Mass#

The block shows the one-dimensional motion of a two ported mass under two external forces in [N], the gravity and friction forces. The block returns velocity in [m/s], motion in [m] and acceleration in [m/s\(^2\)].

The friction force can be simulated using a formula accounting the dry friction friction, static friction, viscous friction and frontal resistance, or more advanced using the Karnopp friction model accounting for: static friction, dry friction, viscous friction, frontal resistance and the Stribeck effect. When using the advanced friction formula, the user can select or not select the Stribeck effect. If it is not selected, the transition from static to dynamic force is immediate. If the Stribeck effect is selected, the change in the slope of the Stribeck effect curve (positive or negative angle) occurs only by changing the static friction force.

The frictionless force is calculated as (1):

(1)#\[ F_{ext}=F_{ext1}+F_{ext2}-9.81\cdot m\cdot sin\left(\theta\right), \]

where:

\(F_{ext}\) - external force on block, [N];

\(F_{ext1}\) – external force on the left port, [N];

\(F_{ext2}\) – external force on the right port, [N];

\(m\) – mass, [kg];

\(\theta\) – angle, [grad].

Taking into account the friction force, it is calculated as follows (2):

(2)#\[ F_{fric}=\left(F_{coul}+\left(F_{stick}-F_{coul}\right)e^{-3\frac{\left|V\right|}{astrib}}\right)sign\left(V\right) \]

where:

\(F_{fric}\) - frictional force, [N];

\(F_{coul}\) – dry friction force, [N];

\(F_{stick}\) – static friction force, [N];

\(astrib\) – Limit, at which static friction force actss, [m/s].

Block acceleration including friction is determined using the formula (3):

(3)#\[ a_{cc} =\frac{1}{m}\left(F_{ext}-F_{fric}\cdot s i g n\left(V\right)-r_{visc}\cdot V-r_{wind}\cdot V\left|V\right|\right) \]

where:

a\(_{cc}\) – block acceleration, [m/s\(^2\)];

r\(_{visc}\) – damping coefficient, [N/(m/s)];

r\(_{wind}\) – head resistance coefficient, [N/(m/s)\(^2\)].

1. Properties#

Property	Default value	Description	Units of measurement
Mass	1.0	-	kg
Gravity	Off	-	-
Inclination, available when selecting `Gravity` - `On`	0.0	-	degrees
Use friction	On	-	-
Advanced friction	Off	-	-
Stribeck effect, available when selecting `Advanced friction` - `On`	Off	-	-
Stribeck constant, available when selecting `Stribeck effect` - `On`	0.001	-	m/s
Stiction force, available when selecting `Use friction` - `On`	0.0	-	N
Coulomb friction force, available when selecting `Use friction` - `On`	0.0	-	N
Damping factor, available when selecting `Use friction` - `On`	0.0	-	\(\frac{N}{m/s}\)
Windage factor, available when selecting `Use friction` - `On`	0.0	-	\(\frac{N}{{(m/s)}^2}\)
Stick velocity threshold, available when selecting `Advanced friction` - `On`	1.0e-6	-	m/s

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Translational force	Input	-	N	Translational motion
Velocity	Output	-	m/s	Translational motion

In order to see the connection capabilities of the block, you need to go to page Description of block ports