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ValentinKaisermayerValentinKaisermayer
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adds missing rotational components
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‎docs/src/API/mechanical.md

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@@ -34,10 +34,22 @@ Inertia
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Spring
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Damper
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IdealGear
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RotationalFriction
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ViscousFriction
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```
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### Rotational Sources
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```@docs
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Torque
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Speed
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```
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### Rotational Sensors
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```@docs
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AngleSensor
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SpeedSensor
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TorqueSensor
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RelSpeedSensor
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```

‎src/Mechanical/Rotational/Rotational.jl

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@@ -3,19 +3,22 @@ Library to model 1-dimensional, rotational mechanical systems
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"""
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module Rotational
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6-
using ModelingToolkit, Symbolics, IfElse, OrdinaryDiffEq
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using ModelingToolkit, Symbolics
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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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export Flange, Support
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include("utils.jl")
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export Fixed, Inertia, Spring, Damper, IdealGear
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export Fixed, Inertia, Spring, Damper, IdealGear, RotationalFriction
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include("components.jl")
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export Torque
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export Torque, Speed
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include("sources.jl")
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export AngleSensor, SpeedSensor, TorqueSensor, RelSpeedSensor
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include("sensors.jl")
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end

‎src/Mechanical/Rotational/components.jl

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@@ -3,8 +3,11 @@
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Flange fixed in housing at a given angle.
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# Connectors:
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- `flange` [Flange](@ref)
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# Parameters:
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- `phi0`: [rad] Fixed offset angle of housing
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- `phi0`: [`rad`] 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()
@@ -18,16 +21,20 @@ end
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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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- `phi`: [`rad`] Absolute rotation angle of component
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- `w`: [`rad/s`] Absolute angular velocity of component (= D(phi))
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- `a`: [`rad/s²`] Absolute angular acceleration of component (= D(w))
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# Connectors:
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- `flange_a` [Flange](@ref) Left flange
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- `flange_b` [Flange](@ref) Right flange
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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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"""
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function Inertia(;name, J, phi_start=0.0, w_start=0.0, a_start=0.0)
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@named flange_a = Flange()
@@ -53,9 +60,17 @@ end
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Linear 1D rotational spring
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# States:
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- `phi_rel(t)`: [`rad`] Relative rotation angle (`flange_b.phi - flange_a.phi`)
65+
- `tau(t)`: [`N.m`] Torque between flanges (`flange_b.tau`)
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# Connectors:
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- `flange_a` [Flange](@ref)
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- `flange_b` [Flange](@ref)
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# Parameters:
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- `c`: [N.m/rad] Spring constant
58-
- `phi_rel0`: Unstretched spring angle
72+
- `c`: [`N.m/rad`] Spring constant
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- `phi_rel0`: [`rad`] Unstretched spring angle
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"""
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function Spring(;name, c, phi_rel0=0.0)
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@named partial_comp = PartialCompliant()
@@ -73,8 +88,18 @@ end
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Linear 1D rotational damper
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# States:
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- `phi_rel(t)`: [`rad`] Relative rotation angle (= flange_b.phi - flange_a.phi)
93+
- `w_rel(t)`: [`rad/s`] Relative angular velocity (= D(phi_rel))
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- `a_rel(t)`: [`rad/s²`] Relative angular acceleration (= D(w_rel))
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- `tau(t)`: [`N.m`] Torque between flanges (= flange_b.tau)
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# Connectors:
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- `flange_a` [Flange](@ref)
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- `flange_b` [Flange](@ref)
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# Parameters:
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- `d`: [N.m.s/rad] Damping constant
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- `d`: [`N.m.s/rad`] Damping constant
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"""
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function Damper(;name, d)
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@named partial_comp = PartialCompliantWithRelativeStates()
@@ -91,6 +116,15 @@ 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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# States:
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- `phi_a(t)`: [`rad`] Relative angle between shaft a and the support
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- `phi_b(t)`: [`rad`] Relative angle between shaft b and the support
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# Connectors:
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- `flange_a` [Flange](@ref)
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- `flange_b` [Flange](@ref)
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- `support` [Support](@ref) if `use_support == true`
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# Parameters:
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- `ratio`: Transmission ratio (flange_a.phi/flange_b.phi)
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- `use_support`: If support flange enabled, otherwise implicitly grounded
@@ -107,4 +141,44 @@ function IdealGear(;name, ratio, use_support=false)
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0 ~ ratio*flange_a.tau + flange_b.tau
108142
]
109143
extend(ODESystem(eqs, t, sts, [ratio]; name=name), partial_element)
110-
end
144+
end
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"""
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RotationalFriction(;name, f, tau_c, w_brk, tau_brk)
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Models rotational friction with Stribeck effect, Coulomb friction and viscous friction between the two flanges.
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The friction torque is a function of the relative angular velocity between flange_a and flange_b.
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Friction model: "Armstrong, B. and C.C. de Wit, Friction Modeling and Compensation, The Control Handbook, CRC Press, 1995."
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# States:
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- `phi_rel(t)`: [`rad`] Relative rotation angle (= flange_b.phi - flange_a.phi)
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- `w_rel(t)`: [`rad/s`] Relative angular velocity (= D(phi_rel))
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- `a_rel(t)`: [`rad/s²`] Relative angular acceleration (= D(w_rel))
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- `tau(t)`: [`N.m`] Torque between flanges (= flange_b.tau)
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# Connectors:
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- `flange_a` [Flange](@ref)
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- `flange_b` [Flange](@ref)
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# Parameters:
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- `f`: [`N⋅m/(rad/s)`] Viscous friction coefficient
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- `tau_c`: [`N⋅m`] Coulomb friction torque
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- `w_brk`: [`rad/s`] Breakaway friction velocity
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- `tau_brk`: [`N⋅m`] Breakaway friction torque
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"""
171+
function RotationalFriction(;name, f, tau_c, w_brk, tau_brk)
172+
@named partial_comp = PartialCompliantWithRelativeStates()
173+
@unpack w_rel, tau = partial_comp
174+
pars = @parameters f=f tau_c=tau_c w_brk=w_brk tau_brk=tau_brk
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176+
str_scale = sqrt(2*exp(1)) * (tau_brk - tau_c)
177+
w_st = w_brk * sqrt(2)
178+
w_coul = w_brk / 10
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180+
eqs = [
181+
tau ~ str_scale * (exp(-(w_rel/w_st)^2) * w_rel / w_st) + tau_c * tanh(w_rel / w_coul) + f * w_rel # Stribeck friction + Coulomb friction + Viscous friction
182+
]
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extend(ODESystem(eqs, t, [], pars; name=name), partial_comp)
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end

‎src/Mechanical/Rotational/sensors.jl

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@@ -0,0 +1,82 @@
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"""
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AngleSensor(;name)
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4+
Ideal sensor to measure the absolute flange angle
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# Connectors:
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- `flange`: [Flange](@ref) Flange of shaft from which sensor information shall be measured
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- `phi`: [RealOutput](@ref) Absolute angle of flange
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"""
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function AngleSensor(;name)
11+
@named flange = Flange()
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@named phi = RealOutput()
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eqs = [
14+
phi.u ~ flange.phi
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flange.tau ~ 0
16+
]
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return ODESystem(eqs, t, [], []; name=name, systems=[flange, phi])
18+
end
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"""
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SpeedSensor(;name)
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23+
Ideal sensor to measure the absolute flange angular velocity
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# Connectors:
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- `flange`: [Flange](@ref) Flange of shaft from which sensor information shall be measured
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- `w`: [RealOutput](@ref) Absolute angular velocity of flange
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"""
29+
function SpeedSensor(;name)
30+
@named flange = Flange()
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@named w = RealOutput()
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eqs = [
33+
D(flange.phi) ~ w.u
34+
flange.tau ~ 0
35+
]
36+
return ODESystem(eqs, t, [], []; name=name, systems=[flange, w])
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end
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39+
"""
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TorqueSensor(;name)
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42+
Ideal sensor to measure the torque between two flanges (`= flange_a.tau`)
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# Connectors:
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- `flange_a`: [Flange](@ref) Left flange of shaft
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- `flange_b`: [Flange](@ref) Left flange of shaft
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- `tau`: [RealOutput](@ref) Torque in flange flange_a and flange_b (`tau = flange_a.tau = -flange_b.tau`)
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"""
49+
function TorqueSensor(;name)
50+
@named flange_a = Flange()
51+
@named flange_b = Flange()
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@named tau = RealOutput()
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eqs = [
54+
flange_a.phi ~ flange_b.phi
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tau.u ~ flange_a.tau
56+
]
57+
return ODESystem(eqs, t, [], []; name=name, systems=[flange_a, flange_b, tau])
58+
end
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60+
"""
61+
RelSpeedSensor(;name)
62+
63+
Ideal sensor to measure the relative angular velocity
64+
65+
# Connectors:
66+
- `flange_a`: [Flange](@ref) Flange of shaft from which sensor information shall be measured
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- `flange_b`: [Flange](@ref) Flange of shaft from which sensor information shall be measured
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- `w`: [RealOutput](@ref) Absolute angular velocity of flange
69+
"""
70+
function RelSpeedSensor(;name)
71+
@named flange_a = Flange()
72+
@named flange_b = Flange()
73+
@named w_rel = RealOutput()
74+
@variables phi_rel(t)=0.0
75+
eqs = [
76+
0 ~ flange_a.tau + flange_b.tau
77+
phi_rel ~ flange_b.phi - flange_a.phi
78+
D(phi_rel) ~ w_rel.u
79+
0 ~ flange_a.tau
80+
]
81+
return ODESystem(eqs, t, [phi_rel], []; name=name, systems=[flange_a, flange_b, w_rel])
82+
end

‎src/Mechanical/Rotational/sources.jl

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Original file line numberDiff line numberDiff line change
@@ -2,11 +2,61 @@
22
Torque(;name)
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Input signal acting as external torque on a flange
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6+
# States:
7+
- `phi_support(t)`: [`rad`] Absolute angle of support flange"
8+
9+
# Connectors:
10+
- `flange` [Flange](@ref)
11+
- `tau` [RealInput](@ref) Accelerating torque acting at flange `-flange.tau`
12+
13+
# Parameters:
14+
- `use_support`
515
"""
616
function Torque(;name, use_support=false)
717
@named partial_element = PartialElementaryOneFlangeAndSupport2(use_support=use_support)
818
@unpack flange = partial_element
9-
@named tau = RealInput() # Accelerating torque acting at flange (= -flange.tau)
19+
@named tau = RealInput()
1020
eqs = [flange.tau ~ -tau.u]
1121
return extend(ODESystem(eqs, t, [], []; name=name, systems=[tau]), partial_element)
22+
end
23+
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25+
26+
"""
27+
Speed(; name, use_support=false, exact=false, f_crit=50)
28+
29+
Forced movement of a flange according to a reference angular velocity signal
30+
31+
# States:
32+
- `phi_support(t)`: [`rad`] Absolute angle of support flange"
33+
34+
# Connectors:
35+
- `flange` [Flange](@ref)
36+
- `w_ref` [RealInput](@ref) Reference angular velocity of flange with respect to support as input signal needs to be continuously differential
37+
38+
# Parameters:
39+
- `use_support`: If support flange enabled, otherwise implicitly grounded
40+
- `exact`: true/false exact treatment/filtering the input signal
41+
- `tau_filt`: [`rad/s`] if exact=false, Time constant of low-pass filter to filter input signal
42+
"""
43+
function Speed(;name, use_support=false, exact=false, tau_filt=50)
44+
@named partial_element = PartialElementaryOneFlangeAndSupport2(use_support=use_support)
45+
@unpack flange, phi_support = partial_element
46+
@named w_ref = RealInput()
47+
@variables phi(t)=0.0 w(t)=0.0 a(t)=0.0
48+
eqs = [
49+
phi ~ flange.phi - phi_support
50+
D(phi) ~ w
51+
]
52+
if exact
53+
pars = []
54+
push!(eqs, w ~ w_ref.u)
55+
push!(eqs, a ~ 0)
56+
else
57+
pars = @parameters tau_filt=tau_filt
58+
push!(eqs, D(w) ~ a)
59+
push!(eqs, a ~ (w_ref.u - w) * tau_filt)
60+
end
61+
return extend(ODESystem(eqs, t, [phi, w, a], pars; name=name, systems=[w_ref]), partial_element)
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end

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