Energy observation in jerk decoupled translatory feed axes
1. Energy optimization in jerk
decoupled translatory feed axes
Muhammad Ammad Ejaz
Under Supervision of Dr. Chen Silu
2. What is jerk decoupling
“Decreasing Vibrations with passive filter i.e a spring and
damper element” which is normally mounted between
movable part of linear motor and frame structure
3. Mechanical Model
Primary part
Secondary Part
Friction forces
Coulomb (Non
velocity dependent)
Reynolds (Velocity
dependent)
Stribeck (Dropping of
friction with higher
velocities in low
velocity range)
4. The slide of primary part Mp is guided with longitudinal ball
rail system and forces acting on it can be given by following
equation
Primary Part
5. The secondary path comprises two bodies . Jerk decoupled
slide and equivalent mass. Following equation can be Set up
for equivalent frame
While forces acting on second body of this path is given by
following equation
Secondary Part
6. Transfer function describes complete mechanical model
comprising primary part , jerk decoupling slide , equivalent
frame and linear motor .Following is the transfer function of
primary equation
In the same manner TF of equivalent and jerk decoupled
frame given
&
Transfer Function
7. Linear motor is being placed between primary path and jerk
decoupling slide of secondary path in order to get TF of linear
motor
Note : TF of linear motor is very important for the designing of
the velocity control circuit
Transfer Function of linear motor
8. Linear motors in machine are based on synchronous principle
for this reason a model of rotating field main machine is
applied .Three different ways of controls are commonly used
Trapezoidal commutation
Sinusoidal commutation
Field oriented control
System Design and Simulation
12. If using one pair of poles , equation for motor model is given as
Drive force can be given as
Note: After calculating these currents and drive force another
transformation from rotor to orthogonal coordinate system needed
-
-
=
Equations for linear motor model
15. Potential differential work and potential work are given as
Kinematic differential work and kinematic work given as
And same for friction energy
Energy equations for Primary part
16. The potential and kinematics energies of EF is similar to
primary one but in this case instead of friction there is
material damping ,work given as
The work stored in the spring can be given as
Energy equations for Equivalent Frame
17. Potential and kinematic works are similar to first two parts
but in this case elastic work
work caused by damping
work caused by friction
Energy equations for Jerk–decoupling slide
18. SO this is how it works
Mechanical
Model
Synchronous
linear direct
drive
Energy
Observer
19. Friction is the tangential reaction force between two surfaces in
contact
The friction force as function of velocity for constant velocity
motion is called Stribeck
The force required to overcome the static friction and start
motion is called Break away force
Friction Phenomena
20. Static friction models
The main idea is that friction opposes motion and it’s magnitude
is independent of velocity and contact area and described as
Fc is proportional to normal load i and it is being described as
coulomb friction
Viscous friction is used for force component and which is
normally described as
25. It was developed to overcome the zero velocity detection problem
and to avoid switching between different state equations for sticking
and sliding .It was developed to overcome different state equations
for sticking and sliding
For velocities within internal state may be non zero but output
block is maintained at zero
Drawback: This model strongly coupled with rest of system
The Karnopp Model
26. When a object is subject to stress the friction force increases
gradually until rupture occurs
Dynamic Models: The Dahl Model
27. The friction force is only position force is only displacement
dependent
For a time domain Dahl model
For
Dynamic Models: The Dahl Model
28. Bilman and sorine stress rate independence .The magnitude
of friction depends only on sign V and given as
The models are expressed as linear systems in space variable
The first order model is given by
First order model
Model by Bliman and Sorine
29. The first order model does’t give stiction nor does it give a
friction peak this can be achieved by second order
The model is parallel connection of fast and slow Dahl Model
Model by Bliman and Sorine
30. Neither Dahl or LuGre model are capable of realizing the
nondrifting property in presliding.There is model named
extension of LuGre model is capable of capturing the
property but it does’t solve the problem of lack of nonlocal
memory
The Leuven model elaborated the LuGre model further by
including hysteresis but hysteresis function Fh while
maintaining the LuGre formulation was not with
implementing difficulties
Relating the existing friction models to Model structure
32. Model can be given as
Z denotes the average bristle deflection .The model behaves like a
spring for small displacement .Linearization of around velocity and
zero state gives
Sigma is the stiffness of bristles and sigma 1 the damping
The LuGre Model
33. This model overcomes the problem we faced earlier
`
Pros: friction characteristics, stribeck effect in sliding frictional
lag , hysteresis behavior with nonlinear memory which is not
shown by LuGre
Maxwell slip model
Editor's Notes
2.tg=active primary part length ,every 2/3 tg a vector for the amplitude of each voltage is calculated , each vector represents amplitude of sin wave n phase shift .secondary is under a axis ,after summation of all voltages ud and uq can be calculated , good working means ud is 0 n voltage uq to current set point
1.The parameter v/h is set to be zero , in case of vertically use we set it to be zero 2. Integration shows the
The sigma sign is stiffness coefficient and alpha determines shape of stress strain curve .normally aplha =1
