Ideal Fixed Gear Transmission

Ideal fixed gear transmission without clutch or synchronization

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• Powertrain Blockset / Transmission / Transmission Systems

Vehicle Dynamics Blockset / Powertrain / Transmission

• Description

The Ideal Fixed Gear Transmission implements an idealized fixed-gear 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 component-sizing, 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.

SettingBlock 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:

• Gear

• Input torque

• Input speed

• Oil temperature

The block uses this equation to determine the transmission dynamics:

$\begin{array}{l}{\stackrel{˙}{\omega }}_{i}\frac{{J}_{N}}{{N}^{2}}={\eta }_{N}\left(\frac{{T}_{o}}{N}+{T}_{i}\right)-\frac{{\omega }_{i}}{{N}^{2}}{b}_{N}\\ {\omega }_{i}=N{\omega }_{o}\end{array}$

The block filters the gear command signal:

$\frac{G}{{G}_{cmd}}\left(s\right)=\frac{1}{{\tau }_{s}s+1}$

Neutral Gear

When is equal to 0, the initial gear is neutral. The block uses these parameters to decouple the input flywheel from the downstream gearing.

The block uses these equations for the neutral gear speed and flywheel.

$\begin{array}{l}{\stackrel{˙}{\omega }}_{neutral}\frac{{J}_{N}}{{N}^{2}}={\eta }_{N}\frac{{T}_{o}}{N}-\frac{{\omega }_{neutral}}{{N}^{2}}{b}_{N}\\ {\omega }_{neutral}=N{\omega }_{o}\end{array}$

$\begin{array}{l}{\stackrel{˙}{\omega }}_{1}{J}_{F}={\eta }_{@N=0}{T}_{i}-{b}_{@N=0}{\omega }_{i}\\ {J}_{F}={J}_{@N=1}-{J}_{@N=0}\end{array}$

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionVariableEquations

PwrInfo

PwrTrnsfrd — Power transferred between blocks

• Positive signals indicate flow into block

• Negative signals indicate flow out of block

PwrEng

Engine power

Peng

${\omega }_{i}{T}_{i}$
PwrDiffrntl

Differential power

Pdiff

${\omega }_{o}{T}_{o}$

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

• Positive signals indicate an input

• Negative signals indicate a loss

PwrEffLoss

Mechanical power loss

Peffloss

${\omega }_{o}{T}_{o}\left({\eta }_{N}-1\right)$
PwrDampLoss

Mechanical damping loss

Pdamploss

PwrStored — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

PwrStoredTrans

Rate change in rotational kinetic energy

Pstr

The equations use these variables.

 bN Engaged gear viscous damping JN Engaged gear rotational inertia JF Flywheel rotational inertia ηN Engaged gear efficiency G Engaged gear number Gcmd Gear number to engage N Engaged gear ratio Ti Applied input torque, typically from the engine crankshaft or dual mass flywheel damper To Applied load torque, typically from the differential or drive shaft ωo Initial input drive shaft rotational velocity ωi, ώi Applied drive shaft angular speed and acceleration ωNo Initial neutral gear input rotational velocity ωneutral Neutral gear drive shaft rotational velocity τs Shift time constant

Ports

Inputs

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Integer value of gear number to engage, Gcmd.

Applied input torque, Ti, typically from the engine crankshaft or dual mass flywheel damper, in N·m.

Applied load torque, To, typically from the differential, in N·m.

Oil temperature, in K. To determine the efficiency, the block uses a 4D lookup table that is a function of:

• Gear

• Input torque

• Input speed

• Oil temperature

Dependencies

To enable this port, set Efficiency factors to Gear, input torque, input speed, and temperature.

Output

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Bus signal containing these block calculations.

SignalDescriptionVariableUnits
EngEngTrq

Applied input torque, typically from the engine crankshaft or dual mass flywheel damper

Ti

N·m

EngSpd

Applied drive shaft angular speed input

ωi

DiffDiffTrq

Applied load torque, typically from the differential

To

N·m

DiffSpd

Drive shaft angular speed output

ωo

TransTransSpdRatio

Input to output speed ratio at time t

Φ(t)

N/A

TransEta

Ratio of output power to input power

ηN

N/A

TransGearCmd

Commanded gear

Ncmd

N/A

TransGear

Engaged gear

N

N/A

PwrInfoPwrTrnsfrd

PwrEng

Engine power

Peng

W
PwrDiffrntl

Differential power

Pdiff

W
PwrNotTrnsfrdPwrEffLoss

Mechanical power loss

Peffloss

W
PwrDampLoss

Mechanical damping loss

Pdamploss

W
PwrStoredPwrStoredTrans

Rate change in rotational kinetic energy

Pstr

W

Applied drive shaft angular speed input, ωi, in rad/s.

Drive shaft angular speed output, ωo, in rad/s.

Parameters

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To specify the block efficiency calculation, for Efficiency factors, select either of these options.

SettingBlock 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:

• Gear

• Input torque

• Input speed

• Oil temperature

Dependencies

Setting Parameter ToEnables
Gear only

Efficiency vector, eta

Gear, input torque, input speed, and temperature

Efficiency torque breakpoints, Trq_bpts

Efficiency speed breakpoints, omega_bpts

Efficiency temperature breakpoints, Temp_bpts

Efficiency lookup table, eta_tbl

Method that the block uses to switch the gear ratio during gear shifting.

Transmission

Vector of integer gear commands used to specify the number of transmission speeds. Neutral gear is 0. For example, you can set these parameter values.

To SpecifySet Gear number, G To
Four transmission speeds, including neutral[0,1,2,3,4]
Three transmission speeds, including neutral and reverse[-1,0,1,2,3]
Five transmission speeds, including neutral and reverse[-1,0,1,2,3,4,5]

Vector dimensions for the Gear number vector, Gear ratio vector, Inertia vector, Damping vector, and Efficiency vector parameters must be equal.

Torque breakpoints for efficiency table.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Speed breakpoints for efficiency table.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Temperature breakpoints for efficiency table.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Vector of gear ratios (that is, input speed to output speed) with indices corresponding to the ratios specified in Gear number, G. For neutral, set the gear ratio to 1. For example, you can set these parameter values.

To Specify Gear Ratios ForSet Gear number, G ToSet Gear ratio, N To
Four transmission speeds, including neutral[0,1,2,3,4][1,4.47,2.47,1.47,1]
Five transmission speeds, including neutral and reverse[-1,0,1,2,3,4,5][-4.47,1,4.47,2.47, 1.47,1,0.8]

Vector dimensions for the Gear number vector, Gear ratio vector, Inertia vector, Damping vector, and Efficiency vector parameters must be equal.

Vector of gear rotational inertias, JN, with indices corresponding to the inertias specified in Gear number, G, in kg*m^2. For example, you can set these parameter values.

To Specify Inertia ForSet Gear number, G ToSet Inertia, J To
Four gears, including neutral[0,1,2,3,4][0.01,2.28,2.04, 0.32,0.028]
Inertia for five gears, including reverse and neutral[-1,0,1,2,3,4,5][2.28,0.01,2.28, 2.04,0.32,0.028,0.01]

Vector dimensions for the Gear number vector, Gear ratio vector, Inertia vector, Damping vector, and Efficiency vector parameters must be equal.

Vector of gear viscous damping coefficients, bN, with indices corresponding to the coefficients specified in Gear number, G, in N·m·s/rad. For example, you can set these parameter values.

To Specify Damping ForSet Gear number, G ToSet Damping, b To
Four gears, including neutral[0,1,2,3,4][0.001,0.003, 0.0025,0.002,0.001]
Five gears, including reverse and neutral[-1,0,1,2,3,4,5][0.003,0.001, 0.003,0.0025, 0.002,0.001,0.001]

Vector dimensions for the Gear number vector, Gear ratio vector, Inertia vector, Damping vector, and Efficiency vector parameters must be equal.

Vector of gear mechanical efficiency, ηN, with indices corresponding to the efficiencies specified in Gear number, G. For example, you can set these parameter values.

To Specify Efficiency ForSet Gear number, G ToSet Efficiency, eta To
Four gears, including neutral[0,1,2,3,4][0.9,0.9,0.9,0.9,0.95]
Five gears, including reverse and neutral[-1,0,1,2,3,4,5][0.9,0.9,0.9, 0.9,0.9,0.95,0.95]

Vector dimensions for the Gear number vector, Gear ratio vector, Inertia vector, Damping vector, and Efficiency vector parameters must be equal.

Dependencies

To enable this parameter, set Efficiency factors to Gear only.

Table of gear mechanical efficiency, ηN as a function of gear, input torque, input speed, and temperature.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Initial gear number, Go, dimensionless.

Transmission initial output rotational velocity, ωo, in rad/s.

Initial neutral gear input rotational velocity, ωNo, in rad/s.

Shift time constant, τs, in s.

Extended Capabilities

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