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ChrisRackauckasChrisRackauckas
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Merge pull request #34 from ValentinKaisermayer/add-mechanics
Adds rotational components
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‎docs/src/API/magnetic.md‎

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# ModelingToolkitStandardLibrary: Magnetic Components
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## Magnetic Utilities
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## Flux Tubes
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### Flux Tube Utilities
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```@docs
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PositiveMagneticPort
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NegativeMagneticPort
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TwoPort
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```
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## Basic Magnetic Blocks
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### Basic Flux Tube Blocks
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```@docs
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Ground
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ElectroMagneticConverter
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```
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## Magnetic Sources
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### Flux Tube Sources
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```@docs
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ConstantMagneticPotentialDifference

‎docs/src/API/mechanical.md‎

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# ModelingToolkit Standard Library: Mechanical Components
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## Rotational Components
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### Rotational Utils
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```@docs
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Flange
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```
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### Rotational Core Components
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```@docs
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Fixed
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Inertia
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Spring
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Damper
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IdealGear
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```
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### Rotational Sources
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```@docs
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Torque
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```

‎docs/src/index.md‎

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- [Basic Blocks](http://mtkstdlib.sciml.ai/dev/API/blocks/)
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- [Electrical Components](http://mtkstdlib.sciml.ai/dev/API/electrical/)
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- [Magnetic Components](http://mtkstdlib.sciml.ai/dev/API/magnetic/)
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- [Mechanical Components](http://mtkstdlib.sciml.ai/dev/API/mechanical/)
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- [Thermal Components](http://mtkstdlib.sciml.ai/dev/API/thermal/)

‎src/Mechanical/Mechanical.jl‎

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"""
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Library of mechanical models.
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"""
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module Mechanical
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using ModelingToolkit
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include("Rotational/Rotational.jl")
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end
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‎src/Mechanical/Rotational/Rotational.jl‎

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"""
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Library to model 1-dimensional, rotational mechanical systems
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"""
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module Rotational
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using ModelingToolkit, Symbolics, IfElse, OrdinaryDiffEq
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using OffsetArrays
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using ...Blocks: RealInput, RealOutput
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@parameters t
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D = Differential(t)
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export Flange
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include("utils.jl")
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export Fixed, Inertia, Spring, Damper, IdealGear
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include("components.jl")
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export Torque
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include("sources.jl")
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end

‎src/Mechanical/Rotational/components.jl‎

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"""
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Fixed(;name, phi0=0.0)
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Flange fixed in housing at a given angle.
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# Parameters:
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- `phi0`: Fixed offset angle of housing
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"""
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function Fixed(;name, phi0=0.0)
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@named flange = Flange()
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@parameters phi0=phi0
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eqs = [flange.phi ~ phi0]
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return compose(ODESystem(eqs, t, [], [phi0]; name=name), flange)
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end
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"""
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Inertia(;name, J=1.0, phi_start=0.0, w_start=0.0, a_start=0.0)
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1D-rotational component with inertia.
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# Parameters:
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- `J`: [kg.m2] Moment of inertia
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- `phi_start`: [rad] Initial value of absolute rotation angle of component
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- `w_start`: [rad/s] Initial value of absolute angular velocity of component
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- `a_start`: [rad/s2] Initial value of absolute angular acceleration of component
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# States:
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- `phi`: [rad] Absolute rotation angle of component
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- `w`: [rad/s] Absolute angular velocity of component (= der(phi))
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- `a`: [rad/s2] Absolute angular acceleration of component (= der(w))
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"""
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function Inertia(;name, J=1.0, phi_start=0.0, w_start=0.0, a_start=0.0)
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@named flange_a = Flange()
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@named flange_b = Flange()
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@parameters J=J
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sts = @variables begin
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phi(t)=phi_start
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w(t)=w_start
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a(t)=a_start
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end
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eqs = [
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phi ~ flange_a.phi
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phi ~ flange_b.phi
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D(phi) ~ w
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D(w) ~ a
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J*a ~ flange_a.tau + flange_b.tau
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]
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return compose(ODESystem(eqs, t, sts, [J]; name=name), flange_a, flange_b)
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end
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"""
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Spring(;name, c, phi_rel0=0.0)
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Linear 1D rotational spring
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# Parameters:
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- `c`: Spring constant
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- `phi_rel0`: Unstretched spring angle
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"""
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function Spring(;name, c=1.0e5, phi_rel0=0.0)
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@named partial_comp = PartialCompliant()
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@unpack phi_rel, tau = partial_comp
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pars = @parameters begin
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c=c
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phi_rel0=phi_rel0
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end
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eqs = [tau ~ c*(phi_rel - phi_rel0)]
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extend(ODESystem(eqs, t, [], pars; name=name), partial_comp)
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end
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"""
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Damper(;name, d=0.0)
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Linear 1D rotational damper
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# Parameters:
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- `d`: Damping constant
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"""
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function Damper(;name, d=0.0)
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@named partial_comp = PartialCompliantWithRelativeStates()
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@unpack w_rel, tau = partial_comp
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pars = @parameters d=d
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eqs = [tau ~ d*w_rel]
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extend(ODESystem(eqs, t, [], pars; name=name), partial_comp)
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end
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"""
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IdealGear(;name, ratio)
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Ideal gear without inertia.
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This element characterizes any type of gear box which is fixed in the ground and which has one driving shaft and one driven shaft.
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# Parameters:
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- `ratio`: Transmission ratio (flange_a.phi/flange_b.phi)
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"""
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function IdealGear(;name, ratio, use_support=false)
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@named partial_element = PartialElementaryTwoFlangesAndSupport2(use_support=use_support)
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@unpack phi_support, flange_a, flange_b = partial_element
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@parameters ratio=ratio
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sts = @variables phi_a(t)=0.0 phi_b(t)=0.0
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eqs = [
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phi_a ~ flange_a.phi - phi_support
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phi_b ~ flange_b.phi - phi_support
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phi_a ~ ratio*phi_b
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0 ~ ratio*flange_a.tau + flange_b.tau
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]
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extend(ODESystem(eqs, t, sts, [ratio]; name=name), partial_element)
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end

‎src/Mechanical/Rotational/sources.jl‎

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"""
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Torque(;name)
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Input signal acting as external torque on a flange
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"""
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function Torque(;name, use_support=false)
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@named partial_element = PartialElementaryOneFlangeAndSupport2(use_support=use_support)
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@unpack flange = partial_element
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@named tau = RealInput() # Accelerating torque acting at flange (= -flange.tau)
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eqs = [flange.tau ~ -tau.u]
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return extend(ODESystem(eqs, t, [], []; name=name, systems=[tau]), partial_element)
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end

‎src/Mechanical/Rotational/utils.jl‎

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@connector function Flange(;name)
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sts = @variables begin
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phi(t)
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tau(t), [connect=Flow]
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end
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ODESystem(Equation[], t, sts, [], name=name, defaults=Dict(phi=>0.0, tau=>0.0))
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end
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Base.@doc """
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Flange(;name)
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1-dim. rotational flange of a shaft.
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# States:
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- `phi`: [rad] Absolute rotation angle of flange
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- `tau`: [Nm] Cut torque in the flange
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""" Flange
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@connector function Support(;name)
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sts = @variables begin
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phi(t)
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tau(t), [connect=Flow]
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end
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ODESystem(Equation[], t, sts, [], name=name, defaults=Dict(phi=>0.0, tau=>0.0))
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end
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Base.@doc """
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Support(;name)
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Support/housing of a 1-dim. rotational shaft
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# States:
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- `phi`: [rad] Absolute rotation angle of the support/housing
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- `tau`: [Nm] Cut torque in the support/housing
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""" Support
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"""
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PartialCompliant(;name, phi_rel_start=0.0, tau_start=0.0)
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Partial model for the compliant connection of two rotational 1-dim. shaft flanges.
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# Parameters:
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- `phi_rel_start`: Initial relative rotation angle
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- `tau_start`: Initial torque between flanges
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# States:
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- `phi_rel`: Relative rotation angle (= flange_b.phi - flange_a.phi)
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- `tau`: Torque between flanges (= flange_b.tau)
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"""
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function PartialCompliant(;name, phi_rel_start=0.0, tau_start=0.0)
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@named flange_a = Flange()
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@named flange_b = Flange()
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sts = @variables begin
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phi_rel(t)=phi_rel_start
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tau(t)=tau_start
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end
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eqs = [
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phi_rel ~ flange_b.phi - flange_a.phi
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flange_b.tau ~ tau
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flange_a.tau ~ -tau
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]
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return compose(ODESystem(eqs, t, sts, []; name=name), flange_a, flange_b)
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end
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"""
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PartialCompliantWithRelativeStates(;name, phi_rel_start=0.0, tau_start=0.0)
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Partial model for the compliant connection of two rotational 1-dim. shaft flanges where the relative angle and speed are used as preferred states
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# Parameters:
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- `phi_rel_start`: Initial relative rotation angle
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- `w_rel_start`: Initial relative angular velocity (= der(phi_rel))
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- `a_rel_start`: Initial relative angular acceleration (= der(w_rel))
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- `tau_start`: Initial torque between flanges
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# States:
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- `phi_rel`: Relative rotation angle (= flange_b.phi - flange_a.phi)
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- `w_rel`: Relative angular velocity (= der(phi_rel))
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- `a_rel`: Relative angular acceleration (= der(w_rel))
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- `tau`: Torque between flanges (= flange_b.tau)
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"""
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function PartialCompliantWithRelativeStates(;name, phi_rel_start=0.0, w_start=0.0, a_start=0.0, tau_start=0.0)
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@named flange_a = Flange()
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@named flange_b = Flange()
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sts = @variables begin
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phi_rel(t)=phi_rel_start
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w_rel(t)=w_start
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a_rel(t)=a_start
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tau(t)=tau_start
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end
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eqs = [
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phi_rel ~ flange_b.phi - flange_a.phi
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D(phi_rel) ~ w_rel
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D(w_rel) ~ a_rel
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flange_b.tau ~ tau
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flange_a.tau ~ -tau
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]
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return compose(ODESystem(eqs, t, sts, []; name=name), flange_a, flange_b)
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end
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"""
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PartialElementaryOneFlangeAndSupport2(;name, use_support=false)
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Partial model for a component with one rotational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models
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# Parameters:
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- `use_support`: If support flange enabled, otherwise implicitly grounded
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# States:
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- `phi_support`: Absolute angle of support flange"
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"""
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function PartialElementaryOneFlangeAndSupport2(;name, use_support=false)
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@named flange = Flange()
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sys = [flange]
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@variables phi_support(t)
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if use_support
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@named support = Support()
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eqs = [
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support.phi ~ phi_support
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support.tau ~ -flange.tau
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]
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push!(sys, support)
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else
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eqs = [phi_support ~ 0]
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end
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return compose(ODESystem(eqs, t, [phi_support], []; name=name), sys)
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end
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"""
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PartialElementaryTwoFlangesAndSupport2(;name, use_support=false)
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Partial model for a component with two rotational 1-dim. shaft flanges and a support used for textual modeling, i.e., for elementary models
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# Parameters:
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- `use_support`: If support flange enabled, otherwise implicitly grounded
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# States:
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- `phi_support`: Absolute angle of support flange"
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"""
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function PartialElementaryTwoFlangesAndSupport2(;name, use_support=false)
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@named flange_a = Flange()
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@named flange_b = Flange()
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sys = [flange_a, flange_b]
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@variables phi_support(t)=0.0
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if use_support
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@named support = Support()
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eqs = [
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support.phi ~ phi_support
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support.tau ~ -flange_a.tau - flange_b.tau
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]
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push!(sys, support)
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else
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eqs = [phi_support ~ 0]
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end
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return compose(ODESystem(eqs, t, [phi_support], []; name=name), sys)
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end

‎src/ModelingToolkitStandardLibrary.jl‎

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module ModelingToolkitStandardLibrary
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include("Blocks/Blocks.jl")
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include("Mechanical/Mechanical.jl")
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include("Electrical/Electrical.jl")
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include("Magnetic/Magnetic.jl")
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include("Thermal/Thermal.jl")

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