ME 322: Instrumentation Lecture 30 April 6, 2015 Professor Miles Greiner

Announcements/Reminders This week in lab – Open ended Lab 9.1 – 1%-of-grade extra-credit for active participation HW 10 due Friday – I will revise the Lab 10 Instructions, so don’t start it until Wednesday.

Piezoelectric accelerometer Seismic mass increases/decreases compression of crystal, – Compression causes electric charge to accumulate on its sides – Changing charge can be measured using a charge amplifier High damping, stiffness and natural frequency – Good for measuring high frequency varying accelerations But not useful for steady acceleration

Accelerometer Model Un-deformed sensor dimension y 0 affected by gravity and sensor size Charge Q is affected by deformation y, which is affected by acceleration a If acceleration is constant or slowly changing, then F = ma = –ky, so – Only the spring is important: y S = (-m/k)a; – Static transfer function What is the dynamic response of y(t) to a(t)? (Damper become important) y0y0 Charge Q=fn(y) = fn(a) a(t) = Measurand k [N/m] [N/(m/s)] y = Reading a y -m/k

Moving Damped Mass/Spring System Inertial Frame z s(t)

Response to Impulse (Step change in v) v t a t

Response

Response to Continuous “Shaking”

Particular Solution

Solution

Compare to Quasi-Steady Solution

Problem (page 421) Consider an accelerometer with a natural frequency of 800 Hz and a damping ratio of 0.6. Determine the vibration frequency above which the amplitude distortion is greater than 0.5%.

Problem (page 421)

Lab 10 Vibration of Weighted Steel and Aluminum Cantilever Beam This lab can be on the course Final Accelerometer Calibration Data – strumentation/Labs/Lab%2010%20Vibrating%20Beam/Lab%20 Index.htm strumentation/Labs/Lab%2010%20Vibrating%20Beam/Lab%20 Index.htm – C = mV/g – Use calibration constant for the issued accelerometer – Inverted Transfer function: a = V*1000/C Measure: E, W, T, L B, L E, L T, M T, M W – Estimate uncertainties of each W L T M T T LBLB LELE Accelerometer Clamp MWMW E (Lab 5)

Table 1 Measured and Calculated Aluminum Beam Properties The value and uncertainty in E were determined in Lab 5 W and T were measured using micrometers whose uncertainty were determined in Lab 4 L T, L E, and L B were measured using a tape measure (readability = 1/16 in) M T and M W were measured using an analytical balance (readability = 0.1 g) UnitsValue 3  Uncertainty Elastic Modulus, E [Pa][GPa]633 Beam Width, W[inch] Beam Thickness, T[inch] Beam Total Length, L T [inch] End Length, L E [inch] Beam Length, L B [inch] Beam Mass, M T [g] Intermediate Mass, M I [g] Combined Mass, M w [g]

Figure 2 VI Block Diagram Very similar to Lab 5 Add Formula Block Suggestion: To get practice and prepare for final, re-write the entire VI

Figure 1 VI Front Panel

Disturb Beam and Measure a(t)

Time and Frequency Dependent Data

Uncertainty Calculation

Dynamic (high speed) Accelerometer Response y(t) y 0 + y(t) s(t) z(t) = s(t) + y(t) + y 0

Lab 10 Vibration of a weighted cantilever Beam

Measure a(t) Find damping coefficient and damped natural frequency, and compare to predictions How to predict? t (s) Fit to data: find b and f