Modelling of the energy supply equipment of the air braking system of a farm tractor

Abstract

Farm tractors are provided with pneumatic systems to control and operate air braking systems as well as pneumatic suspension systems, the latter being increasingly often applied to high-capacity trailers. The excessive consumption of compressed air may adversely affect the braking effectiveness of a tractor-trailer unit; therefore, the impact of performance of the air supply equipment of the tractor on the transient processes taking place in the air braking system of the trailer should be taken into consideration as early as at the design stage. A mathematical model of the air supply equipment, consisting of functional and structural models of individual equipment components such as compressor, pressure regulator, and compressed air reservoir, has been presented in this paper. An example has been included, where the computer model of the supply system, prepared in the Matlab-Simulink program, was used to assess the correctness of compressor selection to the pneumatic system of the Pronar 5110 tractor. The adequacy of the implemented computer model of the air supply equipment, experimentally confirmed, was evaluated with statistical methods, with the use of the Kolmogorov-Smirnov test. The computer model developed may be used as a tool to assess the correctness of selection of parameters of the air supply equipment within the designing process and as a subsystem in order to evaluate, with the use of simulation methods, the transient processes taking place in the air braking systems of agricultural vehicles.

Determination of the functional and service characteristics of the pneumatic system of an agricultural tractor with mechanical brakes using simulation methods

“…The proposal for a programme of agricultural tractor approval testing in respect of braking, presented in study [17], includes the performance testing of the service and parking brake systems [6] The possibilities of using simulation methods for predicting the functional and service characteristics during the model-based design of tractor air brake systems is shown on the example of testing the capacity of the air compressor and the response time of the control device of a Pronar 320AM tractor. The computer models for all of the tractor pneumatic system components were created as S-function graphic subsystems stored in the Matlab program's m-files, derived from described algorithms and procedures [14,16].…”

“…The computer models for all of the tractor pneumatic system components were created as S-function graphic subsystems stored in the Matlab program's m-files, derived from described algorithms and procedures [14,16].…”

“…The mathematical and computer model of this valve considers a number of phenomena, such as heat exchange, the inertia of movable elements, and friction, which are generally omitted already at the stage of physical creation or at the stage of running the computer model for digital simulation [11,23,29]. Whereas, in the case of modelling the energy supply unit described in [16], the most important final model equations are only given. A computer program implemented in Matlab-Simulink was used to estimate selected functional and service characteristics, including the assessment of supply unit compressor performance and the control device response time in accordance to the requirements for brake systems.…”

“… dt dp dt dp (32) Assuming that the compressor discharge pressure is equal to the reservoir pressure p t (a short length and a small capacity of the pipe connecting the compressor with the reservoir), the mass flux k m  [kg/s] of air discharged by the compressor can be described as follows [16]:…”

“…The pressure drop in the system to the preset minimum value p min causes the switching over of the unload valve again and re-charging of the system by compressor. This type of unload valve action can be described by the function of a bi-stable relay with a hysteresis loop of the width equal to p max -p min :   (32) Assuming that the compressor discharge pressure is equal to the reservoir pressure p t (a short length and a small capacity of the pipe connecting the compressor with the reservoir), the mass flux k m  [kg/s] of air discharged by the compressor can be described as follows [16]: Changes in reservoir air pressure and temperature are described by the following equations [16]: …”