63 to 97 and that maintaining the necessary transmission ratio of 1.69 to 1 would result in drive pinions with certain teethertia, slope, air or mechanical friction, we will start from a calculation greater than the 50 km / h necessary and we will place it at 60 km / h.

Through the following formula it will allow us to know the necessary speed for a given wheel diameteresta manera, conociendo la relación de transmisión a aplicar y manteniendo el piñón de arrastre del motor de 11 dientes, procedemos al cálculo de dientes necesario en la corona a través de la siguiente fórmula:

GT= Number of teeth driven / Number of driving teeth

So it turns out that, with a transmission ratio of 1.69 to 1 and a number of 11 teeth on the drive pinion of the motor (driver) we need a crown with 18 teeth .

5. Conclusions:

- The mounting of an 18 tooth crown seems somewhat fair for a rear axle that has a diameter of 50 mm. (See the comparison in the image) and it would almost be necessary to manufacture them since in the market, from what has been observed, crowns between 63 and 97 teeth are common.

- Fitting the smaller 63 tooth ring gear would break the desired gear ratio since, if the motor drive pinion is maintained, it would result in a gear ratio of 5.72 to 1 and the number of rpm in the The output would be reduced to 361'88, which would increase the output torque (we improved acceleration with respect to the previous transmission ratio from 1.69 to 1) at the cost of losing top speed, clearly putting at risk reaching the desired goal 60 km / h.

- Although the assembly of an 18 tooth crown is not an impossible task, we can modify the drive pinion and crown assembly in such a way that the coupling ends up being more feasible.

The following table shows some crowns that we can find from 63 to 97 and that maintaining the necessary transmission ratio of 1.69 to 1 would give us as a result unosin this way, knowing the gear ratio to apply and keeping the drive pinion oin this way, knowing the gear ratio to apply and keeping the drive pinion of the 11-tooth motor, we proceed to calculate the necessary teeth on the crown through from the following fof the 11-tooth motor, we proceed to calculate the necessary teeth on the crown through from the following fo

While it is true that the drive pinion has an internal conical shape (the internal diameter varies along its height to settle on the motor shaft which is also conical and secured with a key, as can be seen in the image below ) that might not fit with another straight internal cut pinion, a solution could be to internally turn the new pinion or proceed to join both pinions by welding.