Method and device for the hysteresis correction of measured values for sensors with extensometers

Abstract

The invention relates to a method and a device for the hysteresis correction of the measured values of one or more sensors (1), which have been determined in a deformation body using extensometers. According to the invention, each measured value x affected by hysteresis is corrected for the hysteresis error. To achieve this, a hysteresis model is created from the registered strain characteristic curve and the theory of dipole density of the aligned elementary hysteresis in the interior of the deformation body. Said model is used, together with the measured values x affected by hysteresis and the recorded strain history, to derive a correction value for correcting the hysteresis error.

Description

[0001] The invention relates to a method for the hysteresis correction of measured values in connection with transducers with strain gages, which detect the strain due to a force influence on a deformation body, according to the preamble of the Patent claim 1, as well as an apparatus for carrying out the method according to the preamble of the Patent claim 10.

[0002] Measured value transducers with strain gages are often utilized for the detection of measured values, whereby the strain gages generate an electrical measuring signal due to a force influence on an elastic deformation body. In this regard, these transducers are predominantly utilized in weighing devices for the measuring of forces, moments or pressures. Such transducers and especially weighing cells or load cells are generally subject to or affected by a hysteresis error, which is recognizable in practice in that two different measured values are provided for the same load, depending on whether the measurement is carried out with a rising or falling load application. The main cause for this ambiguous characteristic curve deviation are frequency-independent damping processes in the material of the deformation body in connection with strains in the elastic range, or a beginning plastification in boundary or limit cases. Besides that, external frictional effects also arise on the force introduction or joint surfaces. Besides other linearity errors, these hysteresis errors are essentially decisive regarding the accuracy of the measurement results.

[0003] In practice, these hysteresis errors are often reduced in connection with weighing or load cells and force transducers in that they are compensated to the extent possible by hysteresis effects in the application of the converter elements (strain gages). For this purpose, the strain gages and corresponding adhesives are selected, which comprise a contrary or counteracting hysteresis to the extent possible and thereby keep the total hysteresis error small. The hysteresis error remaining in this manner is, however, subjected to a series scattering, and cannot be removed or corrected even by subsequent processing. Thus, previously, transducers with very small hysteresis errors were produced simply by selection from the series.

[0004] A method for the reduction of the hysteresis error has similarly become known from the DE 20 40 987 B2, wherein this method, in a mechanical manner, couples together in a transducer two measuring elements with opposed hystereses. While the hysteresis error can be reduced in this manner, whereby, however, also here, a subsequent processing after the fabrication is no longer possible, so that also here all tolerances caused by the fabrication go completely into the measurement result. Moreover, such an apparatus increases the mechanical structure enormously due to the production of a complicated and costly measurement spring.

[0005] Furthermore, for the correction of the hysteresis error, mathematical methods are also previously known from the GB 147912 B and the EP 0,457,134 A2, which mathematical methods are utilized in the output value of the force transducer. Both publications disclose mathematical methods in the form of polynomial approximations, in which, respectively dependent on the loading direction of the weighing system, stored hysteresis correction values are processed with the determined measured values, and thereafter are output as a weight value corrected by the hysteresis error. Since these methods do not take into consideration the local reversal points in the load history, a significant residual error must remain.

[0006] Therefore, it is the underlying object of the invention, to correct a hysteresis error in connection with strain gage transducers, and this at an acceptable expense and effort.

[0007] This object is achieved by the invention recited in the Patent claim 1 and 10. Further developments and advantageous example embodiments are recited in the dependent claims.

[0008] The invention has the advantage that this correction method is utilizable in connection with all hysteresis-affected transducer systems with strain gages. In this context, it is simply necessary to provide a one-time determination of the loading characteristic curve or individual loading values in rising and falling form, which are sufficient for forming or mapping a hysteresis model, whereupon correction values are derivable for each hysteresis-affected measured value in connection with the model.

[0009] Furthermore, the invention has the advantage, for the formation of the respective hysteresis model for the special or specific transducer or the special or specific weighing scale, that only its loading characteristic curve or only a few determinative loading values need to be determined or prescribed, which already takes place for a normal staggered or graduated measurement for the adjustment, without requiring that the entire loading history must be known, so that no particular prior determination of a plurality of coefficients is necessary.

[0010] The invention still additionally has the advantage that the hysteresis correction can be carried out both for one individual transducer as well as for a plurality of transducers circuit-connected together, for example in a complete weighing scale, since the entire hysteresis error takes place through a downstream or subsequently circuit-connected numerical signal preparation or processing. Thereby, it is especially advantageous that this takes place in the simplest manner due to the derivation of the model from the existence of elastic dipoles, and therefore also requires only a very small computational effort or expense.

[0011] In a particular embodiment of the invention it is advantageous that an adaptation to an unsymmetrical envelope of the hysteresis is also possible, through an additional weighting function, without requiring that the hysteresis model must have been altered.

[0012] The invention will be described in further detail in connection with an example embodiment, which is illustrated in the drawing. It is shown by:

[0013] FIG. 1: a block circuit diagram of the invention;

[0014] FIG. 2: a development of the density function dependent on the strain history;

[0015] FIG. 3: the envelope of a hysteresis model, and

[0016] FIG. 4: a computer program of the hysteresis model.

[0017] In FIG. 1 of the drawing, the invention is illustrated in connection with a block circuit diagram, which includes a transducer 1 with a pre-amplifier 2, which provides a measured signal x, of which the hysteresis error is corrected by a model circuit 3, a weighting function circuit 4, a multiplying circuit 5 and a summing circuit 6.

[0018] The transducer 1 is embodied as a weighing or load cell, which includes an elastic deformation body, onto which strain gages are applied. These emit an electrical signal, that is proportional to the weight loading of the load cell 1. Because this load cell 1 includes a deformation body of an iron alloy, the load cell 1 emits a signal that is subject to or affected by a hysteresis error, of which the non-linear course or progression forms a so-called envelope. This hysteresis-affected weight signal x is amplified in a following pre-amplifier 2 and provided to a model computation circuit 3. Loading values are inputted into this model computation circuit 3, wherein these loading values are run through during a loading of the load cell 1 up to a maximum value and a complete unloading. In this context, beginning from an unloaded state, at least one intermediate value is required in the rising branch, and at least one intermediate value is required in the falling branch. Such a staggered or graduated measurement with several measured values generally is already carried out in the adjustment of the load cell 1 or a weighing scale, so that usually no special input of the necessary loading values is required for this purpose. Moreover, such a loading also does not necessarily have to take place in the first use of the load cell 1 or the weighing scale, because all previous hysteresis-causing measured values are written over because of the measurement up to the maximum value, and therefore can remain disregarded or not taken into account.

[0019] The hysteresis model of the model circuit 3 is based on the underlying recognition that the loading history that leads to the hysteresis is developed according to the following steps. For this purpose, a computational model is utilized, that is derived from the geometric interpretation of a bending beam. In the manner of a starting point, one begins in this context from the existence of elastic dipoles, which orient themselves under the influence of an elastic strain field and orient or align themselves in the tension or stress direction similarly like the elementary magnets. In the case of the bending beam, the distribution (dipole density φ) is only to be considered over the height of the spring or of the strain body z. In this context, in a first approximation, all further spatial components can be neglected. Thereby, also the boundary or edge strain εr is detectable or acquirable by measurement technology, and the greatest strains arise in the elastic range on the spring or on the deformation body. Thus, it is assumed for the model, that at this point, a partial aligning or orienting of edge dipoles is forced in the direction of the stress variations. In this context, the edge or boundary orientation behaves according to the following mathematical function:

φ(Zr)=C·εr

[0020] wherein

[0021] φ=dipole density;

[0022] z=spacing distance from the neutral phase in the direction toward the strain edge or boundary;

[0023] r=characteristic parameter for edge or boundary values;

[0024] εr =strain at the edge or boundary area; and

[0025] C=factor for hysteresis strength.

[0026] The dipole density φ of the oriented elementary hystereses in the interior of the body thus arises or is determined from the distortion or deformation history of the deformation body according to the following mathematical function

εr=ΣΔεrn

εrn+1=εrn+Δεrn+1

[0027] wherein

[0028] n=number of the load steps.

[0029] For reasons of symmetry, a piecemeal or piece-wise linear distribution function φ is to be assumed over the height z in a bending beam. Therefore, the development of the density function φ can be developed according to FIG. 2 of the drawing with knowledge of the loading history. The course or progression of a first loading and further loading cycles is illustrated in FIG. 2 of the drawing. One begins with φ=constant=0.0 and εr=0.0. The boundary or edge strain is increased to εr=A. Thereby, the density function becomes adjustingly set to the course or progression A-B. If next the initial condition εr=0.0 is again forced, then the point C arises, and the oriented region 0-C-B remains behind in the interior. If the boundary or edge strain is again increased, thereby the front A′-C′ is formed parallel to A-B. Upon reaching ε1, point C′ transitions into C, whereby a cancellation of both points takes place. A sign reversal in the strain velocity causes a new instability or discontinuity point in φ at the body edge. This point can move or wander only in the direction toward the neutral fiber (NF). Fronts between two instability or discontinuity points are immovable, only the line segment between the edge and the first point is shifted in a parallel manner. Points that run together again mutually cancel each other. With a sufficiently large boundary or edge strain, independent of the sign, every older internal structure is overwritten by the new front B′. If thereby two instability or discontinuity points cancel each other out, there thus arises a kink or bend in the characteristic curve branch. In a weakly damped decaying oscillation, beginning with the maximum amplitude in εr, the entire stored information is cancelled or erased.

[0030] The failure or fault moment of a single individual fiber is to be obtained from the geometric conception, through the density function φ that is multiplied with the fiber spacing z. An internal hysteresis moment Mh or an internal hysteresis force Fh, which is held in equilibrium balance by a boundary or edge strain error εh, is obtainable from the integration over z and a multiplication with the factor C (hysteresis strength). This remaining hysteresis moment Mh or hysteresis force Fh arising out of the loading history, arises or is given according to the following mathematical function: 1$M_h=C_m·{\int }_{-\mathrm{zr}}^{+\mathrm{zr}}\phi \left(z\right)·z·dz\text{or}{F}_h=C_f·{\int }_{-\mathrm{zr}}^{+\mathrm{zr}}\phi \left(z\right)·z·dz$

[0031] In this context, the factor C is first selected so that the relative model hysteresis becomes 100%. The adaptation to the transducer hysteresis that is to be corrected can then additionally be carried out through a weighting function P(x) in a weighting circuit 4. From the thusly developed model, which essentially contains or includes the loading history, a correction or auxiliary value h is calculable for each determined measured value x. In this context, the hysteresis model essentially describes the linearity deviation from a straight line in the teardrop shape of the envelope loop. Such an envelope of the auxiliary value h over the hysteresis-affected measured value x is shown in FIG. 3 of the drawing. Thereby, this envelope 7 represents or illustrates a symmetrical teardrop shaped course or progression, of which the values are respectively calculated in the model circuit 3 according to the program in FIG. 4. In this context, the hysteresis model is described in the programming language “FORTRAN” and is input into the model computation circuit 3, which therewith calculates the respective auxiliary value h for each measured value x. Since the envelope 7 according to the model circuit 3 describes an envelope in ideal teardrop shape according to FIG. 3 of the drawing, an adaptation to unsymmetrical hysteresis curves, which deviate from this teardrop shape 7, can still be carried out. For this purpose, a weighting function is still provided, which describes a linear dependence P(x) through which the unsymmetries of the hysteresis curves can additionally be taken into account in the weighting circuit 4. Since an adapting factor C of the transducer hysteresis is still further contained in this weighting function P(x), the model computation circuit 3 can be used for all hysteresis-affected transducers.

[0032] In a following multiplying circuit 5, the weighting function P(x) as the form of the respective weighting factor w is multiplicatively coupled with the respective auxiliary value h and provided to a summing circuit 6 as a correction factor. This weighting factor w can, in the ideal case for an ideal teardrop shape 7 of the envelope, possess the factor 1 as described above, or can contain an adaptation of the measured hysteresis to the relative model hysteresis. Since also a linear adaptation to a deviation of the ideal teardrop shape 7 of the hysteresis model can be contained by this weighting function, the weighting function circuit 4 still additionally calculates the respective deviation relative to the determined hysteresis-affected measured value x. The total weighting factor w resulting herefrom, multiplied with the auxiliary value h gives, at the output of the multiplier 5, a correction value for taking into account the respective hysteresis error.

[0033] In the summer 5, the determined correction value is additively coupled with the correct sign with the hysteresis-affected measured value x, so that thereafter the measured value y that has been cleaned with respect to the hysteresis error is then available for further processing or for indication at the output of the summer 6.

[0034] Such a correction method can be carried out as well by means of hardware or software-based computational circuits. In this context, such a correction method is suitable both for analog as well as for digital transducer circuits or weighing scales.

[0035] Particularly, it requires no special adaptation to the special embodiment of the transducers or weighing scales, but rather it can simply be carried out by receiving or taking up the falling and rising loading characteristic curves.

Claims

1. Method for the hysteresis correction of measured values in connection with transducers with strain gages, which detect the strain due to a force influence on an elastic deformation body, in which the hysteresis-affected measured values are corrected by a determined hysteresis error, characterized in that a hysteresis model is formed from determined loading values in a rising and a falling loading branch, with the aid of which, and from each determined hysteresis-affected measured value x, a correction value is derivable or calculable, which serves for the correction of the hysteresis error.

2. Method according to claim 1, characterized in that a hysteresis model of the transducer (1) is formed in a model circuit (3) from the dipole density φ of the oriented elementary dipoles in the interior of the deformation body and the determined loading values in the rising and falling loading branch (envelope (7) of the hysteresis).

3. Method according to claim 1 or 2, characterized in that an auxiliary value h is formed from the formed hysteresis model and respectively from a hysteresis-affected measured value x in the model circuit (3), which auxiliary value h represents a value for the relative hysteresis error.

4. Method according to claim 3, characterized in that a weighting factor w is formed from the determined loading values (envelope (7) of the hysteresis) of the transducer (1) in a weighting circuit (4) by means of a weighting function P.

5. Method according to claim 3, characterized in that a weighting factor w is formed from the determined loading values (envelope of the hysteresis) of the transducer (1) and/or from an unsymmetry of the envelope (7) by means of s a weighting function P(x).

6. Method according to claim 4 or 5, characterized in that a weighting factor w is formed from the weighting function P(x) and from a respectively determined hysteresis-affected measured value x in the weighting circuit (4), and this weighting factor is multiplicatively coupled with the auxiliary value h and gives a value for the respective hysteresis error.

7. Method according to claim 6, characterized in that the value of the respective hysteresis error is coupled with the hysteresis-affected measured value x with a correct sign in a summing circuit (6), and gives a measured value y that is corrected by the hysteresis error.

8. Method according to one of the preceding claims, characterized in that the hysteresis-affected measured value x is determined as the output signal of a transducer (1) or as the output signal of several transducers (1) that are circuit-connected together.

9. Method according to one of the preceding claims, characterized in that the output signals x are formed as well from sampled analog signals or as digital values.

10. Apparatus for carrying out the method according to one of the preceding claims, characterized in that a transducer (1) with strain gages is provided, of which the hysteresis-affected measured values x are delivered to a 5 model circuit (3), which therefrom forms an auxiliary value h, which is coupled in a provided multiplication circuit (5) with the weighting factor w formed from a provided weighting circuit (4) to form a correction value, and from which, in a provided summing circuit (6), under consideration of the hysteresis-affected measured value x, at the output of which the corrected measured value y is available for further processing or indication.

11. Apparatus according to claim 10, characterized in that the model circuit (3), the multiplying circuit (5), the weighting circuit (4) and the summing circuit (6) is embodied in a hardware manner as an electronic circuit.

12. Apparatus according to claim 10, characterized in that the functions of the model circuit (3), the multiplying circuit (5), the weighting circuit (4) and/or the summing circuit (6) is embodied as a program-controlled electronic computer circuit.