WOLFRAM SYSTEMMODELER

OneWayClutch

Series connection of freewheel and clutch

Wolfram Language

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SystemModel["Modelica.Mechanics.Rotational.Components.OneWayClutch"]
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Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

This component models a one-way clutch, i.e., a component with two flanges where friction is present between the two flanges and these flanges are pressed together via a normal force. These flanges maybe sliding with respect to each other Parallel connection of ClutchCombi and of FreeWheel. The element is introduced to resolve the ambiguity of the constraint torques of the elements.

A one-way-clutch is an element where a clutch is connected in parallel to a free wheel. This special element is provided, because such a parallel connection introduces an ambiguity into the model (the constraint torques are not uniquely defined when both elements are stuck) and this element resolves it by introducing one constraint torque and not two.

Note, initial values have to be chosen for the model, such that the relative speed of the one-way-clutch >= 0. Otherwise, the configuration is physically not possible and an error occurs.

The normal force fn has to be provided as input signal f_normalized in a normalized form (0 ≤ f_normalized ≤ 1), fn = fn_max*f_normalized, where fn_max has to be provided as parameter. Friction in the clutch is modelled in the following way:

When the relative angular velocity is positive, the friction torque is a function of the velocity dependent friction coefficient mue(w_rel) , of the normal force "fn", and of a geometry constant "cgeo" which takes into account the geometry of the device and the assumptions on the friction distributions:

        frictional_torque = cgeo * mue(w_rel) * fn

Typical values of coefficients of friction:

      dry operation   :  mue = 0.2 .. 0.4
      operating in oil:  mue = 0.05 .. 0.1

When plates are pressed together, where ri is the inner radius, ro is the outer radius and N is the number of friction interfaces, the geometry constant is calculated in the following way under the assumption of a uniform rate of wear at the interfaces:

         cgeo = N*(r0 + ri)/2

The positive part of the friction characteristic mue(w_rel), w_rel >= 0, is defined via table mue_pos (first column = w_rel, second column = mue). Currently, only linear interpolation in the table is supported.

When the relative angular velocity becomes zero, the elements connected by the friction element become stuck, i.e., the relative angle remains constant. In this phase the friction torque is calculated from a torque balance due to the requirement, that the relative acceleration shall be zero. The elements begin to slide when the friction torque exceeds a threshold value, called the maximum static friction torque, computed via:

       frictional_torque = peak * cgeo * mue(w_rel=0) * fn   (peak >= 1)

This procedure is implemented in a "clean" way by state events and leads to continuous/discrete systems of equations if friction elements are dynamically coupled. The method is described in (see also a short sketch in UsersGuide.ModelingOfFriction):

Otter M., Elmqvist H., and Mattsson S.E. (1999):
Hybrid Modeling in Modelica based on the Synchronous Data Flow Principle. CACSD'99, Aug. 22.-26, Hawaii.

See also the discussion State Selection in the User's Guide of the Rotational library.

Connectors (4)

flange_a

Type: Flange_a

Description: Left flange of compliant 1-dim. rotational component

flange_b

Type: Flange_b

Description: Right flange of compliant 1-dim. rotational component

heatPort

Type: HeatPort_a

Description: Optional port to which dissipated losses are transported in form of heat

f_normalized

Type: RealInput

Description: Normalized force signal 0..1 (normal force = fn_max*f_normalized; clutch is engaged if > 0)

Parameters (9)

phi_nominal

Value: 1e-4

Type: Angle (rad)

Description: Nominal value of phi_rel (used for scaling)

stateSelect

Value: StateSelect.prefer

Type: StateSelect

Description: Priority to use phi_rel and w_rel as states

useHeatPort

Value: false

Type: Boolean

Description: =true, if heatPort is enabled

mue_pos

Value: [0, 0.5]

Type: Real[:,2]

Description: [w,mue] positive sliding friction coefficient (w_rel>=0)

peak

Value: 1

Type: Real

Description: peak*mue_pos[1,2] = maximum value of mue for w_rel==0

cgeo

Value: 1

Type: Real

Description: Geometry constant containing friction distribution assumption

fn_max

Value:

Type: Force (N)

Description: Maximum normal force

w_small

Value: 1e10

Type: AngularVelocity (rad/s)

Description: Relative angular velocity near to zero if jumps due to a reinit(..) of the velocity can occur (set to low value only if such impulses can occur)

peak2

Value: max([peak, 1 + eps0])

Type: Real

Description:

Used in Examples (1)

HeatLosses

Demonstrate the modeling of heat losses