Modeling of power and torque curves of a diesel at the design stage

An external speed characteristics outlines the upper limit of the field of possible operating conditions of the engine. With its help, therefore, it is possible to judge the extreme values of the indicators and parameters of the engine when it is running at a specific speed of the crankshaft. It is at theexternal speed characteristics of the engine parts are subjected to the greatest mechanical and thermalloads, the maximum is also the smoke of the exhaust gases of diesel engines. This indicates the particular importance of techniques that allow to determine the performance of the engine in the modes of external speed characteristics. Get external speed characteristics when testing the engine on the test bench. However, this possibility is not always available, especially it is not at the design stage. When calculating the cycle, the engine performance is obtained in two modes – rated power and maximum torque. Therefore, the external speed characteristics, built by calculation is important at the stage of justification of the main indicators and parameters of the designed engine.


Establishing the problem statement
Curves of the external speed characteristics (ESC) shows the limit of the field of possible operating conditions of the engine. With its help, therefore, it is possible to define engine operation parameters when it is running at a certain rotational frequency of the crankshaft. It is at the external speed characteristics of the engine parts are subjected to the greatest mechanical and thermal loads, the maximum is also the smoke of the exhaust gases of diesel engines [1][2][3][4]. These points to the particular importance of techniques that allow to determine the performance of the engine in the ESC modes. Get ESC when testing the engine on the test bench. However, this possibility is not always available, especially it is not at the stage of design. When calculating the cycle, the engine parameters are obtained in two modes -nominal power and maximum torque. Therefore, the ESC, built by calculation is important at the stage of definition of the main indicators and parameters of the designed engine.
The procedure of calculating the effective engine torque Ttq (or mean effective pressure me) and fuel consumption rate B, i.e., the parameters more closely connected with in-cylinder processes, is as follows. Effective power Pe and effective specific fuel consumption rate b at various engine speeds n, etc. can be determined by using the wellknown formula [ (1) . 1000 e P B b (2) For the sake of generality and applicability of the computational procedure to the ESC parameters of engines with diverse power and speed, it is worth to use the dimensionless dependencies: For engine speed nx: For effective engine torque Ttqx: For fuel consumption rate Bx: For effective power Pex: tq tq e eT enom eT ex P P P P P (6) For specific fuel consumption rate bx: Here, tq T and  Figure 1 shows the ES for the diesel with a regulator curve.
In the work [1] the method of tuning the fuel supply control during the diesel refinement using the model of ESC, which allowed to carry out the target formation of indicators of external high-speed characteristics, is given. This once again showed the importance of developing a model for the construction of ESC.
Also, this problem is considered in work [5,6], which is devoted to modeling the pollution of exhaust gases of internal combustion engines depending on the temperature inside the engine cylinder.

The purpose of the study
Power and torque curves on the external speed characteristic (ESC) simulate engine operation on the transportation vehicle during its motion under conditions of variable road resistance but only at a fixed and marginal position of the fuel supply actuator. So, the purpose of the study is to develop methods for modeling the ESC of the piston engine at all modes of operating at the design stage.  for effective engine torque Ttqx: (9) for fuel consumption rate Bx:

Research methods
If parameters Pe and b are modeled, then the values of tq T and B are determined by using equations (1) and (2).
The calculations indicate that the use of dimensionless parameters in coordinates , tq T n B n and b n allows one to obtain the common relative ESC for diesels, gasoline engines, and turbocharged diesels [4][5][6][7][8][9][10]. The analytical dependencies of equations (11) to (14) allow one to plot the common [1] or generalized ES for low-capacity diesels (LCD) (without turbocharging), as well as to model the ES at the design stage. Figure 3 shows , to n by several intervals ( presented in column 9. The specific fuel consumption rate b can be obtained using equation (2).
A good agreement between calculated and measured data allows one to recommend this methodology for modeling the ES at the design stage of LCD.
The proposed method of modeling the external speed characteristics allows to evaluate the capabilities of the newly designed engine, and, in addition, allows you to pre-form a rational external characteristic of the engine for a particular purpose. This will eliminate the dips in the torque curve on the ESC.