Optimal Approximation Method for Diesel Engine External Speed Characteristics
Abstract
This article focuses on selecting an optimal approximation method for the external speed characteristics of diesel engines, a critical step in mathematical modeling for evaluating vehicle performance parameters.
An analysis of modern turbocharged diesel engines with electronic fuel injection systems has shown that they exhibit a constant torque region over a wide range of crankshaft angular velocities. This feature complicates their analytical representation and necessitates the selection of an appropriate approximation method.
Various approximation techniques were examined, including polynomial approximation using Lagrange interpolation and the least squares method, as well as piecewise linear approximation. It was found that polynomial methods provide high accuracy only for torque curves with a smooth increase, peak, and subsequent decline. However, for diesel engines with a constant torque region, these methods introduce significant errors. Increasing the polynomial degree improves accuracy to some extent, but even sixth-degree polynomials fail to accurately capture the constant torque region, introducing artificial oscillations and local extrema.
Results indicate that piecewise linear approximation effectively reconstructs the external speed characteristics of diesel engines with a constant torque region. For the Volkswagen CAYD diesel engine, segmenting the angular velocity range into five sections provided the highest accuracy. Reducing the number of segments to three slightly decreased accuracy but still outperformed sixth-degree polynomial approximation using the least squares method.
Consequently, piecewise linear approximation is identified as the most suitable method for approximating the external speed characteristics of diesel engines with a constant torque region.
Keywords: diesel engine, external speed characteristics, approximation, polynomial approximation, piecewise linear approximation, mathematical modeling.
