Ideal Fixed Gear Transmission
Ideal fixed gear transmission without clutch or synchronization
 Library:
Powertrain Blockset / Transmission / Transmission Systems
Vehicle Dynamics Blockset / Powertrain / Transmission
Description
The Ideal Fixed Gear Transmission implements an idealized fixedgear transmission without a clutch or synchronization. Use the block to model the overall gear ratio and power loss when you do not need a detailed transmission model, for example, in componentsizing, fuel economy, and emission studies. The block implements a transmission model with minimal parameterization or computational cost.
To specify the block efficiency calculation, for Efficiency factors, select either of these options.
Setting  Block Implementation 

Gear only  Efficiency determined from a 1D lookup table that is a function of the gear. 
Gear, input torque, input speed, and temperature  Efficiency determined from a 4D lookup table that is a function of:

The block uses this equation to determine the transmission dynamics:
$$\begin{array}{l}{\dot{\omega}}_{i}\frac{{J}_{N}}{{N}^{2}}={\eta}_{N}\left(\frac{{T}_{o}}{N}+{T}_{i}\right)\frac{{\omega}_{i}}{{N}^{2}}{b}_{N}\\ {\omega}_{i}=N{\omega}_{o}\end{array}$$
The block filters the gear command signal:
$$\frac{G}{{G}_{cmd}}(s)=\frac{1}{{\tau}_{s}s+1}$$
Neutral Gear
When Initial gear number, G_o is equal to
0
, the initial gear is neutral. The block uses these
parameters to decouple the input flywheel from the downstream gearing.
Initial input velocity, omega_o
Initial neutral input velocity, omegainN_o
The block uses these equations for the neutral gear speed and flywheel.
$$\begin{array}{l}{\dot{\omega}}_{neutral}\frac{{J}_{N}}{{N}^{2}}={\eta}_{N}\frac{{T}_{o}}{N}\frac{{\omega}_{neutral}}{{N}^{2}}{b}_{N}\\ {\omega}_{neutral}=N{\omega}_{o}\end{array}$$
$$\begin{array}{l}{\dot{\omega}}_{1}{J}_{F}={\eta}_{@N=0}{T}_{i}{b}_{@N=0}{\omega}_{i}\\ {J}_{F}={J}_{@N=1}{J}_{@N=0}\end{array}$$
Power Accounting
For the power accounting, the block implements these equations.
Bus Signal  Description  Variable  Equations  



 Engine power  P_{eng}  ${\omega}_{i}{T}_{i}$ 
PwrDiffrntl  Differential power  P_{diff}  ${\omega}_{o}{T}_{o}$  
 PwrEffLoss  Mechanical power loss  P_{effloss}  ${\omega}_{o}{T}_{o}\left({\eta}_{N}1\right)$  
PwrDampLoss  Mechanical damping loss  P_{damploss}  $$\begin{array}{l}\text{ForG=0:}\frac{{b}_{N}{\omega}_{i}^{2}}{\left{N}^{2}\right}\\ \\ \text{ForG}\ne \text{0:}{b}_{N}{\omega}_{i}^{2}\text{}\frac{{b}_{N}{\omega}_{neutral}^{2}}{\left{N}^{2}\right}\end{array}$$  
 PwrStoredTrans  Rate change in rotational kinetic energy  P_{str}  $$\begin{array}{l}\text{ForG=0:}\frac{{J}_{N}}{{N}^{2}}{\dot{\omega}}_{i}{\omega}_{i}\\ \\ \text{ForG}\ne \text{0:}{J}_{F}{\dot{\omega}}_{i}{\omega}_{i}+\frac{{J}_{N}}{{N}^{2}}{\dot{\omega}}_{neutral}{\omega}_{neutral}\end{array}$$ 
The equations use these variables.
b_{N}  Engaged gear viscous damping 
J_{N}  Engaged gear rotational inertia 
J_{F}  Flywheel rotational inertia 
η_{N}  Engaged gear efficiency 
G  Engaged gear number 
G_{cmd}  Gear number to engage 
N  Engaged gear ratio 
T_{i}  Applied input torque, typically from the engine crankshaft or dual mass flywheel damper 
T_{o}  Applied load torque, typically from the differential or drive shaft 
ω_{o}  Initial input drive shaft rotational velocity 
ω_{i}, ώ_{i}  Applied drive shaft angular speed and acceleration 
ω_{No}  Initial neutral gear input rotational velocity 
ω_{neutral}  Neutral gear drive shaft rotational velocity 
τ_{s}  Shift time constant 