Figure from article: A mathematical study of the...
 
KEYWORDS
TOPICS
ABSTRACT
Air-fuel ratio measurement is essential for efficient combustion and emission control in internal combustion engines. This study presents a mathematical model for the voltage response of narrowband zirconia lambda sensors, commonly used in older vehicles. These sensors, while cost-effective, are limited by their narrow operating range and strong temperature sensitivity – especially under rich mixture conditions. Using the Nernst equation, the study models the sensor voltage as a function of oxygen partial pressure. The sensor’s heating element was experimentally characterized, and its resistance–temperature relationship was accurately described using a Rational5 function. A modified form of the Nernst equation enabled voltage-to-AFR conversion across a wide mixture spectrum. Data analysis confirmed that in lean conditions, the voltage response is nearly linear and largely unaffected by temperature, enabling accurate closed-loop control. In contrast, rich mixtures produced highly non-linear and temperature-dependent behavior, making interpretation more complex. To address this, an Arrhenius-based model was successfully applied to the rich-side response, significantly improving accuracy after temperature compensation. The model was implemented and tested on a Ford EEC V ECU with a Ford 302 GT40P engine running on LPG. Modifications to the controller allowed stable closed-loop operation up to lambda = 1.35 using only a narrowband sensor. These results show that with proper modeling and calibration, narrowband lambda sensors can effectively monitor lean mixtures and offer limited utility in rich conditions. This opens new possibilities for retrofitting legacy engine systems without expensive hardware upgrades. Further research is needed to enhance rich-side precision and dynamic temperature correction.
REFERENCES (15)
1.
Aravind S, Ragupathi P, Kumar DS, Vignesh G. A numerical investigation of automotive lambda sensor to improve the life span of the sensor using CFD. IOP Conf Ser Mater Sci Eng. 2020;923(1). https://doi.org/10.1088/1757-8....
 
2.
Bosch Engineering GmbH, Lambda Sensor LSU 4.9 datasheet, 51865867 en, 1, 26. Aug. 2025.
 
3.
Collings N, Harris JA, Glover K. Estimating IC engine exhaust gas lambda and oxygen from the response of a universal exhaust gas oxygen sensor. Meas Sci Technol. 2013;24(9):095101. https://doi.org/10.1088/0957-0....
 
4.
Hills B. United States Patent Preparing Fire-Fighting Concentration US 4,464,267 1984;(19).
 
5.
How Oxygen Sensor Works – Automotive Systems https://youtu.be/Fl3aD1qJrEg?s... (accessed on 10.06.2025).
 
6.
Jakliński P, Czarnigowski J, Ścisłowski KJ. Study of the effect of ignition crank angle and mixture composition on the performance of a spark-ignition engine fueled with ethanol. Combustion Engines. 2024;197(2):56-63. https://doi.org/10.19206/CE-17....
 
7.
Klett S, Piesche M, Heinzelmann S, Weyl H, Wiedenmann H, Schneider U et al. Numerical and experimental analysis of the momentum and heat transfer in exhaust gas sensors. SAE Technical Paper 2005-01-0037. 2005. https://doi.org/10.4271/2005-0....
 
8.
Moos R, Izu N, Rettig F, Reiß S, Shin W, Matinfara I. Resistive oxygen gas sensors for harsh environments. Sensors. 2011;11(4):3439-3465. https://doi.org/10.3390/s11040....
 
9.
Nishiyama A, Ikeda Y, Serizawa T. Lean limit expansion up to lambda 2 by multi-point microwave discharge igniter. 2018;247-260. Ignition Systems for Gasoline Engines: 4th International Conference December 6–7, 2018, Berlin. https://doi.org/10.5445/IR/100....
 
10.
Run Lean Emissions Ecco modder forum thread https://ecomodder.com/forum/sh... (accessen on 10.06.2025).
 
11.
Sensing the adequate mixture – the Bosch Lambda Sensor https://www.bosch.com/stories/... (accessed on 10.06.2025).
 
12.
Tang H, Prasad K, Sanjinés R, Lévy F. TiO2 anatase thin films as gas sensors. Sensors and Actuators, B: Chemical. 1995 https://doi.org/10.1016/0925-4....
 
13.
Toema M. Physics-based characterization of lambda sensor output to control emissions from natural gas fueled engines. An Abstract of a Disertation, Kansas State University, 2010.
 
14.
Tutunea D, Dumitru I, Stănciuc-Oţăt OV. Overview of the use of oxygen sensors in automotive applications. IOP Conf Ser Mater Sci Eng. 2024;1303(1):012014. https://doi.org/10.1088/1757-8....
 
15.
Urbański B, Przybyła G, Brodziński Ł, Savitskaya M. Reducing emissions of harmful substances in rally cars. Combustion Engines. 2024;197(2):132-8. https://doi.org/10.19206/CE-18....
 
eISSN:2658-1442
ISSN:2300-9896
Journals System - logo
Scroll to top