What is motion?
the change in the physical position of an object
What are linear and angular displacement devices are capable of?
- measuring displacement against time, and therefore velocity and acceleration (i.e position of gear wheel with respect to time tells you angular velocity and acceleration)
What is displacement?
- the distance measured in a stated direction from a reference point
What is linear displacement and how is it measured?
the distance measured IN A STRAIGHT LINE in a stated direction from a reference
- measured in terms of an angle of rotation about an axis it is called angular displacement
How are large displacements measured?
- requiring highly accurate measurements
- measured by radar, sonar, or sophisticated optical systems.
How is displacement restricted for the purpose of designing simple control systems
restrict the measurement of displacement to less than one metre
Name simple devices used for measuring linear displacement and the advantages and disadvantages
rulers
slip gauges micrometers and vernier gauges
- these are quick and easy to use but their accuracy is heavily dependent on the skill of the operator and cannot be used for remote measurement A mechanical linear displacement device which is generally more accurate is the dial test indicator (DTI).
How can linear displacement be more accurately measured?
using a dial test indicator (DTI)
What is a potentiometer, what does it consist of, what materials are used and why?
- an electrical device which is a form of variable resistor, consisting of a sliding contact which moves over the length of a resistance element
- the sliding contacts are often made of copper alloys which have good electrical conductivity and have good elastic properties which maintain good electrical contact with the element
See lecture notes for example and solution
See lecture notes for example and solution
What is the capacitance C of a parallel plate capacitor given by
C = (ε0 εrA)/d
What is εr?
the relative permittivity of the dielectric between the capacitor plates
What is ε0?
the permittivity of free space (8.85 x 10-12 F/m)
What is A?
the area of overlap between the two plates
What is d?
the plate separation
What does the capacitance of a parallel plate capacitor depend on?
the plate separation
- so a change in this separation produces a change in capacitance
If the separation increases by x (as shown in lecture notes), what does the capacitance become?
C = (ε0 εrA)/(d + x)
What does LVDT stand for?
Linear Variable Differential Transformer
Up to what displacement can the LVDT measure?
300mm
Describe how the LVDT works? (relates to name)
- firstly it is a transformer obeying the principles of electromagnetic induction
- It has one primary and two secondary windings connected to provide the difference in respective voltage levels (differential)
- It is variable since the magnetic coupling between the primary and each of the secondary coils can be varied to affect the magnitude of induced emfs
- Finally the whole assembly is designed to give a linear response in variation
Describe operation of LVDT
- The secondary voltages are in phase and should the winding be connected together they will cancel giving zero voltage
- If the soft iron core is now moved in either direction the flux linkage to one secondary winding will increase while the other will be reduced.
- Eventually the core is wholly within one secondary winding and not the other so the output voltage is at a maximum and unable to increase any further (saturated).
- This limits the effective working range of such a device.
What do bonded strain gauges measure?
- the size of a solid object, due to the object being strained (stretched or compressed)
Why are they bonded to the object?
so that as it changes size so do they
- when they stretch or compress, the resistance changes and this can be analysed in terms of displacement
What is the range of size in a strain gauge?
from fractions of a millimetre to about fifty millimetres
