Mass With Length & Friction (PB)

Mass with length, friction, and gravitational effects

Since R2024b

Libraries:
Simscape / Foundation Library / Translational / Elements

Description

The Mass With Length & Friction (PB) block represents a mass with length, gravitational effects, and friction that moves along an inclined rail. Gravity can induce motion along the rail. Gravity and an optional additional normal force induce friction with the stationary rail.

The Mass With Length & Friction (PB) block is essentially a structural component that consists of a Mass (PB) block connected to a Spacer (PB) block. The Mass (PB) block is also connected to port F of a Translational Friction (PB) block. Port B of the Translational Friction (PB) block is connected to an implicit reference.

Mass with length and friction schematic

The friction force is a function of relative velocity and is assumed to be the sum of Stribeck, Coulomb, and viscous components, as shown in the figure.

Friction force diagram

The force flow equations are:

$f_{a c c} = m \cdot \dot{v}$

$f_{a c c} = f + f_{g p} + f_{f r i c t i o n}$

$f_{g p} = - m \cdot g \cdot \sin (θ)$

$f_{f r i c t i o n} = - \sqrt{2 e} (F_{b r k} - F_{C}) \cdot \exp (- {(\frac{v}{v_{S t}})}^{2}) \cdot \frac{v}{v_{S t}} - F_{C} \cdot \tanh (\frac{v}{v_{C o u l}}) - f_{v} v$

$F_{N} = F_{N, e x t} + f_{g n}$

$f_{g n} = m \cdot g \cdot | \cos (θ) |$

$F_{b r k} = F_{N} \cdot K_{b r k}$

$F_{C} = F_{N} \cdot K_{C}$

$v_{S t} = v_{b r k} \sqrt{2}$

$v_{C o u l} = v_{b r k} / 10$

$l e n g t h = x_{F} - x_{B}$

$x_{L o g} = x_{B} + f r a c t i o n_{L o g} \cdot l e n g t h$

$p o w e r_d i s s i p a t e d = - f_{f r i c t i o n} \cdot v$

where:

f_acc is force proportional to mass acceleration. Positive force accelerates the mass in the positive direction.
f is net force of other mechanical components in the network acting on the mass.
f_gp is force proportional to the parallel component of gravitational acceleration, that is, to gravitational acceleration acting along the rail.
f_gn is force proportional to the normal component of gravitational acceleration, that is, to gravitational acceleration acting in the direction normal to the rail.
f_friction is the friction force.
m is the mass.
v is the mass velocity. Ports B and F have the same velocity, v_B = v_F.
g is the gravitational acceleration.
θ is the rail incline angle.
F_N is the normal force, which acts on the mass in the direction normal to the rail, that is, normal to the direction of the motion. This force is the sum of the external normal force and the force proportional to the normal component of gravitational acceleration.
F_N,ext is the external normal force, which acts on the mass in the direction normal to the rail. This is an optional force due to an external load. You can specify it as an input signal or as a block parameter.
F_C is the Coulomb friction.
K_C is the Coulomb friction coefficient.
F_brk is the breakaway friction.
K_brk is the breakaway friction coefficient.
f_v is the viscous friction coefficient.
v_brk is the breakaway friction velocity.
v_St is the Stribeck velocity threshold.
v_Coul is the Coulomb velocity threshold.
length is the mass length.
x_B and x_F are the absolute positions of ports B and F, respectively.
x_Log is the absolute position of an intermediate point, if you enable the Log the position of an intermediate point option.
fraction_Log is the intermediate point fractional length from port B.
power_dissipated is the power dissipated through the friction.

For example, to log the position of the center of mass, select the Log the position of an intermediate point check box and set the Intermediate point fractional length from B parameter to 0.5.

You can disable frictional effects by setting the Breakaway friction coefficient, Coulomb friction coefficient, and Viscous friction coefficient parameters to 0.

The Mechanical Translational Properties (PB) block specifies the gravitational acceleration and rail incline angle in the network. For more information, see Interpreting Logged Forces in Mass Blocks.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Examples

Gravity and Friction in the Position-Based Translational Domain

Configure gravity and gravity-induced friction effects in a position-based mechanical translational network.

Open Live Script

Ports

Input

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N — External normal force control signal, N
physical signal

Physical signal input port for the control signal that specifies the external normal force. The block calculates the total normal force as the sum of the external normal force and the force proportional to the normal component of gravitational acceleration.

If the signal becomes negative, the block saturates the input value to 0.

Dependencies

To enable this port, set the External normal force specification parameter to Variable.

Conserving

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B — Base port
position-based mechanical translational

Position-based mechanical translational conserving port that represents the base connection.

F — Follower port
position-based mechanical translational

Position-based mechanical translational conserving port that represents the follower connection. For nonzero length, port F has a more positive position than port B.

Parameters

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Mass — Constant mass
`1 kg` (default) | positive scalar

Mass value. The mass is constant during simulation.

Length — Length of mass
`0 m` (default) | nonnegative scalar

Length of mass, that is, distance between ports B and F. This distance is constant during simulation.

Log the position of an intermediate point — Whether to log position of intermediate point
`off` (default) | `on`

Select this check box to log the position of an intermediate point between ports B and F, for example, of the center of the mass. For more information, see Data Logging.

Intermediate point fractional length from B — Fractional length of logged point from port B
`0.5` (default) | unitless scalar between 0 and 1

Fractional distance between port B and the intermediate point being logged.

Dependencies

To enable this parameter, select the Log the position of an intermediate point check box.

External normal force specification — Whether external normal force is constant or variable
`Constant` (default) | `Variable`

Select whether the external normal force applied to the block is constant or variable:

Constant — Specify normal force by using the Constant external normal force parameter value.
Variable — Specify normal force by using the physical signal at port N.

Constant external normal force — Force normal to motion
`0 N` (default) | nonnegative scalar

Force applied to the block in the direction normal to the motion. The block calculates the total normal force as the sum of this value and the force proportional to the normal component of gravitational acceleration. The block then calculates the breakaway friction force and the Coulomb friction force based on the total normal force and the proportionality coefficients, Breakaway friction coefficient and Coulomb friction coefficient.

Dependencies

To enable this parameter, set External normal force specification to Constant.

Breakaway friction coefficient — Proportionality coefficient between normal force and breakaway friction force
`2.5` (default) | nonnegative scalar

Coefficient for calculating the breakaway friction force, which is the sum of the Coulomb and the static frictions, based on the normal force. The parameter value must be greater than or equal to the Coulomb friction coefficient value.

Breakaway friction velocity — Peak velocity for Stribeck friction
`0.1 m/s` (default) | positive scalar

The velocity at which the Stribeck friction is at its peak. At this point, the sum of the Stribeck and Coulomb friction is the breakaway friction force. This parameter specifies the velocity threshold, which affects the tradeoff between the simulation accuracy and speed.

Coulomb friction coefficient — Proportionality coefficient between normal force and friction that opposes motion
`2` (default) | nonnegative scalar

Coefficient for calculating the Coulomb friction force, which is the friction that opposes motion, based on the normal force.

Viscous friction coefficient — Viscous losses proportionality coefficient
`0 N/(m/s)` (default) | nonnegative scalar

Proportionality coefficient between the friction force and the relative velocity. Viscous losses do not depend on the normal force.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024b

Mass With Length & Friction (PB)