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Jeffrey Lang is an electrical engineer whose work concerns electromechanical conversion power balance, control and small-scale devices. MIT's Research Laboratory of Electronics identifies the same professor as Jeffrey H. Lang and describes research on electric motors, electrical generators and microelectromechanical systems, together with teaching in circuits and electromagnetism.^[ref]

The identified MIT profile provides an externally hosted portrait of Jeffrey H. Lang.

For an original motor-scale illustration, a shaft delivering torque $\tau =2\mathrm{mN}\mathrm{m}$ at angular velocity $\omega =1000\mathrm{rad}{\mathrm{s}}^{-1}$ delivers $P_m=\tau \omega =2\mathrm{W}$. If electrical input is $3\mathrm{W}$ and the operating point is steady, the remaining $1\mathrm{W}$ must be accounted for by losses or another specified output. During acceleration some input can instead increase rotational kinetic energy. Reporting only shaft speed would not establish either output power or conversion efficiency.

With Anant Agarwal, Lang is credited on the MIT course material State and Memory by Anant Agarwal and Jeffrey Lang. It explains how a capacitor's state summarizes the part of past input needed to predict its future response.^[ref] For a series RC circuit with a constant later input $V_f$,Two different earlier input histories that leave the same initial capacitor electric potential difference give the same subsequent response under the same future input. For stipulated $RC=1\mathrm{ms}$, $v_C(0)=1\mathrm{V}$ and $V_f=3\mathrm{V}$, the value after one time constant is $3-2/e\approx 2.2642\mathrm{V}$. This original numerical example shows what it means for the state to retain enough of the past without retaining the entire waveform.

A microelectromechanical system combines small mechanical structures with electrical sensing or actuation. Fabrication methods related to semiconductor device fabrication can create suspended beams, membranes and movable masses together with their electrodes. Sensors and actuators can consequently be integrated into compact devices.

A capacitive accelerometer illustrates the mechanism. A suspended proof mass moves relative to its support under acceleration. In a simple spring model, a slowly varying support acceleration $a$ produces a relative displacement $x\approx -ma/k$, where $m$ is the mass and $k$ is the spring constant. Measuring a change of capacitance then measures that displacement. The ADXL335 uses suspended polysilicon structures and a differential capacitor to turn motion into an electrical signal.^[ref]

For an idealized pair of parallel-plate capacitors with equal area $A$ and gaps $g\mp x$, the capacitance difference isThis model explains why a small mechanical displacement can produce a signed electrical measurement; it is not a detailed model of every commercial MEMS geometry.

Nicholas A. Lambert coauthored research on rotating accelerometers for gear damage detection with David G. Lewicki and Robert S. Wagoner. Their2015 NASA report identifies Lambert and Wagoner with Ridgetop Group and Lewicki with Glenn Research Center. The contribution documented there is a joint experimental evaluation of embedded rotating sensing against conventional stationary housing measurements.^[ref]

The apparatus used a microelectromechanical system acceleration-sensing package on the rotating pinion. Its radial channel and two tangential channels did not measure identical combinations of motion. With the reported sensor orientation, adding the tangential channels isolated rotational acceleration, while subtracting them isolated the shared lateral contribution. This makes the experiment an example of choosing measurement geometry to separate motions, rather than interpreting every channel as the same gear vibration spectrum.^[ref]

An idealized algebraic version writes the channels as $T_1=u+r\alpha$ and $T_2=-u+r\alpha$, where $u$ is one projected translational acceleration, $r$ is sensor radius and $\alpha$ is angular acceleration. Then $(T_1+T_2)/(2r)=\alpha$ while $(T_1-T_2)/2=u$. Sensor placement, polarity and matching measurement calibration are what permit those cancellations. This illustrative decomposition explains the measurement principle; it does not assign sole authorship of the apparatus to one coauthor.

Robert S. Wagoner is a coauthor of experimental research using rotating accelerometers to detect damage in transmission gears. In the2015 report with David G. Lewicki and Nicholas A. Lambert, his affiliation is Ridgetop Group. The experiment compared embedded microelectromechanical system sensors with stationary housing sensors while an intentionally notched pinion was run toward tooth failure.^[ref]

A central signal-processing problem was separating repeatable shaft-related motion from unrelated vibration. The study reconstructed a rotation timing signal from a strong periodic component of the measured data and used it for time-synchronous averaging. Its comparison with a measured timing reference tested whether that reconstruction preserved the rotation-related waveform.^[ref]

The underlying averaging idea can be illustrated by records $a_j(\theta )=g(\theta )+{\eta }_j(\theta )$ aligned at the same shaft angle. Averaging $M$ revolutions preserves the repeatable waveform $g$; independent zero-mean noise with common variance ${\sigma }^2$ has mean-record variance ${\sigma }^2/M$. Timing error or changing operating conditions breaks those assumptions. This distinguishes detecting a repeatable vibration feature from proving that it uniquely identifies a tooth defect. The report found that fault indicators generally responded near actual tooth fracture, limiting the demonstrated early-warning interval.^[ref]

A rotating accelerometer is an accelerometer whose sensing axes rotate with a moving component, such as a gear shaft. It can measure motion close to its source, but its output combines the point's actual acceleration with a changing projection direction. Treating its channels as fixed laboratory axes can therefore change the interpretation of a gear vibration spectrum. A NASA transmission experiment mounted a microelectromechanical system sensor package on a pinion and compared it with stationary housing measurements.^[ref]

For a rigid shaft rotating in a plane, let its center have inertial acceleration ${\mathbf{a}}_O$. An attached point at radius $r$ haswhere ${\mathbf{e}}_r,{\mathbf{e}}_t$ rotate with the shaft. The radial contribution is the rotating-accelerometer centripetal term. At constant $\omega =100rad/s$ and $r=0.020\mathrm{m}$, its magnitude is $200m/{\mathrm{s}}^2$ even without vibration of the center. For the ideal specific force convention, the measured vector is ${\mathbf{a}}_P-\mathbf{g}$ projected onto each sensor axis, so gravitational acceleration can also produce a changing projection.

Suppose a laboratory acceleration $A\cos (2\pi f_{m}t)$ projects onto a sensor direction rotating at $f_r$. The product contains components at $f_m-f_r$ and $f_m+f_r$:This measurement geometry can produce modulation sidebands without a damaged tooth. The NASA radial channel showed1854 and2060Hz around a1957Hz mesh frequency with103Hz rotation. Paired tangential channels also allowed different motion contributions to be separated by sums and differences.^[ref] Correct interpretation therefore specifies mounting radius, orientation, measurement calibration and rotation timing, as well as sensor bandwidth.