Research Article

Mixed Integer Linear Programming Based Speed Profile Optimization for Heavy-Haul Trains

Table 2

Notations for model formulation.

NotationDescription

Index of cars
Mass of car
, Number of locomotives and wagons
Mass of the HHT
Speed of the HHT
Position of the HHT
Time of HHT running
, Basic and line resistances
Air brake force
Electric brake force
Unit basic resistance
, , Positive coefficients of basic resistance
Gravity constant
Position of car
Gradient at the position of car
Number of slopes
Gradient of slopes
Starting and ending positions of slopes
Curve radius at the position of car
Number of curves
Radius of curves
Starting and ending positions of curves
Empirical coefficient
Length between cars and
Output ratio of electric brake force
Maximum electric brake force
Number of brake shoes equipped on a car
Pressure acting on one brake shoe of car
Brake shoe friction coefficient of car
Brake cylinder diameter
Braking leverage
Number of brake cylinders equipped on a car
Transmission efficiency of braking device
Brake cylinder pressure of car
Brake cylinder pressure of car during air brake application
Brake cylinder pressure of car during air brake release
Amount of pressure reduction
, Binary variable indicating regimes of the application and release of air braking
, Timing of air brake application and release
, Pressure rise and fall delay times for car
Time required for the pressure to change to zero
Time required for the pressure to change to the maximum value
Maximum value of brake cylinder pressure
, Functions to describe the rise and fall of brake cylinder pressure for each car
Given running time
Application time of air braking
Running distance with the speed limit
Total running distance
, Weight coefficients
Speed limit
Minimum release speed
Air brake release time
Air-filled time
, Starting and ending positions of a neutral section