ElastoBacklash2

Backlash connected in series to linear spring and damper (backlash is modeled with elasticity; at start of contact the flange torque can jump, contrary to the ElastoBacklash model)

    ElastoBacklash2

Library

Mechanics/Rotational/Components

Description

This element consists of a backlash element connected in series to a spring and damper element which are connected in parallel. The spring constant shall be non-zero, otherwise the component cannot be used.

In combination with components IdealGear, the ElastoBacklash2 model can be used to model a gear box with backlash, elasticity and damping.

During initialization, the backlash characteristic is replaced by a continuous approximation in the backlash region, in order to reduce problems during initialization, especially for inverse models.

If the backlash b is smaller as 1e-10 rad (especially, if b=0), then the backlash is ignored and the component reduces to a spring/damper element in parallel.

In the backlash region (-b/2 ≤ flange_b.phi - flange_a.phi - phi_rel0 ≤ b/2) no torque is exerted (flange_b.tau = 0). Outside of this region, contact is present and the contact torque is basically computed with a linear spring/damper characteristic:

   desiredContactTorque = c*phi_contact + d*der(phi_contact)

            phi_contact = phi_rel - phi_rel0 - b/2 if phi_rel - phi_rel0 >  b/2
                        = phi_rel - phi_rel0 + b/2 if phi_rel - phi_rel0 < -b/2

            phi_rel     = flange_b.phi - flange_a.phi;

This torque characteristic leads to the following difficulty:

  • If the damper torque becomes larger as the spring torque and with opposite sign, the contact torque would be "pulling/sticking" which is unphysical, since during contact only pushing torques can occur.

In the literature this issue seems to be not discussed. For this reason, the most simple approach is used in the ElastoBacklash2 model, by slightly changing the linear spring/damper characteristic to:

    // Torque characteristic when phi_rel > phi_rel0
    if phi_rel - phi_rel0 < b/2 then
       tau_c = 0;          // spring torque
       tau_d = 0;          // damper torque
       flange_b.tau = 0;
    else
       tau_c = c*(phi_rel - phi_rel0);    // spring torque
       tau_d = d*der(phi_rel);            // damper torque
       flange_b.tau = if tau_c + tau_d ≤ 0 then 0 else tau_c + tau_d;
    end if;

Note, when sticking would occur (tau_c + tau_d ≤ 0), then the contact torque is explicitly set to zero.

This model of backlash is slightly different to the ElastoBacklash component:

  • An event occurs when contact occurs or when contact is released (contrary to the ElastoBacklash component).
  • When contact occurs, the torque changes discontinuously, due to the damping. The damping is larger as for the ElastoBacklash component (for the same damping coefficient), because the ElastoBacklash component has a heuristic to avoid the discontinuity of the torque when contact occurs.
  • For some models, the ElastoBacklash2 component leads to faster simulations (as compared when using the ElastBacklash component).

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

Parameters

ElastoBacklash2_0

NameLabelDescriptionData TypeValid Values

mo_c

c

Spring constant (c > 0 required)

Scalar

mo_d

d

Damping constant

Scalar

mo_b

b

Total backlash

Scalar

mo_phi_rel0

phi_rel0

Unstretched spring angle

Scalar

mo_useHeatPort

useHeatPort

=true, if heatPort is enabled

Number

0
1

mo_bMax

bMax

Backlash in range bMin <= phi_rel - phi_rel0 <= bMax

Scalar

mo_bMin

bMin

Backlash in range bMin <= phi_rel - phi_rel0 <= bMax

Scalar

mo_bEps

bEps

Minimum backlash

Scalar

ElastoBacklash2_1

NameLabelDescriptionData TypeValid Values

mo_phi_nominal

phi_nominal

Nominal value of phi_rel (used for scaling)

Scalar

mo_stateSelect

stateSelect

Priority to use phi_rel and w_rel as states

Structure

mo_stateSelect/choice1

StateSelect.never

Number

0
1

mo_stateSelect/choice2

StateSelect.avoid

Number

0
1

mo_stateSelect/choice3

StateSelect.default

Number

0
1

mo_stateSelect/choice4

StateSelect.prefer

Number

0
1

mo_stateSelect/choice5

StateSelect.always

Number

0
1

ElastoBacklash2_2

NameLabelDescriptionData TypeValid Values

mo_phi_rel

phi_rel

phi_rel

Structure

mo_phi_rel/fixed

fixed

Cell of scalars

true
false

mo_phi_rel/start

start

Cell of scalars

mo_w_rel

w_rel

w_rel

Structure

mo_w_rel/fixed

fixed

Cell of scalars

true
false

mo_w_rel/start

start

Cell of scalars

mo_a_rel

a_rel

a_rel

Structure

mo_a_rel/fixed

fixed

Cell of scalars

true
false

mo_a_rel/start

start

Cell of scalars

mo_tau

tau

tau

Structure

mo_tau/fixed

fixed

Cell of scalars

true
false

mo_tau/start

start

Cell of scalars

mo_lossPower

lossPower

lossPower

Structure

mo_lossPower/fixed

fixed

Cell of scalars

true
false

mo_lossPower/start

start

Cell of scalars

Ports

NameTypeDescriptionIO TypeNumber

flange_a

implicit

Left flange of compliant 1-dim. rotational component

input

1

flange_b

implicit

Right flange of compliant 1-dim. rotational component

output

1

Port 3

implicit

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

input

mo_useHeatPort