3. Types of Mechanical Sensors

mechanical sensors, the primary signals about the state of the object or process under study are mechanical in nature. These may be: a change in the shape and/or dimensions of bodies; a change in their relative position, i.e. mechanical displacement; a change in the velocity of motion; the occurrence of accelerations; a change in the amplitude, phase or frequency of mechanical oscillations, etc. Accordingly, it makes sense to subdivide mechanical sensors, taking into account the physical nature of the sensing elements and the primary information signals that arise in them, into the following types:

• deformation sensors, in which the primary signals are changes in the shape, volume or dimensions of the sensing element;

• sensors of linear displacement, in which the primary signal is the displacement of the body's centre of mass in space;

• sensors of angular displacement, in which the primary signals are the tilt, turning or rotation of the body;

• accelerometers, in which the primary signal is the occurrence of mechanical acceleration;

• vibration sensors, in which the primary signal is a change in the state of mechanical oscillations of a body or system of bodies;

• chromatographic sensors, in which the primary signals appear as a result of the mechanical movement of molecules (of a liquid or gas) through a porous medium.

.3.1. Deformation sensing elements

The best-known deformation sensing elements are the deformation sensing elements for measuring temperature, force and pressure. In production conditions, for monitoring temperature for the purpose of its regulation, preference is usually given to bimetallic sensing elements. They are bimetallic strips consisting of two firmly bonded layers of metals with substantially different temperature coefficients of linear expansion (TCLE). As the temperature rises, one of the metals elongates more, the other – less. As a result, the bimetallic strip bends toward the metal with the lower TCLE

When measuring the pressure of a liquid or gas, mechanical devices that deform under the action of pressure are often used as sensing elements. The most commonly used of these are – bellows, diaphragms and elastic tubes.

For measuring weight and force, another deformation sensing element is often used – the spring. Springs are usually used as a sensing element only within the limits of linear elastic deformation, when the well-known Hooke's law holds:

(2.1)

where – the coefficient of elasticity, – the applied force, – the length of the unloaded spring, – the amount of extension or compression of the spring.

When applying microsystem technologies, of all the deformation elements listed above, diaphragms are the easiest to implement. They are therefore usually the preferred choice. Silicon strain gauges, which convert mechanical deformation into electrical signals, are formed directly in the silicon diaphragm. Alongside the miniature diaphragm, on the same silicon chip, the microcircuits required for reading and electronic processing of the signals are also formed

3.2. Sensors of linear displacement

A well-known type of mechanical sensing element in which the primary signal appears in the form of linear displacement is the piston.. On one side of the movable piston, in the hermetically sealed part of the cylinder, there is gas, while on the other side there is the medium in which the pressure is being measured. This may also be a gas or a liquid. When the measured pressure increases, the movable piston is displaced, compressing the gas in the closed part of the cylinder until its pressure equalizes with the external one. When the measured pressure decreases, the piston moves in the opposite direction until a new state of equilibrium is reached

The next well-known mechanical sensing element with linear displacement is the float.. Liquid level sensors make use of the fact that the float moves together with the movement of the liquid surface. And its movements can be converted in various ways into electrical, visual or other kinds of signals.

For example, small permanent magnets are placed inside the body of the float. At any given moment, only the switch that is located inside the float, and is therefore subject to the action of the magnets, is triggered. The resistance of the electrical circuit directly depends on the position of the float and, consequently, – on the level of the liquid.

To measure the density of liquids, hydrometers are often used. A hydrometer consists of a hollow glass, metal or plastic capsule to which a thin "neck" with a scale is attached. The capsule is filled with shot in such a calculated amount that the capsule is fully submerged in the liquid being tested, but does not sink, instead floating, with part of the neck bearing the scale protruding above the surface of the liquid. According to Archimedes' principle, the flotation condition of the hydrometer has the form:

(3.2)

• where – the mass of the hydrometer, – the acceleration of gravity, – the density of the liquid, – the volume of the part of the hydrometer submerged in the liquid.

To determine the coefficients of surface tension of liquids , capillary tubes are used, in which the height of the rise or fall of the liquid column h is determined by the value of the surface tension and the density of the liquid:

where – the diameter of the capillary, – the acceleration of gravity.

3.3. Sensors of angular displacement

Among sensors of angular displacement, 2 groups are distinguished: tilt (roll) angle sensors and rotation angle sensors.

Inclinometers

Tilt sensors are also called "inclinometers" (from the Latin incline – to tilt). Most often what is meant is the angular deviation from the vertical or from the horizontal plane. Even the earliest builders used plumb lines, spirit levels, levels for this purpose.

Fig. 3.1 shows a modern optoelectronic design of an inclinometer, which makes it possible to measure two tilt angles simultaneously in mutually perpendicular planes. In housing 1 are placed an LED 2, a silicon chip 3 with photodiodes or phototransistors 4 and amplifiers formed in it, a plastic hemisphere with a transparent liquid 5 and an air bubble 6 left in it. This bubble, refracting the light from LED 2, creates a shadow region 7. When housing 1 is positioned horizontally, the shadow from the bubble covers all 4 photodiodes equally. If the housing tilts slightly, the air bubble shifts. Correspondingly, the shadow from it shifts across the surface of the photodiodes (Fig. 3.1, right). And the signals from the photodiodes become different. Measuring them makes it possible to accurately calculate the tilt angles relative to two orthogonal axes. For this, the sensor is precisely calibrated during production at normal and at the extreme operating temperature values. The calibration data is stored in the microprocessor's memory.

Fig. 3.1. Design and operating principle of a two-axis optoelectronic inclinometer

The error in measuring tilt angles by this method does not exceed 0.01°. This makes it possible to control with high precision the shape of a surface, for example, of the mirrors of large telescopes, the flatness and levelness of the guide rails of large high-precision coordinate tables, etc.

Absolute encoders

Rotation angle sensors have come a long way in their development. Over many centuries of technological development, quite a few different methods and devices have been created. At first these were exclusively mechanical devices. In them, using mechanical gearing, the angle of rotation or the number of revolutions performed was converted and displayed either as the movement of a pointer along a scale with degree divisions or as a number formed in a transparent window by a system of wheels with digits marked on their rims.

In the middle of the twentieth century, magnetic and electrical sensors of rotation angle or number of revolutions became more popular. Nowadays, for measuring rotation angles and the number of revolutions, optoelectronic encoders are increasingly used. By operating principle, it is customary to distinguish between so-called "absolute" and "incremental" encoders.

Absolute encoders output digital codes at their output that correspond to the absolute value of the rotation angle relative to a position taken as zero. The operating principle of an absolute encoder designed for one revolution. A code disk is mounted on a shaft that is fixed on two precision bearings and kinematically connected to the assembly whose rotation is being monitored. On the latter, concentric tracks with transparent and opaque sections are marked out.. Light passes freely through the transparent sections of the tracks and, upon reaching the corresponding photodetectors, causes a "1" signal to appear at the outputs of the corresponding amplifiers. Light does not pass through the opaque sections of the tracks, and "0" signals are formed at the outputs of the corresponding amplifiers.

The total number of possible n-bit binary codes is 2n. Therefore, the accuracy of determining the angular position of the disk equals (360° : 2n+1).

In absolute encoders, information about the angular position of the shaft is retained even when the power is switched off, since it is fixed physically by the position of the code disks. When using an ordinary binary code to encode the shaft position, the transition to an adjacent position can cause several bits to change simultaneously. For example, in the transition from 0111 to 1000, 4 bits change simultaneously. Therefore, near the transition position, due to some asynchrony in the change of the bits, incorrect codes may briefly be output.

This can be avoided by using the well-known Gray code for encoding.

Incremental encoders

In incremental encoders, the counting disk usually has just one track, on which transparent and opaque sections alternate. And correspondingly, instead of a row of photodetectors, only 1 or 2 photodetectors are used – depending on whether the disk can rotate in only one direction or in both directions. At the sensor's output, a sequence of pulses is formed with a period inversely proportional to the rotational speed of the disk..

where – the deviation of the proof mass M from the equilibrium position; – the damping coefficient due to damping; – the stiffness coefficient of the elastic element; – the current acceleration of the object on which the accelerometer is mounted.

The damper is usually adjusted so that the damping coefficient reaches a critical value. In this case, the response time of the accelerometer to a change in acceleration turns out to be the smallest, and even with a step change in acceleration , oscillations around the new equilibrium position do not arise. To determine the acceleration , it is sufficient to measure the deviation from the equilibrium position or the force , which acts on the elastic element.

Thus, the proof mass M provides for the conversion of the primary information signal in the form of linear acceleration into mechanical displacement or into the deforming force on the elastic element. The elastic element ensures linearity, or at least a one-to-one correspondence, of the conversion. And the damper prevents the occurrence of prolonged oscillatory processes. It turns out that all of them are necessary constituent elements of the accelerometer.

Fig. 3.3 shows the design of a capacitive accelerometer, manufactured using MST. In silicon crystal 1, sections 2 are etched away so that a substantial proof mass 3 is mechanically separated from the other parts of the accelerometer. It is connected to them only by thin bridges 4, which play the role of elastic elements. At a small distance (~ 10 µm) from the silicon crystal, above and below, metal electrodes 5 and 6 are located. The role of the damper is played by a viscous non-conductive liquid, which fills the space between the electrodes and the silicon.

Fig. 3.3. Design of a capacitive accelerometer

In such a design, proof mass 3 can move only vertically. The electrical capacitances between it and the upper (lower) electrodes are connected in opposite arms of an AC bridge circuit. It is balanced so that, in the absence of acceleration, the output signal equals zero. When the object on which the accelerometer is mounted moves with acceleration directed along the axis of the sensor, proof mass 3 is displaced from the equilibrium position, as a result of which one of the capacitances increases while the other decreases. Because of the resulting imbalance, a voltage of the corresponding sign appears at the output of the bridge circuit, and the greater it is, the greater the acceleration. The bridge circuit, the necessary electronic switches, amplifiers, temperature-compensation elements – everything required for signal processing and calibration of the accelerometer – is nowadays formed by MST (microsystem technology) methods on the same silicon crystal.

In the design of the accelerometer described above, the acceleration, which is here the primary information signal, is first converted into linear displacement of the proof mass. The displacement, in turn, is converted into a change in the capacitance of the upper and lower capacitors, and the latter – into an electrical signal.

In piezoresistive accelerometers it is not the linear displacement of the inertial mass that is measured, but the force acting on the elastic element. To measure this force, silicon piezoresistors are formed in the elastic elements.

Angular accelerometers

To measure angular accelerations, a rotor 1 with a sufficiently large moment of inertia (Fig. 3.4) relative to the axis of rotation 2 is required. This rotation must be opposed by an elastic torsion element 3, which creates a moment of force proportional to the twist angle. A damper is also needed to dissipate the energy of the resulting torsional oscillations. Then, when an angular acceleration of the controlled object arises in the direction of the accelerometer's axis, rotor 1, under the action of the moment of inertia, turns through a certain angle.

Fig. 3.4. Mechanical diagram of an angular accelerometer: 1 - rotor; 2 - axis of rotation; 3 - elastic element; 4 - lower support; 5 - upper support

The rotation of the rotor is described by a differential equation analogous to (4.1), in which the mass must be replaced by the moment of inertia of the rotor, the linear displacement by the angle of rotation, and the linear acceleration – by the angular acceleration. The role of the damper is played by an adjustable moment of friction forces between the rotor axis and the supports. By measuring the twist angle or the moment of force on the elastic element, the magnitude of the angular acceleration can be determined.

With the use of microsystem technologies, angular accelerometers are nowadays also made in a microminiature design.

3.5 Vibration measuring sensors

In these sensors, the primary information signal is a change in the state of mechanical oscillations of a body or a system of bodies. Mechanical oscillatory systems can be very sensitive to various influencing factors, which is exploited in building vibration sensors.

The section "Electrical sensors" discussed methods for exciting undamped mechanical and electrical oscillations of a piezoelectric crystal by synchronous energy pumping, for example through a transistor using positive feedback. These oscillations occur at the crystal's own resonant frequency, which usually lies in the range of units to tens of megahertz and depends on its geometric dimensions and mass. If the latter change, the oscillation frequency changes too.

To compensate for the influence of temperature changes and other disturbances, two identical piezoelectric vibrators are installed side by side. One of them – the reference one – remains free of the influence, while the controlled factor acts on the other. To determine the magnitude of this factor's influence, the difference between the oscillation frequencies of the measuring and reference vibrators is measured. It is practically independent of temperature changes and of other extraneous disturbances that affect the frequency of both vibrators equally.

Most often, the influencing factor is the addition of a small mass to the piezoelement, the magnitude of which needs to be determined. In that case, such a vibration sensor works as microscales, whose sensitivity is on the order of 1 microgram. The change in frequency (in Hz) over the operating interval is usually described by the formula

where – the initial oscillation frequency (MHz); – the mass increment (g); – the electrode area of the piezocrystal (cm2).

If the dimension is given in the International System of Units SI, then the following formula must be used:

where – in Hz; –in kg; – in m2.

If a specific receptor layer – a thin film of a material that selectively adsorbs (attaches) molecules of some gas – is applied to the surface of two piezoelectric crystals, and one of the crystals is brought into contact with the atmosphere, then as a result of adsorption of molecules of the corresponding gas the mass of that crystal increases slightly. The frequency of its natural oscillations changes accordingly. By measuring the difference in oscillation frequencies, one can determine the specific content of the corresponding gas in the atmosphere. For example, if a thin film of gold is applied to the surface of the crystal, the sensor becomes sensitive to the presence of mercury vapor in the surrounding atmosphere. If mercury vapor is present, its atoms are adsorbed by the gold film, forming an amalgam. The mass of the film increases slightly, which can be detected from the change in the frequency of the piezocrystal's mechanical and electrical oscillations. Naturally, the mass of adsorbed vapor depends on the specific content of the corresponding gas in the monitored medium and on the "exposure" time.

Cantilevers

With the use of modern microsystem technologies, mechanical oscillatory systems can now be made in astonishingly small sizes. Especially popular in this area have become the so-called cantilevers (cantilever) – elastic long beams fixed at one end, resembling in shape the diving boards from which athletes jump into water. As an example, Fig. 3.5 shows three cantilevers 1, formed by MST methods in a silicon crystal 2.

Fig. 3.5

Example of the design of silicon cantilevers: 1 - cantilevers; 2 - main body of silicon; right – enlarged image of a cantilever; 3 - sensitive zone; 4 - piezoresistor; 5 and 6 - electrodes for exciting and sustaining mechanical oscillations

On the right, one of the cantilevers is shown enlarged. On its upper surface a sensitive zone 3 and a piezoresistor 4 are formed, and below – electrode 5. To excite and sustain undamped mechanical oscillations of the cantilevers 1, electrostatic forces are usually used, created by applying an alternating voltage between the cantilever and the excitation electrode 6, formed on a silicon substrate.

. The necessary positive feedback is provided by piezoresistors 4, formed near the fixed end of the cantilever, where the greatest deformations are concentrated. The mechanical oscillations are automatically maintained at the resonant frequency of the cantilever's free oscillations. This frequency is usually a few megahertz. Excitation and sustaining of undamped mechanical oscillations of cantilevers can also be carried out by other methods: magnetic, electromagnetic, etc.

A "receptor layer" is applied to the sensitive zone 3 – a coating selectively sensitive to a controlled chemical substance or to a particular protein, virus, or other analyte. If this analyte is present in the medium the cantilever is in contact with (gas, liquid), some of its atoms (molecules, particles) chemically bind to the sensitive coating 3. Because of the resulting slight change in mass, the frequency of the cantilever's mechanical oscillations changes. The frequency of the signals from piezoresistor 4 changes accordingly. These signals are picked up and processed by electronic circuits formed in the same silicon crystal. Since the cantilever's own mass is very small and even very slight frequency changes are detected, the sensitivity of such vibration sensors turns out to be quite high.

Vibration analyzers

Not only piezocrystals, membranes, and cantilevers have their own resonant frequency. Every mechanical structure has its own resonant frequencies, its own characteristic oscillatory properties. And with any mechanical damage or deformation, the pattern of their natural oscillations changes. This creates a fundamental possibility of detecting undesirable changes and defects that have appeared in a structure from changes in the pattern of mechanical oscillations. The scientific and technical discipline concerned with this is called vibration diagnostics, and the instruments for measuring and analyzing mechanical oscillations are called vibrometers and vibration analyzers.