DE3512180A1 - Vibrating-frame sensor for vectorial measurement of magnetic fields - Google Patents

Abstract

For the purpose of vectorial measurement of magnetic fields, use is made of a vibrating frame whose stretched surface is periodically varied by flexural vibrations, likewise periodic, of the frame, as a result of which periodic fluctuations also occur in the magnetic flux of the frame. Consequently, an alternating voltage is induced in a coil, which is proportional to the magnetic field and whose phase angle indicates the direction of the magnetic field.

Description

The invention relates to an electromechanical transducer with which it is possible to measure a magnetic field according to its size and direction.

In principle there are two ways of measuring.

Firstly, the measurement with a transducer, which is successively brought into three mutually perpendicular positions, whereby three directional vectors are measured, which are then used by a computer to calculate the resulting field vector.

Secondly, the measurement with three transducers arranged perpendicular to one another, which simultaneously measure the three direction vectors, which are also used by the computer to further calculate the resulting field vector.

The purpose of this invention was originally the vectorial detection of the earth's magnetic field in a grid arrangement over properties in order to detect, for example, biologically effective disturbances such as underground watercourses or strong fracture zones in the subsurface, etc.

The storage of larger amounts in comparison to the surroundings of different types of minerals, which have different magnetic properties, can lead to local disturbances of the otherwise homogeneous geomagnetic field and thus be measurable.

It was important to be able to get off the ground quickly and with as much as possible To enable a vectorial magnetic field measurement with little expenditure on technical equipment and energy.

The measured values should be prepared in such a way that a clear grid evaluation by computer is possible immediately or later.

These requirements are met with my arrangement, whereby large areas could even be covered by systematic exploration, e.g. by overflying or underwater towing.

With this oscillating frame sensor it is also possible to build an electronic compass.

Such a compass would have the advantage that it practically does not need any time to settle; its time constants can be set as desired using software in the computer program. Another important advantage would be that disturbances, e.g. caused by ship magnetism, can be corrected by means of suitable programs on the software side, so that magnetic corrections are not necessary.

Finally, many services such as the calculation of standard deviations of the course, calculation and evaluation of roll and yaw movements or even the automatic, position-dependent consideration of geological misalignments can be used by software. All measured values can be automatically called up and processed by a computer.

Of course, technical magnetic fields can also be measured with the arrangement. The magnetic field to be measured does not have to be stationary, but its permissible rate of change must not exceed a maximum size, which is generally limited mainly by the data rate of the computer.

Magnetic field sensors based on the Hall principle are known,

Field plates (resistance principle) and rotating coils (dynamo principle).

The method presented here is in principle dynamic, with high frequencies and with the decisive advantage that no mechanically moving parts and no sliding contacts are required.

The procedure described below is fully implemented in a test device, the function is confirmed.

The device was also tested in the field, only a small NC accumulator is required for operation. In addition, a program has been created with which raster measured values from series measurements are processed and then graphically displayed.

It is important that the field direction and field strength can be determined very quickly with the device, even without the help of a computer, by looking for the maximum of the measurement voltage depending on the direction.

The test device consists of two units, the measuring head with the dimensions 5 x 10 x 12 cm [high] 3 and the electronics with a similar volume.

The device can, however, be made much smaller.

The vibration frame sensor works as follows.

As is known, an electrical voltage is induced in a coil enclosing a magnetic flux, which voltage is proportional to the number of turns and the change in the magnetic flux over time, or it is represented mathematically:

Gl. 1

e = -N d diameter / dt

N = number of turns

Diameter = magnetic flux

e = induction voltage

If one introduces the magnetic induction "B" and the area "A" wrapped around by the coil, one can write with diameter = B times A.

Gl. 2

e = -N d (B times A) / dt = -N (A times dB / dt + B times dA / dt)

As you can see, the voltage depends on the change in the magnetic induction over time and on the change in the area wrapped around it.

If the magnetic field is stationary or quasi stationary,

so [high] dB / dt = 0 and it becomes

Gl. 3

e = -N times B times dA / dt

i.e. "e" is proportional to the magnetic induction "B" and proportional to the rate of change of area "[high] dA / dt".

In my principle, according to the invention, the change in area is achieved in that a closed oscillating frame made of non-ferrous metal is excited to periodic flexural vibrations which correspond to one of its mechanical resonance frequencies and which are automatically excited by suitable feedback methods in conjunction with an electronic oscillator circuit and an electromechanical converter.

A piezo oxide is used as an electromechanical converter in my sample structure.

The flexural vibrations of the oscillating frame are excited in such a way that they act in the direction of the area spanned by the oscillating frame, whereby the effective area of the area spanned by the oscillating frame changes periodically synchronously with the exciting frequency.

The oscillating frame alone now acts as a coil with one turn, which also functions as the primary coil of a coreless transformer.

A second coil with "N" turns, arranged within the surface of the oscillating frame, acts as a secondary coil from which the induced voltage is tapped. This induced voltage is first amplified in an amplifier and then fed to a synchronous detector, where the magnitude and polarity of the voltage are determined. This signed voltage is already the input variable for the computer; it can be queried automatically or entered manually.

In order to obtain all the data for calculating the vector magnetic field, only the three directional components that are perpendicular to one another need to be measured.

The arrangement with a mechanically oscillating frame is particularly suitable because, firstly, there is no mechanical wear and therefore no maintenance is required. The transducer can be completely encapsulated in non-ferrous metal, which means that it is protected against interference and environmental influences.

Second, the resonance frequency of the oscillator, which can be defined by its geometric dimensions, is relatively large. This enables a simple, interference-free amplification of the induced voltage.

In my model structure is a rectangular swing frame with the external dimensions 80 mm x 50 mm, a width of 9.3 mm and a material thickness of 4 mm made of aluminum. The excited natural frequency is practically exactly 3000 Hz.

The type of excited oscillation is somewhat more complicated, but the theoretical description agrees very well with the measured values.

Figure 1 shows the basic arrangement of my oscillator and the extreme oscillation states shown in dashed lines.

However, many other fashions are possible and useful. Other oscillating frame shapes are also possible and it is also possible to manufacture the oscillating frame from an insulating material, e.g. quartz glass, and to apply the secondary coil to its surface, e.g. by vapor deposition. In this form, the vibrating frame and the piezoelectric transducer can be built in an integrated manner.

The theoretical description of the oscillating frame leads to the oscillation behavior of a rod firmly clamped on both sides with the length "L" as shown in Figure 2.

For example, the rod is excited with its fourth eigenvalue condition. You have to imagine this rod folded into a rectangle, with the piezo-oxide transducer engaging in the center of the rod and the middle piece forming a short side of the rectangle according to Figure 1. In the middle of the opposite side of the rectangle, the two firmly clamped ends of the elongated rod meet. This then results in the waveform as shown in Figure 1.

The equation of motion of the undamped rod firmly clamped on both sides is the differential equation

Gl. 4th small omega = deflection

x = place

t = time

small gamma = specific weight of the rod material

F = area of the bar

E = dynamic modulus of elasticity of the rod material

I = area moment of inertia

g = acceleration due to gravity

The solution for the displacement "small omega" of this equation can be written in product form, whereby one factor only depends on the time "t" and the second factor only depends on the location "x".

Gl. 5

small omega (x, t) = W (x) times T (t)

are in it

Gl. 6th

W (x) = C [deep] 1 times cos (ax) + C [deep] 2 times sin (ax) + C [deep] 3 times cosh (ax) + C [deep] 4 times sinh (ax)

and

Gl. 7th

T (t) = A times Cos small omega t + B times sin small omega t

with the coefficient "a" where is.

With the help of the boundary conditions W = 0 and W '= 0 at firmly clamped ends, this results.

Gl. 8 W (0) = 0 = C [low] 1 + C [low] 3

Gl. 9 W '(0) = 0 = C [low] 2 + C [low] 4

Gl. 10 W (L) = 0 = C [deep] 1 times (cosa times l-cosha times l) + C [deep] 2 times (sina times L-sinha times L)

Gl. 11 (W '(L) = 0 = -C [deep] 1 times a times (sina times L + sinha times L) + C [deep] 2 times a times (cosa times L-cosha times L)

this finally results in the conditional equation

Gl. 12th

2-2 times cosaL times coshaL / (cosaL - coshaL) times (sinaL + sinhaL) = 0

respectively

Gl. 13th

cos large omega = 1 / cosh large omega with large omega = aL

This equation has any number of solutions, we are interested in the fifth solution

Gl. 14th

large omega = a [deep] 5 times L = 14,147165

This means that the fifth natural frequency of the oscillator can now be determined, too

Gl. 15th

In this specific case, that leads to

Gl. 16

F = 9.3 by 4 mm [high] 2

g = 9810 mm / s [high] 2

E = 7000 kg / mm [high] 2

I = 9.3 by 4 mm [high] 4/12 small gamma = 2.85 kg / 10 [high] 6 mm [high] 3

L = 244 mm

The measured value of the excited frequency of 3000 Hz therefore deviates only insignificantly from the theoretically expected value f = 3028 Hz.

In order to determine the change in area of the oscillating frame, the position function of the deflection W (x) must be considered.

Gl. 17th

W (X) = C [deep] 1 times (cosa [deep] 5 times x - cosha [deep] 5 times x) + C [deep] 2 times (sina [deep] 5 times x - sinha [deep] 5 times x)

Gl. 18th

with C [deep] 1 = -C [deep] 2 times sina [deep] 5 times L-sinha [deep] 5 times L / cosa [deep] 5 times L-cosha [deep] 5 times L = -C [deep ] 2 times 1 becomes

Gl. 19th

W (x) = C [deep] 2 times (sina [deep] 5 times x - sinha [deep] 5 times x - cosa [deep] 5 times x + cosha [deep] 5 times x)

= C [low] 2 times (sina [low] 5 times x - cosa [low] 5 times x + B [high] -a [low] s times x)

The equation is a determining equation for C [deep] 2 if the deflection by the piezo-oxide transducer is introduced at the point x = L / 2 with Co.

Co, in turn, is determined by the control voltage at the piezo oxide and its electrodynamic properties.

So that will

Gl. 20th

W (L / 2) = C [deep] 0 = C [deep] 2 times (sina [deep] 5 times L / 2 -cosa [deep] 5 L / 2 + B [high] -a [deep] 5 L / 2) = C [low] 2 times 8.5 times 10 [high] -4

which results

Gl. 21

C [low] 2 = C [low] 0 times 1.1764 times 10 [high] 3 and thus

Gl. 22nd

W (x) = C [low] 0 times 1.1764 times 10 [high] 3 times (sina [low] 5 times x - cosa [low] 5 times x + e [high] -a [low5s times x)

As can be seen in Figure 2, the area under the stretched vibrating rod is characterized by three positive maxima and two negative maxima or by two positive maxima and three negative maxima, depending on the phase position.

The integral over the position function W (x) in the two extreme oscillation states is thus, depending on the phase position, one time greater than "0" that is positive and one time less than "0" that is negative. The maximum change in area is therefore equal to twice the value of the integral over W (x).

Gl. 23

= C [low] 0 times 2.353 times 10 [high] 3 times 1 / a [low] 5

= C [low] 0 times 2.353 times 10 [high] 3 / 14.137 times L

in the concrete structure with L = 244mm

Gl. 24

A = C [deep] 0 by 4.06 by 10 [high] 4 mm

The piezo oxide used by Valvo, of the material type PXE 5 with a thickness of 3 mm, works practically mechanically unloaded on a high-resistance system in resonance and thus follows the equation

Gl. 25th

S = d times E [deep] 1 which describes the relationship between electrical and mechanical quantities.

"S" is the relative change in thickness C [deep] 0 / D,

"d" is the piezoelectric charge constant and

"E [deep] 1" is the electric field strength U / D

with the control voltage "U".

With d = 384 times 10 [high] -9 mm / V one can write

Gl. 26th

C [low] 0 / D = 384 times 10 [high] -9 mm / V times U / D

Gl. 27

C [low] 0 = 3.84 times 10 [high] -9 mm / V times U

"C [deep] 0" in equation Eq. 24 inserted and "U" replaced by U [deep] 0 times sin small omega [deep] 5 times t leads to

Gl. 28

A (t) = 3.84 times 10 [high] -9 mm / V 4.06 times 10 [high] 4 mm times U [deep] 0 times sin small omega [deep] 5 times t

= 1.559 times 10 [high] -2 mm [high] 2 / V times U [low] 0 times sin small omega [low] 5 times t

with a peak control voltage of approx. 300V, A (t) results in

Gl. 29

A (t) = 4.677 mm [high] 2 times sin small omega [deep] 5 times t

and

Gl. 30th

dA (t) / dt = 4.677 mm [high] 2 times small omega [deep] 5 times cos small omega [deep] 5 times t = 4.677 mm [high] 2 times 2 times small pi times 3028 [deep] [high] -1 times cos small omega [deep] 5 times t

= 8.9 times 10 [high] 4 times mm [high] 2 / s times cos small omega [deep] 5 times t

Gl. 30 in Eq. 3 inserted finally results in the

Oscillating frame induced voltage "e" which is proportional to the magnetic induction "B". "N" is implemented with 100 in the model structure.

Gl. 31

e = -N times B times dA (t) / dt = -100 times B times 8.9 times 10 [high] 4 mm [high] 2 / s times cos small omega [deep] 5 times t

= -B times 8.9 times 10 [high] 6 mm [high] 2 / s times cos small omega [deep] 5 times t

The magnetic field strength "H" is approximately near the earth

H [deep] earth = 15 A / m = 1.5 times 10 [high] -2 A / mm

The magnetic induction "B" and the field strength "H" are related by the equation

Gl. 32

B = µ [deep] r times µ [deep] 0 times H

where µ [deep] r for air = 1 and the field constant µ [deep] 0 is µ0 = 1.256 times 10 [high] -9 Vs / Amm

The quantities in Eq. 32 inserted result

Gl. 33

e = -1.256 times 10 [high] -9 Vs / Amm 1.5 times 10 [high] -2 A / mm times 8.9 times 10 [high] 6 mm [high] 2 / s times cos small omega [low ] 5 times t

= -1.68 times 10 [high] -4 V times cos small omega [low] s times t

i.e. a voltage of approx. 0.168 mV is generated when the magnetic field passes perpendicularly through the area spanned by the oscillating frame.

The induced voltage "e" is phase shifted by 90 ° with respect to the frame oscillation.

If the passage angle deviates by "small beta" from 90 °, the induction is effective

Gl. 34

B (small beta) = B times cos small beta

At Eq. 34 it can be seen that the generated voltage "e" including the sign is dependent on the projected quantity B (small beta), that is, it represents the vector "B".

The voltage "e", which is proportional to the vector "B", is amplified and demodulated synchronously so that relative output voltage values in the range -5V less than or equal to U less than or equal to 5V are generated in my model during earth field measurements. These voltages are suitable for automatic data processing with the aid of analog-digital converters.

It should be noted that, for example, a triangular oscillating frame, which is excited in the 3rd harmonic, works around a factor of 15 more effectively than the rectangular oscillating frame described above for the same area.

In conclusion, it must be said that the oscillating frame can also be operated in reverse operation.

For this purpose, an alternating voltage is applied to the coil, as a result of which an alternating magnetic field is generated in the vibrating frame, which now stimulates the vibrating frame to mechanical bending vibrations through its reaction (mutual inductance).

Claims (4)

1. Oscillating frame sensor for the vectorial measurement of magnetic fields, characterized in that a suitably shaped closed frame either made of non-ferrous metal or a non-conductive material is excited at a suitable point to mechanical resonance bending vibrations, which lead to the effective Area changes periodically, whereby a magnetic flux flowing vertically through the frame also experiences periodic changes, which leads to an alternating electrical voltage being induced on a stationary coil stretched either within the non-ferrous metal frame or on a co-oscillating coil attached to the non-conductive frame, which is induced by the magnetic Flux is proportional, oscillates with the frequency of the mechanical frame oscillation and whose voltage and phase position is used to identify the magnetic field. 2. The oscillating frame sensor according to claim 1, characterized in that the component which stimulates mechanical oscillations in the frame is a piezoelectric transducer which is either mechanically connected to the frame at a suitable point or which is created in the form of an integrated oscillator at the same time as the non-conductive frame is manufactured will. 3. oscillating frame sensor according to claim 1 and 2, characterized in that two or three each Frame arrangements oriented perpendicular to one another are mechanically excited at the same time. 4. Oscillating frame sensor according to 1 and 2, characterized in that in a reversal of action, the oscillating frame generates an alternating magnetic field by applying an alternating voltage oscillating with the frame resonance frequency, the reaction of which in turn causes the frame to resonate flexural vibrations and is detectable in the complex electrical input resistance at the coil is.