2103483 Automotive System Design (2022/2)

one speed transmission

Since our motors can break traction all the way to maximum RPM and still provide sufficient top speed for FSAE racing, we see no benefit to a multi-speed transmission. Thus, our transmission will be used only to transfer the torque from the motor to the wheel with a suitable ratio.

the gears

To transmit torque to the wheel, the gears must be able to withstand the torque that the motor can produce. So, the first step in designing the transmission will be to design the gearset.

teeth type

We have a choice of using helical gear or spur gear. Helical gear is stronger but produce axial load and require additional supports. Spur gear is more efficient and produce less heat than helical gear but produce more noise. Since we want the gearbox to be as compact as possible to fit into the narrow section of the frame, the additional support required for helical gear would make the gearbox too wide so we will use spur gear for in the transmission.

gear layout

The gears can be arranged in a planetary set to transmit power axially or in parallel to transmit power laterally. From our black box design, the motor and the output shaft need to have an offset so a traditional parallel gearset will be adopted.

teeth and layout

Because of our packaging limitation, we will use a simple straight cut gear train. The lack of axial support will reduce the size of the gearbox and power will be transmitted down from the motor.

teeth size

Gear size is measured by “module” which is standard across the globe. For gears with the same diameter a smaller module will have more teeth allowing smoother power delivery but larger module with a smaller number of teeth will have larger teeth which is stronger and can withstand more torque. For the best power delivery, we will use the smallest module that can withstand the load from the motor. We will calculate the load of 480Nm since that is the final torque that will be output to the wheel. We will be aiming for a safety factor of 4 because the transmission is an important component that is very hard to replace during the race and in case of failure, we want it to be the last part that broke. In case of a wheel lockup that produce excessive torque in the drivetrain we designed the drivetrain so that the axle will break before the transmission. That’s why the transmission is designed with such a high factor of safety.

The material of the gear is forged steel which is not uncommon in motorsport and can be ordered from many manufacturers. From calculation and simulation, we found that an M2.5 module gear with a thickness of 20mm can withstand a load of 480Nm with safety factor of 4.77. So, our gearset will use M2.5x20mm gears.

teeth number

To produce a smooth power delivery the industry standard, say 17 teeth on a gear will produce an acceptable level of smoothness in most use case. But to produce the ratio of 4.8 the driven gear will have to have 81 teeth which will make the whole gearbox too large to fit in the car.

To fit in the car the total length of the gearset must be less than 245mm, but for the output shaft to clear the body of the motor including tripod housing the total center distance of the gearset must be longer than 126mm.

To satisfy these physical constraints a compound layout is adopted for the gearset. Gear reduction is done over two sets of gear and from calculation to satisfy every requirement two sets of 17:37 gears will be use.

Two sets of 17:37 gears will produce a final ratio of 4.737 which is within target, and each gear has prime number teeth which will distribute wear better.

lightweighting

The 17 teeth M2.5x20mm gear is too small to make any lightweighting so it will be used as is. The weight of the 17 teeth gear is 124 grams each. We will focus the lightweighting effort on the 37 teeth gear.

There are two ways to lightweight a gear canaling, and hole punching. Canaling is when a surface of the gear is machined equally to make a circular canal, this method is relatively easy to manufacture and produce no mass imbalance but produce an unoptimized shape. Hole punching is when holes is drilled into the gear, the holes are spaced out equally on the gear and the final product looks like a spoke on a wheel. Hole punching produce a better strength to weight ratio since the shape is more optimized but is more time consuming to manufacture.

Easier to manufacture
Balanced
Not optimised
Bad planar stiffness

Better strength to weight
No planar wobble
More manufacturing process
Compromise surface finish of forged product

topology study

Previous simulation showed that the stress is mostly concentrated on the surface of the gear teeth, and on other part of the gear the stress increase near the center of the gear. Using topology study the shape that the AI produced utilized both canaling and hole punching. The thickness of canaling and size of hole punching is roughly carried over into our final design which use 7.5mm canaling on both side with 7 20mm holes punch located around the outer edge of the gear, which is in line with our observation from previous simulation which suggest that the stress is greater in the middle of the gear.

final gear design

The final design has a safety factor of 4.43 of the surfaces of the teeth, which remained unchanged after the lightweighting, and an evenly distributed safety factor of 5 to 6 in the middle of the gear. And the final weight is reduced from 990 grams per gear down to 445 grams each.

Before

SF 4.77

990 grams

max stress at teeth

After

SF 4.43

445 grams

more even stress distribution

shaft and bearing

The shaft transmits the internal torque between the gears. The shaft and bearing receive lateral loads produced by the gears and hold the gears in place. A simple calculation is used to find the loads produced by the gears and determine the size of the shaft and bearing with safety actor of 4.

To with stand the loads the shaft should have a diameter larger the 17mm, but to fit a tripod housing to the end of the shaft some section of the shaft needs to have a diameter of 35mm.

From the SKF angular contact bearing catalogue the smallest bearing that can withstand the load has an internal bore of 20mm.

*Note that the mass of the gear is very small compared to the load produced, so in the calculation the mass of the gears is negligable.

final design

The final size of the shaft is as followed. In the final design gears are set in the shaft first, then locked in place with snap rings. Then the bearing is pressed onto each end of the shaft and the whole assembly is fitted into the transmission housing.

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