![Figure 4 The friction–velocity relation observed in [31]. The friction force is lower for decreasing velocities than for increasing velocities. The hysteresis loop becomes wider as the velocity variations become faster.](/figures/figure-4-the-friction-velocity-relation-observed-in-31-the-24uc2rsn.webp)
![Figure 3 Pre-Sliding displacement as found by [16]. The result agrees with Figure 1 for small displacements. Releasing the applied force results in a permanent displacement as indicated by the dashed lines.](/figures/figure-3-pre-sliding-displacement-as-found-by-16-the-result-zolhmi5e.webp)
Q2. What is the force of the bond between the two surfaces?
As the surfaces move relative to each other the strain in the bond increases and the bristles act as springs giving rise to a friction force.
Q3. Why is there a trend that current loops are implemented with computer control?
Because of the price and performance of micro electronics there is a trend that current loops are implemented with computer control.
Q4. Why are many of the ad hoc fixes used?
Many of the ad hoc fixes traditionally used, e.g. interpolation at low velocities, filtering etc., are also1997-11-28 16:52 31avoided because of the inherent dynamics in the friction model.
Q5. What is the main disadvantage when using a model such as (5)?
1997-11-28 16:52 8The main disadvantage when using a model such as (5), for simulations or control purposes, is the problem of detecting when the velocity is zero.
Q6. What is the problem with a shaft encoder?
The sensor problem can be considerable with a shaft encoder because there will be a variable delay in estimation of the velocity.
Q7. Why is it difficult to make meaningful experiments with a torque that changes sign?
Because of the gear box it is difficult to make meaningful experiments with a torque that changes sign because the backlash in the gear box may hide the friction effects.
Q8. What is the friction force for zero velocity?
Fe if v 0 and tFet < FSFS sgn(Fe) if v 0 and tFet ≥ FS (4)The friction force for zero velocity is a function of the external force and not the velocity.
Q9. Why has there been a significant interest in dynamic friction models?
This has been driven by intellectual curiosity, demands for precision servos and advances in hardware that makes it possible to implement friction compensators.
Q10. What is the RMS error for a friction observer?
The RMS error is reduced to 7.85 ⋅ 10−3 by friction compensation based on a Coulomb friction model and further to 2.65 ⋅ 10−3 with a compensator based on the LuGre model.
Q11. What is the relative damping for the LuGre model?
The relative damping for the LuGre model isζ σ 1 +α 2 2 √ Jσ 0 , (29)The damping thus depend on the parameter σ 1 which can be chosen freely independent of the viscous friction coefficient α
Q12. What is the ideal model trajectory for vs without sign reversal?
The ideal model trajectory going from steady state for −vs to steady state for vs without sign reversal in velocity is writtenF∗(s, vs) CeAs ( A−1 + ∫ s0 e−Aσ dσ) Bvs. (24)This trajectory is also defined by the unique solution xs(0) −F ○ ofmax xs(0), sF(s), (25)for constant vs, i.e. (24) is the trajectory giving the largest break-away friction force.
Q13. What is the simplest way to describe the behavior of the friction model?
Introducing F σ z the model can be written asdz dt v − σ tvt Fc z,F σ z. (11)Haessig and Friedland introduced a friction model in [28], which attempted to capture the behavior of the microscopical contact points between two surfaces.
Q14. What is the friction coefficient in a lubricated system?
As a result the friction coefficient in lubricated systems normally de-1997-11-28 16:52 3creases when the velocity increases from zero.