## INTRODUCTION

The aim of this project is to create a model of a five-speed transmission for motorcycles and perform simulations of the gear shifting during acceleration with LMS Virtual Lab software modeling.

A transmission is a mechanical component that has the function to modify the characteristic curve of the output power of an engine, similarly to a reducer, but allowing to select each time a different transmission ratio, from the range of gear ratios available.

The type used on motorcycles is the sequential manual transmission where gears are selected in order, and direct access to specific gears is not possible.

Sequential manual transmissions work by providing the driver with the ability to select the gear directly before or after the gear currently engaged. Usually the shift lever is pulled back to select the adjacent lower gear and pushed forwards to select the adjacent higher gear.

On a sequential gearbox, the shift lever operates a ratchet mechanism that converts the back and forth movement of the shift lever into a rotary motion.This rotary action turns a selector drum (sometimes called a barrel) which has three or four tracks machined around its circumference. Running in the tracks are the selector forks, either directly, or via selector rods. These tracks deviate around the circumference and as the drum rotates, the selector forks running in the tracks are moved to select the required gear.

## OBJECTIVES

The aim of this project is to create a model of a five-speed gearbox for motorcycles and perform simulations of the gear shifting during acceleration with LMS Virtual Lab software modeling.

## MODELING

Already having the CAD drawings of all the pieces of the transmission, realized according to the manufacturer’s specifications, it was possible to start directly with the assembling.

The first step was to examine the real part, which made it possible to understand which joint to use.

Gearbox is essentially composed of two shafts, a primary connected to the engine through clutch, and a secondary ending with the sprocket; on these shafts are positioned the gear wheels (five for each shaft since the transmission is a five speed transmission) that are divided into axially fixed and axially free wheels and free in rotation and fixed in rotation wheels.

Axially free wheels (three) are moved by the forks, in turn driven by the selector drum as was explained previously, to select the desired gear.

When a fork moves the toothed wheel to the right or left, it engages with the adjacent wheel through grooves.

In the schemes below are represented the positions of the gear wheels in each selected gear.

For assembling the free in rotation wheels was used a revolute joint between the shaft and the gear, for the axially free wheels was used a bracket joint between the shaft and the gear, releasing the degree of freedom relative to the axial translation, and finally for the fixed wheels and the sprocket was used a bracket joint between the shaft and the gear.

For assembling the two shafts, two fixed to the ground axes were created, each shaft was then coupled to the respective axis through a revolute joint.

To model the engagement between the gear wheels was used the “Three-Body Relative Constraint”.Then was inserted into the required parameters, the right gear ratio provided by the manufacturer.

The following table shows the gear ratios for the different gears.

After several tests, it was concluded that the most close to reality method for modeling the joint between the wheels on the same shaft at the time of selection of the gear was to raise a contact force of the type “Sphere-to-Extruded Surface Contact ” as it can be seen in these images.

The plane element has been bound to the wheel through a bracket joint, in the same way the sphere element has been bound with the other wheel through a bracket joint.

In this way, when the wheel connected to the fork and fixed in rotation approaches the freewheel a collision occurs between the sphere and plane as happens in reality in the joint between the two wheels.

To proceed with the simulations was necessary to assume an engine’s torque curve.

So it was created an expression, dependent on engine speed and bounded above to 12500 rpm, and given as input to a RSDA placed on the revolute joint of the main shaft.

Then has been set inertia equal to 0.12kgxm ^ 2 to the primary shaft, calculated taking into account the inertia of the engine and the one of the shaft (values taken from “Motorcycle dynamics”) and was assumed equivalent inertia, concentrated on the sprocket, equal to 2.5kgxm ^ 2.

Subsequently was applied a resistive torque to the counter shaft calculated as:

Resistive Torque= 1/2*ρair*Cx*Ar*(sprocket_speed*(zp/zc)*Rr)^2

Assuming:

- ρair=1.18 kg/m^3 air’s density
- Cx=0.2 drag coefficient
- Ar=1 m^2 frontal area
- zp=13 number of sprocket’s teeth
- zc=58 number of crown’s teeth
- Rr=0.3 m wheel’s radius

Was finally sets an initial speed of 800 rpm to countershaft to make the simulation more realistic.In fact, the clutch, which is necessary for the standing start, has not been modeled.

## SIMULATIONS AND ANALYSIS OF RESULTS

The last step was the validation of the model built. For this purpose was made an acceleration test in which they were changed all gears.

In this video it can be seen the engagement.

In this video it can be seen full simulation.

First of all it was verified the respect of speed ratios.

The graph shows the evolution of the speed of mainshaft and countershaft.

It can be seen as the ratio between the two speeds remain constant and equal to the gear ratio.

In this zoom it can be seen the first-to-second step.The first slope corresponds to the speed of the first gear, the second corresponds to the neutral position (in fact in the sequential manual gearbox for changing gear must always switch to the neutral position) then occurs the engagement and the curve continues with the slope of the second gear.

This graph shows the torque characteristic. The red curve represents the sprocket’s torque, the green one represents the resistive torque and the blue one the engine’s torque. As the speed increases the resistive torque increases and the vehicle stops to accelerate.

Finally, some values have been calculated on paper, then they were compared with the software’s results for validating the model.

Maximum vehicle’s speed.

Calculated 305,503 km/h

Software output 305,503 km/h

Maximum engine’s power

Calculated 80,994 kW

Software output 80.993 kW

## CONCLUSIONS

The acceleration test has allowed to validate the model implemented on LMS Virtual Lab Software modeling. The gearbox responds to gear changes as expected and program’s output values correspond to those calculated. The gear ratios are respected and the torque is transmitted as expected.

Some parameters, such as the frontal area, the drag coefficient and the crown-pinion ratio, should be reviewed. The model could be extended by introducing the clutch and could be included in the model of a motorcycle.