New MapleSim Applications

Shoot the Ball

Dr. Gilbert Lai — Fri, 27 Jan 2012 05:00:00 Z

This model stimulates a ball being shot with an initial speed and initial angle (relative to the ground) and determines if the ball hits one of the three predefined targets.

This application is related to a blog post on MaplePrimes: Rebound Rumble: MapleSim Ball Shooting Model for FIRST Robotics 2012

Flow Dynamics in Connected Liquid Tanks

Maplesoft — Mon, 09 Jan 2012 05:00:00 Z

This models investigates the flow dynamics between three liquid tanks connected by two pipes (the first pipe connecting Tank 1 and 2, and the second pipe connecting Tank 2 and 3).

The liquid level in each tank oscillates due to the flow inertia in each pipe. Flow inertia is damped by pipe friction, and eventually the liquid height in each tank reaches an equilibrium.

A Maple worksheet that models the system from a first-principle momentum balance is also attached (see Project > Attachments > Documents > OscillatingTanks.mw). In the Maple worksheet, differential equations that describe a momentum balance and the dynamic change in liquid height in each tank are solved numerically.

The results of the MapleSim model and Maple worksheet agree.

Water Hammer

Maplesoft — Mon, 09 Jan 2012 05:00:00 Z

When a valve at the end of a pipeline rapidly closes, a pressure surge hits the valve, and a pressure wave travels along the pipeline. This is known as Water Hammer.

In this model, a discretized pipeline (with inertial and resistive properties) is initially pressurized at one end to create flow. After two seconds, a valve at the other end is closed. A pressure surge at the valve is observed.

Probes can be placed at various points to investigate the pressure dynamics along the pipeline.

The valve dynamics can be altered to reduce the magnitude of the pressure surge. Moreover, an accumulator can be enabled to further reduce the pressure surge.

Additionally, a Maple worksheet that models Water Hammer by solving the governing PDEs (through spatial discretization, giving a set of ODEs) is included as an attachment (see Project > Attachments > Documents > Water Hammer Application.mw.

The MapleSim model and Maple worksheet give consistent results, and the maximum pressure (for fully shut valves) corresponds to the Joukowsky pressure. This provides assurance that both approaches are correct.

Electro-Hydraulic Clutch Actuator

Wed, 14 Dec 2011 05:00:00 Z

This is a model of a typical clutch actuation system found in an automatic transmission. The transmission controller sends an on/off signal to a solenoid that opens/closes a hydraulic valve. The hydraulic pressure is supplied by an oil pump connected to the engine drive shaft and will vary with engine speed. A pressure relief valve is used to regulate the supply pressure to the clutch actuator.

Solar Array

Wed, 14 Dec 2011 05:00:00 Z

In this model, a solar array is modeled using both multibody and electrical components. First, the solar radiation on a panel is calculated based on the tilt of the panel as well as the elevation angle of the sun which varies throughout the day. This is used as input to an equivalent circuit model of a single junction solar cell for estimation of the array's power generation. In the second model, the same solar array model is used but this time its tilt angle tracks the sun with the goal of maximizing power generation.

Tracking Gimbal Radar

Fri, 09 Dec 2011 05:00:00 Z

In this model, the required elevation and azimuth angles are determined for a radar gimbal tracking system. This inverse kinematics problem is solved using the inverse kinematics equations generated by MapleSim. Servo drives are implemented to tune the required parameters of the tracking gimbal.

5 Degrees of Freedom Robot – Minimum Time Control

Maplesoft — Fri, 09 Dec 2011 05:00:00 Z

This is an extension of the 2-link robot model that includes body rotation, wrist and end effector. Each component has a 3-D CAD object attached to it to create a visualization of the full robot. The movement of the manipulator is controlled to minimize the time required for a set path.

Holiday Tree Powered by MapleSim

Fri, 09 Dec 2011 05:00:00 Z

Season’s Greetings and a Happy New Year from all of us at Maplesoft! To celebrate, we’ve created a Holiday Tree powered by MapleSim. MapleSim is a physical modeling and simulation tool built on a foundation of symbolic computation technology. MapleSim reduces model development time from months to days while producing high-fidelity, high-performance models.

Planetary Rover

Maplesoft — Fri, 09 Dec 2011 05:00:00 Z

In this model, planetary rover behaviour on rough terrain is simulated in an extensive multi-domain environment. Various behaviours are simulated, including rover motion, wheel/soil interaction, and energy consumption. Further analysis is possible in Maple, allowing for power optimization and path planning.

Aircraft Aerodynamics

Maplesoft — Fri, 09 Dec 2011 05:00:00 Z

This model simulates the aerodynamics of an aircraft, incorporating the aircraft body model, aerodynamic data, and controller design. The aircraft body is characterized through a mass and inertia matrix, and driven through applied forces to the rigid body centre of mass frame. Nonlinear functions of angle-of-attack, air density variations, and more are implemented with lookup table data.

Quadrocopter

Maplesoft — Fri, 09 Dec 2011 05:00:00 Z

In this model, a quadrocopter is modeled and its flight is visualized. The forces and torques in the body subsystem are created by four rotors, each driven by a DC motor. The lift and drag of each rotor are computed from the angular speed. A controller subsystem is used to maintain the altitude of the quadrocopter at a reference of 50m. A one second failure is simulated at the 20 second mark in order to create a perturbation, and as can be seen in the simulation, the model stabilizes shortly thereafter.