Method for determining the static bending stiffness of an object from dynamic acceleration measurements after vibration excitation of the object.

Abstract

Method for determining a static bending stiffness (C B,stat ) of an object (1) which is vibrationally decoupled from an environment and arranged on at least two support means (2, 3), from dynamic acceleration measurements after vibration excitation of the object (1), comprising the steps a) Establishing a plurality of force application points (4) on the object (1), b) Arranging a number of accelerometer means (5) on the object (1), c) Exciting the object (1) at the force application points (4) determined in step a) using vibration generating means and determining a number of frequency response functions from the accelerations measured using the acceleration sensor means (5), d) Calculating an acceleration vector of the object (1) from the frequency response functions obtained in step c), e) Calculating a displacement vector from the acceleration vector determined in step d), f) Calculating a number of dynamic bending stiffness curves from the forces acting at the force application points (4) and the deflections of the object (1) induced by the displacements with the displacement vector, g) Extrapolating at least one of the dynamic bending stiffness curves obtained in step f) to a frequency f=0 Hz to obtain the static bending stiffness (C B,stat ) of the object (1).

Description

[0001] The present invention relates to a method for determining the static bending stiffness of an object which is vibrationally decoupled from its environment and arranged on at least two support means, from dynamic acceleration measurements after vibration excitation of the object.

[0002] The stiffness of an object is generally a measure of its resistance to elastic deformation under the influence of an external force or torque and depends directly on the elasticity of the material from which the object is made, as well as on the object's geometry. Depending on the type of external load, a general distinction is made between tensile stiffness, torsional stiffness, and bending stiffness.

[0003] Stiffness is of great importance in automotive engineering, for example. The torsional and bending stiffness of a vehicle body significantly influences comfort and the perceived quality of a vehicle. Torsional stiffness also has a considerable impact on the vehicle's handling and is therefore particularly relevant in the development of sports cars.

[0004] The comfort and perceived quality of a motor vehicle are primarily determined by its dynamic stiffness, or more precisely, the position of its natural frequencies. The position of these natural frequencies is determined by the static stiffness c and the mass m. The following applies: f=12πcm

[0005] The primary goal in the design of a motor vehicle is to shift the resonance frequencies to the highest possible frequencies, as these occur significantly less frequently than lower frequencies during typical everyday driving. Furthermore, the occurrence of natural frequencies in the range of typical excitation frequencies, such as those caused by driving on uneven roads, should be avoided.

[0006] Torsional stiffness and bending stiffness are spring constants from a mechanical perspective. Torsional stiffness is defined as the quotient of the torque M and the bending stiffness. T The torsional stiffness depends on the force that causes the object to twist and the angle of twist induced by the torque. It also depends on the modulus of elasticity of the material from which the object is made, the object's geometry, and the distance between the axes of twist.

[0007] The bending stiffness of an object is defined as the quotient of a force F causing the deflection and the maximum deflection w. maxIn bending tests, the object under investigation is mounted on at least two spaced-apart supports, ideally vibration-free and decoupled from its surroundings. A force is then applied to the object, causing it to deflect. The bending stiffness is found to depend on the elastic modulus of the material from which the object is made, the object's geometry, and the distance between the supports. Furthermore, the type of load influences the object's bending stiffness. For example, it makes a difference whether the object is subjected to a single force acting midway between the two supports, an eccentric single force, a linear load acting between the supports, or a distributed load.

[0008] Methods for determining the static bending stiffness of an object are known from the prior art, in which the object is rigidly clamped and subjected to an external force. Using high-precision displacement measuring devices, in particular dial gauges, the deflection of the object due to the external force is recorded along a deflection curve. The static bending stiffness (expressed in N / mm) is then determined at the position where the deflection of the object is at its maximum. Another possibility for determining the static bending stiffness of an object is through computer-aided simulation methods.

[0009] Methods for determining the dynamic bending stiffness of an object are already known in the art. The object under investigation is vibrationally decoupled from its environment and set into vibration using at least one vibration generator. The vibration excitation is achieved by the action of structure-borne sound, which is generated, for example, by a hammer blow or by electrodynamic or hydrodynamic vibration generators. Subsequently, a transfer function is calculated between the external force generating the vibrations and the measured acceleration of the object, which represents the object's structural response to the external vibration excitation. This transfer function provides a mathematical relationship between the external force as the excitation quantity and the object's acceleration in the frequency domain.It describes the object under investigation very accurately in its frequency response. After a fast Fourier transform (FFT) of all measured transfer functions, the frequency positions of the dynamic bending modes and the dynamic torsional modes can be determined.

[0010] DE 101 54 337 A1 discloses a method for objectifying the dynamic properties of a motor vehicle or parts thereof, in particular for optimizing the dynamic design of the chassis and body, wherein vibrations occurring during a journey or on a test bench on the vehicle or parts thereof are recorded metrologically as measurement data and the measurement data are subjected to a signal analysis in which the vibrations occurring during the movement are decomposed into rigid and / or elastic global motion modes.

[0011] German patent DE 10 2006 057 888 B3 discloses a method for obtaining data for the certification of an aircraft. A finite element model (FE model) of the aircraft structure is created. Then, as part of roll tests for the qualification of the aircraft's landing gear, vibration tests are carried out to validate the FE model. In these tests, the aircraft structure is excited to vibrate by the rolling of the landing gear over uneven ground, and the excited vibrations of the aircraft structure are measured. Based on the validated FE model, a flutter stability analysis of the aircraft structure is then performed.

[0012] DE 26 28 954 C3 describes a method for simulating mass and / or stiffness on elastomechanical vibration systems, wherein accelerations and / or displacements, but also velocities, are measured and evaluated on the vibration system, which is preferably designed as an elastomechanical continuum.

[0013] EP 2 444 787 A1 discloses a method for diagnosing the condition of a bridge structure.

[0014] The present invention aims to provide a method for determining the static bending stiffness of an object from dynamic acceleration measurements after vibration excitation of the object, which is characterized in particular by high accuracy.

[0015] This problem is solved by a method having the features of claim 1. The dependent claims relate to advantageous embodiments of the invention.

[0016] A method according to the invention for determining the static bending stiffness of an object that is vibrationally decoupled from its environment and arranged on at least two support means, from dynamic acceleration measurements after vibration excitation of the object, comprises the steps a) Establishing multiple points of force application on the object, b) Arranging a number of accelerometers on the object, c) Excitation of the object at the force application points determined in step a) using vibration generating devices and determination of a number of frequency response functions from the accelerations measured using the accelerometer devices, d) Calculating an acceleration vector of the object from the frequency response functions obtained in step c), e) Calculating a displacement vector from the acceleration vector determined in step d), f) Calculating a number of dynamic bending stiffness curves from the forces acting at the points of force application and the deflections of the object induced by the displacements with the displacement vector, g) Extrapolating at least one of the dynamic bending stiffness curves obtained in step f) to a frequency f=0 Hz to obtain the static bending stiffness of the object.

[0017] The invention is based on the fundamental idea of ​​calculating selected frequency response functions after vibration excitation of the object, which form transfer functions, in such a way that the bending of the object can be described by a single dynamic bending stiffness curve. Due to decoupling modes of the object, this real measurement curve is erroneous in a low-frequency region of the frequency response and is therefore extrapolated to a frequency f=0 Hz in order to obtain the static bending stiffness. Surprisingly, it has been found that the static bending stiffness obtained by extrapolating the dynamic bending stiffness curve to f=0 Hz corresponds, within the range of usual error tolerances, to the static bending stiffness measured using displacement measuring devices, in particular dial gauges, or calculated in simulations.The method presented here is particularly suitable for determining the static bending stiffness of complex objects, such as car body shells or so-called "trimmed bodies". An advantage of the method described here is that the bending stiffness can be obtained almost as a byproduct of a modal analysis, without having to change the experimental setup.

[0018] In an advantageous embodiment, it is proposed that for extrapolation in process step f), the dynamic bending stiffness curve with the lowest curve profile of all dynamic bending stiffness curves is used. Investigations have shown that this dynamic bending stiffness curve is best suited for extrapolation to the frequency f=0 Hz, and results for the static bending stiffness are obtained that are very close to the values ​​calculated for this quantity using simulation models.

[0019] It has been shown that the bending stiffness curve in the low-frequency range can be described by a third- or fourth-degree polynomial. In a particularly advantageous embodiment, it is therefore proposed that the dynamic bending stiffness curve be extrapolated to the frequency f=0 Hz using a third- or fourth-degree polynomial. In this context, it has proven advantageous to extrapolate the dynamic bending stiffness curve using a third- or fourth-degree polynomial P that has a slope P'=0 at the frequency f=0 Hz.

[0020] Advantageously, at least three (preferably uniaxial) accelerometers are used, with one accelerometer being positioned at each of the two outer reference points of the object and at a position where maximum deflection is expected. The two outer reference points can preferably be formed by the positions of the two support points. For objects where the point of maximum deflection is unknown or only very vaguely known, it has proven advantageous to use additional accelerometers. These additional accelerometers also have the advantage of being able to detect possible asymmetries in the object's deflection curve.

[0021] In order to minimize the influence of local disturbances, a preferred embodiment may provide that the acceleration sensor means are arranged at a distance from the force application points on the object.

[0022] In a particularly advantageous embodiment of the method, it is possible that in step d) an inertia matrix is ​​formed which is multiplied by a force vector, formed from the forces acting at the points of force application during vibration excitation, to determine the acceleration vector.

[0023] In a further advantageous embodiment, it can be provided that line loads or area loads acting on the object are simulated by a number of force application points spaced apart from each other in a row or in an area.

[0024] Preferably, impact hammers or electrodynamic or hydrodynamic vibration generating devices, in particular so-called "shakers", can be used as vibration generating means, which act on the points of force application and set the object into vibration.

[0025] Further features and advantages of the present invention will become clear from the following description of preferred embodiments with reference to the accompanying figures. Fig. 1 a schematic representation of a beam-shaped object that is subjected to a force and thereby experiences a deflection, Fig. 2. A functional flow diagram of a method for determining the static bending stiffness of an object from dynamic acceleration measurements after vibration excitation of the object. Fig. 3 a schematically simplified representation of a beam-shaped object with a longitudinally variable cross-section and with a number of force application points and a number of acceleration sensor means, Fig. 4 an inertia matrix consisting of measurements on the in Fig. The object shown in section 3 can be obtained. Fig. 5 a reduced inertia matrix, Fig. 6 A side view of a motor vehicle body shell with the schematically indicated positions of several force application points and several acceleration sensor means.

[0026] In developing the method presented here for determining the static bending stiffness of an object 1 from dynamic acceleration measurements after vibration excitation of the object 1, geometrically very simple objects 1 were initially investigated. The method was adapted and validated. Subsequently, the investigation was extended to a car body shell, which represents an extremely complex object 1. To facilitate understanding of the method, some basic mechanical concepts will first be explained below.

[0027] In Fig. Figure 1 shows a beam-shaped object 1 with a constant cross-section, which is vibrationally decoupled from its surroundings and arranged on two spaced-apart supports 2, 3. Mechanical decoupling from the surroundings can be achieved, in particular, using expanders or elastic bands. A compressive force F acts at the midpoint between the two supports 2, 3, causing a deflection of the object 1. A maximum deflection w max is visible in the center of object 1. The force system is in static equilibrium. Three force application points 4 can be identified where the forces acting in static equilibrium act. For the bending stiffness c B applies cB=Fwmax

[0028] The bending stiffness of object 1 depends on the modulus of elasticity of the material from which object 1 is made, the object geometry, and the distance between the supports 2 and 3. Furthermore, the type of load influences the bending stiffness of object 1. For example, it makes a difference whether object 1—as in Fig. 1 shown - with a single force acting in the middle between the two support means 2, 3 or with an off-center single force or with a load acting linearly between the support means 2, 3 or with a surface load.

[0029] The following will be discussed with further reference to Fig. 2. The functional sequence of the procedure will be explained in more detail.

[0030] In a first step, the load case to be investigated is selected from a multitude of possible load cases. By selecting the load case, those areas of object 1 are chosen on which a force acts during the subsequent test, potentially leading to vibration excitation of object 1. These areas will subsequently be referred to as force application points 4. Preferably, the locations of the force application points 4 (and thus the load case) can be freely chosen. However, the rules of statics must be observed when selecting the force application points 4. It must therefore be ensured that static equilibrium exists. The magnitude of the external force F itself has no influence on the bending stiffness.

[0031] At the in Fig. The beam-shaped object 1 shown, which rests on the two spaced-apart support means 2, 3 and is subjected to a force in the middle between the support means 2, 3, allows a relatively valid statement about the bending stiffness c to be made without much effort. B This can be obtained. If the object under investigation 1 is, for example, flat and essentially plate-shaped, a line load acting centrally between the supports 2, 3 can be simulated using several individual forces. The larger number of individual forces reduces local effects. However, the effort required for the measurements and the evaluation of the measurement data increases.

[0032] In a second step 200, the measurement setup is defined. Object 1 is to be excited with external forces at the positions defined in the first step 100, i.e., at the defined force application points 4. With reference to Fig. Figure 3, in which a beam-shaped object 1 with a cross-section that varies in the longitudinal direction (x-direction) is shown, shows at least three accelerometers 5 attached to the object 1. Two of the accelerometers 5 are located at two outer reference points of the object 1 (preferably in the area of ​​the support means 2, 3, which are shown in Figure 3). Fig. 3 (not explicitly shown for the sake of simplicity) are attached. At least one further acceleration sensor 5 is attached to the object 1 at the position where the maximum deflection w occurs. max of object 1 is presumed. For objects 1 where the point of maximum deflection is unknown or only vaguely known, the following should be done - as in Fig. Figure 3 shows that additional accelerometers 5 can be advantageously used to increase accuracy. To avoid local interference or to minimize its influence on the measurement results, it is particularly advantageous if the accelerometers 5 are spaced away from the force application points 4. Preferably, uniaxial accelerometers 5 are used.

[0033] In a third process step 300, the actual measurement takes place. Here, object 1 is excited at the force application points 4 defined in the first process step 100. The structure-borne sound generated by the mechanical impulses acting on object 1 excites the object 1 and sets it into mechanical vibration. For geometrically simple objects 1 (for example, beam-shaped or plate-shaped objects 1), so-called impulse hammers are used to excite the vibrations. For more complex objects, such as a car body shell, electrodynamic or hydrodynamic vibration generators, in particular so-called "shakers," are used. In the latter case, the test setup includes amplifiers for controlling the shakers. The acceleration sensors 5 locally detect the resulting accelerations.In this way, a number of so-called frequency response functions (FRFs) are obtained. The experimental setup includes appropriate means for processing the force and acceleration signals. The evaluation of the measurement and test data is software-based and performed using a computer unit that executes the corresponding computer program.

[0034] The number n of frequency response functions is obtained from the product of the number i of accelerometer centers 5 and the number j of force application points 4 where a force acts on the object 1 and excites it to oscillations. Therefore, the number n of frequency response functions is given by... n=i⋅j

[0035] Mathematically, frequency response functions have a real part and an imaginary part. However, only the real part of the frequency response functions is considered for the evaluation of the measurement results.

[0036] With renewed reference to Fig. In Figure 3, five force application points 4 are used to investigate the beam-shaped object 1 with a variable cross-section. Two of these points are located at the support means 2, 3 (not explicitly shown here), and seven acceleration sensor means 5 are used. Two of the acceleration sensor means 5 are located in the area of ​​the support means 2, 3. In this way, several different load cases can be simulated. This measurement setup then yields n=35 frequency response functions. As in Fig. As can be seen in Figure 3, several positions P1-P9 can be defined on object 1 in the x-direction, at which either a force application point 4 or an acceleration sensor 5, or both a force application point 4 and an acceleration sensor 5, are present. To avoid interference, the acceleration sensor 5 at those positions P1, P5, P9 where they coincide with the force application points 4 in the x-direction are offset in the y-direction (i.e., into the plane of the drawing) from the force application points 4.

[0037] In a fourth process step 400, an inertia matrix h is first calculated. ij formed, which in Fig. 4 for the in Fig. The object 1 shown in Figure 3 is depicted. The indices i indicate the positions of the accelerometer means 5. The indices j indicate the positions of the force application points 4. Based on the in Fig. In example 3, it becomes clear that although accelerometers 5 are present at positions P3, P4, P6, and P7, no excitations occur there. The corresponding columns can therefore be derived from the inertia matrix h. ij will be removed. Furthermore, the following will be removed: Fig. 3 clearly shows that no accelerometers 5 are present at points P2 and P8, even though excitations occur there. Therefore, the corresponding rows are also removed from the inertia matrix. This reduces the original 9x9 inertia matrix to a 7x5 inertia matrix, as shown in Fig. 5 is shown.

[0038] By defining the inertia matrix h ij Subsequently, multiplying this with the force vector formed from the magnitudes of the forces F1, F2, F3, F4, F5 acting at the individual (in this case five) points of force application yields an acceleration vector with the components a1, a2, a3, a4, a5, a6, a7.

[0039] In a fifth step, 500, a displacement vector is calculated. z→ calculated. The following applies to this one: z→=a→ω2=a→(2πf)2

[0040] The quantity ω denotes the angular frequency (the quantity f is the measured frequency).

[0041] In a sixth step 600, at least one dynamic bending stiffness curve (usually several dynamic bending stiffness curves) is determined.

[0042] For the dynamic bending stiffness c B,dyn applies cB,dyn=Fw(x)

[0043] For the deflection w(x) at position x (in the longitudinal direction of object 1) the following applies: w(x)=|z(x)−z0(x)|−(x−x0)⋅|z0−zl|xl−x0

[0044] In this formula, z(x) describes the displacement of object 1 in the z-direction at position x. Furthermore, z0 and z give l the rigid body displacements of object 1 at locations x0 and x lthe displacements z(x) of object 1 at positions x can thus be used to determine the deflection w(x) at these positions.

[0045] In this way, several dynamic bending stiffness curves are typically obtained in the sixth process step. The "true" dynamic bending stiffness c B,dyn This corresponds to the bending stiffness curve with the lowest curve profile, since the bending stiffness c B applies cB=Fwmax

[0046] Therefore, of the bending stiffness curves determined in the manner described above, the one with the lowest curve profile is selected for further processing in the seventh process step 700.

[0047] In this seventh and final process step 700, the static bending stiffness C is determined. B,statThe dynamic bending stiffness curve determined in step 600 with the lowest curve profile is extrapolated. The dynamic bending stiffness curve is extrapolated to a frequency f=0 Hz. Preferably, a third-degree or fourth-degree polynomial P with a slope P'=0 at the frequency f=0 Hz is used for this purpose.

[0048] It has been shown that the static bending stiffness C obtained by extrapolating the dynamic bending stiffness curve to f=0 Hz B,stat within the scope of usual error tolerances of the static bending stiffness measured by the use of displacement measuring devices, in particular dial gauges, or calculated in the context of simulations.

[0049] The method presented here is also suitable for determining the static bending stiffness of complex objects 1, such as the body shells 10 of motor vehicles or so-called “trimmed bodies”. Fig.Figure 6 shows an exemplary body shell 10 of a motor vehicle with three force application points 4 and nine acceleration sensor means 5 for carrying out the method described above. The body shell 10 has two damper domes 11, 12 spaced apart longitudinally (in the x-direction), each comprising a force application point 4 and an acceleration sensor means 5 near the respective force application point 4. Another force application point 4 is provided on a sill flange 13 of the body shell 10 in the middle between the damper domes 11, 12. An acceleration sensor means 5 is also arranged near this sill-side force application point 4. The remaining six acceleration sensor means 5 are arranged in a line below the door cutouts of the body shell 10 (for example at intervals of + / -100 mm, 200 mm, 300 mm from the center) between the damper domes 11, 12.

Claims

[1] Method for determining a static bending stiffness (C B,stat ) of an object (1) which is vibrationally decoupled from an environment and arranged on at least two support means (2, 3), from dynamic acceleration measurements after vibration excitation of the object (1), comprising the steps a) Establishing a plurality of force application points (4) on the object (1), b) Arranging a number of accelerometer means (5) on the object (1), c) Exciting the object (1) at the force application points (4) determined in step a) using vibration generating means and determining a number of frequency response functions from the accelerations measured using the acceleration sensor means (5), d) Calculating an acceleration vector of the object (1) from the frequency response functions obtained in step c), e) Calculating a displacement vector from the acceleration vector determined in step d), f) Calculating a number of dynamic bending stiffness curves from the forces acting at the force application points (4) and the deflections of the object (1) induced by the displacements with the displacement vector, g) Extrapolating at least one of the dynamic bending stiffness curves obtained in step f) to a frequency f=0 Hz to obtain the static bending stiffness (C B,stat ) of the object (1). [2] Method according to claim 1, characterized by , that for extrapolation in process step f) the dynamic bending stiffness curve is used which has the lowest curve profile of all dynamic bending stiffness curves. [3] Method according to one of claims 1 or 2, characterized by , that the dynamic bending stiffness curve is extrapolated using a third- or fourth-degree polynomial (P). [4] Method according to claim 3, characterized by , that the dynamic bending stiffness curve is extrapolated with a third or fourth degree polynomial (P) which has a slope P'=0 at the frequency f=0 Hz. [5] Method according to any one of claims 1 to 4, characterized by , that at least three accelerometer means (5) are used, wherein one accelerometer means (5) is attached at two outer reference points of the object (1) and at a position where maximum deflection is expected. [6] Method according to any one of claims 1 to 5, characterized by , that the acceleration sensor means (5) are arranged at a distance from the force application points (4) on the object (1). [7] Method according to any one of claims 1 to 6, characterized by, that in step d) an inertia matrix is ​​formed which is multiplied to determine the acceleration vector by a force vector formed from the forces acting at the force application points (4) during vibration excitation. [8] Method according to any one of claims 1 to 7, characterized by , that line loads or area loads acting on the object (1) are simulated by a number of force application points (4) spaced apart from each other in a row or in an area. [9] Method according to any one of claims 1 to 8, characterized by , that impulse hammers or electrodynamic or hydrodynamic vibration generating devices are used as vibration generating means, acting on the force application points (4) and causing the object (1) to vibrate.

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