How do you model mechanical systems?

1 Identify the system

The first step of modeling is to identify the system you want to model and define its boundaries, inputs, outputs, and assumptions. The system can be a single component, such as a spring or a gear, or a complex assembly, such as a car or a robot. The boundaries separate the system from its environment and determine what influences the system and what the system influences. The inputs are the external forces or signals that act on the system, such as gravity, torque, or voltage. The outputs are the responses or effects of the system, such as displacement, velocity, or current. The assumptions are the simplifications or idealizations that you make to reduce the complexity of the system, such as neglecting friction, air resistance, or nonlinearities.

2 Choose the model type

The second step of modeling is to choose the type of model that best suits your purpose and available data. There are different types of models that can capture different aspects of mechanical systems, such as kinematic, dynamic, static, linear, nonlinear, deterministic, stochastic, or hybrid models. Kinematic models describe the geometry and motion of the system without considering the forces or energy involved. Dynamic models describe the forces and energy that cause and result from the motion of the system. Static models describe the equilibrium conditions of the system when there is no motion. Linear models describe the system behavior using linear equations that obey the superposition principle. Nonlinear models describe the system behavior using nonlinear equations that do not obey the superposition principle. Deterministic models describe the system behavior using fixed or known inputs and outputs. Stochastic models describe the system behavior using random or uncertain inputs and outputs. Hybrid models combine different types of models to capture the system behavior in different domains or modes.

3 Formulate the model equations

The third step of modeling is to formulate the model equations that relate the inputs and outputs of the system using the principles of mechanics, such as Newton's laws, conservation of energy, or conservation of momentum. The model equations can be differential, algebraic, or integral equations, depending on the type of model and the variables involved. Differential equations describe the rate of change of a variable with respect to another variable, such as time or position. Algebraic equations describe the relationship between variables without involving derivatives, such as force balance or voltage balance. Integral equations describe the accumulation or total effect of a variable over a range of another variable, such as work or power. The model equations can be written in different forms, such as scalar, vector, matrix, or state-space form, depending on the number and nature of the variables and equations.

4 Solve the model equations

The fourth step of modeling is to solve the model equations to obtain the values of the outputs or the behavior of the system for given inputs or initial conditions. The solution of the model equations can be analytical or numerical, depending on the complexity and type of the equations and the desired accuracy and speed. Analytical solutions involve finding exact or approximate expressions for the outputs using mathematical methods, such as integration, differentiation, or series expansion. Numerical solutions involve finding approximate values for the outputs using computational methods, such as finite difference, finite element, or Runge-Kutta methods.

5 Validate and refine the model

The fifth step of modeling is to validate and refine the model to ensure that it matches the reality or the expectations of the system. Validation involves comparing the model outputs with the experimental data or the empirical evidence from the real system or a similar system. Validation can help you assess the accuracy, reliability, and applicability of the model, as well as identify and correct any errors or discrepancies. Refinement involves improving the model by adding or removing variables, equations, or assumptions, or by changing the model type, form, or parameters. Refinement can help you increase the fidelity, robustness, and efficiency of the model, as well as adapt the model to different situations or requirements.

6 Use the model

The sixth step of modeling is to use the model for your intended purpose, such as design, analysis, optimization, or control of mechanical systems. Using the model can help you understand how the system works, how it responds to different inputs or disturbances, how it can be improved or modified, or how it can be regulated or manipulated. Using the model can also help you communicate, visualize, or demonstrate your ideas, concepts, or solutions to others.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?