Gelöste Aufgaben/JUMP/Car-Body - Versionsgeschichte

Mechaniker: /* Structure */

2021-03-24T13:08:55Z

Structure

← Nächstältere Version		Version vom 24. März 2021, 13:08 Uhr
Zeile 333:		Zeile 333:
	The latter part for ''F<sub>L</sub>'' represents a force that is required to push the elastic wheel through elasto-plastic ground. We'll keep it simple and phrase it to be		The latter part for ''F<sub>L</sub>'' represents a force that is required to push the elastic wheel through elasto-plastic ground. We'll keep it simple and phrase it to be

	::<math>F_L = \mu \cdot N_a \cdot \frac{\displaystyle 2}{\displaystyle \pi} atan\left( \frac{\displaystyle v_T}{\displaystyle v_{T 0}}\right) </math>		::<math>F_L = \mu \cdot N_a \cdot \frac{\displaystyle 2}{\displaystyle \pi} \text{atan}\left( \frac{\displaystyle v_T}{\displaystyle v_{T 0}}\right) </math>

	with the new loss-velocity ''v<sub>T0<sub>''.		with the new loss-velocity ''v<sub>T0<sub>''. The atan-function looks somewhat displaced here - it ensures that the rolling loss-force does not exceed the traction force.
	\|code=		\|code=
	<syntaxhighlight lang="lisp" line start=1>		<syntaxhighlight lang="lisp" line start=1>

Mechaniker: /* Structure */

2021-03-24T13:07:21Z

Structure

← Nächstältere Version		Version vom 24. März 2021, 13:07 Uhr
Zeile 333:		Zeile 333:
	The latter part for ''F<sub>L</sub>'' represents a force that is required to push the elastic wheel through elasto-plastic ground. We'll keep it simple and phrase it to be		The latter part for ''F<sub>L</sub>'' represents a force that is required to push the elastic wheel through elasto-plastic ground. We'll keep it simple and phrase it to be

	::<math>F_L = \mu \cdot N_a \cdot \frac{\displaystyle 2}{\displaystyle \pi} \atan\left( \frac{\displaystyle v_T}{\displaystyle v_{T 0}}\right) </math>		::<math>F_L = \mu \cdot N_a \cdot \frac{\displaystyle 2}{\displaystyle \pi} atan\left( \frac{\displaystyle v_T}{\displaystyle v_{T 0}}\right) </math>

	with the new loss-velocity ''v<sub>T0<sub>''.		with the new loss-velocity ''v<sub>T0<sub>''.

Mechaniker: /* Structure */

2021-03-24T13:06:39Z

Structure

← Nächstältere Version		Version vom 24. März 2021, 13:06 Uhr
Zeile 333:		Zeile 333:
	The latter part for ''F<sub>L</sub>'' represents a force that is required to push the elastic wheel through elasto-plastic ground. We'll keep it simple and phrase it to be		The latter part for ''F<sub>L</sub>'' represents a force that is required to push the elastic wheel through elasto-plastic ground. We'll keep it simple and phrase it to be

	::<math>F_L = \mu \cdot N_a \cdot \frac{\displaystyle v_T}{\displaystyle v_{T 0}} </math>		::<math>F_L = \mu \cdot N_a \cdot \frac{\displaystyle 2}{\displaystyle \pi} \atan\left( \frac{\displaystyle v_T}{\displaystyle v_{T 0}}\right) </math>

	with the new loss-velocity ''v<sub>T0<sub>''.		with the new loss-velocity ''v<sub>T0<sub>''.

Mechaniker: /* Structure */

2021-03-22T16:10:17Z

Structure

← Nächstältere Version		Version vom 22. März 2021, 16:10 Uhr
Zeile 325:		Zeile 325:
	::<math>\begin{array}{ll}		::<math>\begin{array}{ll}
	F &= F(N_a,v_{rel})\\		F &= F(N_a,v_{rel})\\
	& = \mu(v_{rel})\cdot N_a		& = \mu(v_{rel})\cdot N_a - F_L
	\end{array}</math>		\end{array}</math>

	and introduce a point-symmetric characteristic for this relationship ''μ''(''v<sub>rel</sub>''):[[Datei:JUMP-carbody-slide22.png\|mini\|Friction characteristic\|alternativtext=\|ohne]]It mimics the key properties of dry friction with a stick-coefficient ''μ<sub>0</sub>'' for very low relative velocities and ''μ'' else. To simplify implementation, we’ll be using the same mechanism as for the tracks to compose this characteristic from lines and transition parabolas.		with the standard-formulation with ''μ''(''v<sub>rel</sub>'') for dry friction and a loss-related force ''F<sub>L</sub>''.
			For the first part, we introduce a point-symmetric characteristic for this relationship ''μ''(''v<sub>rel</sub>''):[[Datei:JUMP-carbody-slide22.png\|mini\|Friction characteristic\|alternativtext=\|ohne]]It mimics the key properties of dry friction with a stick-coefficient ''μ<sub>0</sub>'' for very low relative velocities and ''μ'' else. To simplify implementation, we’ll be using the same mechanism as for the tracks to compose this characteristic from lines and transition parabolas.

			The latter part for ''F<sub>L</sub>'' represents a force that is required to push the elastic wheel through elasto-plastic ground. We'll keep it simple and phrase it to be

			::<math>F_L = \mu \cdot N_a \cdot \frac{\displaystyle v_T}{\displaystyle v_{T 0}} </math>

			with the new loss-velocity ''v<sub>T0<sub>''.
	\|code=		\|code=
	<syntaxhighlight lang="lisp" line start=1>		<syntaxhighlight lang="lisp" line start=1>

Mechaniker: /* Variables */

2021-03-22T07:56:54Z

Variables

← Nächstältere Version		Version vom 22. März 2021, 07:56 Uhr
Zeile 695:		Zeile 695:
	\|m		\|m
	\|-		\|-
	\|''φ''		\|''ϕ''
	\|rotation of car-body		\|rotation of car-body
	\|rad		\|rad

Mechaniker: /* Parameter */

2021-03-22T07:56:39Z

Parameter

← Nächstältere Version		Version vom 22. März 2021, 07:56 Uhr
Zeile 761:		Zeile 761:
	\|N/m		\|N/m
	\|-		\|-
	\|spring stiffness rear;<br/> if "0" is given, compute it so that the static ''φ=0''		\|spring stiffness rear;<br/> if "0" is given, compute it so that the static ''ϕ=0''
	\|''k<sub>2</sub>''		\|''k<sub>2</sub>''
	\|0		\|0

Mechaniker: /* Variables */

2021-03-22T07:55:48Z

Variables

← Nächstältere Version		Version vom 22. März 2021, 07:55 Uhr
Zeile 697:		Zeile 697:
	\|''φ''		\|''φ''
	\|rotation of car-body		\|rotation of car-body
	\|m		\|rad
	\|-		\|-
	\|''ψ''		\|''ψ''
	\|rotation of wheel (absolute - not relative to car-body)		\|rotation of wheel (absolute - not relative to car-body)
	\|m		\|rad
	\|}		\|}

Mechaniker: /* Variables */

2021-03-22T07:55:01Z

Variables

← Nächstältere Version		Version vom 22. März 2021, 07:55 Uhr
Zeile 679:		Zeile 679:
	!unit		!unit
	\|-		\|-
	\|''m<sub>C</sub>''		\|''u<sub>1</sub>''
	\|		\|center of mass displacement in x-direction
	\|		\|m
	\|-		\|-
	\|		\|''u<sub>2</sub>''
	\|		\|center of mass displacement in y-direction
	\|		\|m
	\|-		\|-
	\|		\|''u<sub>3</sub>''
	\|		\|spring compression at front axis
	\|		\|m
			\|-
			\|''u<sub>4</sub>''
			\|spring compression at rear axis
			\|m
			\|-
			\|''φ''
			\|rotation of car-body
			\|m
			\|-
			\|''ψ''
			\|rotation of wheel (absolute - not relative to car-body)
			\|m
	\|}		\|}

Mechaniker: /* Parameter */

2021-03-22T07:50:01Z

Parameter

← Nächstältere Version		Version vom 22. März 2021, 07:50 Uhr
Zeile 693:		Zeile 693:

	== Parameter ==		== Parameter ==
	{\| class="wikitable~~" style="border-collapse: collapse;~~"		{\| class="wikitable"
	!~~style="border-right: solid 0px;"\|~~name		!name
	!symbol		!symbol
	!value		!value
	!unit		!unit
	\|-		\|-
	\|~~battery~~ mass		\|axis distance
	\|''m<sub>B</sub>''		\|''a<sub>0</sub>''
	\|~~340~~		\|40
	\|g		\|cm
	\|}		\|-
			\|distance front axis center of mass
			\|''a<sub>1</sub>''
			\|10
	{\| ~~class="wikitable"~~		\|cm
	~~!name~~		\|- a[3] 0.1 m
	~~!symbol~~		\|vertical distance from wheel-hub to center of mass for relaxed springs
	~~!unit~~		\|''a<sub>3</sub>''
			\|10
			\|cm
			\|-
			\|wheel radius
			\|''R''
			\|58.42
			\|mm
	\|-		\|-
	\|~~mass of~~ car-body		\|car-body mass
	\|m<sub>C</sub>		\|''m<sub>C</sub>''
			\|4
	\|kg		\|kg
	\|-		\|-
	\|~~mass of~~ wheel-~~pair "''A~~''"		\|wheel-set mass
	\|m<sub>A</sub>		\|''m<sub>W</sub>''
			\|0.3
	\|kg		\|kg
	\|-		\|-
	\|~~mass of~~ wheel-~~pair~~ "''A''"		\|inertia-radius for body with <math>J_C = m_C \cdot r_C^2</math>
	\|m<sub>B</sub>		\|''r<sub>C</sub>''
	\|kg		\|15
			\|cm
			\|-
			\|inertia-radius wheel-set
			\|''r<sub>W</sub>''
			\|4
			\|cm
			\|-
			\|track-stiffness
			\|''k<sub>T</sub>''
			\|1.00E+04
			\|N/m
			\|-
			\|spring stiffness front
			\|''k<sub>1</sub>''
			\|500
			\|N/m
			\|-
			\|spring stiffness rear;<br/> if "0" is given, compute it so that the static ''φ=0''
			\|''k<sub>2</sub>''
			\|0
			\|N/m
			\|-
			\|spring damping front
			\|''b<sub>1</sub>''
			\|100
			\|N/(m/s)
			\|-
			\|spring damping rear
			\|''b<sub>2</sub>''
			\|100
			\|N/(m/s)
			\|-
			\|smoothening radius for spring characteristic
			\|''ε''
			\|1
			\|mm
			\|-
			\|friction coefficient
			\|''μ''
			\|0.4
			\|1
			\|-
			\|rounding radius for friction coefficient
			\|''μ<sub>ε</sub>''
			\|0.01
			\|1
			\|-
			\|stick coefficient
			\|''μ<sub>0</sub>''
			\|0.6
			\|1
			\|-
			\|reference velocity for damping at springs
			\|''v<sub>ref</sub>''
			\|5
			\|m/s
	\|-		\|-
	\| ~~colspan="1" \|mass-moment of car-body~~		\|loss velocity for rolling contact
	~~\| colspan="1"~~ \|''J<sub>C</sub>''		\|''v<sub>T0</sub>''
	\| ~~colspan="1"~~ \|kg m~~<sup>2<~~/~~sup>~~		\|5
			\|m/s
	\|}		\|}

	[[Gelöste Aufgaben/JUMP/Driver Controls\|next workpackage: driver-controls →]]		[[Gelöste Aufgaben/JUMP/Driver Controls\|next workpackage: driver-controls →]]

Mechaniker: /* Parameter */

2021-03-22T07:07:29Z

Parameter

@@ Zeile 693: / Zeile 693: @@
 == Parameter ==
 {| class="wikitable"
 !name