Measurement Techniques for Engineers Motion and Vibration Measurement
Introduction Quantities that may need to be measured are velocity, acceleration and vibration amplitude Quantities useful in predicting fatigue failure of a particular part or machine or analysis to reduce structural vibrations or noise
Introduction Need to determine appropriate quantities in reference to a specified state ie velocity, displacement or acceleration in relation to ground Ideally want a transducer that connects to body in motion and provides output proportional to vibrational input
Introduction Ideal transducer independent of location should work whether vibrating structure is on ground, in air or in space Sound can be classified as a vibratory phenomena, especially important in building and equipment design (specialised and course does not cover this)
Simple Vibration Instruments Simple Wedge - attached to vibrating wall, at rest see a single wedge Wall is vibrating up and down in figure When vibration occurs see movement of wedge and can measure overlap distance shown in figure Using trigonometry the amplitude of the vibration can be calculated
Simple Vibration Instruments Cantilever beam - mounted on block placed against vibrating surface and length is able to be varied beam length is adjusted so the beam vibrates at natural frequency - resonance
Simple Vibration Instruments frequency of motion can be calculated based on Young s modulus of material, moment of inertia of beam, mass and length, which are all known
Principles of Seismic Instrument Used to measure motion of surfaces to which they are fixed sensitive to motion along one axis only therefore if motion 3D need 3 pickups along 3 mutually perpendicular axes Essential component is a seismic mass
inertia of seismic mass (tendency to remain fixed in spatial position) causes it to lag behind the motion of the casing when casing accelerated - causes deflection in support Principles of Seismic Instrument Seismic mass - body of metal suspended from a resilient support resilient support - one which deflection is proportional to the force applied to it
Principles of Seismic Instrument Deflection forms input to transducer which produces output signal figure 9.3 shows a potentiometer but any kind of transducer can be used Another example, seismic instrument in form of an accelerometer using a transducer in the form of an unbonded strain gauge
Principles of Seismic Instrument Dashpot in figure 9.3 represents damping which may come from hysteresis of supporting material or by filling casing with silicone fluid of suitable viscosity Select mass, stiffness of support and damping and by choosing appropriate transducer can be designed as a displacement pickup or a acceleration pickup (accelerometer)
Principles of Seismic Instrument Generally large mass and soft springs for vibrational displacement and small mass and stiff spring for acceleration indications Seismic pickup is essentially a damped spring mass system and natural frequency of vibration is calculated from spring stiffness and mass of seismic mass
Displacement Pickups Used to measure displacement of vibrating body when no fixed reference point available (eg movement of car body) Therefore want seismic mass to behave as if fixed in space Use large seismic mass and relatively floppy resilient support
Displacement Pickups Gives low natural angular frequency for system figure 9.4 shows frequency response of ζ = Actualdamp displacement pickup with various values of damping ratio (ζ) ζ=actual Damping Critical Damping
Displacement Pickups Critical damping = value of damping which allows displaced mass to return to original position without overshooting If ζ>1 mass returns slowly without overshooting If ζ<1 mass returns more quickly but overshoots and oscilates
Displacement Pickups For frequencies of vibration above natural frequency displacement of casing and mass are equal but opposite Seismic mass therefore virtually stands still Optimum ζ=0.707 in terms of least variation in displacement ratio so displacement pickups designed to have damping ratio of 0.7
Displacement Pickups At ζ=0.7 can bring ω/ω n down to 1.75 before error in displacement measurement exceeds 5%
Velocity Pickups Signal proportional to velocity may be obtained from a vibration by differentiating the signal from a displacement pickup by passing it through a differentiating circuit integrating the signal from an accelerometer by passing it through an integrating circuit using a seismic velocity pickup
Velocity Pickups Seismic velocity pickup - similar to figure 9.3 but with a velocity transducer instead of a displacement transducer Integrating from an accelerometer gives a much more accurate result than differentiating from a displacement pickup - differentiation amplifies errors in signal but integration diminishes them
Velocity Pickups Velocity pickup - gives a direct velocity signal, this can be passed through an integrating circuit to give a displacement signal as well Velocity pickup designed to have a low value of ω n and to operate at angular frequencies well above this
Velocity Pickups So motion of seismic mass is virtually the same as that of the casing but opposite in phase Transducer is usually coil of wire carried by seismic mass
Velocity Pickups coil suspended in radial magnetic field so voltage is proportional to velocity generated in coil when it is vibrated axially Seismic mass consists of central rod plus nuts washers and coil former Rod connects together two flexible diaphragms whose stiffness add to form the spring
Velocity Pickups Coil former suspends coil in narrow annular slot in cylindrical magnet - field acting radially across slot Coil former may be made of metal so eddy currents are generated in it to provide eddy current damping
Acceleration pickups By designing the pickup system in figure 9.3 to have a low value of ω n could be used as displacement or velocity pickup for angular frequencies well above ω n For acceleration pickup have to go to opposite extreme
Acceleration pickups Fig 9.4 shows that for angular frequencies well below ω n the displacement of the seismic mass relative to the casing tends to zero Therefore at much lower frequencies seismic mass must be accelerating with same acceleration as casing therefore corresponding forces must apply to spring
Acceleration pickups Can use spring as transducer to tell us force applied to known mass and hence acceleration of mass and casing Fig 9.6 show the ratio of acceleration of seismic mass to acceleration of casing against ω/ ω n for values of ζ
Acceleration pickups Curve in fig 9.6 indicates that provided the damping ratio does not exceed 1.0 accurate readings will be obtained for frequencies of vibration from 0 to 0.2 of undamped natural frequency for heavier damping upper frequency limit will be less
Acceleration pickups Most accelerometers use a piezoelectric crystal as combined spring and transducer damping ratio of crystal almost zero ζ=0.01 ideal damping ration ζ=0.7 would give accurate reading up to 0.5 ω n
Acceleration pickups for accelerometer want highest undamped natural frequency (high spring stiffness and low mass) So piezoelectric crystal usually used as connection between seismic mass and casing as has high modulus of elasticity and so very high spring stiffness
Acceleration pickups Disadvantage at low frequencies of vibration charge leaks so limit to low frequency use (about 5 Hz)