Micromechanical spring

Abstract

A micromechanical spring including at least two bar sections which, in the undeflected state of the spring, are oriented substantially parallel to one another or are at an angle of less than 45 with respect to one another, and one or more connecting sections which connect the bar sections to one another, wherein the bar sections can be displaced relative to one another in their longitudinal direction, and wherein the spring has, in the direction of its bar sections, a substantially adjustable, in particular linear force-deflecting behavior.

Claims

1. A micromechanical spring system comprising: at least two bar sections which, in an undeflected state of the spring, are oriented substantially parallel to one another or are oriented at an angle of less than 45 with respect to one another, and at least one connecting section which connects the bar sections to one another, wherein the bar sections are configured to be displaced relative to one another in their longitudinal direction, and wherein a spring stiffness of the micromechanical spring system is substantially constant throughout a deflection range of one of the bar sections and wherein the dimensions of the micromechanical spring are selected to ensure constant spring stiffness throughout the deflection range of the bar section.

2. The spring system as claimed in claim 1, wherein the micromechanical spring is coupled to at least one micromechanical spring element or is coupled at least to a substrate, and has, for a purpose of coupling, in each case a coupling region or at least one coupling element which comprises the at least one micromechanical spring element, wherein the micromechanical spring element is coupled in a substantially rigid fashion to the spring.

3. The spring system as claimed in claim 1, wherein the micromechanical spring is coupled to one or more micromechanical spring elements via a seismic mass, and the micromechanical spring system has a substantially adjustable deflection behavior in a direction of the bar sections.

4. The spring system as claimed in claim 1, wherein fabrication parameters of the spring, comprising at least spatial dimensions (d,l,w) have values such that the spring has, in a direction of the bar sections, a substantially adjustable deflection behavior, at least within a defined deflection interval.

5. The spring system as claimed in claim 1, wherein a set of parameters comprising a length of the bar sections (l), a distance between the bar sections (d) and a length of the at least one connecting section and of at least one coupling region or of at least one coupling element have values such that the spring has, in a direction of the bar sections, a deflection behavior particular to no more than one of the parameters, at least within a defined deflection interval.

6. The spring system as claimed in claim 1, wherein the bar sections and the at least one connecting section of the spring are embodied and arranged so as to be substantially u-shaped or v-shaped or s-shaped in the undeflected state.

7. The spring system as claimed in claim 1, wherein the substantially adjustable deflection behavior of the spring is determined at least by an embodiment of the bar sections with defined lengths (l) and widths (w) and by an arrangement of the at least two bar sections at a defined distance (d) from one another.

8. The spring system as claimed in claim 1, wherein said spring is composed substantially of monocrystalline silicon.

9. The spring system as claimed in claim 1, wherein each bar section comprises a non-linearity of a second order and wherein an absolute value of the second order non-linearity coefficient () of spring stiffness with respect to a deflection substantially in a direction of the bar sections is less than 2,000,000 1/m.sup.2.

10. The spring system as claimed in claim 9, wherein the absolute value of the second order non-linearity coefficient () of spring stiffness with respect to the deflection substantially in a direction of the bar sections is less than 300,000 1/m.sup.2.

11. A micromechanical spring system comprising: at least two bar sections which, in an undeflected state of the spring, are oriented substantially parallel to one another or are oriented at an angle of less than 45 with respect to one another, and at least one connecting section which connects the bar sections to one another, wherein the bar sections are configured to be displaced relative to one another in their longitudinal direction, wherein a spring stiffness of the micromechanical spring is substantially constant with respect to a deflection substantially in a direction of the bar sections within a defined deflection interval, and wherein said spring has a negative second order non-linearity coefficient of spring stiffness with respect to the deflection or the deflection of at least one of the bar sections in the direction of the bar sections.

12. The spring system as claimed in claim 1, wherein said spring has at least one coupling element comprising at least one spring element, a spring stiffness of the at least one spring element changes within the defined deflection interval, wherein the entire spring is embodied in such a way that the changing spring stiffness of the at least one spring element is compensated overall.

13. The spring system as claimed in claim 1, wherein force-deflecting behavior is linear.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is best understood from the following detailed description when read in connection with the accompanying drawings. Included in the drawings are the following figures:

(2) FIG. 1 shows an exemplary embodiment of a simple rotation rate sensor with bar springs,

(3) FIG. 2 shows an exemplary, simple rotation rate sensor with meandering springs,

(4) FIG. 3 shows the exemplary profile of the normalized spring stiffness

(5) $\hat{k}\left(x_0\right)=k\left(x_0\right)/k_0$
or a bar spring and of a meandering spring as a function of the deflection,

(6) FIG. 4 shows exemplary amplitude responses x.sub.0(f.sub.ext) of the deflection of different non-linear oscillators,

(7) FIG. 5 shows a spring element which is embodied in an exemplary way, with a substantially linear deflection behavior,

(8) FIG. 6 shows different profile examples of the normalized spring stiffness as a function of the deflection for different embodiments of the substantially linear spring,

(9) FIG. 7 shows the dependence of the non-linearity coefficient of the second order of the spring constant of a spring exemplary embodiment on its dimensions d and l,

(10) FIG. 8 shows a number of different exemplary embodiments of substantially linear micromechanical spring systems,

(11) FIG. 9 shows exemplary embodiments of combined linear springs which are connected to one another, and exemplary embodiments of combinations of linear springs with additional coupling elements and/or an additional spring element,

(12) FIG. 10 shows an exemplary embodiment of the implementation of a rotary oscillation system with four linear springs,

(13) FIG. 11 shows a micromechanical spring which comprises 3 additional spring elements which are coupled via a seismic mass,

(14) FIG. 12 shows an exemplary meandering spring for direct comparison with an exemplary linear spring shown in FIG. 13,

(15) FIG. 13 shows an exemplary linear spring, and

(16) FIG. 14 shows the comparative profiles of the normalized spring stiffnesses as a function of the deflection of these two exemplary embodiments.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(17) FIG. 1 illustrates by way of example a simple rotation rate sensor with a seismic mass 1 which is suspended from two bar springs 2 on a substrate (not illustrated). FIG. 1b) illustrates the driving mode of the rotation rate sensor, which comprises deflections of the seismic mass 1 and of the bar springs 2. FIG. 1c) shows a section through FIG. 1a) in the x-z plane, wherein the seismic mass 1 is deflected in the z direction and oscillates, for example, in its reading mode. It is known that the illustrated, very simple spring geometry has a strong non-linear relationship between the deflection of the seismic mass 1 and the restoring force acting thereon. As the deflection increases, additional mechanical stresses occur, said stresses occurring due to the clamping-in conditions in the longitudinal direction of the bar and leading to hardening of the bar spring.

(18) FIG. 2 shows exemplary springs which have a meandering structure 3 and from which the seismic mass 1 of an exemplary, simple rotation rate sensor is suspended. The use of such meandering springs 3 reduces the dependence of the normalized spring stiffness {circumflex over (k)}(x.sub.0) on the deflection of the springs.

(19) The black curve in FIG. 3 shows the typical exemplary behavior of a simple bar spring with respect to its normalized spring stiffness

(20) $\hat{k}\left(x_0\right)=k\left(x_0\right)/k_0$
as a function of a deflection in the x direction which is related to the limiting value of the spring stiffness k.sub.0 for small deflections. The outline curve shows an exemplary typical profile of the normalized spring stiffness of an oscillator with meandering bar springs as a function of the deflection, which oscillator has the same primary frequency as the oscillator with the original bar geometries which is illustrated in FIG. 1.

(21) The problem of such non-linear primary oscillators is that they can be deflected only up to a certain maximum amplitude before instabilities occur. FIG. 4 shows exemplary amplitude responses x.sub.0(f.sub.ext) of different non-linear oscillators. While the black curve a shows the well-known behavior of a linear, harmonically excited and damped harmonic oscillator with the natural frequency f.sub.prim, as the non-linearity increases the curve b deviates from the ideal curve (shown in FIG. 4 as curve b) until regions occur (dashed) curve c in which there are bistable states with the result that for certain excitation frequencies f.sub.ext there are a plurality of stable oscillation states between which the system can jump due to minimum external interference. Such non-linear oscillators have a typical hysteresis behavior: starting from low excitation frequencies (f.sub.ext<f.sub.prim) the system passes through P1, P2 and P4, while starting from high excitation frequencies (f.sub.ext>f.sub.prim) the system passes through points P4, P3 and P1. In order, therefore, to design rotation rate sensors which operate in a stable way and which have a high amplitude and therefore a high rotation rate amplification, the spring elements which define the primary oscillation must be as linear as possible.

(22) FIG. 5 illustrates an exemplary spring element which has the advantage of being insensitive to certain process fluctuations which cause, in particular, undesired deflections (not illustrated) in the direction which is perpendicular to the actual, desired deflection. It has been found that the spring element 10, if suitably dimensioned, has the property of being linear in any desired way. The spring element 10 comprises, for example, two bar sections 11 which are substantially parallel to one another in the undeflected state, as illustrated in FIG. 5b), and which are connected via a connecting section 12. In the course of a deflection, as illustrated in FIGS. 5a) and c), bar sections 11 are displaced with respect to one another.

(23) A further possible advantage is that the structure can be configured in such a way that, as the deflection increases, softening of the spring stiffness is brought about, instead of hardening of the spring stiffness occurring, as is known from conventional springs.

(24) Calculations and measurements have shown that by adjusting the geometry of this exemplary spring element 10 it is possible to generate any desired, in particular linear, deflection behavior and also stiffness-reducing behavior.

(25) FIG. 6 shows, for different exemplary embodiments of the spring element 10, typical profiles of the normalized spring constant {circumflex over (k)}(x.sub.0) as a function of the deflection. If the normalized spring stiffness {circumflex over (k)}(x.sub.0) is approximated with the formula {circumflex over (k)}(x.sub.0)=1+x.sub.0.sup.2, it is possible to interpret as being the degree of non-linearity. The greater the absolute value, the greater the degree by which the spring stiffness for large deflections deviates from the linear behavior. The sign of ultimately indicates whether the spring stiffness becomes greater (+) or becomes weaker () as deflections increase.

(26) FIG. 7 illustrates by way of example the relationship between the dimensions d and l for a certain spring geometry, corresponding to the exemplary embodiment in FIG. 5, and the non-linearity coefficient . In this context it has been ensured that the spring stiffness k.sub.0 is identical for all combinations d and l. This therefore permits the non-linearity to be adjusted to a positive, negative or minimal setting for a desired spring stiffness, within certain peripheral conditions.

(27) FIG. 8 shows a number of exemplary embodiments of substantially linear spring systems which differ from one another in terms of the number and embodiment of the bar sections, of the connecting sections and of the coupling regions 40 or coupling elements 42.

(28) FIGS. 9a) and b) illustrate exemplary embodiments in which a plurality of substantially linear springs are firmly and rigidly connected to one another, for example by means of the seismic mass l, and can be correspondingly used in combination. FIGS. 9c) to e) show exemplary embodiments with coupling elements. Here, combinations of individual linear springs with conventional bar springs 21, 22 are illustrated in FIGS. 9c) and d), the free ends of which are rigidly connected to one another, and are illustrated with an additional, differently oriented non-linear spring 23 in FIG. 9e).

(29) Here, the rigid connection in FIG. 9d) and that in FIG. 9e) respectively comprise a seismic mass 1. For example, the stiffness in the deflection direction is primarily provided by the substantially linear springs 20.

(30) FIG. 10 illustrates, for example, a seismic mass 1 which is suspended from four linear springs 10 and can therefore be deflected, for example, substantially linearly or rotationally.

(31) FIG. 11 is an exemplary embodiment of a micromechanical spring system, depicted as a linear spring 20, which is at the same time an oscillator and comprises the seismic mass 1 and bar spring elements 22, and is suspended from the substrate 30. The linear properties of the linear spring 20 are based substantially on the exemplary embodiment of the bar sections 11 and of the connecting section 12 with which the non-linear deflection properties of the bar spring elements 22 are compensated in the direction of the bar sections.

(32) In the text which follows, exemplary methods for implementing and/or developing linear springs as shown above and/or for developing micromechanical springs with an adjustable deflection behavior are described:

(33) Method by Means of Finite Elements:

(34) The method of finite elements provides the possibility of describing in a computer-supported fashion spring properties of a bar arrangement composed of a certain material whose elastic properties are known. It is possible, for example, to describe the spring stiffness values in all the spatial directions and/or about all the spatial axes. For this purpose, the position of the spring system, which corresponds to an end of the spring system which is held in a secured fashion or clamped in, is provided with a corresponding peripheral condition, and the position which corresponds to an end which is held in a free or deflectable fashion, is deflected by way of example by a specific amount in a spatial direction or about a spatial axis. From the result of the analysis, for example by determining the reaction force acting on the deflection travel, the stiffness of the spring can be calculated. In order to determine the spring stiffness, it is also possible to use other known methods such as, for example, the effect of a force on the free end or of an acceleration on a suspended mass. In addition, for example non-linear material properties and geometric non-linearities can be depicted completely in the finite element analysis. It is therefore possible, with given dimensions of a material arrangement, to determine the deflection-dependent spring stiffness and therefore the linearity behavior. In the text which follows, a method is described with which the desired deflection behavior can be achieved and/or adjusted.

(35) At first, one or more certain embodiments of a spring system are selected, and the following investigations are carried out for each individual embodiment. After the analysis of the individual investigations, it is possible to decide on the optimum spring embodiment.

(36) For a spring embodiment, the dimensions which can be varied are then selected. If n free geometry parameters .sub.1 (i=1 . . . n), which are represented by the vector {right arrow over ()}=(.sub.1, .sub.2, . . . .sub.n) are available, an n-dimensional parameter field is created as a result. Typically, certain restrictions apply to the parameters .sub.i.sub.i in terms of the values which they can assume. Said values can lie, for example, within an interval having the limiting values a.sub..sub.i and b.sub..sub.i: .sub.ia.sub..sub.i;b.sub..sub.i.

(37) Finally, a number of m.sub.i values which lie within the range a.sub..sub.i;b.sub..sub.i are selected for each geometry parameter .sub.i: .sub.i,1, .sub.i,2, . . . .sub.i,m.sub.i. This results in a set of

(38) $\underset{i=1}{\overset{n}{.Math.}}{m}_i$
of different parameter vectors (.sub.1,j.sub.1, .sub.2,j.sub.2, . . . .sub.n,j.sub.n) where j.sub.i[1, 2, . . . m.sub.i]. For each possible combination of (j.sub.1, j.sub.2, . . . j.sub.n) there is an associated parameter set (.sub.i,j.sub.1, .sub.2,j.sub.2, . . . .sub.n,j.sub.n) to which a certain set of geometrical dimensions corresponds. For each individual set of geometrical dimensions it is then possible to carry out the desired simulations. In order to determine the deflection behavior, at least three simulations, for example, are necessary for this, in which simulations the free end is displaced by at least three different values x.sub.1, x.sub.2, . . . x.sub.p (p3) in the desired deflection direction. The result is at least three reaction forces acting on the deflected free end counter to the deflection direction: F(x.sub.1), F(x.sub.2), . . . F(x.sub.p).

(39) From these it is possible to calculate the spring stiffness values

(40) $K\left(x_q\right)=F\left(x_q\right)/x_q$
where q[1, 2, . . . p]. The parameters k.sub.0, and of the function k(x.sub.0)=k.sub.0(1+x.sub.0+x.sub.0.sup.2) can then be determined in such a way that the spring constants K(x.sub.q) are approximated by K(x.sub.q), for example according to the principle of the least mean square error. The linear spring constant k.sub.0 and the non-linearity coefficient are therefore obtained for each parameter set (.sub.1,j.sub.1, .sub.2,j.sub.2, . . . .sub.n,j.sub.n).

(41) If the non-linearity coefficient has then been determined for all the parameter sets of all the spring embodiments, the parameter sets and/or spring embodiments which have the desired properties in terms of the stiffness and the non-linearity coefficient etc. can be selected.

(42) Method of Analytical Modeling:

(43) If one restricts themselves to simple bar geometries, it is possible to design an analytical model according to the bar theory which describes the desired properties. The adjustment of the non-linearity coefficient can be done by parameter optimization of the geometry dimensions within the analytical model.

(44) Experimental Selection:

(45) A further possibility is experimental investigation of variants of selected spring concepts. For example, it is possible to investigate oscillators with masses which are suspended from the spring elements to be investigated. It is possible to draw conclusions about the non-linearity coefficient from this. However, owing to the expenditure on production and measurement it is only possible to analyze relatively small sets of dimensions in this way.

(46) In the text which follows, an exemplary micromechanical linear spring will be described in more detail and compared with a conventional micromechanical meandering spring with optimized linearity. The peripheral conditions adopted are:

(47) (A) The structural height h is 100 m.

(48) (B) The material used is monocrystalline silicon, wherein the coordinate system, which is given by the crystal directions, is rotated through 45 degrees about the wafer perpendicular with respect to the coordinate system of the element.

(49) (C) The spring stiffness in the deflection direction is intended to be 400 Nm.sup.1. If a mass of 2 g is held by two springs, a natural frequency in the deflection direction of 20 kHz occurs.

(50) A conventional meandering spring having the dimensions l.sub.M=436 m, w.sub.M=18 m and d.sub.M=20 m has a spring stiffness of 400 Nm.sup.1. The silicon surface occupied by the meandering structure is 0.024 mm.sup.2. FIG. 12 shows this exemplary meandering spring.

(51) FIG. 13 shows, for the purpose of comparison, an exemplary, substantially linear spring having the dimensions l=250 m, which corresponds substantially to the length of the two bar sections 11, the width w=15.3 m, and the distance between the two bar sections d=250 m, wherein this spring also has a stiffness of 400 Nm.sup.1. By virtue of the above-described method of finite elements, the dimensions were selected such that the non-linearity coefficient is as small as possible. The silicon area which is occupied by the spring structure is only 0.014 mm.sup.2 here.

(52) The different linearity behavior of these two different springs from FIGS. 12 and 13 is illustrated in FIG. 14. Here, the normalized spring constant {circumflex over (k)}(x.sub.0) in the deflection direction was plotted against the deflection. While the meandering spring has a non-linearity coefficient of 1.3 10.sup.6 in the deflection region illustrated, the non-linearity coefficient of the new spring structure is smaller in absolute terms than 300 000. In particular, in the new spring structure illustrated, the non-linearity coefficient is negative, with the result that spring-stiffening non-linearities occurring due to additional effects could be compensated. An oscillator with the meandering structure can be operated only up to approximately 9 m amplitude without instability regions, but with the novel spring structure stable oscillations up to amplitudes of 23 m are possible. In addition, the area for the meandering structure is significantly larger compared to the area required for the exemplary linear spring.