How do I select the right motor and gear ratio for a mid-drive e-Bike?

• evbkezz
In summary: They need a gear to reduce the rpm to a usable level. The ideal RPM for this motor would be around 60, but if you reduce it to 60 the torque will still be high.
evbkezz
TL;DR Summary
Need help finding the correct motor and gear configuration for a 250W mid-drive.
Hey all!

I am working on my first ebike build and posted a question about friction drives earlier. Now, I have decided to go with a Mid-drive. I made calculations and found out the torque and rpm required for the build. But I am having difficulty find the right motor and gear ratio. I am trying to build something like the Brose S Mag, the size of the drive is so small but the power it delivers is insane. It delivers a torque of 90Nm. They said they use a planetary gear box. As per my understanding, they have used a high rpm motor and geared it to achieve the required torque and RPM. The place I live has a legal power limit of 250W and speed limit of 25Kmh for ebikes.

These are the specs of my bike:
GVW= 105kg
Max Speed = 25kmhI calculated the air resistance using the formula:

RA = rhoCdAV^2/2 where rho is density of air, Cd is the drag coefficient(0.88), A is area of contact in m^2(0.4) and v is velocity in m/s(6.94)
RA = 10.38NI calculated rolling resistance using the formula:

RR = GVW*Crr where GVW is total vehicle weight(105Kgs) and Crr is rolling resistance of tire on asphalt road(0.004)
RR = 4.12NI calculated grade resistance using the formula:

RG = GVW*sin theta where sin theta = 0.196 for 20% gradeablity
RR = 202.09N

The acceleration force required for 25kmh in 5 secs is 145.74N

The torque required when considering grade resistance is 83.6Nm
The torque required on flat roads is 37.15Nm
The RPM required for 25kmh with a wheel dia of 26" is 240 after including a fudge factor of 20%

I should now select a motor that can achieve the above figures and the rated power has to be below 250W and size of motor should be really small. I think using a high rpm motor with planetary gear reduction can help me achieve these numbers. I am planning to use a 36V 10A controller so the peak power can be till 306W assuming a 85% efficiency of the motor.
Idk what motor should I choose and what gear ratio I should use. Will RC motors work as they provide very high rpms and are small too?

A user on the other forum told me that I would have to design a gearbox such the peak power of the motor is delivered at 60RPM since the bicycle drivetrains are built for the average human rpm which is around 60. But when I look for motors online, manufactures aren't giving the peak power inform. How do I find the rpm and torque at the peak power? I should build a gear to reduce it to 60 RPM? What should be the ideal torque or RPM values before reduction? If I reduce the RPM to 60 will still be able to achieve 25Kmh?
Should I design it such that it exceeds the 83.6Nm torque at the highest gear?

Please do let me know if my calculations are right.

Thanks

Why a gear? A BLDC motor plus its digital controller work over a large range of RPM including zero. Electric motorcycles and scooters use them. They come in many sizes, and they are relatively affordable.

Edit: incorrect paragraph removed.

anorlunda said:
Why a gear? A BLDC motor plus its digital controller work over a large range of RPM including zero. Electric motorcycles and scooters use them. They come in many sizes, and they are relatively affordable.

Edit: incorrect paragraph removed.

Gear because the small BLDC motors don't provide enough torque.

1. How do I determine the power requirements for my mid-drive e-Bike?

To determine the power requirements for your mid-drive e-Bike, you will need to consider factors such as the weight of the rider and any additional cargo, the terrain you will be riding on, and the desired speed and acceleration. You can use online calculators or consult with experienced e-Bike riders to get a better idea of the power needed for your specific needs.

2. What is the importance of selecting the right motor for a mid-drive e-Bike?

The motor is the heart of an e-Bike and plays a crucial role in its performance. Selecting the right motor for your mid-drive e-Bike is important because it will determine the power and torque output, as well as the overall efficiency and range of your e-Bike. It is essential to choose a motor that can handle the power requirements and is compatible with your e-Bike's battery and controller.

3. How do I calculate the gear ratio for a mid-drive e-Bike?

To calculate the gear ratio for your mid-drive e-Bike, you will need to know the motor's RPM (revolutions per minute) and the wheel's RPM. The gear ratio is the ratio of the number of rotations of the motor to the number of rotations of the wheel. You can use an online calculator or manually calculate it by dividing the motor's RPM by the wheel's RPM.

4. What factors should I consider when selecting a gear ratio for a mid-drive e-Bike?

When selecting a gear ratio for your mid-drive e-Bike, you should consider the terrain you will be riding on, the desired speed and acceleration, and the motor's power and torque output. A lower gear ratio will provide more torque and better hill-climbing abilities, while a higher gear ratio will offer better speed and efficiency on flat terrain. It is essential to choose a gear ratio that suits your riding style and needs.

5. Can I change the gear ratio on my mid-drive e-Bike?

Yes, it is possible to change the gear ratio on a mid-drive e-Bike. However, it may require some technical knowledge and tools. You can change the gear ratio by adjusting the size of the front and rear sprockets or by changing the size of the chainring and cassette. It is recommended to consult with a professional or do thorough research before attempting to change the gear ratio on your e-Bike.

• Mechanical Engineering
Replies
2
Views
3K
• Classical Physics
Replies
16
Views
2K
• Mechanical Engineering
Replies
2
Views
1K
• Mechanical Engineering
Replies
19
Views
792
• Mechanical Engineering
Replies
1
Views
575
• Mechanical Engineering
Replies
3
Views
3K
• Engineering and Comp Sci Homework Help
Replies
2
Views
1K
• Other Physics Topics
Replies
8
Views
15K
• Mechanical Engineering
Replies
17
Views
3K
• Mechanical Engineering
Replies
10
Views
3K