FIELD OF THE INVENTION
The present invention relates to a micromechanical motion sensor capable of detecting a deflection imparted to an oscillatably mounted bar spring element excited to permanent periodic oscillation by an electrostatic oscillating drive to which a periodic drive voltage is applied. Such a micromechanical motion sensor which uses bar springs and comb drives among other things is described in U.S. Pat. No. 5,025,346.
BACKGROUND INFORMATION
Bar springs exhibit non-linear effects when subjected to high deflections. In a yaw rate sensor manufactured by the applicant (Robert Bosch GmbH model MM2R), a rotor is suspended in its center of rotation on an X spring (see appended FIG. 3). This non-linear effect is clearly detectable even for deflections as small as ±4°. It is manifested in a shift of the resonance frequency of the system. In addition, areas exhibiting a plurality of stable operating states may appear as a result of the non-linearity. If a sudden transition occurs between the stable states during operation due to minor interference, for example, the performance of the yaw rate sensor may be considerably impaired.
In the yaw rate sensor (model MM2R) manufactured by the present Applicant and schematically illustrated in FIG. 3, due to a centrally mounted X spring 2, the bar spring element has a centrally mounted and centrally symmetric flywheel mass 1 which is excited to a periodic rotary oscillation in a lateral plane x, y having positive and negative deflections i, a of the same magnitude about a rest position O (angle γ designates the deflection angle in positive direction i) by symmetrically acting comb drives. A first comb drive pair has two comb drive units KI1 and KA1 opposite one another, which act upon a first drive point P1 situated on a circular arc-shaped peripheral segment of flywheel mass 1. These two first comb drive units KI1 and KA1, which are provided for a deflection in positive direction i and negative direction a, respectively, are situated parallel to a an imaginary straight line connecting the center of X spring 2 to the rest position of flywheel mass 1. A second pair of comb drive units KI2, KA2 for positive deflections i and negative deflections a, respectively, situated centrally symmetrically to the first pair of comb drive units KI1, KA, acts upon a second point of application P2 diametrically opposite first point of application P1 on flywheel mass 1. The latter two comb drive units KI2 and KA2 are situated parallel to an imaginary straight line connecting the center of flywheel mass 1 to point O denoting the rest position.
A control unit 3 generates drive voltages UPKI,drive and UPKA,drive for comb drive units KI1 and KI2 (for excitation in positive deflection direction i) and for comb drive units KA1 and KA2 (for excitation in negative deflection direction a), respectively, as shown in appended FIG. 4. FIG. 4 shows in top part A the periodic and, in the ideal case, harmonic excitation function γ(t) of flywheel mass 1 in positive direction i and negative direction a, which has the period 2π.
In center FIG. 4B, a dashed line shows the square pulse-shaped drive voltage UPKA,drive for comb drive units KA1 and KA2 for deflection in negative direction a, while bottom FIG. 4C shows drive voltage UPKI,drive for comb drive units KI1, KI2 for positive deflection in phase opposition to drive voltage UPKA,drive, the positive deflection also having square pulses having the periodicity of periodic excitation oscillation γ(t) shown in FIG. 4A.
In addition, FIG. 4 shows that the pulses of drive voltage UPKA,drive for positive deflection i according to FIG. 4C are generated symmetrically to the positive zero crossings of periodic oscillation γ(t) of flywheel mass 1, while the pulses of drive voltage UPKA,drive for negative deflection i according to FIG. 4B are generated symmetrically to the negative zero crossings of periodic excitation oscillation γ(t) according to FIG. 4A. Since the comb drive units (KI and KA) schematically shown in FIG. 3 are each able to exert a force in one direction only, a plurality of comb drive units are needed to set the rotor in an oscillating motion.
For practical reasons, a square-wave voltage is generated for the drive voltage applied by control unit 3 instead of the sinus curve. This is accomplishable using a control logic and a voltage pump in control unit 3. In principle, a voltage pump is made up of a capacitor which is charged. This allows higher voltages than the operating voltage to be generated for a short period. This voltage is used if needed.
The non-linear bending of the bar is describable using Duffing's differential equation. Since this is a known differential equation, a detailed analysis of the dynamic properties is not necessary. Instead, the two main effects (frequency shift and instability) are briefly explained with reference to appended FIGS. 1 and 2. The mechanical non-linearity of the X spring may be described using Duffing's differential equation
Mdrive=Jzγ+bt,zγ+ktz,0·(1+ktz,NLγ2)γ (1)
or
Mdrive=Jz·γ+bt,zγ+ktz,0·γ+ktz,0ktz,NLγ3 (2)
The parameters are determined via the appropriate finite-element computations.
As can be seen from equation (2), this is a second-order differential equation for oscillation, having linear attenuation term bt,z (velocity-proportional attenuation). γ denotes the angle describing the deflection of the rotor. The only difference with respect to the “standard differential equation for oscillation” is additional non-linear term ktz,0ktz,NLγ3. Term ktz,0 is the linear spring constant (torsion). Term ktz,NL describes the non-linearity. Jz denotes the moment of inertia of the rotor about the z axis. The rotor oscillation is excited via drive moment Mdrive.
Appended FIG. 1 shows the resonance curve of the gain in the linear case with attenuation. The gain factor attains its maximum at the exact moment when the system is excited by its intrinsic frequency. In the non-linear case, the maximum of the resonance curve is shifted to the right. As can be seen from appended FIG. 2, the resonance curve tends additionally to the right. The one-to-one correspondence between gain and excitation frequency is thus lost. The gain in each individual case depends on the previous history. For example, in the case of a smooth increase in the excitation frequency, there is a slow transition from area I to area II and thus to point 1 in FIG. 2. In the case of supercritical excitation and a slower reduction in the drive frequency, the operating state migrates from area III to point 2 in area II. This makes two different states possible for one drive frequency. In general, this is an undesirable effect, because, for example, interference pulses may cause a sudden transition from point 1 to point 2. The risk of a sudden change exists in the entire area II (shaded in FIG. 2).
Only the basic analytical equation in principle is given here as the operating principle of comb drives:
Fs≈ε0ΔU2(h/d0) (3)
The following relationships are discernible from equation 3:
- The greater voltage difference (ΔU) on the capacitor plates of the comb drive, the greater drive force Fx.
- The greater height h of the comb drive structure, the greater drive force Fx.
- The smaller distance do between the capacitor plates of the comb drive, the greater drive force Fx.
These are only the basic relationships. Detailed examination shows that the force is caused by the formation of stray fields. Therefore, in a more accurate analysis, the field lines must be used for computing the force. For more complex geometries, the relationships may be determined using finite element computations.
SUMMARY OF THE INVENTION
As explained previously, the object of the present invention is to avoid the above-described problems in a micromechanical motion sensor, in particular in a yaw rate sensor equipped with comb drive units or in a linear oscillator due to mechanical non-linearity, and to provide such a micromechanical motion sensor in which non-linearities are compensated.
According to an essential aspect, a micromechanical motion sensor for achieving this object according to the present invention is characterized in that electrostatic compensation drive means acting upon the bar spring element are provided, to which a suitable periodic compensation voltage is applied to compensate the non-linearity of the resonance frequency response of the bar spring element.
If such a micromechanical motion sensor is configured as a yaw rate sensor on the basis of the aforementioned basic structure of the yaw rate sensor manufactured by the present Applicant, the bar spring element has a centrally symmetric flywheel mass (rotor) which is centrally mounted with the help of a centrally situated X spring and is excited by the oscillation drive to a rotary oscillation in a lateral X-Y plane for positive and negative deflections of the same magnitude about a rest position; the oscillation drive has at least one comb drive unit controlled by a control unit using the periodic drive voltage for exciting the flywheel mass for positive and negative deflections, whose drive forces act upon the flywheel mass tangentially at at least one first point of application situated in the same X-Y plane in such a way that they excite, i.e., drive the flywheel mass symmetrically about its rest position; and the compensation drive means have at least one comb drive unit for compensating the non-linearities in the positive and negative deflection directions, which acts upon the same point of application and/or upon a second point of application situated diametrically opposite thereto at the same distance from the center of the flywheel mass.
In one embodiment, the compensation comb drive units may be identical to at least one of the pairs of comb drive units. In another embodiment, at least one additional pair of compensation comb drive units are provided for compensation in addition to the comb drive units used for normal excitation.
If a micromechanical motion sensor of this type is configured as a linear oscillator, the bar spring element has a system of a plurality of flywheel masses connected by a centrally situated coupling spring and mounted by a symmetric spring suspension so it is able to perform linear oscillations, the system being excited by the oscillation drive to a linear oscillation in a lateral plane with positive and negative deflections of the same magnitude about a central rest position; for exciting the flywheel mass system in the positive and negative deflection directions, the oscillation drive has at least one comb drive unit controlled by a control unit, the drive forces of the comb drive unit acting upon the flywheel mass system at a plurality of points of application situated in the same lateral plane and opposite one another on each flywheel mass of the system in such a way that they excite the flywheel masses of the system about their respective rest positions; and the compensation drive means have for each flywheel mass of the system at least one comb drive unit which acts upon at least one of the points of application of each flywheel mass.
Due to the use proposed according to the present invention of comb drive units for compensating the non-linearity, the overall structure made up of bar spring element and comb drive units has a linear characteristic. This eliminates the above-described problems possibly caused by non-linearities.
The above and additional advantageous features of a micromechanical motion sensor according to the present invention, in particular of a yaw rate sensor and a linear oscillator, are elucidated in more detail in the subsequent description of preferred exemplary embodiments with reference to the drawing.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 graphically shows the frequency response of the gain (resonance curve) in the linear case with attenuation.
FIG. 2 graphically shows the frequency response of the gain in the non-linear case in which, as explained above, the maximum of the resonance curve tends to the right.
FIG. 3 shows a schematic top view of the above-described yaw rate sensor configured as a micromechanical motion sensor and indicates at the same time a first exemplary embodiment of the yaw rate sensor (compensated) according to the present invention.
FIGS. 4A, B, and C, respectively, graphically show the idealized oscillation curve of the centrally mounted flywheel mass according to FIG. 3, the drive voltage for the comb drive unit for the negative deflection direction, and the drive voltage for the comb drive units for the positive deflection direction as generated by the control unit according to FIG. 3.
FIG. 5 shows a schematic top view of a second exemplary embodiment according to the present invention, in which additional compensation comb drive units are provided for compensating the non-linearity.
FIGS. 6A-6F graphically show, in addition to the time diagrams according to FIGS. 6A, 6B, and 6C already shown in FIGS. 4A-4C, an oscillation curve of a compensation voltage signal for negative deflection (FIG. 6D), an oscillation curve of a compensation voltage signal for positive deflection (FIG. 6E), and in FIG. 6F a sum of the respective drive voltage signals and the corresponding compensation voltage signal.
FIG. 7 shows a schematic top view of a third exemplary embodiment of a micromechanical motion sensor according to the present invention in the form of a linear oscillator in which additional compensation comb drive units are provided for compensating the non-linearity.
DETAILED DESCRIPTION
To compensate for the mechanical non-linearity of the bending bar, in addition to the previous drive signal (see FIG. 4), a compensation voltage is applied to the comb drive, which accurately compensates for the non-linear term of differential equation 2. It must be kept in mind that comb drives are able to apply forces in one direction only due to their operating principle. Thus, in the case of a positive deflection i, comb drive KA is responsible for the compensation, and in the case of negative deflection a, it is comb drive KI.
The compensation voltage curve results from the analytical relationships for the yaw rate sensor. The moment to be compensated results from equation 2.
Mcomp=ktz,0ktzNLγ3 (4)
If this moment is to be applied via the available comb drives (KI1, KI2 and KA1, KA2), the following equation results:
where Kstray is a correction factor for taking into account stray field effects; ncomb is the number of combs, and reff is the resulting effective radius for calculating the drive moment. UPCM denotes the common reference potential of all comb drives.
Equation 5 may be solved for voltage UUKI (voltage applied to comb drive units KI1, KI2) or UPKA (voltage applied to comb drive units KA1, KA2), to obtain the compensation voltage
Adding drive voltage UPKI, PKA,drive (see FIG. 4) and compensation voltage UPKI, PKA,comp computed in equation 6 yields the ideal voltage curve applied to comb drives UPKI,PKA,tot. In practical applications, this curve must be approximated by a stepped graph.
Thus, in a first exemplary embodiment, total voltage UPKA,tot and UPKI,tot according to FIG. 6F, formed from the sum of the respective drive voltages UPKA,drive and UPKI,drive (FIGS. 6B and C) and the respective compensation voltages UPKA,comp and UPKI,comp according to FIGS. 6D and E, are supplied to the respective comb drive units KA1, KA2 and KI1, KI2 according to FIG. 3 to compensate the non-linearity. To do so, control unit 3 generates the total voltages UPKA,tot and UPKI,tot shown, respectively, in FIG. 6F in dashed and solid lines (indicated with dashed lines in FIG. 3) and applies them to corresponding comb drive units KA1, KA2 and KI1, KI2.
In the exemplary embodiment of a yaw rate sensor according to the present invention shown in FIG. 3, the oscillation drive has four comb drive units KA1, KA2 and KI1, KI2, of which a first and second comb drive unit for positive i and negative a deflection form a first pair (KI1, KA1), which has a first shared point of application P1 on flywheel mass 1. A third and fourth comb drive unit KI1 and KA2 form a second pair, which act upon the opposite shared point of application on the flywheel mass. The two comb drive units KI1, KA1 and KI2, KA2 are situated opposite one another, parallel to an imaginary line which defines rest position O of flywheel mass 1 and passes through the center of the very flywheel mass. In this way, the drive forces of the comb drive units for positive deflection i and the drive forces of the comb drive units for negative deflection a are added up.
According to parts B and C of FIGS. 4 and 6, drive voltage signals UPKA,drive and UPKI,drive generated by control unit 3 are square voltage pulses in phase opposition; control unit 3 generates square voltage pulses UPKI,drive for positive deflection i symmetrically to the positive zero crossings of oscillation curve γ(t) shown in FIG. 4A and square voltage pulses UPKA,drive for comb drive units KA1 and KA2 for negative deflection symmetrically to the negative zero crossings of oscillation curve γ(t).
Compensation voltage signals UPKA,comp and UPKI,comp according to FIGS. 6D and 6E, generated by control unit 3, are also in phase opposition with respect to one another but are symmetric to the deflection maximums in the positive and negative deflection directions, respectively, of oscillation curve γ(t). Thus, compensation voltage signal UPKA,comp for negative deflection is delayed by 90° (π/2) with respect to drive voltage signal UPKI,drive for positive deflection, and compensation voltage signal UPKI,comp according to FIG. 6E is also delayed by 90° (π/2) with respect to drive voltage signal UPKA,drive.
To check the practical suitability of a yaw rate sensor compensated as described above, the above equation 6 may be converted into a simulation model using Simulink standard blocks. This simulation model calculates the resulting total voltage from the input signals:
- deflection angle γ of flywheel mass 1,
- reference potential UPCM, and
- drive voltage UPKI,drive, UPKA,drive.
The simulation results have shown that, in order to achieve sufficient compensation of the non-linearity, the total voltages on the comb drive units shown in FIG. 6F and indicated as dashed lines in FIG. 3 must assume a very high voltage level at which conventional comb drive units no longer operate. The recognition of this fact resulted in the second exemplary embodiment shown in FIG. 5, which, in addition to the four comb drive units KI1, KI2 and KA1, KA2 shown in FIG. 3, has four compensation comb drive units KIK1, KIK2 and KAK1, KAK2, which are controlled by control unit 3 exclusively via corresponding compensation voltage signal UPKI,comp or UPKA,comp according to FIGS. 6E and D. In contrast, comb drive units KI1, KI2 and KA1, KA2 of the drive means receive only drive voltage signals UPKI,drive and UPKA,drive shown in FIGS. 6B and 6C from control unit 3, so that the problem of an excessive voltage being applied to a comb drive unit is avoided.
In the exemplary embodiment shown in FIG. 5, it is apparent that the additional compensation comb drive units KIK1, KIK2, KAK1, and KAK2 are also arranged in pairs and act upon the same points of application P1 and P2 of the flywheel mass, situated diametrically opposite one another. The arrangement of four additional compensation comb drive units KIK1, KAK1 and KIK2, KAK2 in pairs used in this exemplary embodiment makes the configuration of this yaw rate sensor completely symmetric. Of course, the non-linearity may also be compensated using only two additional compensation comb drive units, for example, using compensation comb drive units KAK1 and KIK1 or compensation comb drive units KAK2 and KIK2. A system having only two compensation comb drive units KIK1 and KAK2 or KAK1 and KIK2 is also possible.
The above-mentioned simulation has also shown that the amplitude of the compensation voltage signal increases approximately linearly with deflection angle γ if, when designing the yaw rate sensor drive, it is ensured that the smallest possible deflection amplitudes are needed. The smallest possible non-linearity must be observed when designing the spring geometry. The additional compensation comb drive units described in the second exemplary embodiment offer the advantage compared to the first exemplary embodiment in the currently used yaw rate sensor technology that the comb drive units provided for the drive means may be designed for lower voltage amplitudes.
FIG. 7 shows a schematic top view of a third exemplary embodiment of a micromechanical motion sensor according to the present invention in the form of a linear oscillator in which additional compensation comb drive units are provided for compensating the non-linearity.
According to FIG. 7, the bar spring element has a system connected via a centrally located coupling spring FC and mounted via a symmetric spring suspension F1-F4 so it is able to perform linear oscillations, the system being composed in this case of two flywheel masses ml, m2, which are excited by comb drive units KI1, KA1, KI2, KA2 to a linear oscillation in a lateral x-y plane to perform positive and negative deflections i1, i2 and a1, a2 of the same magnitude about their particular rest positions O1, O2. The oscillation drive thus has four comb drive units controlled by a control unit 3 for exciting the two flywheel masses m1, m2 of the flywheel mass system, the drive forces of the comb drive units acting upon the two flywheel masses at opposite points of application in the same lateral x-y plane in such a way that they excite flywheel masses m1, m2 of the system about their particular rest positions O1, O2. Both coupling spring FC and spring suspension F1-F4 cause oscillation non-linearities, which are compensated according to the present invention. To compensate for non-linearity, the compensation drive means for each flywheel mass m1, m2 of the system also have two compensation comb drive units KIK1, KAK1 and KIK2, KAK2, which act upon the same points of application of each flywheel mass m1 and m2 as the comb drive units of the oscillation drive. For the drive and compensation voltage signals supplied by control unit 3, to the latter and to the compensation comb drive units, the same applies in principle as explained above with reference to the second exemplary embodiment illustrated in FIG. 5.
The control unit is able to advantageously approximate the oscillation curve of the compensation voltage signals via step signals having fine steps.
To achieve greater compensation moments with the same voltage, it is advantageous in the exemplary embodiments having separate compensation comb drive units to make the effective radius or effective distance of the compensation comb drive units greater than the effective radius or the effective distance of the oscillation drive comb drive units.