title: Tutorial 904: Mechanical Systems¶

Tutorial 904: Mechanical Systems¶

Overview¶

Model mechanical systems and their coupling with electrical domains. Learn to simulate motor loads, gearboxes, and electromechanical dynamics.

Level: Advanced (3/3)

Duration: 45-60 minutes

Series: Magnetics & Mechanical

Status: Placeholder - Circuit files to be added

Learning Objectives¶

Understand mechanical-electrical analogies
Model rotational inertia and friction
Simulate motor-load dynamics
Design for mechanical resonance avoidance

Mechanical-Electrical Analogy¶

Mechanical (Rotational)	Symbol	Electrical	Symbol
Torque	τ	Current	I
Angular velocity	ω	Voltage	V
Inertia	J	Capacitance	C
Friction (damping)	B	Conductance	G
Stiffness (spring)	K	Inductance⁻¹	1/L

Mechanical Model¶

    Motor Torque (τm)
         │
         ▼
    ┌────┴────┐
    │    J    │  Inertia (motor + load)
    │  (rotor)│
    └────┬────┘
         │
    ┌────┴────┐
    │    B    │  Friction/Damping
    │         │
    └────┬────┘
         │
    ┌────┴────┐
    │    K    │  Shaft stiffness (if flexible)
    │ (shaft) │
    └────┬────┘
         │
         ▼
    Load Torque (τL)

Equations of Motion¶

Simple Inertial Load¶

J × dω/dt = τm - τL - B×ω

Two-Mass System (Flexible Shaft)¶

J1 × dω1/dt = τm - K×(θ1-θ2) - B1×ω1
J2 × dω2/dt = K×(θ1-θ2) - τL - B2×ω2

Gearbox Modeling¶

Ideal Gear¶

ω2 = ω1 / n  (speed reduction)
τ2 = τ1 × n  (torque multiplication)

With Efficiency¶

τ2 = τ1 × n × η

Reflected Inertia¶

J_reflected = J_load / n²

Common Mechanical Loads¶

Load Type	Torque Characteristic
Constant torque	τL = constant (conveyors, hoists)
Linear (friction)	τL = B × ω (viscous loads)
Quadratic (fan)	τL = k × ω² (fans, pumps)
Constant power	τL = P / ω (machine tools)

Exercises¶

Exercise 1: Motor Startup¶

Model PMSM with inertial load
Simulate acceleration from standstill
Calculate acceleration time: t = J×Δω / (τm - τL)

Exercise 2: Gearbox¶

Add 10:1 gearbox between motor and load
Compare motor torque with direct drive
Observe speed reduction

Exercise 3: Resonance¶

Model two-mass system with flexible shaft
Find mechanical resonance frequency: fr = √(K/J)/(2π)
Avoid exciting resonance with control

Circuit Files¶

Status: Placeholder - motor_inertial_load.ipes - two_mass_system.ipes - gearbox_model.ipes

Tutorial Version: 1.0 (Placeholder)