Module: physics

The physics library includes helper functions and data related to physics models and parameters; for rigid body inertia, see rigidBodyUtilities

  • Date: 2021-01-20

Function: StribeckFunction

StribeckFunction(vel, muDynamic, muStaticOffset, muViscous = 0, expVel = 1e-3, regVel = 1e-3)

  • function description: describes regularized Stribeck function with optial viscous part for given velocity, \(f(v) = \begin{cases} (\mu_d + \mu_{s_{off}}) v, \quad \mathrm{if} \quad |v| <= v_{reg}\\ \mathrm{Sign}(v)\left( \mu_d + \mu_{s_{off}} \mathrm{e}^{-(|v|-v_{reg})/v_{exp}} + \mu_v (|v|-v_{reg}) \right), \quad \mathrm{else}\end{cases}\)

  • input:

    • vel: input velocity \(v\)

    • muDynamic: dynamic friction coefficient \(\mu_d\)

    • muStaticOffset: \(\mu_{s_{off}}\), offset to dynamic friction, which gives muStaticFriction = muDynamic + muStaticOffset

    • muViscous: \(\mu_v\), viscous part, acting proportional to velocity except for regVel

    • regVel: \(v_{reg}\), small regularization velocity in which the friction is linear around zero velocity (e.g., to get Newton converged)

    • expVel: \(v_{exp}\), velocity (relative to regVel, at which the muStaticOffset decreases exponentially, at vel=expVel, the factor to muStaticOffset is exp(-1) = 36.8%)

  • output: returns velocity dependent friction coefficient (if muDynamic and muStaticOffset are friction coefficients) or friction force (if muDynamic and muStaticOffset are on force level)

  • notes: see Isermann (2008) and Armstrong-Helouvry (1991)

Relevant Examples (Ex) and TestModels (TM) with weblink to github: massSpringFrictionInteractive.py (Ex), springMassFriction.py (Ex)

Function: RegularizedFrictionStep

RegularizedFrictionStep(x, x0, h0, x1, h1)

  • function description: helper function for RegularizedFriction(…)

Function: RegularizedFriction

RegularizedFriction(vel, muDynamic, muStaticOffset, velStatic, velDynamic, muViscous = 0)

  • function description: describes regularized friction function, with increased static friction, dynamic friction and optional viscous part

  • input:

    • vel: input velocity

    • muDynamic: dynamic friction coefficient

    • muStaticOffset: offset to dynamic friction, which gives muStaticFriction = muDynamic + muStaticOffset

    • muViscous: viscous part, acting proportional to velocity for velocities larger than velDynamic; extension to mentioned references

    • velStatic: small regularization velocity at which exactly the staticFriction is reached; for smaller velocities, the friction is smooth and zero-crossing (unphysical!) (e.g., to get Newton converged)

    • velDynamic: velocity at which muDynamic is reached for first time

  • output: returns velocity dependent friction coefficient (if muDynamic and muStaticOffset are friction coefficients) or friction force (if muDynamic and muStaticOffset are on force level)

  • notes: see references: Flores et al. Flores2008, Qian et al. Qian2018

Relevant Examples (Ex) and TestModels (TM) with weblink to github: massSpringFrictionInteractive.py (Ex)

Function: VonMisesStress

VonMisesStress(stress6D)

  • function description: compute equivalent von-Mises stress given 6 stress components or list of stress6D (or stress6D in rows of np.array)

  • input:

    • stress6D: 6 stress components as list or np.array, using ordering \([\sigma_{xx}\), \(\sigma_{yy}\), \(\sigma_{zz}\), \(\sigma_{yz}\), \(\sigma_{xz}\), \(\sigma_{xy}]\)

  • output: returns scalar equivalent von-Mises stress or np.array of von-Mises stresses for all stress6D

Function: UFvonMisesStress

UFvonMisesStress(mbs, t, sensorNumbers, factors, configuration)

  • function description: Sensor user function to compute equivalent von-Mises stress from sensor with Stress or StressLocal OutputVariableType; if more than 1 sensor is given in sensorNumbers, then the maximum stress is computed

  • input: arguments according to SensorUserFunction; factors are ignored

  • output: returns scalar (maximum) equivalent von-Mises stress

example:

  #assuming s0, s1, s2 being sensor numbers with StressLocal components
  sUser = mbs.AddSensor(SensorUserFunction(sensorNumbers=[s0,s1,s2],
                                           fileName='solution/sensorMisesStress.txt',
                                           sensorUserFunction=UFvonMisesStress))