DE19748294A1 - Device for measuring the rotation with a vibrating, mechanical resonator - Google Patents

Abstract

A mechanical resonator 10 provided with transducers 15 1 and 15 2 enables an axially-symmetrical standing wave to be set up in the resonator. The apparatus also comprises sensors 16 for measuring the elongation of the resonator vibration in at least two particular directions and a monitoring and control circuit 12 for sustaining the vibrations and for detemining the locations of the vibration nodes and anti-nodes. The monitoring and control circuit powers the transducers to generate two contra-rotating travelling waves in the resonator with the phase difference between them being representative of the angle of rotation of the resonator about its axis of revolution. The amplitudes of the waves are such that when combined they give rise to a standing wave of determined in-phase amplitude and of quadrature amplitude that is substantially zero. The apparatus can be applied to any form of resonator e.g. a disk or a bowl.

Description

The present invention relates in general to devices for measurement of ro with:

• - a mechanical element called a resonator, which has an axial Has symmetry, the axis of which is the sensitive axis of the device and that is able to vibrate in a mechanical resonance,
• - Transducers that are sensitive to the deflection of the vibration of the Elements in at least two specific directions,
• - and transducers for applying forces to the resonator in the two certain directions, especially the control of vibration to serve.

A number of devices with resonators of this type already exist, d. H. that vibrate; they use the Coriolis acceleration, which is due to a vibrie element works when its body rotates. The Coriolis Acceleration becomes perpendicular to the rotational speed as well as to the Vi direction and it has a modifying effect on the alignment  of the vibration network, proportional to the rotation of the element around the sensitive che axis.

Such devices use resonators that are pronounced under can take different forms. The resonator can be annular Have structure; it can be made from a circular or square plate det be; it can take the form of a shell attached to the floor, the Transducers and transducers are distributed around the edge of the shell; he may also include an array of four vibrating carriers, each because are distributed around the angles of a rectangle (EP-A-0 578 519).

It has also been known since at least 1923 that a stationary shaft can be viewed in a resonator with an axial symmetry, such as. B. the Compilation of two contrarotative progressive waves from the same waves length. This option is used in optical gyrometers with rings (laser Gyrometer) implemented. The two contrarotative waves can change their phase when the resonator rotates around its sensitive axis.

Likewise, this compilation was suggested in the case of Pre to use directions that have an annular resonator (EP-A-609 929) or with a corrugated cylindrical surface (US-A-4,384,409). The provided However, devices still make circuits necessary Carry out complex calculations and / or a large number of converters.

Similarly to this day, these calculations and the arrangement All transducers and transducers can be connected to a single type of Resona gate adjusted. For example, the resonator with a ring, the subject of EP-A-609 929, which has already been cited, is replaced by transducers speaking the particular directions, relative to the directions of the recording mer controlled, for a vibration mode in which n 2 corresponds to what the Ver  use of the control electronics of the resonator for another Vibra mode or for another type of resonator.

The invention aims in particular to circumvent these disadvantages.

It is known that in the case of a mechanical resonance of any resonator, there is the possibility of analytically representing the vibration field on a basis that has two separate reference modes. The vibration can be described by the following system of equations:

Equation 1

the solution of which is a description of the vibration.
In these equations:

η _i (with i = 1 or 2): coordinates in the plane of the eigenmodes,
ξ _i : coefficients of reduced modal amortization,
m _i : modal masses,
ω _i : self-pulsations,
α _i : coefficients of the gyroscopic coupling,
Ω _{w / i} : inertial rotation speed of the resonator,
f _i : generalized forces.

These relations are used by arranging the transducers and transducers in a way that:  

• the transducers emit the components of the two vibrations according to the axes η ₁ and η ₂ ,
• - The transducers allow the application of the forces f ₁ and f ₂ along the same axes.

The position and number of transducers and transducers, which depends on the shape of the resonator and their connection, always makes it possible to obtain the outputs η ₁ and η ₂ and to allow the inputs f ₁ and f _{2 in} accordance with FIG. 1 and to use the control / control electronics, as proposed in this figure, which remains independent of the shape of the resonator and which, moreover, does not require any adaptation to the frequency of the resonance used.

It is found that the axes η ₁ and η ₂ mechanically form an angle corresponding to π / 2n, where n is an integer greater than or equal to 1. For example, for a circle that deforms into an ellipse, n = 2 and the two natural waves form an angle of π / 4 = 45 °.

The invention uses these principles and equations for the first time to be able to provide an electronic module that is considered universal can qualify, which is the control of mechanical resonators with any kind of axial symmetry according to all common vibration modes allowed to move an angle or a rotational speed according to their emp deliver sensitive axis.

A universal module is a module that you do not have to modify, if you change the mode or the resonator, only the transducers and transducers have to be adapted to what their starting or Sensitivity level and their positions with respect to the resonator according to the mechanical frame of reference that corresponds to the chosen resonance mode corresponds.  

The present invention also provides an apparatus for measuring the Rotation of the type defined above, which requires the use of only one minimal number of transducers and transducers and a relatively simple one Allows electronics that can be completely analog. In line with this goal the invention proposes a device according to claim 1.

Thanks to maintaining the amplitude in phase with a particular he aimed at value, for example by regulating the energy of the contra rotative waves as well as thanks to the cancellation of the quadratic amplitude possible to use a relatively reduced number of converters. The brisk can be ensured by using only those without difficulty in the Form of a wired circuit implementable elements of the comp used without a microprocessor, in particular because the comp trigonometric functions is only optional.

The device can easily be made to be a gyro as well skop or a gyrometer can form. For use as a gyrometer the stationary shaft held in place by a forced precision sion is provoked. In case of use as a gyroscope they are for the Function as a gyrometer is not necessary for certain means, but they allow performing periodic calibration for increased precision.

The above characteristics as well as going beyond result in particular ser from the following description of a preferred embodiment, which is exemplary and not limiting. The description refers to the accompanying drawings, in which:

Fig. 1 is a synoptic diagram, determined to represent the control / control mode of the device with a universal module;

Fig. 1A is a schematic diagram illustrating a possible distribution of the transducers on a resonator with circular periphery at rest, the connections of the transducers and transducers with a circuit for measurement and excitation, and a network of stationary waves, which in the resonator according to a mode second Order was provoked;

FIG. 2 shows a representation of the vibration of a point of the resonator of FIG. 1, in a reference system η ₁ , η ₂ , which corresponds to the mode;

Fig. 3 is a synoptic of the measuring means of the phase shift and the cancellation of the phase shift, can be used for the implementation of the invention;

Fig. 4 is a synoptic, which shows the operators that can be used to maintain the amplitude of the contrarotative waves in a resonator;

Figure 5 is a synoptic of usable operators to generate a re presentative signal of anzuwen to provoke a precision Denden forces.

Fig. 6 is a synoptic of the entire electronics of a device for measuring the rotation according to the invention, which can work as a gyrometer or gyro scope.

Before a detailed description of the implementation of the invention, it seems useful to realize that the network of the nth order stationary waves (second order in the given example) can be broken down into two progressive waves. In the case of an annular resonator, the rotation tends to drive the network of stationary waves when the resonator rotates about its axis. This leads to the fact that the two progressive waves, which allow a re-composition of the stationary wave, have a frequency difference ω ₁ -ω ₂ , which corresponds to the rotational speed Ω, and a phase difference, which speaks to the angle of rotation starting from an origin.

The invention uses this fact by connecting transducers to measure the extension of the resonator at several locations around the axis and transducers to generate forces to compensate for the damping with electronics that emit two output signals with frequencies whose difference in rotational speed corresponds (and whose phase difference corresponds to the angle) and which supplies the transducers in such a way that these forces are generated which:

• - keep the amplitude of the vibration in phase with a constant value;
• - cancel the component that is out of phase by 10 °.

The mechanical resonator can have very different configurations. By way of example, FIG. 1A shows a resonator 10 , which in particular can have the shape of a disk or a shell made of a material, so that the resonator has low losses. In the idle state, the resonator is circular or has a structure which mechanically corresponds to a circular area, as shown in FIG. 1 in a solid line. When the resonator vibrates in its second order mode, it takes on the two extreme forms shown in broken line and greatly enlarged scale in Fig. 1A when excited by an electronic circuit 12 to its resonant frequency which is in opposite phase supplies two transducers 14 , which are arranged offset from one another by 90 °. In practice, each converter 14 is supplied with a parallel converter, which is not shown for the sake of simplicity. Two other pairs of electrodes 15 ₁ , 15 ₂ are arranged at 45 ° with respect to the aforementioned in the reference system of the modes.

The radial offset is measured in the described case at the same Winkelanord in which the transducers are arranged. For this purpose, for example, two pairs of transducers 16 (only the connections of a single transducer are shown) allow a measurement of the amplitude of the vibration and make it possible to supply the electronic circuit 12 with the signals of the measurement. The circuitry is provided to power the transducers in a manner to maintain a constant amplitude of vibration, as will be seen later.

These indications as well as the following would be equally valid for everyone in Vibra tion offset resonators according to a mode of order ≧ 1, the An order of the transducer and the transducer is slightly modified.

The same device 12 can therefore also be used for a resonator with four parallel, vibrating carriers, such as. B. described in the document EP-A-0 578 519, which has already been mentioned.

When the container holding the resonator rotates at a certain angle by the arrow Ω, the vibration field tends to shift under the influence of the Coriolis forces, and the vibration node 18 also shifts if not is counteracted by the action of an electronic circuit 12 and at the moment t, for example, assumes an angle Θ. This angle is proportional to the rotation which the container is subject to, with a constant ratio which is ≦ 1, depending on the type of resonator.

Depending on the type of mechanical resonator, provided that it has a stationary vibration mode with at least order 1, the offset of a point M in the reference system of modes η ₁ , η _{2 can be represented} by the diagram in FIG. 2. The offset of a movable point M can be represented in the parametric form given above. In the following, the formulas are developed using the following notations:

η ₁ and η ₂ : reference axes and coordinates in the reference system,
ω angular frequency of vibration of the resonator,
Ω rotation speed of the container,
α shape coefficient, <1.
f ₁ and f ₂ : Along the axes η ₁ and η ₂ , forces applied, primarily intended to compensate for the losses and to correct the anisotropy of the frequency, and in the second line never to change the function mode and to correct the function through use stored error models,
M: moving point representing the state of vibration,
ω ₁ and ω ₂ : angular frequencies of the two progressive waves, resulting from the decomposition of the stationary wave with the angular frequency ω.
Θ: inclination of the main axis of the ellipse, which corresponds to the vibration in the plane of the modes, in the reference axes η ₁ and η ₂ , connected to the container of the resonator,
or: a vector representing the movable point M at the marking η ₁ , η ₂ ,
2a and 2b: major and minor axes of the ellipse corresponding to the vibration,
VCO ₁ and VCO ₂ : voltage controlled oscillators operating at frequencies ω ₁ and ω ₂ ,
₁ and ₂ : vectors with the respective modules r ₁ and r ₂ , which rotate at the frequencies ω ₁ and ω ₂ ,
ft ₁ and ft ₂ : tangential forces acting on the resonator to drive the amplitudes in phase with a constant value,
for ₁ and for ₂ : radial forces which are exerted on the resonator in order to remove the amplitudes which are phase-shifted by 90 °,
Ω: rotational speed of the resonator container,
Ω _p : precession speed, corresponds to (ω ₁ and ω ₂ ) / 2,
C _p : control signal of precession.

Fig. 2 shows the rotational speed Ω of the container, which carries the Reso nator, with the effect of rotating the vibration field and the main axis 2 a of the ellipse, which represents the movement of the point, for example, to rotate an angle Θ . For the functioning of the gyroscope, the angle through which the container of the resonator is rotated is deduced from a measurement of Θ by using a scale factor α, which is dependent on the resonator and the order of the mode.

FIG. 2 shows the vibration in the form of an ellipse, which has a main axis of the value 2a and a small axis of the value 2b. The variations of the coordinates η ₁ and η _{2 of} a movable point M as a function of time can be as follows:

η ₁ = a cos ωt cos Θ - b sin ωt sin Θ
η ₂ = a cos ωt cos Θ + b sin ωt sin Θ.

The component of the vibration with the amplitude b, which is also called the quadrature of the Space, the appearance of parasitic waste provokes vibration field, which determines the quality of the measurements during the work of the Gyroscopes worsen.  

According to the invention, two controls are provided for driving the vibration in all cases for:

• - maintaining the amplitude a (or a ² + b ² , ie the energy) by compensating for the losses;
• - Reduction of the square of space b to zero.

In addition, a third control is necessary for the functioning of the gyrometer or for calibration:

• - an external precision controller to make the axis of the vibration rotate at a precision speed Ω _p , which is defined below.

To break it down into two progressive waves of different frequencies
To enable ω ₁ and ω ₂ , it should be noted that the vector can be regarded as the result of ₁ + ₂ , where the vector _{1 of} the beam r ₁ = (a - b) / 2 rotates at the speed + ω and where the vector _{2 of} the beam r ₂ = (a - b) / 2 rotates at the speed -ω when the container is stationary.

If the container is rotated at a speed of Ω, the speeds of vectors ₁ and _{2 are} corresponding to ω ₁ = ω - Ω and ω ₂ = ω + Ω.

The vibration can be driven by the control of two oscillators, each of which provides two alternative square signals in a way that their outputs, which are applied to the electrons, form two vectors with the frequencies ω ₁ and ω ₂ turn. Vectors ₁ and ₂ represent the outputs of the two controlled oscillators VCO ₁ and VCO ₂ , which have to be controlled in positions ₁ and ₂ . This implies measuring or calculating the phase shift between ₁ and ₁ and between ₂ and ₂ .

Measurement and cancellation of the phase shift

To measure the phase shift, it is suggested to use the peculiarity of the vectorial product to be zero when the two vectors are aligned. In the case of the vector V ₁ :

₁ ∧ = ₁ ∧ ( ₁ + ₂ )
= ₁ ∧ ₁ + ₁ ∧ ₂ .

The expression ₁ ∧ ₂ results in a signal 0 after filtering, since the vectors ₁ and ₂ rotate in the opposite direction, from which:

₁ ∧ = sin ( ₁ , _2. ) = Arg ( ₁ , ₁ )) = ξ ₁ , with ξ ₁ as an error signal, or:

₁ ∧ = η ₂ . cosω ₁ t - η ₁ . sinω ₁ t.

Under the condition of using the oscillators, which provide square-wave signals of amplitude 1 , the multiplication is simply carried out with the aid of the multipliers with +1 and -1 and an addition unit which, if the signals are analog, can be an operational amplifier. An identical compilation is used for the second way.

As a consequence, the means for measuring the phase shift and the cancellation of the phase shift can be those shown in FIG. 3. The input η ₂ denotes the totality of the signals that represent the vector = ₁ + ₂ .

The components 20 ₁ and 20 ₂ , which form the vectorial products, due to the multiplication of the input values, alternatively by +1 or -1, and the additions, follow a filtering. The error signals ε1 and ε2 are again applied to VCO ₁ and VCO ₂ .

This gives two outputs 22 ₁ and 22 ₂ , the phases of which are controlled by two vectors ₁ and ₂ , which form the elliptical vibration and whose phase shift corresponds to 2versch.

Measurement and regulation of the amplitude of the two waves

The amplitude of each of the two contrarotative waves is carried out by forming a scalar product instead of a vectorial product. One can use two operators 24 ₁ and 24 ₂ as shown in FIG. 4.

The algebraic equation remains a type with two multiplications of real size and an addition, the two modulators and an algebraic addition makes necessary.

If you assume that VCO ₁ and VCO _{2 provide} amplitude signals equal to 1, you have for 24 ₁ :

_1st = ₁ . ( ₁ + ₂ )
= ₁ . ₁ + ₁ . _2nd
= r ₁ . cos ( ₁ , ₁ ) + r ₂ cos ( ₁ , ₂ ).

After filtering, the result is r ₁ ; r ₂ is obtained in the same way; one therefore plans:

• two components η ₁ and η _{2 of} the vector,
• - two components of the rotating vectors ₁ and ₂ twice.

One can therefore keep the amplitude of each of the contrarotative waves at an instruction value by sending the normal driving forces f _t to the vectors, ie tangents to the circular paths. The compensation forces must be equal to the amortization forces and be opposed to them, which are induced by the speed vector.

The principle of the control is shown in Fig. 4. The values r ₁ and r ₂ are introduced into the adders 26 ₁ and 26 ₂ and compared with the instructions r ₀₁ and 2 ₀₂ . The outputs of the adders are amplified with an input k at 28 ₁ and 28 ₂ and sent to the multipliers 30 ₁ and 30 ₂ , which perform simple multiplications. The rotation of vectors ₁ and ₂ , which were previously sent to the multipliers, is carried out in 32 ₁ and 32 ₂ by a simple inversion of the coordinates and possibly by changing the sign.

Removal of the quadrature

This lifting is easy. It is sufficient to give the same value r ₀ to the instructions r ₀₁ and r ₀₂ to control the two amplitudes. The effect is b = r ₁ - r ₂ .

Precession control

Controlling the precession is necessary for functioning as a gyrometer and / or for calibration. For this purpose, a precession Ω _{p of} the gyroscope is created and:

• - The speed ω _{1 is increased} by ₁ by Ω _p
• - Reduces the speed ω ₂ of ₂ by the same amount Ω _p because:
  Θ = + Ω _p . t
  ω ₁ = ω + Ω _p
  ω ₂ = ω - Ω _p .

For this purpose, a force f _{r is} introduced that is normal to the path and therefore performs zero parallel to the vector R and a work.

The tangential velocity v corresponds to ω. r. It can be seen that the Coriolis formula is obtained in this way:

f _p = 2 m. Ω _p ωr

with m = k / ω ²

The precession forces, which are parallel to vectors ₁ and ₂ , are obtained by simply multiplying vectors ₂ or ₂ by a scalar C _p , which results in a modulation; the additions to be added to the outputs of multipliers 30 ₁ and 30 ₂ of FIG. 4 can be generated by operators of the type shown in FIG. 5. The multipliers 34 ₁ and 34 ₂ receive the external precession control C _p .

If one arranges the vectors ₁ and ₂ , one can deduce the sin 2θ and cos 2θ from it, by a vector product of the vectors ₂ ∧ ₁ = sin 2θ and a scalar product ₂ . ₁ = cos 2θ.

The global schematic of the circuit may be that shown in Fig. 6, where the elements already described have the same reference numerals.

In the overview in FIG. 6, the paths of the analog signals are indicated by simple solid lines. The numerical signals coded in n-bits are indexed by the lines bearing the number of bits. The double lines finally indicate the orbits of the pairs of values that represent a vector, such as. B. ₁ , ₂ etc.

In Fig. 6, the means already shown in Fig. 3 can be found, which serve the measurement and maintenance of the vibration amplitude and which receive the outputs of the added or subtracted transducers 16 in addition to the input signals, depending on their relative position. The interconnection of the VCO includes a numbering circuit. By composition of the thus obtained digital signals can be ten the value of 2Θ preserver in a Additionator 36, wherein Θ is given by a simple shift bits.

The energy level of the vibration is adjustable by the introduction of an instruction value r ₀ by an external control in the adders 26 ₁ and 26 ₂ . This instruction value is chosen as a function of the mechanical characteristics of the resonator.

The components for ₁ and ft ₁ are combined in a double addition 46 ₁ . The same components for ₂ and ft ₂ are combined in 46 ₂ . The combination of the values of the resulting forces is carried out in an adder 50 , which divides them into the signals f ₁ and f ₂ , which correspond to the forces to be exerted on the transducers 14 and 15 .

FIG. 6 also shows an operator 38 ₁ for calculating sin 2θ by a vector product of ₁ and ₂ and an operator 28 ₂ for calculating cos 2θ by a scalar product of vectors ₁ and ₂ .

Finally, the device shown in FIG. 6 comprises devices for generating the resonance frequency F ₀ , starting from vectors ₁ and ₂ . These directions comprise two multipliers 40 ₁ and 40 ₂ . The multiplier 40 ₁ receives the signals corresponding to the vector ₂ and a signal of an individual component of the interconnection formed by the vector multiplier 42 and a amplifier 44 . The vectorial multiplier receives the output of the two multipliers 40 ₁ and 40 ₂ , the latter being symmetrical about 40 ₁ .

Claims (7)

1. Device for measuring the rotation about a sensitive axis, with a mechanical resonator, which is equipped with transducers that allow the generation of a stationary vibration wave in the resonator and are arranged axially symmetrically, and with sensors for measuring the extension of the vibration of the resonator in at least two determined directions and with a control / control circuit for driving the vibrations and for determining the arrangement of the nodes and expansion of the vibration around the axis, characterized in that the control / control circuit comprises devices for supplying the transducers , To generate two pro gressive contrarotative waves in the resonator, the phase difference of which corresponds to the angle of rotation of the resonator about its axis of rotation and the amplitudes are such that their composition provokes a stationary wave, which has a certain amplitude in phase and a phase-shifted amplitude e, which is essentially zero. 2. Device according to claim 1, characterized in that it at least least a pair of transducers and at least a pair of transducers summarizes, which are distributed by uniform angles to a network of stationary Generate waves with an order n greater than or equal to 1. 3. Apparatus according to claim 1 or 2, characterized in that the control circuit comprises means for measuring the cancellation of the phase shift, with two oscillators (VCO ₁ , VCO ₂ ) which are voltage-controlled and provide square-wave signals of a uniform amplitude as well as vectorial multipliers ( 20 ₁ , 20 ₂ ), each providing the product of the output of a respective oscillator and a cor responding signal from the pickups, the output being present at the input of the control of the oscillator. 4. The device according to claim 3, characterized in that the control / control circuit comprises means for measuring the amplitude of the two waves and for maintaining the same at the same instruction value (r ₀ ), with addition units ( 26 ₁ , 26 ₁ ) record the instruction value at an addition input and the scalar product of the signal emitted by the transducers and the output of the corresponding controlled oscillator at the other input, which corresponds to the real amplitude. 5. The device according to claim 4, characterized in that the outputs from the addition unit to the multipliers ( 30 ₁ , 30 ₂ ) given who, and a multiplication of the outputs of the oscillators, shifted by 90 °, by simple inversion of the coordinates and possibly by changing the sign. 6. Device according to one of the preceding claims, characterized ge indicates that the circuit additionally controls the precession force with regard to operation as a gyrometer sums up. 7. The device according to claim 6, characterized in that the devices for controlling the precession multipliers ( 34 ₁ , 34 ₂ ) of the outputs of the respective oscillators by a scalar C _p , corresponding to the precision.