AE 416 T2

Thrust term m˙Ve\dot{m}V_em˙Ve​ represents?

Momentum thrust

Total impulse definition

Integral of thrust over burn duration

Mach number at throat for choked flow

1

Underexpanded nozzle condition

Exit pressure higher than ambient

Solid grain geometry affects

Burn duration and chamber pressure

A transducer converts to what

Electrical signal

ADC converts

Analog voltages to digital numbers

Faraday cage blocks

External electric fields

Rapidly changing magnetic fields do what?

Penetrate a Faraday cage

333 kS/s equals

333,000 samples per second

Equation of motion

mx¨+cx˙+kx=F(t)

Natural frequency

ωn​=sqrt(k/m)

ζ<1 means

Underdamped

Resonance occurs when

Forcing frequency ≈ natural frequency

Catastrophic vibration failure from

Sustained forcing at resonance

Strobe freezes motion by

Matching flash frequency to motion

Xenon flash brightness cause

Rapid electron excitation & de-excitation

Power of 150 J flash over 0.001 s

150 kW

Shakers simulate

Sine, random, shock vibrations

Accelerometers measure

Acceleration

NDE assumption

Larger flaws easier to detect

Active NDE

Ultrasonics

Passive NDE?

Leak testing

X-ray attenuation equation

I=I0​e^(−μx)

Radiographic cracks appear

Dark

Penetrant relies on

Capillary action

Fluorescent penetrants require

UV light

Thermography measures

Infrared radiation

Borescopes used for

Inspecting inaccessible regions

Ultrasonic method uses

High-frequency sound waves

Strain-gage beam acts as

Load cell

Load cell calibration needs

Known masses

Manufacturer thrust curves used to

Compare with collected data

Time reconstruction needed because

Sample numbers must convert to time

Low-pass filter helps

Remove high-frequency noise

Critical damping does what?

Fastest return without oscillation

Overdamped systems

Slow return to equilibrium

Underdamped systems

Vibrate with decreasing amplitude

Forced vibration equation includes

Mass, damping, stiffness, forcing

Light stiff structures have

Higher natural frequency

Shaker testing determines

Resonance behavior

High flash energy from

Rapid capacitor discharge

Volumetric NDE

Radiography & ultrasonics

Specific impulse

Impulse ÷ propellant weight

Signal conditioning includes

Attenuation and isolation

When pe​−p0​=0

Exit pressure equals ambient

Design condition nozzle

Perfect expansion to ambient

Solid motor propellant

Solid grain with fuel + oxidizer + binder

Specific impulse increases when

Exit velocity increases

Thrust stand measures

Force produced by the motor

16-bit ADC levels

2^16

Increasing sampling rate reduces

Aliasing

Acceleration-to-voltage sensor

Accelerometer

Faraday cage least effective against

Slowly varying magnetic fields

Nyquist requirement

≥ twice highest frequency

Undamped free vibration motion

Pure sinusoid

ζ=1

Critically damped

Increase k, constant m

Natural frequency increases

Large oscillations when

Forcing frequency ≈ natural frequency

Phase lag increases as

Forcing frequency → resonance

Strobe determines

Rotational frequency

Xenon tube triggered by

High voltage instantaneously

Strobe freezing occurs when

Flash rate = object’s motion frequency

Shakers convert

Voltage to mechanical force

Piezo accelerometer produces charge when

Material is deformed

Why NDE

Does not damage the part

Eddy current works on

Conductive materials

Ultrasonic good for

Internal flaws/voids

Visual inspection tool

Borescope

Developer function

Draw penetrant out of cracks

Attenuation increases with

Higher material density

μ in attenuation equation

Linear attenuation coefficient

Thermal cameras detect

Infrared radiation

Acoustic emission listens for

Crack growth signals

CT scanning advantage

2D/3D internal reconstruction

Load cells must be

Rigidly mounted

Thrust integrated with respect to

Time

Overexpanded nozzle produces

Oblique shock at exit

pe​<p0​ =

Overexpanded

Nozzle throat purpose

Reach Mach 1

Filtering prevents

Aliasing

Amplification improves

SNR (signal-to-noise ratio)

Wheatstone bridge used for

Strain gages

Underdamped decay shape

Exponential envelope

Forced vibration amplitude decreases when?

Damping increases

Longitudinal waves travel

Faster than shear waves

CT scanning uses?

Rotating x-ray source + detectors

Penetrant cannot detect?

Buried internal defects

Overdamped if?

ζ>1

Increasing mass does what to ωn\omega_nωn​

Decreases natural frequency