Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string

Typically, component-oriented acausal hybrid modeling of complex dynamic systems is implemented by specialized modeling languages. A well-known example is the Modelica language. The specialized nature, complexity of implementation and learning of such languages somewhat limits their development and wide use by developers who know only general-purpose languages. The paper suggests the principle of developing simple to understand and modify Modelica-like system based on the general-purpose programming language Python. The principle consists in: (1) Python classes are used to describe components and their systems, (2) declarative symbolic tools SymPy are used to describe components behavior by difference or differential equations, (3) the solution procedure uses a function initially created using the SymPy lambdify function and computes unknown values in the current step using known values from the previous step, (4) Python imperative constructs are used for simple events handling, (5) external solvers of differential-algebraic equations can optionally be applied via the Assimulo interface, (6) SymPy package allows to arbitrarily manipulate model equations, generate code and solve some equations symbolically. The basic set of mechanical components (1D translational “mass”, “spring-damper” and “force”) is developed. The models of a sucker rods string are developed and simulated using these components. The comparison of results of the sucker rod string simulations with practical dynamometer cards and Modelica results verify the adequacy of the models. The proposed approach simplifies the understanding of the system, its modification and improvement, adaptation for other purposes, makes it available to a much larger community, simplifies integration into third-party software.

Modelica and Functional Mock-Up Interface: Open Standards for Gas Turbine Simulation

This paper introduces two physical modeling standards in the gas turbine and cycle analysis context. Modelica is the defacto standard for physical system modeling and simulation. The Functional Mock-Up Interface is a domain-independent standard for model exchange (“engine decks”). The paper summarizes key language concepts and discusses important design patterns in the application of gas turbine simulation concepts to the acausal modeling language. To substantiate how open standards are applicable to gas turbine simulation, the paper closes with two application examples, a conventional unmixed turbofan thermodynamic cycle and weight analysis as well as an electrically boosted geared turbofan.

Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string

As a rule, the limitations of specialized modeling languages for acausal modeling of the complex dynamical systems are: limited applicability, poor interoperability with the third party software packages, the high cost of learning, the complexity of the implementation of hybrid modeling and modeling systems with the variable structure, the complexity of the modifications and improvements. In order to solve these problems, it is proposed to develop the easy-to-understand and to modify component-oriented acausal hybrid modeling system that is based on: (1) the general-purpose programming language Python, (2) the description of components by Python classes, (3) the description of components behavior by difference equations using declarative tools SymPy, (4) the event generation using Python imperative constructs, (5) composing and solving the system of algebraic equations in each discrete time point of the simulation. The classes that allow creating the models in Python without the need to study and apply specialized modeling languages are developed. These classes can also be used to automate the construction of the system of difference equations, describing the behavior of the model in a symbolic form. The basic set of mechanical components is developed — 1D translational components "mass", "spring-damper", "force". Using these components, the models of sucker rods string are developed and simulated. These simulation results are compared with the simulation results in Modelica language. The replacement of differential equations by difference equations allow simplifying the implementation of the hybrid modeling and the requirements for the modules for symbolic mathematics and for solving equations.

Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string

As a rule, the limitations of specialized modeling languages for acausal modeling of the complex dynamical systems are: limited applicability, poor interoperability with the third party software packages, the high cost of learning, the complexity of the implementation of hybrid modeling and modeling systems with the variable structure, the complexity of the modifications and improvements. In order to solve these problems, it is proposed to develop the easy-to-understand and to modify component-oriented acausal hybrid modeling system that is based on: (1) the general-purpose programming language Python, (2) the description of components by Python classes, (3) the description of components behavior by difference equations using declarative tools SymPy, (4) the event generation using Python imperative constructs, (5) composing and solving the system of algebraic equations in each discrete time point of the simulation. The classes that allow creating the models in Python without the need to study and apply specialized modeling languages are developed. These classes can also be used to automate the construction of the system of difference equations, describing the behavior of the model in a symbolic form. The basic set of mechanical components is developed — 1D translational components "mass", "spring-damper", "force". Using these components, the models of sucker rods string are developed and simulated. These simulation results are compared with the simulation results in Modelica language. The replacement of differential equations by difference equations allow simplifying the implementation of the hybrid modeling and the requirements for the modules for symbolic mathematics and for solving equations.

Modeling Torque Converter Characteristics in Automatic Drivelines: Lock-up Clutch and Engine Braking Simulation

A torque converter, which is a hydrodynamic clutch in automatic transmissions, transmits power from the engine shaft to the transmission shaft either by dynamically multiplying the engine torque or by rigidly coupling the engine and transmission shafts. The torque converter is a critical element in the automatic driveline, and it affects the vehicle’s fuel consumption and longitudinal dynamics. This paper presents a math-based torque converter model that is able to capture both transient and steady-state characteristics. The torque converter is connected to a mean-value engine model, transmission model, and longitudinal dynamics model in the MapleSim environment, which uses the advantages of an acausal modeling approach. A lock-up clutch is added to the torque converter model to improve the efficiency of the powertrain in higher gear ratios, and its effect on the vehicle longitudinal dynamics (forward velocity and acceleration) is studied. We show that the proposed model can capture the transition from the forward flow to the reverse flow operations during engine braking or coasting. The simulation results also show that the engine braking phenomenon (due to the flow reversal) can effectively assist the braking system to slow down the vehicle.