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CI Engine Torque Structure Model

The CI core engine torque structure model determines the engine torque by reducing the maximum engine torque potential as these engine conditions vary from nominal:

  • Start of injection (SOI) timing

  • Exhaust back-pressure

  • Burned fuel mass

  • Intake manifold gas pressure, temperature, and oxygen percentage

  • Fuel rail pressure

To account for the effect of post-inject fuel on torque, the model uses a calibrated torque offset table.

To determine the engine torque, the CI core engine torque structure model implements the equations specified in these steps.



Step 1: Determine nominal engine inputs and states

Model uses lookup tables to determine these nominal engine inputs and states as a function of compression stroke injected fuel mass, F, and engine speed, N:

  • Main start of injection timing, SOI = ƒSOIc(F,N)

  • Intake manifold gas temperature, MAT = ƒMAT(F,N)

  • Intake manifold gas pressure, MAP = ƒMAP(F,N)

  • Intake manifold oxygen percentage, O2PCT = ƒO2(F,N)

  • Fuel rail pressure, FUELP = ƒfuelp(F,N)

Step 2: Calculate relative engine states

To determine these relative engine states, the model calculates deviations from their nominal values.

  • Main start of injection timing delta, ΔSOIc= ƒSOI(F,N)- SOI

  • Intake manifold gas temperature delta, ΔMAT = ƒMAT(F,N) - MAT

  • Intake manifold oxygen percentage delta, ΔO2PCT = ƒO2(F,N) - O2PCT

  • Fuel rail pressure delta, ΔFUELP = ƒfuelp(F,N) - FUELP

For the intake manifold gas pressure, the block uses a pressure ratio to determine the relative state. The pressure ratio is the intake manifold gas pressure to the steady-state operating point gas pressure.


Step 3: Determine efficiency multipliers

Model uses gross indicated mean effective pressure (IMEPG)[1] efficiency multipliers to reduce the maximum average pressure potential of combustion. The efficiency multipliers are lookup tables that are functions of the relative engine states.

  • Main start of injection timing efficiency multiplier, SOIeff = ƒSOIeff(ΔSOI,N)

  • Intake manifold gas temperature efficiency multiplier, MATeff = ƒMATeff(ΔMAT,N)

  • Intake manifold gas pressure efficiency multiplier, MAPeff = ƒMAPeff(MAPratio,λ)

  • Intake manifold oxygen percentage efficiency multiplier, O2Peff = ƒO2Peff(ΔO2P,N)

  • Fuel rail pressure efficiency multiplier, FUELPeff = ƒFUELPeff(ΔFUELP,N)

Step 4: Determine indicated mean effective cylinder pressure (IMEP) available for torque production

To determine the IMEP available for torque production, the model implements these equations.


The model multiplies the efficiency multipliers from step 3 by the IMEPG. The model implements IMEPG as lookup table that is a function of the compression stroke injected fuel mass, F, and engine speed, N.

Step 5: Account for losses due to friction

To account for friction effects, the model uses the nominal friction mean effective pressure (FMEP)[1] to implement this equation.


The model implements FMEP as lookup table that is a function of the compression stroke injected fuel mass, F, and engine speed, N. To account for the temperature effect on friction, the model use a lookup table that is a function of oil temperature, Toil, and N.

Step 6: Account for pressure loss due to pumping

To account for pressure losses due to pumping, the model uses the nominal pumping mean effective pressure (PMEP)[1] to implement these equations.


The model implements MAP and EMAP as lookup tables that are functions of the compression stroke injected fuel mass, F, and engine speed, N. Under normal operating conditions, PMEP is negative, indicating a loss of cylinder pressure.

Step 7: Account for late fuel injection SOI timing on IMEP

To account for late fuel injection SOI timing on IMEP, ΔIMEPpost, the model uses a lookup table that is a function of the effective pressure post inject SOI timing centroid, SOIpost, and the post inject mass sum, Fpost.


Step 8: Calculate engine brake torque

To calculate the engine brake torque, Tbrake, the model converts the brake mean effective pressure (BMEP)[1] to engine brake torque using these equations. The BMEP calculation accounts for all gross mean effective pressure losses. Vd is displaced cylinder volume. Cps is the number of power strokes per revolution.


Fuel Injection

In the CI Core Engine and CI Controller blocks, you can represent multiple injections with the start of injection (SOI) and fuel mass inputs to the model. To specify the type of injection, use the Fuel mass injection type identifier parameter.

Type of InjectionParameter Value









The model considers Passed fuel injections and fuel injected later than a threshold to be unburned fuel. Use the Maximum start of injection angle for burned fuel, f_tqs_f_burned_soi_limit parameter to specify the threshold.

Percent Oxygen

The model uses this equation to calculate the oxygen percent, O2p. yin,air is the unburned air mass fraction.


Exhaust Temperature

The exhaust temperature calculation depends on the torque model. For both torque models, the block implements lookup tables.

Torque Model



Simple Torque Lookup

Exhaust temperature lookup table is a function of the injected fuel mass and engine speed.


Torque Structure

The nominal exhaust temperature, Texhnom, is a product of these exhaust temperature efficiencies:

  • SOI timing

  • Intake manifold gas pressure

  • Intake manifold gas temperature

  • Intake manifold gas oxygen percentage

  • Fuel rail pressure

  • Optimal temperature

The exhaust temperature, Texhnom, is offset by a post temperature effect, ΔTpost, that accounts for post and late injections during the expansion and exhaust strokes.


The equations use these variables.


Compression stroke injected fuel mass


Engine speed


Exhaust manifold gas temperature


Optimal exhaust manifold gas temperature

ΔTpostPost injection temperature effect
TexhnomNominal exhaust temperature


Main SOI exhaust temperature efficiency multiplier


Main SOI timing relative to optimal timing


Intake manifold gas pressure exhaust temperature efficiency multiplier


Intake manifold gas pressure ratio relative to optimal pressure ratio


Intake manifold gas lambda


Intake manifold gas temperature exhaust temperature efficiency multiplier


Intake manifold gas temperature relative to optimal temperature


Intake manifold gas oxygen exhaust temperature efficiency multiplier


Intake gas oxygen percent relative to optimal


Fuel rail pressure exhaust temperature efficiency multiplier


Fuel rail pressure relative to optimal


[1] Heywood, John B. Internal Engine Combustion Fundamentals. New York: McGraw-Hill, 1988.

See Also


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