Sensor device and method for determining a natural frequency of a spring-mass system of a sensor device

Abstract

In a method for determining a natural frequency of a spring-mass system of a sensor device, a plurality of measurements are taken, wherein a mass of the spring-mass system is deflected out of a rest position by a deflection force during each measurement and returns to the rest position after the deflection force has been switched off. A respective deflection curve over time is ascertained by ascertaining deflection values of the mass at corresponding sampling times at a specified sampling rate. For each deflection curve, deflection values are selected within a time period after the deflection force has been switched off. An averaged deflection curve is generated on the basis of the deflection curves for the plurality of measurements. The natural frequency of the spring-mass system is ascertained on the basis of the averaged deflection curve.

Description

[0001] Description

[0002] title

[0003] Sensor device and method for determining a natural frequency of a spring-mass system of a sensor device

[0004] The invention relates to a sensor device and a method for determining a natural frequency of a spring-mass system of a sensor device.

[0005] State of the art

[0006] Rotation rate sensors or acceleration sensors can be designed as micromechanical systems which have movable elements that can be set into vibration.

[0007] For example, a gyroscope is known from DE 10 2007 054 505 B4, wherein movable substructures are coupled to a common spring element.

[0008] Knowledge of the oscillator characteristics is advantageous, particularly the natural frequency, the quality factor Q, or the damping factor DL. This allows the determination of the frequency dependence of the sensitivity and noise dependence, which can be taken into account during calibration or trimming. The natural frequency, in particular, is a parameter that can be used to calibrate the fundamental sensing characteristic of the sensors.

[0009] Disclosure of the invention: The invention provides a sensor device and a method for determining a natural frequency of a spring-mass system of a sensor device with the features of the independent claims.

[0010] Preferred embodiments are the subject of the respective dependent claims.

[0011] According to a first aspect, the invention relates to a method for determining the natural frequency of a spring-mass system of a sensor device. A multitude of measurements are performed, wherein, in each measurement, a mass of the spring-mass system is deflected from its rest position by a deflection force and returns to its rest position after the deflection force is switched off. A respective time-dependent deflection profile is determined by ascertaining deflection values ​​of the mass at corresponding sampling times using a predetermined sampling rate. Within each deflection profile, deflection values ​​within a time interval after the deflection force has been switched off are selected for further evaluation. An averaged deflection profile is generated from the deflection profiles of the multitude of measurements. The natural frequency of the spring-mass system is determined from this averaged deflection profile.

[0012] According to a second aspect, the invention relates to a sensor device with a spring-mass system comprising a mass. The sensor device further includes an actuator and a measuring device that performs a multitude of measurements. At each measurement, the actuator deflects the mass of the spring-mass system from its rest position by applying a deflection force. The mass of the spring-mass system returns to its rest position after the deflection force is released. The measuring device determines the respective deflection profile over time by measuring deflection values ​​of the mass at corresponding sampling times with a predetermined sampling rate. For each deflection profile, the measuring device selects deflection values ​​within a time range after the deflection force is released for further evaluation. The measuring device determines an average deflection profile based on the deflection profiles from the multitude of measurements.The measuring device further determines a natural frequency of the spring-mass system based on the averaged deflection curve.

[0013] Advantages of the invention

[0014] In contrast to undercritically damped systems, determining the natural frequency, damping factors, and quality factors is more difficult in overdamped systems because no oscillation is visible. The inventive method for determining the natural frequency of a spring-mass system enables such a determination even for overdamped systems.

[0015] When the deflection force is switched off, a downward transient occurs, meaning the amplitudes of the deflection values ​​initially decrease sharply. If the spring-mass system is described by differential equations, then the natural frequency is only particularly influential for a short period after the deflection force is switched off. According to the invention, values ​​are therefore selected within a time interval after the deflection force has been switched off. Further evaluation, i.e., in particular the generation of the averaged deflection curve, is performed using the selected values. Thus, only deflection values ​​with a high downward slope are considered.

[0016] Furthermore, the accuracy of determining the natural frequency is improved by repeating the measurements.

[0017] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, the mass of the spring-mass system returns to its equilibrium position with an overdamped oscillation after the deflection force is switched off. An overdamped oscillation is understood to be an aperiodic oscillation without oscillatory components. The method according to the invention enables the determination of the natural frequency of the spring-mass system even if the exact time of the switch-off of the deflection force with respect to the sampling times is unknown.

[0018] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, the time interval following the deactivation of the deflection force is determined for each measurement based on a change in the deflection values. In particular, the approximate time interval of the deactivation of the deflection force can be identified if the change in the deflection values ​​exceeds a predetermined threshold.

[0019] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, a time at which the deflection force is switched off is first determined (i.e., a switch-off time). This can be determined approximately by ascertaining that the deflection values ​​fall below a predetermined threshold, for example, 80 percent of the initial deflection.

[0020] To determine the natural frequency of the spring-mass system, the subsequent displacement values ​​are selected, for example, all values ​​within a predefined range, such as less than 80 percent of the initial displacement and more than 20 percent before the equilibrium position. This signal segment is well-suited for synchronization because the signal transient has a high (negative) slope and is only relatively slightly disturbed by the given statistical noise behavior.

[0021] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, a plurality of N signal transients are recorded, where N is a natural number, each with signal waveforms sufficiently before the force is cut off and sufficiently close to the signal decaying in the rest position. Displacement values ​​can be selected which lie within a predetermined range, depending on a maximum initial displacement, approximately 80 percent to 20 percent of the initial displacement.

[0022] According to one embodiment of the method for determining a natural frequency of the spring-mass system of the sensor device, the deflection profiles are interpolated before generating the averaged deflection profile.

[0023] The N deflection curves do not necessarily have to be measured with periodic sampling and do not have to match each other in the sampling grid.

[0024] Through interpolation and / or subsequent synchronization, e.g. with a convolution algorithm, both the synchronization of the curve progressions and an averaging of the curve sequences can be achieved.

[0025] A non-matching sampling grid can be advantageous because it reconstructs the curve's behavior even at intermediate points. The sampling grid is preferably chosen to be sufficiently dense enough to oversample the period of the natural frequency according to the Nyquist-Shannon sampling theorem.

[0026] From the multitude of N recorded signal transients, the area with the highest signal transients (e.g., the aforementioned 80%-20% range, which can be referred to as the synchronization segment) is selected, and the curves in this area are time-synchronized. To achieve this, the signal curves in this synchronization segment are superimposed, for example, by convolution analysis.

[0027] Synchronization accuracy can be increased by artificially interpolating the N curves at a higher sampling rate and then performing the synchronization operation. This statistically reduces the influence of signal noise and any non-deterministic sequence of sampling time and force cut-off. According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, the displacement profiles are shifted relative to each other in time using a convolution algorithm before generating the averaged displacement profile. The averaged displacement profile is then determined based on the time-shifted displacement profiles. Using, for example, the convolution algorithm, the design profiles can be synchronized relative to each other, thus achieving correct averaging of the displacement profile. This results in noise reduction.

[0028] Using the N synchronization values ​​determined from the synchronization segments, the entire signal curves, including the time periods around the crucial switch-off point, are then time-corrected. Finally, the N individual curves are averaged to form a single overall curve. This results in synchronization of the individual curves and, in particular, good noise suppression in the flat curve region around the switch-off point, where the sensor's natural frequency f0 is most accurately encoded.

[0029] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, determining the natural frequency of the spring-mass system based on the averaged deflection profile further comprises scanning the averaged deflection profile. The natural frequency is determined by fitting parameters of a predefined fit function to the scanned averaged deflection profile.

[0030] The natural frequency f0 of the spring-mass system of the sensor device is most accurately encoded around the switch-off time, and the fit algorithm determines it there with good accuracy. The signal waveform of the previous synchronization segment is determined by a normally inseparable entanglement of the natural frequency f0 and the damping DL of the mass. However, since the natural frequency f0 of the mass around the switch-off time (and also the switch-off time itself) can now be determined with sufficient accuracy, the fit algorithm can also determine the damping DL of the mass from the synchronization segment.

[0031] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, a damping factor of the spring-mass system and a point in time at which the deflection force is switched off are further determined based on the averaged deflection profile. Knowledge of the damping factor DL ​​is advantageous for assessing the integrity of the sensor device, since a defective seal and the ingress of air, or even steam or water, can alter the damping factor DL ​​in the sensor device and lead to degradation and corrosion.

[0032] With gyroscopes, the knowledge of the damping also allows the gain of the useful signal to be recorded during operation and recalibrated if it changes.

[0033] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, the deflection values ​​of the averaged deflection curve are weighted differently when determining the natural frequency of the spring-mass system. In particular, earlier values ​​can be weighted more heavily than later ones, since the natural frequency has the greatest influence on the deflection immediately after the start of the oscillation process.

[0034] According to one embodiment of the method for determining a natural frequency of the spring-mass system of the sensor device, the sensor device is an acceleration sensor or angular rate sensor.

[0035] According to one embodiment of the method for determining the natural frequency of the spring-mass system of the sensor device, the determined natural frequency is used to calibrate or trim the sensor device. Further advantages, features, and details of the invention will become apparent from the following description, in which various exemplary embodiments are described in detail with reference to the drawings.

[0036] Brief description of the drawings

[0037] They show:

[0038] Figure 1 shows a schematic block diagram of a sensor device according to an embodiment of the invention;

[0039] Figure 2 shows a schematic representation of a spring-mass system and an actuator of a sensor device according to an embodiment of the invention;

[0040] Figure 3 shows an overall displacement profile of the mass during a multitude of displacements;

[0041] Figure 4 shows exemplary deflection curves;

[0042] Figure 5 shows an exemplary averaged deflection curve; and

[0043] Figure 6 shows a flowchart of a method for determining a natural frequency of a spring-mass system of a sensor device according to an embodiment of the invention.

[0044] In all figures, identical or functionally equivalent elements and devices are designated with the same reference numerals. The numbering of process steps serves for clarity and generally does not imply a specific chronological order. In particular, several process steps can be performed simultaneously.

[0045] Description of the exemplary embodiments Figure 1 shows a schematic block diagram of a sensor device 1 with a spring-mass system 2 comprising a mass 5. The sensor device 1 further includes an actuator 3, which can deflect the mass 5 of the spring-mass system 2 from a rest position by means of a deflection force. For example, the actuator 3 can apply a voltage to electrodes so that the mass is deflected against a spring force from the springs of the spring-mass system 2 and thereby assumes a new static position. The sensor device 1 further includes a measuring device 4, which performs a multitude of measurements. The actuator 3 deflects the mass 5 of the spring-mass system 2 from a rest position by means of a deflection force during each measurement. The mass 5 of the spring-mass system 2 returns to its rest position after the deflection force is switched off.In particular, after the deflection force is switched off, the mass 5 of the spring-mass system 2 can return to the rest position with an overdamped oscillation.

[0046] The measuring device 4 determines the respective time-dependent displacement profile by measuring displacement values ​​of the mass 5 at corresponding sampling times using a predefined sampling rate. The measuring device 4 can, for example, measure an electrical voltage or an electrical current, which correspond to displacement values.

[0047] The sensor device 1 further comprises a control and processing unit 6, which triggers deflection actions and coordinates and evaluates curve recording. The control and processing unit 6 can optionally be arranged externally on a measurement station computer. Alternatively, the control and processing unit 6 can be arranged internally, allowing analysis and any necessary recalibration to be performed while the sensor device 1 is in use.

[0048] The control and processing unit 6 controls the actuator 3 and the measuring device 4, so that a multitude N of displacement and relaxation processes are actuated. The measuring device 4 records these in a memory as a waveform. In each case, the mass 5 is moved into a statically stable displacement and returns to a static rest position via a switch-off transient. In typical circuits, the actuation and measurement sampling are not synchronized, and the displacement and relaxation phases may not be of equal length or may only be approximately equal.

[0049] A steep transient section is suitable for the temporal synchronization of the N recorded deflection curves, since here the unavoidable noise meets a strong real signal transient.

[0050] To perform the synchronization, the measuring device 4 can therefore discard signal components outside the steep range.

[0051] When discarding the deflection values ​​outside the time range following the switching off of the deflection force, at least one deflection value can be discarded, in particular, after the change in the deflection values ​​has already exceeded a predetermined value, i.e., which lies after a (presumed) start of the oscillation process.

[0052] Measuring device 4 interpolates the entire deflection profile. For this purpose, a polynomial of order n can be used, for example with n between four and eight.

[0053] The displacement profiles within the synchronization range are shifted relative to each other in time using a convolution algorithm. This synchronizes the displacement profiles with an accuracy of, for example, t$ / n, where ts denotes the original sampling time (i.e., the time between two samples).

[0054] Measuring device 4 determines an averaged deflection profile based on the deflection profiles from the numerous measurements. For each measurement, the relative time correction to all other N curves within the synchronization range is determined. This allows measuring device 4 to align all N sub-curves within the synchronization range and synchronize the overall curves with each other. Thus, measuring device 4 can average across all deflection profiles.

[0055] The measuring device 4 further determines a natural frequency of the spring-mass system 2 based on the averaged displacement profile. The averaged displacement profile is determined from the time-shifted displacement profiles.

[0056] Determining the natural frequency of the spring-mass system 2 based on the averaged displacement profile can involve sampling the averaged displacement profile at the specified sampling rate. This allows for a downward sampling of the averaged displacement profile back to the original sampling time ts.

[0057] The natural frequency can be determined by fitting the parameters of a predefined fit function to the sampled averaged displacement profile. The fit function can be a solution function of a differential equation describing the oscillation behavior, particularly a solution function of a damped oscillation. This solution function can depend on the natural frequency. The natural frequency can then be determined by optimization, i.e., by minimizing the error between the fit function and the averaged displacement profile.

[0058] With a perfectly known turn-off time (tow) relative to the sample times (ts), the fitting procedure only includes the parameters of the oscillator system to be characterized, e.g., the natural frequency (fo) and the damping (DL). However, since the exact turn-off time within the sample grid (ts) of the measured values ​​is unknown in typical circuits, the fitting algorithm can determine the turn-off time (tow) as precisely as possible, in addition to the oscillator characteristics. The fitting task thus determines more parameters than the physical sensor system describes: {fo, DL + ton}. The fitting task is significantly more difficult due to the increased number of free parameters. The averaging process described above can solve the problem of the lack of synchronization between actuation and sampling.

[0059] The measuring device 4 can further measure a damping factor or damping degree DL of the spring-mass system 2 and a time t. OThe point at which the deflection force is switched off can be determined based on the averaged deflection curve. These quantities can also be parameters of the fitting function.

[0060] The measuring device 4 can weight the deflection values ​​of the averaged deflection curve differently when determining the natural frequency of the spring-mass system 2. For example, selected deflection values, such as a predetermined number of deflection values ​​after the transient process (e.g., three deflection values), can be weighted significantly higher, as these deflection values ​​are most important for the correct identification of the natural frequency.

[0061] Figure 2 shows a schematic representation of a spring-mass system 2 and an actuator 3 of a sensor device. The actuator 3 applies a step voltage U(t) to a first electrode 7 and a second electrode 8, such that the mass 5 is deflected by an electrical force against the force of the (not shown) springs, where the parameter "x" denotes the deflection from the rest position. After the voltage drops to zero, the mass 5 returns to its rest position.

[0062] Figure 3 shows the overall displacement profile of the mass over a multitude of displacements, i.e., the displacement A as a function of time t. The displacements occur sequentially and are not yet synchronized.

[0063] Figure 4 shows exemplary displacement profiles as a function of time t for a multitude of measurements. Each profile has a first time interval 10 in which the mass is displaced from its equilibrium position by means of the displacement force, with the displacement x having a constant value. A second time interval 20 immediately after the displacement force is switched off is of particular importance for determining the natural frequency of the spring-mass system 2, since the natural frequency strongly influences the displacement at this time. A third time interval 30 can be advantageous for further synchronization, whereby the second time interval 20 and the third time interval 30 may overlap.

[0064] Figure 5 shows an exemplary averaged displacement curve 40. In a first time interval 50 immediately after the displacement force is switched off, the influence of the natural frequency of the spring-mass system 2 on the displacement x is particularly strong, so that the measuring device 4 can give particular weight to displacement values ​​in the first time interval 50 when determining the natural frequency of the spring-mass system 2. In a further time interval 60, the influence of the damping factor DL ​​SO is so large that the natural frequency is difficult to extract. This further time interval 60 is determined by both parameters, namely natural frequency fo and damping DL, in combination, but neither parameter can be determined separately from the curve.

[0065] Figure 6 shows a flowchart of a method for determining a natural frequency of a spring-mass system 2 of a sensor device.

[0066] In a first step S1, several measurements are performed, whereby a mass 5 of the spring-mass system 2 is deflected from its rest position by a deflection force in each measurement and returns to its rest position after the deflection force is switched off. In particular, the mass 5 of the spring-mass system 2 can return to its rest position with an overdamped oscillation after the deflection force is switched off.

[0067] A large number N of displacement and relaxation processes are performed, allowing for the determination of numerous displacement profiles over time. This is achieved by measuring displacement values ​​of mass 5 at corresponding sampling times using a predefined sampling rate. For each displacement profile, displacement values ​​within a time interval following the removal of the displacement force are selected to determine the mutual synchronization. For each measurement, the time interval following the removal of the displacement force is determined based on a change in the displacement values.

[0068] The deflection curves are interpolated within the time range following the switching off of the deflection force.

[0069] The deflection curves are shifted relative to each other in time using a convolution algorithm.

[0070] In step S2, an averaged deflection profile is generated based on the deflection profiles from the multitude of measurements.

[0071] In step S3, the natural frequency of the spring-mass system 2 is determined based on the averaged displacement profile. The averaged displacement profile is determined from the time-shifted displacement profiles.

[0072] Determining the natural frequency of the spring-mass system 2 based on the averaged displacement profile can involve sampling the averaged displacement profile at a specified sampling rate. The natural frequency is then determined by fitting parameters of a predefined fit function to the sampled averaged displacement profile.

[0073] Furthermore, a damping factor of the spring-mass system 2 and a time of switching off the deflection force can be determined based on the averaged deflection curve.

[0074] When determining the natural frequency of the spring-mass system 2, the deflection values ​​of the averaged deflection curve can be weighted differently. The natural frequency of the mass-spring system can be determined, for example, during the production process of the sensor device 1. The natural frequency can then be used to check whether the sensor device is suitable for the intended operation. For example, sensor devices 1 with a natural frequency outside a predefined range can be rejected.

Claims

Claims 1. Method for determining a natural frequency of a spring-mass system (2) of a sensor device (1), comprising the steps: Performing (S1) a plurality of measurements, wherein a mass (5) of the spring-mass system (2) is deflected from a rest position by a deflection force at each measurement and returns to the rest position after the deflection force is switched off, wherein a respective temporal deflection profile is determined by determining deflection values ​​of the mass (5) at corresponding sampling times with a predetermined sampling rate, and wherein, in the respective deflection profile, deflection values ​​within a time range after the deflection force has been switched off are selected for further evaluation; Generating (S2) an averaged deflection profile based on the deflection profiles from the multitude of measurements; and Determine (S3) the natural frequency of the spring-mass system (2) based on the averaged deflection profile.

2. Method according to claim 1, wherein the mass (5) of the spring-mass system (2) returns to the rest position with an overdamped oscillating movement after the deflection force is switched off.

3. Method according to claim 1 or 2, wherein for each measurement the time range after the switching off of the deflection force is determined on the basis of a change in the deflection values.

4. Method according to claim 3, wherein deflection values ​​are selected which lie within a predetermined range of values ​​which depends on a maximum initial deflection of the mass (5).

5. Method according to one of the preceding claims, wherein, prior to generating the averaged deflection profile, the deflection profiles within the time range after the switching off of the deflection force are interpolated.

6. Method according to one of the preceding claims, wherein, prior to generating the averaged deflection profile, the deflection profiles are shifted relative to each other in time using a convolution algorithm, and wherein the averaged deflection profile is determined based on the time-shifted deflection profiles.

7. Method according to one of the preceding claims, wherein determining the natural frequency of the spring-mass system (2) based on the averaged deflection profile further comprises: Sampling the averaged displacement profile at the specified sampling rate; and Determining the natural frequency by fitting parameters of a predefined fit function to the sampled averaged displacement curve.

8. Method according to one of the preceding claims, wherein a damping factor of the spring-mass system (2) and a time of switching off the deflection force are further determined on the basis of the averaged deflection profile.

9. Method according to one of the preceding claims, wherein, when determining the natural frequency of the spring-mass system (2), deflection values The averaged deflection curve is weighted differently.

10. Sensor device (1), comprising: a spring-mass system (2) with a mass (5); an actuator (3); and a measuring device (4), which is configured to perform a plurality of measurements, wherein the actuator (3) is configured to deflect the mass (5) of the spring-mass system (2) from a rest position by means of a deflection force at each measurement, wherein the mass (5) of the spring-mass system (2) returns to the rest position after the deflection force is switched off, wherein the measuring device (4) is configured to determine a respective temporal deflection profile by determining deflection values ​​of the mass (5) at corresponding sampling times at a predetermined sampling rate, and wherein the measuring device (4) is configured to select deflection values ​​within a time range after the deflection force has been switched off for the respective deflection profile;wherein the measuring device (4) is further configured to determine an averaged deflection profile based on the deflection profiles during the multitude of measurements, and to determine a natural frequency of the spring-mass system (2) based on the averaged deflection profile.

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