SI Engine Torque Structure Model

The spark-ignition (SI) engine implements a simplified version of the SI engine torque structure calculation used in a Bosch Engine Management System (EMS). For the torque structure estimation calculation, the block requires calibration tables for:

• Inner torque — Maximum torque potential of the engine at a given speed and load

• Friction torque — Torque losses due to friction

• Optimal spark — Spark advance for optimal inner torque

• Spark efficiency — Torque loss due to spark retard from optimal

• Lambda efficiency — Torque loss due to lambda change from optimal

• Pumping torque — Torque loss due to pumping

The tables available with Powertrain Blockset™ were developed with the Model-Based Calibration Toolbox™.

Lookup Table	Used to Determine	Plot
Inner torque, $f_{Tqinr}$	$T{q}_{inr}=f_{Tqinr}(L,N)$	The inner torque lookup table, $f_{Tqinr}$, is a function of engine speed and engine load, $T{q}_{inr}=f_{Tqinr}(L,N)$, where: $T{q}_{inr}$ is inner torque based on gross indicated mean effective pressure, in N·m. L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless. N is engine speed, in rpm.
Friction torque, $f_{Tfric}$	$$T_{fric}=f_{Tfric}\left(L,N\right)$$	The friction torque lookup table, $f_{Tfric}$, is a function of engine speed and engine load, $$T_{fric}=f_{Tfric}\left(L,N\right)$$, where: $T_{fric}$ is friction torque offset to inner torque, in N·m. L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless. N is engine speed, in rpm.
Pumping torque, ƒTpump	Tpump=ƒTpump(L,N)	The pumping torque lookup table, ƒTpump, is a function of engine load and engine speed, Tpump=ƒTpump(L,N), where: Tpump is pumping torque, in N·m. L is engine load, as a normalized cylinder air mass, dimensionless. N is engine speed, in rpm.
Optimal spark, $f_{SAopt}$	$S{A}_{opt}=f_{SAopt}(L,N)$	The optimal spark lookup table, $f_{SAopt}$, is a function of engine speed and engine load, $S{A}_{opt}=f_{SAopt}(L,N)$, where: SAopt is optimal spark advance timing for maximum inner torque at stoichiometric air-fuel ratio (AFR), in deg. L is engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles, dimensionless. N is engine speed, in rpm.
Spark efficiency, $f_{Msa}$	$\begin{array}{l}{M}_{sa}=f_{Msa}(\Delta SA)\\ \Delta SA=S{A}_{opt}-SA\end{array}$	The spark efficiency lookup table, $f_{Msa}$, is a function of the spark retard from optimal $\begin{array}{l}{M}_{sa}=f_{Msa}(\Delta SA)\\ \Delta SA=S{A}_{opt}-SA\end{array}$ where: $M_{sa}$ is the spark retard efficiency multiplier, dimensionless. $\Delta SA$is the spark retard timing distance from optimal spark advance, in deg.
Lambda efficiency, $f_{M\lambda }$	$M_{\lambda }=f_{M\lambda }(\lambda )$	The lambda efficiency lookup table, $f_{M\lambda }$, is a function of lambda, $M_{\lambda }=f_{M\lambda }(\lambda )$, where: $M_{\lambda }$ is the lambda multiplier on inner torque to account for the air-fuel ratio (AFR) effect, dimensionless. $\lambda$ is lambda, AFR normalized to stoichiometric fuel AFR, dimensionless.

The engine brake torque is a based on inner torque with lambda efficiency, spark retard efficiency multipliers, pumping torque, and a friction torque offset

$T_{brake}=M_{\lambda }{M}_{sa}T{q}_{inr}-T_{fric}-T_{pump}$

To account for thermal effects, the torque structure model corrects the friction torque calculation as a function of coolant temperature.

$$\begin{array}{l}{T}_{fric}=M_{fric}{f}_{Tfric}(L,N)\\ M_{fric}=f_{fric,temp}(T_{coolant})\end{array}$$

The pumping torque is a function of engine speed and engine speed.

$$T_{pump}=f_{Tpump}(L,N)$$

$S{A}_{opt}$	Optimal spark advance timing for maximum inner torque at stoichiometric air-fuel ratio (AFR)
$\Delta SA$	Spark retard timing distance from optimal spark advance
$SA$	Spark advance timing
$L$	Engine load at arbitrary cam phaser angles, corrected for final steady-state cam phaser angles
N	Engine speed
$M_{\lambda }$	Lambda multiplier on inner torque to account for the AFR effect
$\lambda$	Lambda, AFR normalized to stoichiometric fuel AFR
$M_{sa}$	Spark retard efficiency multiplier
$f_{Msa}$	Spark efficiency lookup table to account for torque loss due to spark retard from optimal
$f_{Tfric}$	Friction torque lookup table to account for torque losses due to friction
$f_{M\lambda }$	Lambda efficiency lookup table to account for torque loss due to lambda change from optimal
$f_{SAopt}$	Optimal spark lookup table, for maximum inner torque as a function of engine speed and load
$f_{Tqinr}$	Inner torque lookup table, for maximum torque potential of the engine at a given speed and load
$T_{brake}$	Engine brake torque after accounting for spark advance, AFR, and friction effects
$T_{fric}$	Friction torque offset to inner torque
$T{q}_{inr}$	Inner torque based on gross indicated mean effective pressure
Tpump	Pumping torque
Mfric	Friction torque modifier
Tcoolant	Coolant temperature

References

[1] Gerhardt, J., Hönninger, H., and Bischof, H., A New Approach to Functional and Software Structure for Engine Management Systems – BOSCH ME7. SAE Technical Paper 980801, 1998.