energy observation in jerk decoupled translatory feed axes
TRANSCRIPT
Energy optimization in jerk decoupled translatory feed axes
Muhammad Ammad Ejaz
Under Supervision of Dr. Chen Silu
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
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)
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
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
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
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
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
Stator coordinate system
Rotor coordinate system
Motor Model
Rotor coordinate system
Field oriented synchronous linear motor
To get rotor voltages
For getting direct and quadratic voltages
Conversion from stator voltage to direct &quadratic voltages
Model of Linear Motor
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
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-
=
Equations for linear motor model
Visualizing a field oriented control
Energy Observer
Primary & secondary
Part ‘s
Potential Energy
Kinetic Energy
Friction Energy
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
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
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
SO this is how it works
Mechanical Model
Synchronous linear direct drive
Energy Observer
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
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
Static Model Examples
Static Model Examples
Static Model Examples
Static Model Examples
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
When a object is subject to stress the friction force increases gradually until rupture occurs
Dynamic Models: The Dahl Model
The friction force is only position force is only displacement dependent
For a time domain Dahl model
For
Dynamic Models: The Dahl Model
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
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
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
The LuGre Model
Rate depende
nt friction
Phenomena of surfaces are pushed
aprt by lubricant
Stribeck effect
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
This model overcomes the problem we faced earlier
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Pros: friction characteristics, stribeck effect in sliding
frictional lag , hysteresis behavior with nonlinear memory which is not shown by LuGre
Maxwell slip model