Open AccessIn most structures a transmission of the transport-technological machine (TTM) is controlled by automatic systems. In their creating it is necessary to specify the appropriate parameters and algorithms. In the total balance of the machine run time the acceleration mode is the most important. Therefore, an algorithm of the transmission gear ratio change during acceleration largely provides desirable rating of machines.
It is known that the process of acceleration is estimated by its dynamic quality and fuel economy. To reach the best rating of both simultaneously is impossible. Therefore, as the criteria of estimate, were chosen the time and fuel consumption during acceleration to a fixed speed value.
From a mathematical point of view, these criteria represent the sum of integrals, each of which defines the time or the fuel consumption during acceleration with a certain transmission gear ratio. The problem is formulated as follows: to determine the speed values of the TTM at the moments when the transmission gear ratio is changed providing the minimum values during fixed fuel supply for the estimate criteria. The latter condition in a certain way limits the task, but in explicit form there is no this control action in the dependence data.
Given the variety of possible design options for the TTM, the solution is given by a specific example that simplifies the mathematics and makes it easier to understand the results obtained. As a TTM, is considered a passenger car with petrol engine and automatic transmission, which includes a hydrodynamic transformer and three-speed gearbox.
A chosen way of solving the problem involves using the theory of ordinary maxima and minima, which allows finding the unknown values of independent variables. The expressions of sub-integral functions are in explicit form obtained and studied for meeting the necessary and sufficient conditions for existence of the extreme point. The result was a proof that in the case of evaluation process of TTM acceleration, according to the criteria of time and fuel consumption, there are the speed values, corresponding to the moments of the gear ratio change, which provide the minimum values for them.