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                                      Optical Type Pressure Sensor

The circuit diagram shows that if any instant uncovering area of the photo diode is Am, and that of reference one is Ar, with other notations shown in the figure, the ratiometric output would be

Vf/VR = G(Am/Ar – a)

G – Span adjusted

a – Zero adjustment co-efficient

Calibration may be made directly in pressure. The ratiometric technique is often preferred for avoiding drift error in electronic components as they are likely to be equally affected and cancelled. The vane movement or the diaphragm movement is kept small for negligible hysteresis and good precision. Diode signals have non-linearities which may also vary from unit to unit. The non-linearities are often linearised using look up table in programmable read only memories during A/D conversion process. The range may be adjusted from (0-400)MPa with an accuracy of 0.1 percent scan. Temperature, though compensated, affects measurement to a certain extent which, in zero scale may be compensated by auto-zeroing facility.

This system is often used as a null detecting one in a force balance type pressure measurement, where the servo-system brings the sensor to the zero balance point.

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For basics of strain gauge click here:  Strain Gauges

The figure below shows the arrangement of strain gauges that are mounted on a cantilever spring which is operated by a pair of opposing bellow elements. The cantilever is properly chosen in dimension for compensation in the change in the Young’s modulus due to temperature changes.

The figure below shows an arrangement if strain gauges on to a flat diaphragm. Usually four gauges are   mounted as shown and they are connected in a bridge circuit as shown in the figure. Radial and tangential stresses are developed in the diaphragm gauges complicating the measurement of true pressure.

In recent years miniaturization is effected where the discrete gauges are replaced by a rosette which is available in various sizes. The rosettes may be configured such that the radial strains at the edge of the diaphragm and tangential strain near the centre are easily picked up while the solder points/tabs are located in a low strain region.

Unbounded strain gauges can also be adopted for measuring strain and in consequence pressure with a diaphragm. A simple schematic of such a pressure measurement is shown in the figure below. Emperical calibration for all the above cases is always preferred.

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A capacitance pressure transducer is based on the fact that dielectric constants of liquids, solids and gases change under pressure. The figure below shows an arrangement of a cylindrical capacitor that can withstand large pressure. As the change in dielectric constant is quite small (only about ½ percent change for a pressure change of about 10 MPa), it is usable only at large change in pressure. Besides, the capacitance-pressure relation is non-linear and is affected by temperature variation. The measurement of this capacitance is done by a resonance circuit. The schematic is shown below. The oscillogram giving the variation of the output voltage with capacitance is also shown below.

You may also like: Electrical Pressure Transducers and Pressure Transducers

Capacitive Transducer

A basic capacitive transducer has already been explained (Refer: Capacitive Transducers). It consists of a pair of parallel plates with the middle plate moving with pressure and producing a differential capacitor system. The figure below shows a pressure gauge of this type. Spherical depression of the glass plate is less than 0.0025 centimetres. When a differential pressure exists, the thin steel diaphragm moves towards the low pressure side and the output voltage e0 measured as the difference of voltage e1 and e2 across the two capacitors formed with this movable plate is given by the equation

e0 = e1-e2 = Ex/d

x – Displacement of the diaphragm

d – Diameter

Such transducers are frequently used in pressure transmitter.

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You may also like: Electrical Pressure Transducers

There are two optical fibre bundles called guides – input and output – arranged as shown in the end view, giving the proper perspective. Chopped light from source is focused on to input guide, which on emergence is reflected from a flexible membrane. The membrane may be made of aluminized plastic formed as a film. With pressures, P1 and P2 equal, the position of the membrane with respect to the input guide is so kept that 50% of the reflected light falls on the surrounding annular output guide. With P2 greater than P1, the membrane becomes convex towards the guides and more light falls on the output guide, while with P1 less than P2, the reverse occurs. A detector set at the other end of the output guide correspondingly receives varied amount of light with changing pressure. The detector can be calibrated for pressure.

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You may also like: Electrical Pressure Transducers

One method of using the delay line as a practical sensor is to introduce it in the feedback path of an amplifier to obtain an oscillator with its frequency as a function of the stress. The figure is shown below.

As in most devices, temperature affects the performance by changing the property of the material. However, every quartz crystal cut appropriately has a turnover temperature at which the effect of temperature is minimum. Also, if surface wave is proportional on both faces of the substrate using two pairs of IDT’s, the sensitivity increases and effect of temperature is reduced.

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The same method can be extended to develop a null-balance type instrument as shown in the figure below. Feedback through the force coil produces the wanted balance while the output is taken across resistor R and is of value K*(p1-p2), K being a constant.

Some of the most commonly used electrical pressure sensors are:

• Strain Gauge Pressure Transducer
• Capacitance Pressure Gauge
• Piezo-electric Type Pressure Sensor
• Optical Type Pressure Sensor
• Fibre-optic Type Pressure Measurement
• Surface Acoustic Wave (SAW) Sensor
• Bridgeman Pressure Gauge

A high accuracy stable pressure transducer often recommended as calibration standard for gas pressure and density, is obtained by making a thin walled cylinder oscillate continuously in one of its vibration modes – specifically circumferential mode using limit cycle feedback system. Any change in the pressure causes change in the oscillation frequency and the reluctance type pick-up cum drive system produces an output signal which is processed and displayed by electronic means. Provision for temperature compensation is also made where a solid state temperature sensor picks up temperature change and a microprocessor system makes the relevant compensation.

In resistive pressure transducers, the pressure operates the primary sensors as in a bourdon tube, a diaphragm or a bellows element or even the liquid column in a manometer. The mechanical movement of this primary sensor is then converted into electrical signals by resistance variations as shown in the figures below. Figure (4) shows a liquid contact type resistance pressure gauge where with increasing pressure more and more resistances are shortened and the resistance R is decreased. A current meter will directly indicate the pressure.

The modified system is shown in the figure below where a resistance ratio element is used. Long resistance wires are introduced into two manometer legs containing a conducting fluid. The unbalance current in galvanometer directly indicates the pressure difference (p1-p2).

Bridgeman Pressure Gauge

When a wire is subjected to pressure from all sides its electrical resistance changes. This principle can be utilized to obtain a primary type resistive pressure sensor and is called as a Bridgeman pressure sensor. The distortion produced in the crystal lattice due to the external pressure causes the change in resistance. In most common metal wires, the resistance decreases with increase in pressure, while for antimony, bismuth, lithium, and manganin, it increases. In cesium, it initially decreases for small values of pressure changes and reaches a minimum, beyond which it increases with increase in pressure. But these metals cannot be used for practical purposes in a bridgeman gauge. The gauge must be used at a constant temperature, and has a range from 0 to 1000 MPa, but usable only at high pressure, as, at low values of pressure the change in resistance value is very small because of the small value of the pressure co-efficient of resistance.

The constructional features of bridgeman gauge has improves since it was first proposed. The basic construction is shown in the figure below. It has a bone ring shape with an insulated manganin wire having a pressure co-efficient of resistance of 23×10^-7 cm²/kg so that the total resistance of the wire is 100 ohm. The winding is generally bifilar for avoiding inductive effect. Carbon can also be used for pressure measurement in the form of granules or discs. With pressure, its resistance also changes, but non-linearly and is not suitable for a linear scale measurement. The carbon resistance pressure gauge diagram is shown below.

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Metallic diaphragms are known to have good spring characteristics and non-metallic types have no elastic characteristics. Thus, non-metallic types are used rarely, and are usually opposed by a calibrated coil spring or any other elastic type gauge. The non-metallic types are also called slack diaphragm.

Working

The diagram of a diaphragm pressure gauge is shown below. When a force acts against a thin stretched diaphragm, it causes a deflection of the diaphragm with its centre deflecting the most.

Diaphragm Gauge

Since the elastic limit has to be maintained, the deflection of the diaphragm must be kept in a restricted manner. This can be done by cascading many diaphragm capsules as shown in the figure below. A main capsule is designed by joining two diaphragms at the periphery. A pressure inlet line is provided at the central position. When the pressure enters the capsule, the deflection will be the sum of deflections of all the individual capsules. As shown in figure (3), corrugated diaphragms are also used instead of the conventional ones.

Diaphragm Pressure Transducer

Corrugated designs help in providing a linear deflection and also increase the member strength. The total amount of deflection for a given pressure differential is known by the following factors:

• Number and depth of corrugation
• Number of capsules
• Capsule diameter
• Shell thickness
• Material characteristics

Materials used for the metal diaphragms are the same as those used for Bourdon Tube.

Non-metallic or slack diaphragms are used for measuring very small pressures. The commonly used materials for making the diaphragm are polythene, neoprene, animal membrane, silk, and synthetic materials. Due to their non-elastic characteristics, the device will have to be opposed with external springs for calibration and precise operation. The common range for pressure measurement varies between 50 Pa to 0.1 MPa.

The best example for a slack diaphragm is the draft gauge. They are used in boilers for indication of the boiler draft. The device can control both combustion and flue. With the draft, usually of pressure less than the atmosphere, connected, the power diaphragm moves to the left and its motion is transmitted through the sealing diaphragm, sealed link and pointer drive to the pointer.

The power diaphragm is balanced with the help of a calibrated leaf spring. The effective length of the spring and hence the range is determined by the range adjusting screw. By adjusting the zero adjustment screw, the right hand end of the power diaphragm support link as also the free end of the leaf spring, is adjusted for zero adjustment through the cradle.

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• By turning from a solid stock of metal
• By soldering or welding stamped annular rings
• Rolling a tube
• By hydraulically forming a drawn tubing

Working

The action of bending and tension operates the elastic members. For proper working, the tension should be least. The design ideas given for a diaphragm is applied to bowels as well. The manufacturer describes the bellows with two characters – maximum stroke and maximum allowable pressure. The force obtained can be increased by increasing the diameter. The stroke length can be increased by increasing the folds or convolutions.

For selecting a specific material for an elastic member like bellows, the parameters to be checked are:

• Range of pressure
• Hysteresis
• Fatigue on dynamic operation
• Corrosion
• Fabrication ease
• Sensitivity to fluctuating pressures

Out of these hysteresis and sensitivity to fluctuating pressures are the most important ones. Hysteresis can be minimized by following a proper manufacturing technique. For instance, a diaphragm when machined from a solid stock shows less hysteresis compared to the one produced by stamping. The same technique could be adopted for bellows as well. In the latter case, the dynamic nature of the variable is likely to induce resonance quickly depending on the natural frequency of the system. The natural frequency is calculable from the dimensions of the system and the gauge.

For strong bellows, the carbon steel is selected as the main element. But the material gets easily corroded and is difficult to machine. For better hysteresis properties you can use trumpet bass, phosphor bronze, or silicon bronze. Better dynamic performance can be achieved by using beryllium copper. Stainless steel is corrosion resistive, but does not have good elastic properties. For easy fabrication soft materials are sought after.

All bellow elements are used with separate calibrating springs. The springs can be aligned in two ways – in compression or in expansion when in use. Both these types, with internal compression springs or external tension springs, are commercially known as receiver elements and are used universally in pneumatic control loops. The figures below show the compressed and expanded type. Spring opposed bellows are also shown below. The open side of a bellows element is usually rigidly held to the instrument casing and because of the rigid fixing, the effective or active length of the bellows element is smaller than its actual length. This device is used in cases where the control pressure range is between 0.2 to 1 kg/cm².

Because of the device’s dynamic operation, the life of a bellow is an important consideration. Nomograms are available with the manufacturers, wherefrom the life in circles can be read directly knowing the per cent maximum pressure and per cent maximum stroke.

In terms of choice of elastic material for the sensors, the corrosive medium requires special precaution. Besides this, there are other factors showing that the medium should not come in direct contact with the measuring element. They are shown below:

• The direct impact of static head on the measuring element may cause error in response.
• Direct touch of the medium may cause corrosion, high viscosity fluids may cause response error and entrailed materials in the medium may clog in the element.
• In some critical processes in food processing and pharmaceutical industries, cleaning of the measuring system is necessitated.
• Removal of the measuring element for servicing should be convenient.

All these factors suggest that a type of seal should be placed between the process fluid and the measuring element. The best example is the diaphragm seal. It consists of a flexible diaphragm made of corrosion resistance material and sealed within a chamber, that can connect the process on one side and the measuring element on the other.

The effective area of an elastic element like diaphragm or bellows element is generally less than the geometrical area. For finding out the effective area, a known load change is made externally o the centre of the element and the corresponding deflection noted. The differential pressure is then found out for the same deflection.

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There are basically two types of manometers.

1. U-Tube Manometer
2. Well Type Manometer

There are also variations of the above said basic types called Enlarged-Leg Type Manometer, and Inclined Tube Manometer. Another manometer used commercially is the Ring-Balance Type Manometer.

U-Tube Manometer

A simple u-tube manometer is shown below. If ‘dm‘is the manometric fluid density, ‘d1’ is the density of the fluid over the manometer, ‘P2’ is the atmospheric pressure (for general measurement of gas pressure) and ‘P1’ is the gas pressure, and also if d1<<dm, then the differential pressure can be obtained by the relation

p1-p2 = h (dm-d1)

U-Tube Manometer

An enhanced version of a manometer is shown below with a seal liquid over the manometer liquid to separate the process fluid from the manometer fluid for any probable source of trouble like absorption, mixing or explosion and so on. Seal pots with large diameters are also placed for increasing the range. The equation for differential pressure is the same as mentioned above.

Manometer With Large Seal Pots

Well-Type Manometer

The main difference between a U-tube manometer and a well type manometer is that the U-tube is substituted by a large well such that the variation in the level in the well will be negligible and instead of measuring a differential height, a single height in the remaining column is measured. If a1 and a2 are the areas of the well and the capillary, and if (h1-h2) is the difference in height in the well due to the pressure difference (p1-p2) as shown, at balance, then

p1-p2 = dm.h (1+a2/a1)

The figure of a well-type manometer is shown below.

Well-Type Manometer

Enlarged-Leg Manometer

In the enlarged-leg manometer, a2 is not negligible compared to a1. It has a float in the enlarged-leg which is utilized for indication or recording. The two legs can be changed for changing the measurement span. Thus, the equation becomes,

p1-p2 = dm.h

The figure of an enlarged-leg manometer is shown below.

Enlarged Leg Manometer

Inclined Tube Manometer

The inclined tube manometer is an enlarged leg manometer with its measuring leg inclined to the vertical axis by an angle b. This is done to expand the scale and thereby to increase the sensitivity. The differential pressure can be written by the equation,

p1-p2 = dm.h.Cosb (1+a2/a1)

The factor cosb expands the scale of the instrument. When b is quite large, h can be increased such that (h.cosb) remains constant. The figure of an inclined tube manometer is shown below.

Inclined Tube Manometer

Micromanometer

The micromanometer is another variation of liquid column manometers that is based on the principle of inclined tube manometer and is used for the measurement of extremely small differences of pressure. The meniscus of the inclined tube is at a reference level as shown in the figure below, viewing through a magnifier provided with cross hair line. This is done for the condition, p1=p2. The adjustment is done by moving the well up and down a micrometer. For the condition p1 not equal to p2, the shift in the meniscus position is restored to zero by raising or lowering the well as before and the difference between these two readings gives the pressure difference in terms of height.

Micromanometer

Manometer is shown above as a static measuring device. Its dynamics can rarely be ignored. Considering manometric fluid as a free body, the forces acting on it are

• The weight distributed over the entire fluid.
• The drag force due to its motion and the corresponding tube wall shearing stress.
• The force due to differential pressure.
• Surface tension force at the two ends.

Ring-Balance Manometer

This device cannot be actually called a manometer, but it is often considered so. The tube is made of polythene or other light and transparent material. This tube is bent into in to the form of a ring and is supported at the centre by a suitable pivot. The tubular chamber is divided in to two parts by spilling, sealing, and filling with a suitable light liquid like kerosene or paraffin oil for isolating the two pressures. Pressure taps are made with two flexible tubings. Pressures p1 and p2 act against the sealed walls as shown in the figure below, and rotate the ring which is balanced by the counter weight w.

Of the various manometric fluids used, mercury has many advantages like low vapour pressure, non-sticky nature, and wide temperature range from -20 degree Celsius to 350 degree Celsius. Its high density is disadvantageous for low differential pressure measurements. The device installation and maintenance is known to be quite expensive.

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The device was invented by Eugene Bourdon in the year 1849. The basic idea behind the device is that, cross-sectional tubing when deformed in any way will tend to regain its circular form under the action of pressure. The bourdon pressure gauges used today have a slight elliptical cross-section and the tube is generally bent into a C-shape or arc length of about 27 degrees. The detailed diagram of the bourdon tube is shown below.

As seen in the figure, the pressure input is given to a socket which is soldered to the tube at the base. The other end or free end of the device is sealed by a tip. This tip is connected to a segmental lever through an adjustable length link. The lever length may also be adjustable. The segmental lever is suitably pivoted and the spindle holds the pointer as shown in the figure. A hair spring is sometimes used to fasten the spindle of the frame of the instrument to provide necessary tension for proper meshing of the gear teeth and thereby freeing the system from the backlash. Any error due to friction in the spindle bearings is known as lost motion. The mechanical construction has to be highly accurate in the case of a Bourdon Tube Gauge. If we consider a cross-section of the tube, its outer edge will have a larger surface than the inner portion. The tube walls will have a thickness between 0.01 and 0.05 inches.

Working

As the fluid pressure enters the bourdon tube, it tries to be reformed and because of a free tip available, this action causes the tip to travel in free space and the tube unwinds. The simultaneous actions of bending and tension due to the internal pressure make a non-linear movement of the free tip. This travel is suitable guided and amplified for the measurement of the internal pressure. But the main requirement of the device is that whenever the same pressure is applied, the movement of the tip should be the same and on withdrawal of the pressure the tip should return to the initial point.

A lot of compound stresses originate in the tube as soon as the pressure is applied. This makes the travel of the tip to be non-linear in nature. If the tip travel is considerably small, the stresses can be considered to produce a linear motion that is parallel to the axis of the link. The small linear tip movement is matched with a rotational pointer movement. This is known as multiplication, which can be adjusted by adjusting the length of the lever. For the same amount of tip travel, a shorter lever gives larger rotation. The approximately linear motion of the tip when converted to a circular motion with the link-lever and pinion attachment, a one-to-one correspondence between them may not occur and distortion results. This is known as angularity which can be minimized by adjusting the length of the link.

Other than C-type, bourdon gauges can also be constructed in the form of a helix or a spiral. The types are varied for specific uses and space accommodations, for better linearity and larger sensitivity. For thorough repeatability, the bourdon tubes materials must have good elastic or spring characteristics. The surrounding in which the process is carried out is also important as corrosive atmosphere or fluid would require a material which is corrosion proof. The commonly used materials are phosphor-bronze, silicon-bronze, beryllium-copper, inconel, and other C-Cr-Ni-Mo alloys, and so on.

In the case of forming processes, empirical relations are known to choose the tube size, shape and thickness and the radius of the C-tube. Because of the internal pressure, the near elliptic or rather the flattened section of the tube tries to expand as shown by the dotted line in the figure below (a). The same expansion lengthwise is shown in figure (b). The arrangement of the tube, however forces an expansion on the outer surface and a compression on the inner surface, thus allowing the tube to unwind. This is shown in figure (c).

Like all elastic elements a bourdon tube also has some hysteresis in a given pressure cycle. By proper choice of material and its heat treatment, this may be kept to within 0.1 and 0.5 percent of the maximum pressure cycle. Sensitivity of the tip movement of a bourdon element without restraint can be as high as 0.01 percent of full range pressure reducing to 0.1 percent with restraint at the central pivot.

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