Proof mass

Sensors for measurements of physical parameters such as pressure, rotation or acceleration are commonly based on elongation or vibration of membranes, cantilevers or other proof masses. The electrochemical processes used to achieve these micromechanical structures are commonly etch-stop techniques, as discussed in Section 4.5, or sacrificial layer techniques, discussed in Section 10.7. 

An example of the practical consequences of vertical deflection is shown in Figure 5.5.2 for a comb-type accelerometer fabricated with polysilicon. In Fig. 5.5.2a, a positive stress gradient leads to an upward deflection of the fixed outer beams and a downward deflection of the proof mass. In Fig. 5.5.2b, the situation is reversed due to a negative stress gradient in the material [11]. 

Fig. 5.5.2 Close-up of the proof mass of an acceleration sensor made of a material with a positive and b negative stress gradient...

Finally the proof-mass potential is raised to Vstep (Fig. 6.1.15c). Only a mismatch of the sense capacitors (or other mismatch in the circuit, e.g., between the integrating capacitors) results in a non-zero differential output voltage AV0. Note, however, that for identical sense capacitors the output is zero, as is required. Thermal noise sampled onto Cs and Qnt is effectively cancelled. 

Typically, an accelerometer (or g-cell) consists of a proof mass that is suspended with a spring, or compliant beam, in the presence of some damping, and anchored to a fixed reference. Coupling this mass-spring-dashpot model (Fig. 7.1.2)... 

Finally, mechanical noise is the result of Brownian motion of gases around the proof mass. This noise component can be described by... 

Mechanical shock is one of the automotive reliability tests that an accelerometer must survive. Often, these excursions are specified beyond the maximum g-range of the device. Mechanically, this shock magnitude creates the possibility of substantial proof mass movement. To maintain integrity of the mechanical structure in this environment, many accelerometers use another structural material layer to provide a stop to the proof mass that inhibits the movement. An example of an overtravel stop on a lateral accelerometer is shown in Fig. 7.1.12g. 

Fig. 3.7 Dielectric elastomer ocean wave power generator based on a proof mass, system tested at sea (top) and CAD model of a final system that might be used for supplying power to navigation and scientific buoys (bottom)...

This generator was based on a suspended, proof-mass approach that used concatenated roll transducers. 

Based on its operation principle, the resonator can be modeled as a simple spring-mass-dashpot system, as shown in Fig. 2, with the shuttle being the proof mass, folder beams being the spring, and the surrounding air being the dashpot damper. The displacement of the proof mass can then be obtained by solving the second-order differential equation... 

To solve Eqs. 12 and 13 with oscUlating velocity boundary conditions, simple models such as the Couette flow model and ID Stokes model have been used. These models ignore the finite size and edge effects, as both of them model the device as two infinitely large parallel plates with one (the proof mass) oscillating on the top of the other (substrate). The Couette model further assumes a steady flow, resulting in a linear velocity profile between the plates. As shown later, the quality factor obtained by these two models is overpredicted by a factor of two, indicating the importance of 3D effects. 

A thermal flow sensor using porous Si thermal isolation as the one described above was also used in a Si thermal accelerometer without solid proof mass (Goustouridis et al. 2007) and in a Si thermoelectric generator (Hourdakis and Nassiopoulou 2013). 

Goustouridis D, Kaltsas G, Nassiopoulou AG (2007) A sihcon thermal accelerometer without solid proof mass using porous sihcon thermal isolation. IEEE Sens J 7(7) 983 Hourdakis E, Nassiopoulou AG (2013) A thermoelectric generator using porous Si thermal isolation. Sensors. 13 13596... 

Fig. 5.6. Root locus curve (real and imaginary axis) for active damping via proof mass actuators in the secondary mirror support truss (Ci percentage of critical damping)...

To achieve vibration damping, the piezo actuator can be combined with an accelerometer [18]. A first solution consists of using a piezoelectric actuated proof mass damper (Fig. 6.25), in which the compliance of the proof mass corresponds to the piezoelectric compliance. The force provided by the piezo actuator is F = N V, where N is the force factor and V the applied voltage. This method is generally adapted to high frequency mode (e. g. 100. .. 400 Hz), as it remains difficult to build a piezo proof mass (PPM) at low frequency. 

An example of an automotive crash sensor that could be used to deploy an air-bag safety system is shown in Figure 2.18. Here a proof mass is suspended by four fixed-guided support arms of length L that are attached to a stiff frame. The frame is rigidly attached to the car. 

A typical process sequence for the fabrication of a MEMS device is shown in Figure 1.4. At the end of the fabrication cycle the MEMS part is released from the substrate by etching a sacrificial layer in a surface micromachining process, or by etching selected regions of the substrate in a bulk micromachining process. This enables a micromechanical element such as a proof-mass or an actuator to move independently of... 

Inertial sensors consist of a frame and a proof mass suspended within the frame. Movement of the frame is sensed by sensing differential motion between the frame and the proof mass. The suspension usually constrains the proof mass to have one or more degrees of freedom, which can be either rotational or translational. If these degrees of freedom are purely rotational, the instrument is called a rotational seismometer or a gyroscope (see Lee et al. 2012). 

Modem short-period seismometers and geophones are passive inertial sensors which consist of a pendulum with a velocity transducer with sensitivity G in V-s/m mounted so as to measure the relative velocity xt of a proof mass M and frame of the sensor, as shown in Fig. 3. The spring constant of the mainspring and suspension combined K and the viscous damping B determine the transfer function of the pendulum, required to relate the output voltage Vg to the input motion of the frame, x . 

A force-feedback or active seismometer solves these problems by taking a mechanical system like that of the passive seismometer, as shown in Fig. 3, and adding a displacement transducer T, as shown in Fig. 5. In an active seismometer, the voice coil G is used to produce a force on the proof mass by driving it with a feedback current if instead of using it to produce a voltage proportional to the velocity of the proof mass. 

Feedback control systems have the property that as long as the loop gain is sufficiently high (and the system is stable), the transfer function of the system is the inverse of the feedback transfer function (Phillips and Harbor 1991). In the case of an inertial sensor, this means that the transfer function is determined by electronic components in the feedback network not the physical characteristics of the pendulum. Furthermore this same feedback holds the proof mass substantially at rest with respect to the frame of the sensor, greatly reducing the impact of nonlinearities in the suspension and transducers. 

Broadband seismometers generally use displacement transducers to measure the relative displacement of the proof mass and the frame. The proof mass and its suspension together make a pendulum which has a response which is flat to acceleration and independent of its natural frequency above the natural frequency. 

A seismometer not contained within a pressure vessel will exhibit strong pressure sensitivity on the vertical output due to buoyancy of the proof mass. Consider a proof mass with a density Pproof = 8 g/cm at a temperature Tair = 293 K in dry air with a specific gas constant of / air = 287 J/kg K in standard gravity go- For such a seismometer, the vertical sensitivity to air pressure changes due to buoyancy is (Ziim and Wielandt 2007)... 

The primary function of the mainspring that suspends the proof mass is to apply a restoring force to the mass in the direction of its center position, so that when the mass is deflected by some acceleration acting on it, the spring acts in the opposite direction to restore the position of the mass. The spring constant (the force the spring applies per unit of deflection) is generally as weak as can be practically achieved, so as to... 

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