WO2001033183A1

WO2001033183A1 - An equipment and a method for testing bodies

Info

Publication number: WO2001033183A1
Application number: PCT/NO2000/000362
Authority: WO
Inventors: Dag Hermann Andersen; Egil Lundberg
Original assignee: Norsk Hydro Asa
Priority date: 1999-11-05
Filing date: 2000-11-01
Publication date: 2001-05-10
Also published as: NO995416D0; NO312527B1; AU1180401A; NO995416L

Abstract

The present invention concerns an equipment and a method for testing bodies made of a material which expediently has a uniform structure. The present invention may advantageously be used to test carbon electrodes which are to be used in an electrolysis process and is based on mapping the natural frequencies and damping factors (modal parameters) of the electrode. These parameters are used to provide information on whether the electrode has global or local defects, for instance cracks or density gradients.

Description

An Equipment and a Method for Testing Bodies

The present invention concerns an equipment and a method for testing bodies with regard to mapping physical defects and inhomogeneities in the form of cracks and density variations. The material tested will expediently have a simple structure. An application of the invention is to test carbon electrodes for use in an electrolysis process.

Electrodes produced from materials containing carbon are used in connection with the production of aluminium in accordance with the Hall-Heroult principle. The electrodes are usually produced from coke or grafite and a binder being mixed to form a so-called "green" paste. The paste is subsequently given the desired shape either by extrusion or by being placed in a mould which is subjected to vibration or compression. The "green" electrode produced in this way is then subjected to a calcination process before use in the electrolysis cell. When it is inserted in the electrolysis cell, it is very important that it has good thermal and mechanical properties and that its electrical resistance is not too high.

In connection with the production of carbon bodies as stated above, inhomogeneity may occur in the material which is not visible from the outside of the body. Such defects may, in particular, involve cracks, cavities and areas with a lower degree of binding than required.

The purpose of the present invention is to be able to determine whether such defects are present in a body and the extent and orientation of the defects. For carbon electrodes such testing may preferably be done after the calcination process, but before it is inserted in the electrolysis cell.

The present invention will be described in further detail in the following using examples and figures, where:

Figure 1 shows the first natural frequencies of an anode carbon,

Figure 2 shows the first mode shapes for a simulated anode carbon, more precisely the first three natural frequencies, Figure 3 shows a schematic measurement setup for mapping the orientation of the cracks.

The natural frequencies and damping factors (modal parameters) of a body such as a carbon electrode, provide information on local defects such as cracks or density gradients. They will also be able to provide information on how serious these defects are. In order to map the orientation of the cracks in the carbon with modal testing, it is necessary also to map the mode shapes of the carbon (the movement of the carbon for the various natural frequencies) in addition to the modal parameters. This will require a measurement setup which is described schematically in Figure 3.

Regarding finding information on defects in the body , it is possible, on the basis of a "modal point of view", to divide the information which can be found into 4 categories:

1 ) Acquiring information on physical defects in all types of bodies produced from a material with a homogeneous structure.

2) Acquiring information on physical defects in all types of bodies produced from a material, where physical defects here are defined as: Inhomogeneous physical defects; density gradients and/or elasticity gradients in the body are outside their natural variation ranges. Homogeneous physical defects; the mean density and/or elasticity of the body are/is outside their natural variation ranges.

3) Determining the extent, orientation and position of the physical defects in all types of bodies on the basis of measured natural frequencies, damping factors and mode shapes of the body, where physical defects here are defined as:

Inhomogeneous physical defects; density gradients and/or elasticity gradients (cracks, porosity) in the body are outside their natural variation ranges.

Homogeneous physical defects; the mean density and/or elasticity of the body are/is outside their natural variation ranges. 4) Determining the extent, orientation and position of the physical defects in electrodes used in the aluminium process, both in baked and green states, on the basis of measured natural frequencies, damping factors and mode shapes of the electrode, where physical defects here are defined as:

Inhomogeneous physical defects; density gradients and/or elasticity gradients in the body are outside their natural variation ranges. Homogeneous physical defects; the mean density and/or elasticity of the body are/is outside their natural variation ranges.

Elasticity gradients can be caused by cracks, porosity, etc. Density gradients can be caused by porosity, cavities, etc.

Parameters which describe a body's elasticity may be Young's modulus, shear modulus, bulk modulus, Poisson number, etc.

Physical defects which will be detected are defects characterised by a change in the density and/or elasticity of the anode carbon as well as a change in the physical dimensions of the carbon. Cracks which occur in the carbon will reduce elasticity locally.

The simpler the structure of the body, the greater the possibilities of finding all types of information on physical defects (extent, orientation and position of the defect). This means that the present invention will produce better results for bodies which have a simpler structure and are approximately symmetrical about at least one plane. The simpler structure of the body also means that the method and equipment for testing can be simplified. In turn, this means that the technique can be realised more easily, for example on production lines on which products have a simple structure.

Since the dimensions of a type of electrode carbon are approximately constant, the dimensions will not influence changes in the modal parameters beyond a typical standard deviation for the modal parameters. The modal test will also offer the opportunity of distinguishing between inhomogeneous and homogeneous defects. If the density is generally higher for the entire carbon, this will be a "homogeneous defect". This may be due to normal process variations. A crack will lead to an inhomogeneous defect as elasticity is reduced locally in the carbon.

Inhomogeneous defects will disturb the percentage frequency gaps between the resonance frequencies. Homogeneous defects just displace the resonance frequencies. However, the percentage frequency gaps between the resonance frequencies are maintained with a typical standard deviation.

The extent of an inhomogeneous defect is mapped by seeing how much individual resonance frequencies have decreased/increased in value in relation to other resonance frequencies. This information combined with mapping of damping factors makes an important contribution to the information.

There are several methods for mapping the plane in which the defect is extensive. The simplest method is to study how the mode shape of the first 3-6 resonance frequencies has changed. The mode shapes are mapped by mapping the imaginear amplitude at resonance in various positions on the carbon. At least two sensor positions will be necessary to map the mode shapes of the very first resonance frequencies of the carbon electrode (in each sensor position, acceleration is measured in 3 directions).

Carbon electrodes are symmetrical about several lines. This will also lead to symmetrical modes of oscillation if the carbon is physically homogeneous. An inhomogeneous defect thus creates asymmetrical mode shape. Therefore, it will also be of interest to study the mode shapes in order to detect inhomogenous defects. The interaction of the damping factors will be able to contribute important information here too.

Regarding the piece of information stated under 3 above, it is necessary to map asymmetrical mode shapes with greater resolution, i.e. several sensor positions. For example, 3 accelerometers can be moved to 4 positions. In connection with a further description of the present invention, an anode carbon with the dimensions 70cm_x 56cm_x lAOcm _was simulated using a modal analysis module in software called ANSYS. The model assumed free undamped vibrations. This meant that the damping factors were not simulated, just the natural frequencies of the carbon. In order to save time when constructing the model in ANSYS, the nipple holes were modelled square instead of round. The element size was selected as 8 cm. A lower element size increases the level of accuracy but also the calculation time. An element size of 8 cm was selected here for reasons of cost. One disadvantage of this is that the model becomes less sensitive to cracks as the element size increases.

The anode carbon was simulated with a Young's modulus of 9ΛGPa _and _a density of \.55 gl cm _ τh_e first 19 natural frequencies of the anode carbon are shown in Figure 1.

From Figure 1 , the first natural frequency is 474 Hz, the second is 499 Hz, the third is 567 Hz, etc. Each natural frequency represents a mode of oscillation.

In Figure 2, the modes of oscillation or mode shapes are shown for the first 3 natural frequencies. The first mode shape shown in Figure 2a-b is a torsional mode with a frequency of 474 Hz. The mode shape shown in Figure 2c-d has a frequency of 499 Hz and the third mode shape (figure 2e-f) has a frequency of 567 Hz.

In theory, the natural frequencies for a rectangular body with cross-section A= h x b, where the mode forms are not torsional modes will in accordance with "E.M. Uygur, Nondestructive Dynamic Testing, Chapter 6, Vol. 4, Research Techniques in Nondestructive Testing. R. S. Sharp, Ed., Academic Press, 1984", be given as:

f^{r ~} Klπ - J ^' I^ Ap (1.1 )

where k = constant, different for each individual mode L = length

E = Young's modulus / = "second moment of area" = bh³/12 (£>=width, h = height) g = acceleration due to gravity A - cross-section p = density

The carbon electrodes have a natural variation range with regard to the natural frequencies since carbon is normally produced with slightly varying dimensions, elasticity and density. The natural standard deviations of the carbon electrodes will thus be given as a function of the standard deviations of Young's modulus, the dimensions and the density. Regarding dimensions, the height of the carbon in particular has the greatest uncertainty. Uncertainty with regard to the length and width is ignored here. The standard deviations of the natural frequencies will thus be given as:

^sr^, = (!__^{■ ' SE +} d^ ^{' s}pJ + C h^{" ' 5/}') (1 2)

In this equation, the expression in (1.1 ) has been partially derived with regard to Young's modulus, density and height.

With S_E~ 400MPa (typical standard deviation for Young's modulus), S_/ ~ 20kg/m³ (typical standard deviation for density) and S/< ~ 0.003m (typical standard deviation for height), the natural standard deviations for the natural frequencies are as follows:

S_/_ ~ 12Hz for natural frequencies of approximately 500 Ηz Sz, « 24Hz for natural frequencies of approximately 1000Hz S_t, « 36Hz for natural frequencies of approximately 1500 Ηz

The standard deviation of a natural frequency is thus 2.4 % of the value of the natural frequency. If the natural range of variation is defined as ^±2S the natural frequencies will have a natural variation range of fr, refe ence ±4.8%_^ |f natural frequencies outside this range are measured, there is reason to believe that a defect has been introduced into the carbon.

If a crack occurs in the carbon, we can see from equation (1.1 ) that only Young's modulus can be affected in the equation. The dimensions and density will be virtually unaffected regardless of whether there is a crack or not. If we ignore the natural variations in the natural frequencies, the natural frequencies will be proportional to

f_r a Ε (1 .3)

for modes which are not torsional modes, and

(1 .4)

for torsional modes, where S is the shear modulus.

A crack in the carbon will reduce the rigidity in one direction or other in the carbon. Young's modulus or the shear modulus will then decrease in this direction. If we have global defects so that Young's modulus decreases in all directions in the carbon, this means that all mode forms are affected in such a way that the natural frequencies for each individual mode form decrease. The natural changes in density, dimensions and Young's modulus from the process will generally apply globally to the entire carbon. This means that if the percentage gaps between the natural frequencies are much the same from carbon to carbon, even if the natural frequencies have decreased in value, this is probably due to natural changes caused by the process and not defects such as density gradients and cracks. If the percentage gaps between the modes vary from carbon to carbon, this is on account of local defects such as cracks or local density gradients. For example, a crack will never be able to reduce Young's modulus equally in all directions in the carbon. This will lead to the percentage gaps between the modes changing.

Global changes in Young's modulus, density and dimensions will not affect the percentage frequency gap between the modes. Only gradients of density or Young's modulus type will affect the percentage frequency gaps between the modes.

Regarding defects such as density gradients, this affects the natural frequencies by the density changing locally in the carbon. The effective oscillating weight for individual modes will then be changed. Since density gradients are also of a "local nature", this will affect the percentage gaps between the modes.

Equation (1.1 ) was tested with the model in ANSYS by checking whether all natural frequencies decreased quadratically with a reduction in Young's modulus. The tests showed that when we reduced Young's modulus for the entire carbon by 11.0 % (from 9.1 GPa to 8.1 GPa), all 19 modes (from Figure 1 ) were reduced by 5.5 %. When Young's modulus for the entire carbon was reduced by 34 % (from 9.1 GPa to 6.0 GPa), all modes were reduced by 18.8%.

When the density of the entire carbon was reduced by 3 % (from 1.55 to 1.50 g/cm3), the natural frequencies for all modes increased by 1.6 %. When the density of the entire carbon was increased by 3 % (from 1.55 to 1.60 g/cm3), all natural frequencies decreased by 1.6 %.

We see here that a global change such as changing Young's modulus or the density for the entire carbon will not affect the percentage frequency gap between the modes. Only local gradients in the form of elasticity or density can do this.

The damping factors for each mode form provide information on how fast the various modes of oscillation die out. In accordance with "E.M. Uygur, Nondestructive Dynamic Testing, Chapter 6, Vol. 4, Research Techniques in Nondestructive Testing. R. S. Sharp, Ed., Academic Press, 1984", this can be expressed as:

= π-At-f_r

(1 -5)

where ^Δ/ is the time it takes until the vibration amplitude (acceleration) has fallen to 63.2 % of its original value. Obstructions in materials cause this time to be reduced as vibrational energy is transformed more quickly into, for example, thermal energy on account of friction in the obstructions. A carbon with local defects will, therefore, lead to a higher damping factor for individual modes.

The modal parameters were found by mapping the body's transfer functions, which here describe the relationship between acceleration and the force applied to the body. For example, the transfer function, H(aix/F), will describe the relationship between the acceleration measured in the x direction at position 1 and the force applied.

To map the transfer functions, equipment is required to:

1 ) Generate forces against the body which contain relevant frequency components: As will be seen from figure 3, a signal generator module 8 of type 3107 is used for this. It is connected to a power amplifier 6 of type 2712, which is connected to a vibration source 2 of type 4808. The vibration source is pressed against the carbon at a 45° angle in the x, y, and z directions. The vibration source is pressed against one corner (the corner is ground so that the ground surface is normal to the direction of the force).

2) Measure the forces applied to the body: A force sensor 3 of type 8200 is used here. It is connected to a charge amplifier 5 of type 2635, which is, in turn, connected to an input module 7 of type 3022.

3) Measure the acceleration at various points of the body for the x, y and z directions: A 3-axis accelerometer 4 of type 4504 is used here. It is connected to an input module 7 of type 3022. The accelerometer measures acceleration in the x, y and z directions.

4) Analyse the frequency of the signals measured: A software FFT analyser is selected here.

A PC 9 with Labshop 4.0 software co-ordinates and starts/stops/configures the signal generator and FFT analyser and calculates the transfer functions. Bruel & Kjaer equipment was chosen. The type designation is given for each piece of equipment.

A standard anode carbon was tested to find out which requirements should be made for a measurement setup which results in the modal parameters being measured with sufficient accuracy and sensitivity and which can be realised operationally.

The aim of the excitation source is for it to excite a force against the carbon which provokes the natural frequencies of the carbon optimally. Firstly, this means that the force against the carbon should be a "random" signal which contains the frequency components in the range in which the natural frequencies are expected to exist. For the anode carbon, a frequency range of 300-1900 Hz is selected. Selecting a "random" signal means that the first 20 natural frequencies of the carbon will be covered with certainty. The frequency analyser for the PULSE system sketched in Figure 3 can manage a resolution of maximum 1 Hz in a frequency range of 1600 Hz. If it is necessary to increase the resolution, the frequency range to be analysed must be reduced.

Another important point is how the direction of the excitation force is selected. To select a force direction which provokes all modes, it is necessary to have a direction in which the force has components in the x, y and z directions of the carbon (see Figure 3). This means that the excitation must be diagonal. The ideal method is to place the excitation source so that the force has a direction which is ⁴⁵° to the x, y and z directions of the carbon. The measurement setup is shown in Figure 3, in which the excitation source 2 is placed so that it produces an equal force component in the x, y and z directions against the carbon 1. At the same time it is placed against an end.

Figure 3 shows that the force excited against the anode carbon 1 is excited at 45° to the x, y and z directions. In order to realise this, one edge of the anode was ground so as to form a surface against which vibration was applied. The force will be normal to this ground surface. This test was not fully nondestructive as one edge of the anode was ground. This simplifies the measurement setup considerably.

During the tests, one corner of the carbon was ground down so that excitation was possible against a plane on the carbon which was ⁴⁵° to the top surface, short side and long side. The excitation source 2 was adjusted with an adjustable ramp made specially for the tests (the carbon is turned upside down in the tests). The ground surface did not need to be larger than a few square centimetres.

The tests showed that it was unnecessary to screw the excitation source to the surface of the carbon. No extra noise was introduced by the excitation source being pressed against the surface (explanation later). The excitation source could produce a maximum of 112 N. In all the tests, the source was pressed against the carbon so that the source produced a maximum of 102 N against the carbon. This could be measured as the force sensor 3 was placed between the carbon and the excitation source as shown in Figure 3. The signal-to-noise ratio was greatest (or the coherence →¹) when the maximum force was applied. The excitation source of type 5 4808 used in the measurements is the most powerful Bruel og Kjaer vibration source with which it is still possible to use a standard 220 Volt power supply. In accordance with Figure 3, a force sensor 3, connected to a charge amplifier 5, is arranged between the excitation source and the carbon. The charge amplifier is also connected to a 4-channel input module 7, which is also connected to a 3-axis 0 accelerometer 4. A generator module 8 is connected to the excitation source 2 via a power amplifier 6. A computer 9 is also connected to the generator module 8 and the 4-channel input module.

The measurement station can be installed on a conveyor line after the baked state or 5 af te r th e g ree n state .

1 ) The electrode is placed on a rubber mat (for example, wear-resistant rubber).

2) The surface is ground in one corner so that forces can be excited at 45° to the x, y 0 and z directions. For anodes, the surface can be produced in vibration moulds in the mass factory.

3) The vibration source is pressed against the ground surface.

5 4) A mounting for the accelerometers is pressed against the electrode while the accelerometer itself is magnetically fastened to the mounting (alternatively, contactless laser transducers can be used).

5) The signal generator starts and emits a random signal in the desired frequency 0 range. The electrode has random forces applied to it.

6) The measurements start by the FFT analyser starting. The transfer functions are thus found. 7) Software calculates the modal parameters on the basis of the transfer functions and returns information on physical defects to the user on the basis of the modal parameters. The modal parameters may be saved in operational databases.

8) The vibration source/accelerometers and mounting are removed from the electrode.

9) The electrode is taken off the rubber mat and continues along the production line.

The measurement time will be approximately 30 - 60 seconds per product, depending on how many acceleration positions are selected.

Software has already been developed which finds and calculates the modal parameters on the basis of the transfer functions found. Algorithms have been developed which safeguard against incorrect measurement, cable breakdown, defective accelerometers and poor level of accuracy in the measurements.

The software can contain algorithms which indicate the status of the body on the basis of the modal parameters measured. The modal parameters must be analysed with the operating parameters and other parameters which describe the physical state of the body in order to develop algorithms which return a status report to the user on whether the electrode has physical defects.

The accelerometer 4 was placed in a position in which it was expected that the modes had the greatest acceleration. For most modes, this will be against one end of the carbon. The accelerometer was therefore placed diagonally in relation to the excitation source against one end of the wearing surface (see Figure 3), 12 cm in on the carbon from the long side and 12 cm in from the short side.

The accelerometer is a 3-axis accelerometer which contains 3 sensors, each of which measures acceleration in 3 directions, which are the x, y and z directions shown in Figure 3. By measuring acceleration in 3 directions, it is ensured to measure all modes even if some modes do not have acceleration components in one of the directions at the point of measurement. One accelerometer will therefore be sufficient for mapping the modal parameters of the carbon in particular when the accelerometer is of a 3-axis accelerometer type. However, one accelerometer is not sufficient if it is also necessary to map the mode shapes of the various modes. This requires a set of sensors (5-6 along the surface of one carbon) so that the acceleration at each point is read off. In reality, this means:

With a 3-axis accelerometer, the modal parameters are mapped for the carbon (natural frequencies and damping factors). This means that global and local defects in the carbon can be mapped. This concerns defects which affect elasticity and density such as cracks and density gradients. The orientation of the defect can be found to a certain degree by demonstrating that the defect has a probable extent in the xy, yz or xz plane (the crack is either horizontal or vertical).

A 3-axis accelerometer in one position can, to a certain degree, tell something about the mode shape and thus give information on the orientation of cracks.

With a set (5-6) of sensors placed along one side of the carbon, the orientation of the defect can be mapped in more detail and with greater certainty as, in addition to the modal parameters, it will also be mapped the mode shapes for each natural frequency.

In the tests, the 3-axis accelerometer was fastened magnetically to a thin metal plate which was packed in grease on the carbon.

The measurement setup described above was tested. In this connection, the carbon was placed on a rubber mat which was 0.5c/?. _Λ- 100cm x 80c.... τ_ne rubber mat was placed under the carbon so that the carbon was in the centre of it. The excitation source and accelerometer were placed as shown in Figure 3.

A comparison of the simulated natural frequencies in Figure 1 with those measured in the test showed a striking similarity. The natural frequencies measured show clear 3-decibel bandwidths, which proves that the noise is minimal with this measurement setup.

Based on the above principle, it is possible to set up a measurement station on a conveyor line or production line in connection with a production unit for carbon electrodes. Alternatively, the measurement station can be installed on a conveyor line in connection with the electrolysis system. It is expected that a man skilled in the art will be able to set up such a measurement station on the basis of the above description. Therefore, it will not be described in further detail here.

Claims

1. Equipment for testing bodies (1), in particular bodies made of a material with a simple structure, such as carbon electrodes for use in an electrolysis process, characterised in that the equipment comprises at least one excitation source (2) designed to apply a mechanical excitation to the body and at least one accelerometer (4) designed to measure the body's movements, together with means (3, 5, 7, 9) for comparing the movements measured with the excitation applied.

2. Equipment in accordance with claim 1 , characterised in that the excitation source(s) (2) is(are) located at some distance from the accelerometer(s) (4).

3. Equipment in accordance with claim 1, characterised in that it may form an integral part of a conveyor line in an electrode factory or an electrolysis system.

4. A method for testing bodies (1), in particular bodies made of a material with a uniform simple structure such as carbon electrodes for use in an electrolysis process, characterised in that the body is subjected to mechanical excitation and that the body's movements are measured and compared with the excitation applied.

5. A method in accordance with claim 4, characterised in that the excitation is applied at one or more locations on the body's (1) surface and that the body's (1) movements are measured at one or more locations at some distance from where the excitation is applied.

6. A method in accordance with claim 4, characterised in that the excitation is applied at a frequency equivalent to one of the body's (1) natural frequencies.

7. A method in accordance with claim 4, characterised in that defects in the structure of the body are discovered by measuring the percentage frequency gaps between the resonant frequencies of the structure in combination with measured damping factors, whereby this information is interpreted in terms of type and extension of defects based on accumulated knowledge of defects and correponding measuring results.

8. A method in accordance with claim 7, characterised in that homogeneous defects are revealed by measurements and analysis of the extent of mutual displacement in percent of the resonance frequencies.

9. A method in accordance with claim 7, characterised in that the orientation of a defect is revealed by measuring the amplitude ratios at resonance frequencies of the transferfunctions (functions between measured accelleration and excited force) at different positions of the body.

10. A method in accordance with any of preceeding claims 4-9, characterised in that the bodies are tested in line as an integral step in a process for the production and/or the use of the bodies.