Ideal Fixed Gear Transmission

Ideal fixed gear transmission without clutch or synchronization

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Libraries:
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.

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: Gear Input torque Input speed Oil temperature

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
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	$$\begin{array}{l}\text{For G=0: }-\frac{b_N{\omega }_i^2}{\left|N^2\right|}\\ \\ \text{For G}\ne \text{0: }-b_N{\omega }_i^2-\frac{b_N{\omega }_{neutral}^2}{\left|N^2\right|}\end{array}$$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredTrans	Rate change in rotational kinetic energy	Pstr	$$\begin{array}{l}\text{For G=0: }\frac{J_N}{N^2}{\dot{\omega }}_i{\omega }_i\\ \\ \text{For G}\ne \text{0: }{J}_F{\dot{\omega }}_i{\omega }_i+\frac{J_N}{N^2}{\dot{\omega }}_{neutral}{\omega }_{neutral}\end{array}$$

The equations use these variables.

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

Gear — Gear number to engage

scalar

Integer value of gear number to engage, G_cmd.

EngTrq — Applied input torque

scalar

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

DiffTrq — Applied load torque

scalar

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

Temp — Oil temperature

scalar

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

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Variable	Units
Eng	EngTrq		Applied input torque, typically from the engine crankshaft or dual mass flywheel damper	Ti	N·m
	EngSpd		Applied drive shaft angular speed input	ωi	rad/s
Diff	DiffTrq		Applied load torque, typically from the differential	To	N·m
	DiffSpd		Drive shaft angular speed output	ωo	rad/s
Trans	TransSpdRatio		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
PwrInfo	PwrTrnsfrd	PwrEng	Engine power	Peng	W
		PwrDiffrntl	Differential power	Pdiff	W
	PwrNotTrnsfrd	PwrEffLoss	Mechanical power loss	Peffloss	W
		PwrDampLoss	Mechanical damping loss	Pdamploss	W
	PwrStored	PwrStoredTrans	Rate change in rotational kinetic energy	Pstr	W

EngSpd — Angular speed

scalar

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

DiffSpd — Angular speed

scalar

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

Parameters

Efficiency factors — Specify efficiency calculation

Gear only (default) | Gear, input torque, input speed, and temperature

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: Gear Input torque Input speed Oil temperature

Dependencies

Setting Parameter To	Enables
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

Gear property interpolation method — Interpolation

Nearest (default) | Linear | Flat | Cubic spline

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

Transmission

Gear number vector, G — Specify number of transmission speeds

[-1,0,1,2,3,4,5] (default) | vector

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 Specify	Set 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.

Efficiency torque breakpoints, Trq_bpts — Breakpoints

[25,50,75,100,150,200,250] (default) | vector

Torque breakpoints for efficiency table.

Dependencies

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

Efficiency speed breakpoints, omega_bpts — Breakpoints

[52.4 78.5 105 131 157 183 209 262 314 419 524] (default) | vector

Speed breakpoints for efficiency table.

Dependencies

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

Efficiency temperature breakpoints, Temp_bpts — Breakpoints

[313 358] (default) | vector

Temperature breakpoints for efficiency table.

Dependencies

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

Gear ratio vector, N — Ratio of input speed to output speed

[-4.47,4.47,4.47,2.47,1.47,1,0.8] (default) | vector

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 For	Set Gear number, G To	Set 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.

Inertia vector, Jout — Gear rotational inertia

[0.128 0.01 0.128 0.1 0.062 0.028 0.01] (default) | vector

Vector of gear rotational inertias, J_N, 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 For	Set Gear number, G To	Set 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.

Damping vector, bout — Gear viscous damping coefficient

[.003 .001 .003 .0025 .002 .001 .001] (default) | vector

Vector of gear viscous damping coefficients, b_N, 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 For	Set Gear number, G To	Set 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.

Efficiency vector, eta — Gear efficiency

[0.9,0.9,0.9,0.9,0.9,0.95,0.95] (default) | vector

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

To Specify Efficiency For	Set Gear number, G To	Set 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.

Efficiency lookup table, eta_tbl — Gear efficiency

array

Table of gear mechanical efficiency, η_N 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, G_o — Gear

0 (default) | scalar

Initial gear number, G_o, dimensionless.

Initial output velocity, omega_o — Output speed

0 (default) | scalar

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

Initial neutral input velocity, omegainN_o — Neutral gear input speed

0 (default) | scalar

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

Shift time constant, tau_s — Time

.01 (default) | scalar

Shift time constant, τ_s, in s.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017a