Mechanical Measurements
Mechanical Measurements tests sensor principles, calibration, uncertainty, bridge circuits, signal conditioning, and data acquisition.
Core rules and concepts
- Accuracy is closeness to true value; precision is repeatability. Calibration establishes a traceable relation between input and output.
- Uncertainty propagates: for y=f(x_i), u_y^2=sum((partial f/partial x_i)^2 u_xi^2) for independent inputs.
- Strain gauges: delta R/R=GF epsilon. A quarter-bridge output is approximately V_out=V_ex/4 times delta R/R for small strains.
- Thermocouples require cold-junction compensation; RTDs are more stable but slower; thermistors are sensitive over a narrow range.
- Sampling must satisfy Nyquist: f_s>2 f_max; anti-alias filtering is required before sampling.
Worked example
A 120 ohm strain gauge with GF=2.0 experiences 500 microstrain in a quarter bridge with 4 V excitation. delta R/R=GF epsilon=2.0 x 500 x 10^-6=1.0 x 10^-3. Bridge output is about V_ex/4 times delta R/R=4/4 x 1.0 x 10^-3=1.0 mV. The small signal needs amplification and filtering. If lead resistance is significant, a three-wire or four-wire connection reduces error.
Traps
Using gauge factor as a voltage sensitivity, ignoring bridge nonlinearity at large strain, omitting cold-junction compensation, and sampling without anti-alias filtering are common. Distinguish resolution from accuracy.