Master's Degree Thesis ISRN: BTH-AMT-EX--2011/D-05--SE
Supervisors: Ansel Berghuvud, BTH
Magnus Nilsson, MRT System International AB
Department of Mechanical Engineering Blekinge Institute of Technology
Karlskrona, Sweden 2011
Farshad Shafieian
Investigation on Failure of a Crusher Disk in a Mercury
Recovery Device
Investigation on failure of a crusher disk in a mercury
recovery device
Farshad Shafieian
Department of Mechanical Engineering Blekinge Institute of Technology
Karlskrona, Sweden 2011
Thesis submitted for completion of Master of Science in Mechanical Engineering with emphasis on Structural Mechanics at the Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden.
Abstract:
The disc in a rotary crusher of glass and metal in a mercury recycling system encounters fracture failure due to unknown reason. Possible causes are identified and investigated both numerically by finite element analysis and experimentally including modal analysis and materials, acoustic signature and destructive load characterisation. Knowledge is developed on the conditions needed for failure. It is concluded that the observed fracture during operation occur due to a large force rather than fatigue, and a hypothesis on how this may be realized is put forward.
Key words:
Crusher, Fracture, Fatigue, Modal Analysis, Finite element, Acoustic signature
Acknowledgements
This thesis work is carried out at the Department of Mechanical Engineering of Blekinge Institute of Technology (BTH) and MRT System International AB, in Karlskrona, Sweden, under supervision of Dr.Ansel Berghuvud.
I would like to express my sincere appreciations and gratitude to Dr. Ansel Berghuvud, Andreas Josefsson and Torbjörn Melin for their invaluable help, guidance and motivation during the work on this thesis.
I want also to thank Mr. Magnus Nilsson at MRT System International AB, which always helped and provided all the information was needed for this thesis at the shortest time.
Karlskrona, August 2011 Farshad Shafieian
Contents
1 NOTATIONS 6 2 INTRODUCTION 7
2.1 Problem Addressed 7
2.2 Aim and Scope 8
2.3 Method 8
3 STUDIED SYSTEM 10
3.1 The crusher 10
3.2 Failure 12
3.3 Potential Problems 12
4 THEORY 16 4.1 Introduction to Finite Element Method (FEM) 16
4.2 Modal Testing 17
4.2.1 Introduction to Modal Testing 17
4.2.2 Measurement planning 18
4.2.3 Modal Analysis and Modal Model 18
4.2.4 Power spectral density (PSD) 20
4.3 Introduction to ABAQUS 20
4.4 Ring test 21
4.5 Hardness Testing 22
5 INVESTIGATIONS 23
5.1 Ring test 23
5.1.1 Results 24
5.1.2 Discussion and Conclusion 27
5.2 Modal testing 27
5.2.1 Results 28
5.2.2 Discussion and Conclusion 36
5.3 Curve fitting 37
5.3.1 Results 37
5.3.2 Discussion and Conclusion 39
5.4 Running the machine 40
5.4.1 Results 41
5.4.2 Discussion and Conclusion 42
5.5 Hardness test 43
5.5.1 Results 43
5.5.2 Discussion and Conclusion 43
5.6 Destructive test 44
5.6.1 Results 47
5.6.2 Discussion and Conclusion 53
6 CONCLUSION 54
6.1 Further works 54
7 REFERENCES 56
Appendices
A Plots of the ring test B Coherence function from Modal testing
1 Notations
Residue matrix
Conjugate of residue matrix C Actual system damping
Critical system damping F(s) Force
[H] Mobility matrix H(s) Transfer function K stiffness M mass
Q Scaling constant S Laplace transform X(s) Response function
Poles
Conjugate of poles Relative damping
Undamped factor (rad/sec)
Ω Undamped natural frequency (rad/sec) Eigenvector (mode shape vector) Transpose of eigenvector
Damped natural frequency
Indices
c Damping ratio r number of mode
2 Introduction
Since Industrial Revolution human has kept using the earth’s natural resources without bearing in mind the costs and consequences of this exploit, decreasing of these sources and the side effects of this abuse of natural resources like global warming and so on caused scientists to think of new ways to develop sustainable industries by producing less waste and recycle the used material in order to reduce the consumption of fresh raw materials. One of the most dangerous materials for nature is mercury which is used enormously in different kind of lamps and monitors. After ultimate useful life of products society needs to do something with these wastes which contain mercury and portend disaster for nature which long-term accumulation results in environmental degradation and can affect future human life. MRT System International AB is one of the leading companies in this area and by developing a recycling machine it is possible to separate the mercury and glass and the purpose is to develop and increase the efficiency of this industry as much as possible.
2.1 Problem Addressed
The system which is going to be studied is part of a mercury recovery device which has the duty of crushing of the fed material in order to facilitate the process of recovery, after separating the metal part from the glass they are fed to two different crushers (shown in the picture) and distillers for recovering mercury and also reusing the metal and glass. The reason of studying on this part is that due to some unknown reasons the crusher disk smash into pieces during the work. The challenge is that regardless the working hour and material fed to the device, failure can happen during the few first working hours or after working for a couple of months.
The materials fed to the device are all different parts of HID lamps, CRTs, Batteries and other Hg Waste; the crushing process is done by the same manufactured disk installed on two different motors with different rotation speed, one using for glass parts and the other crush metal parts.
Figure 2.1. Crusher assembly which crush glass and metals.
2.2 Aim and Scope
Based on problem the important issue is how to address the potential reason to reach a good answer. There are different reasons which may cause this problem and it will be mention later. The point is that one thesis work cannot cover all this subjects and for a better result it is needed to narrow down some specific reason and by doing some theoretical and experimental analysis and tests try to get answer. The main focus is on the rotary disk itself in order to check the casting process; hardness and also checking to see how similar the produced parts are. This needed to be done between the parts from different produced batches but the problem was that currently all parts were from a same batch.
2.3 Method
The total work is consisting of four different investigations on the rotary disk. First of all the easiest and quick way to find out is there are crack in the part or not is to use ring test. This test needs kind of experiment on sound of a proper part. In order to be able to document this experiment the sound was recorded and then the data was plotted by the help of MATLAB.
Second, because the first experiment gives results showing no visible problem, in order to make the experiment more accurate modal testing was carried out and resonance frequencies was specified in order to check if the resonance of the motor can motivate and affect the part during the work or
not. Afterward the power distribution of the crusher device was recorded also to check the effect of working condition on rotary disk. The accuracy of the data was checked by using the curve fitting method. The hardness was checked by the company and the results will be shown later. The last experiment was destructive test. According to the companies information they had tried in different ways to break the rotary disk and the failed to do that, so based on a broken part which was send from one of the customers the situations was tried to be simulated by the help of ABAQUS and finding the approximate force needed to break the disk.
3 Studied system
The system has the duty of crushing glass and metals to recover mercury and recycle the material to use them again. The feeding of the material to the system does not have a specific pattern so the load can be applied to the part randomly according to the amount and the material fed to the crusher.
The rotary disk is mounted on to different motors with different RPMs separately use for glass and metal.
3.1 The crusher
The final aim is to find the problem and solve it in order to increase the working performance and customer satisfaction. But for starting it is needed to specify the possible options causes disk breakage and a comprehensive list of all major potential risk factors should be identified, then start to eliminate those which seems to be less likely the reason and then investigate some potential errors further and document them in order to be useful for more investigation until the problem is solved completely.
The rotary disk which has the duty of crushing materials and sometimes breaks during the operation is made of ductile cast iron (ASTM-A536). The part is fully casted without welding along with a plate is fixed to keep four rings which do the crushing.
Figure 3.1. Disk, rings and plate.
In order to get the expected quality two other process of hardening and machining are also operated on each part. The chemical properties of the part according to the Swedish production company are as follow [Data provided from MRT System International AB]:
Table 3.1.Chemical composition
Analys Oven Gods
C 3,50 – 3,70 3,40 +/- 0,10 Si 1,40 +/- 0,05 2,40 +/- 0,10 Mn 0,20 – 0,25 0,20 – 0,25 P Max 0,06 Max 0,06 S Max 0,015 Max 0,015 Cu 0,39 – 0,40 -
Cr Max 0,05 Max 0,05 Ni Max 0,10 Max 0,10 Mg - 0,05 +/-0,01 The other properties are shown in the following table [1].
Table 3.2.Properties of ductile cast iron
Property Value in metric unit
Density 7.2 10
Modulus of elasticity 172 Poisson’s ratio 0.275
Thermal expansion(20°C) 11.6 10 °
Specific heat capacity 506 Thermal conductivity 32.3 Electric resistivity 6.0 10 Tensile strength 496
Yield strength 345
Shrink 0.5 1.0 %
Shear strength 372
Fatigue strength 290 Hardness (Brinell) 200 260
Wear resistance Low
Corrosion resistance Low
Weld ability Low
Machinability Good
Cast ability Good
Shock resistance Medium
This rotary disk is mounted on two different motors which one is used for crushing the glass and the other one is for metals.
The one use for metal has a power of 4 kW and speed of 950 rpm and the other one is 3 kW and the speed is limited to 710 rpm.
3.2 Failure
In order to be able to go forward accurately it is needed to know what had happened to the previous broken parts and in which condition and for how long they had worked. But unfortunately the documentation is not accurate enough because it happens sometimes the customers do not report the failure or even if they report they do not tell what happened exactly so this makes the process a bit more difficult on the other hand this problem is not very common to happen regularly that allow us to start gathering a good report.
There are 13 numbers of reports from the customers which 12 had mentioned that those had been fed metal and aluminum end caps and other metals to crush. The one who had used the disk to crush has given no more information about the working condition and how it happens.
This means that most of the failure happens while the machine is working with hard materials.
3.3 Potential Problems
The final aim is to find the problem and solve it in order to increase the working performance and customer satisfaction. But for starting it is needed
to specify the possible options causes disk breakage and a comprehensive list of all major potential risk factors should be identified, then start to eliminate those which seems to be less likely the reason and then investigate some potential errors further and document them in order to be useful for more investigation until the problem is solved completely.
The potential reasons which may cause failure and break of the rotary disk can be estimated as follow:
1. Design of the part.
2. Basic materials for producing the part.
3. Poor assembly.
4. Casting process.
5. Extra vibration effects.
6. Hardening process.
7. Temperature of the working area.
8. Poor maintenance.
9. Machining process.
10. Electrical fluctuation.
11. Wrong feeding material.
12. Humidity of the working area.
13. Shipping deficiency.
Possible works regarding the potential reasons:
1. What is needed here is to check the designed part and. One way is to check and analyze it by computer aided design programs like ABAQUS, or Autodesk Inventor in which we have the possibility to mesh the part and by the help of finite element method and then applying random loads in different directions and points study the parts behavior.
2. Considering the working condition and feeding materials it is essential to investigate what is the appropriate material for producing the crusher, what is going on now is that for both glass and metal part of the recovery process crusher is the same. It can be more economical if we find out that we can build a cheaper crusher by using cheaper material
with less resistance for the glass crusher and for crushing the harder part may be using more strong materials.
3. Because of the rotation of crusher, it is important to mount the part accurately and in the middle so there is equal space between the disk and the outer case. It is of great importance to check and keep the main shaft nut fastened in order to avoid extra vibrations.
4. Casting process is playing a critical role in the part. The way of cooling has a great importance which can lead to a fine-grained casting if the cooling time is fast and it can be a coarse-grained casting for area which cools slowly and this can affect strength and fatigue life. The problem is that it is possible to check the surface of a casted product with a naked eye but usually the problem occurs in the middle of the part which get cooled at a low speed and for analyzing this part we need to do some NDT tests like acoustic test or comparing the FRF of some different disks from the same and different batches by the help of modal analysis to get some knowledge about the part.
5. External forces should be analyzed carefully and also it is important how and where the crusher is located. If the crusher is not fixed on the ground the rotation of the rotary disk can cause vibration to whole crusher part which is unstable on the ground and this can consequently affect the crushing forces and at last uneven load distribution to rotary disk while crushing fed materials.
6. Surface hardening is the process of hardening the surface of metal, after a low carbon steel has been formed into its final shape. Meanwhile this can make the part brittle which it can break more easily, if the hardening is more than what is necessary for the working condition. For testing the hardening of the part some indentation hardness tests, the Vickers hardness test, Brinell scale or Rockwell hardness test may be used, on the other hand we need to find out the maximum pressure or load and other factors to investigate what is the appropriate hardness for the target part.
7. All materials have a limit for its working condition. High temperature or low temperature can make change to the characteristics of the part so the optimum working temperature should be defined and clearly announced to the customer for a perfect and efficient work.
8. All products need maintenance and services periodically to work properly with better efficiency, there is a possibility of getting some
material stuck in the crusher when you stop working and by running it for the next time the crusher needs more power than what is usually needed and again crack occurs in the part.
9. Machining can also cause some defect on ductile and grey cast iron like hydrogen pinhole, nitrogen blowhole, carbon monoxide blowhole, shrinkage which these are needed to be studied in detail and find out the characteristic of each deficiency and its way of solution.
10. As far as the rotation of crusher is done by an electrical motor, electrical fluctuation can lead to rotary speed changes and this can cause some sudden shocks considering the amount of material crusher has been fed.
In this case the load is more than what is expected so it can easily cause a fracture in the part or got overloaded and break the part immediately.
11. The materials which are going to be fed to the crusher should always be checked because sometimes there are extra materials which by mistake have been fed to crusher and according to its resistance it can cause failure for device.
12. Considering the world wide area product distribution it can be interesting to check if the humidity in parallel to the other factors like temperature can affect the life time of the part or not.
13. This is one of the common problems for the cargos which have long journey and for example falling down can cause a small fracture on the part which can greatly decrease the part’s life time.
4 Theory
In order to get better results from experiments it is better always to go theoretically along with experiment. Considering the condition and part one of the best ways to analyse the part is using finite element method that is one of numerical methods which make complicated problems easier to solve and some of the CAD programs like ABAQUS using the same method to solve the problem. Another theory which is used is Modal analysis which helps to find the natural frequencies of the system and this was used to compare how similar different parts are. Finding the natural frequencies gives us only information about the part itself but when the part is mounted on the crusher device then the situation is different and it is better to check the power distribution in a range of frequency and check if this can affect the resonance frequency of the rotary disk or not and for this purpose power spectral density (PSD) has been used.
4.1 Introduction to Finite Element Method (FEM)
In the field of engineering there are lots of physical phenomena which can be described in terms of partial differential equations (PDE) and these cannot be solve by analytical method when it becomes complicated, it is also hard to find out the exact answer of a complicated polynomial equations, so one way is using numerical methods to approach to the answer with minimum errors like FEM. This can be done by eliminating the differential equation for steady state problems or make an approximation of ordinary differential equation and using methods like Galerkin, Runge-Kuta or Euler’s method for solution [2].
The basic concept is to discretise a structure or part to smaller elements dimension with specific number called finite elements. These connected elements produce number of joints which is called Nodes and each element should be to somehow formulate such a way that gives the same property as the whole structure. Then by assembling the equation for each element form the global domain to be solved easily [2]. To solve the problem on paper although it is easier in compare to analytical method meanwhile it can be demanding and time taking. One of the reliable software using finite element method to give deformation of structure on a specified load and
boundary conditions, driving the stress and specifying weak points of the structure is ABAQUS which can be also helpful for improving design of the part.
4.2 Modal Testing
4.2.1 Introduction to Modal Testing
The Modal Testing can be accomplished in two different types of test. The first is a test where the component or part is vibrated with a known excitation usually out of its normal service environment; the second is one where responses and vibrations are measured using the original forces of the working condition while the structure is on operation. For studying a specific part the first test is more accurate and can provide more detailed information to use as it is possible to create a controlled condition in comparison to the second one [3].
The important concern is to evoke the reason of doing such a test. What is the desire outcome from the modal test and what we are going to study by the information? This can lead us to the desired result to get the maximum use from what we have achieved during the test.
In general the modal tests embark on to achieve a mathematical model of the part or structure but in reality it is used in different ways according to the requirements of the process. The most commonly used application is to get some information by vibrating the structure and then compare these measurements by a theoretical model like FEM. But prior to this some rudimentary information is needed to start the experiment in order to increase the accuracy of the experiment. In some other cases the experiment is done for the purpose of comparison of the gathered information from the different vibrated structure to increase the mathematical model for model refinement. There are also other purposes for the experimental modal testing which are not pursued in this thesis work [3].
In order to have a comparison between simulated model and the real model it is possible to follow the curve fitting technique and by the help of some MATLAB toolboxes it is possible to drive the mode shapes at different resonant frequencies.
4.2.2 Measurement planning
It is important for the modal analysis how to prepare the experiment and how to perform the test because everything can affect the test and gives inaccurate data. The following points should be considered when modal testing will be done.
1. How to suspend the test part.
2. Specifying the excitation points.
3. Specifying the accelerometer mounting point considering not putting accelerometer on node to get good information.
4. Using impact hammer with appropriate tip considering the frequency range [3].
Figure 4.1. Impact hammer.
The rule of thumb should be remembered also which says: “The mass of the accelerometer should be less that 10% of the apparent mass in the measurement point”. But in this thesis the main purpose is to find out if there are any differences between the same rotary disks which have been produced or not [4,5].
4.2.3 Modal Analysis and Modal Model
In modal testing the object should be vibrated by applying a force F(s), following the force, system will response to it X(s). The ratio between system response and the force give us transfer function H(s).
Considering Laplace transform for MDOF system it can be written:
(4.1) By solving the system characteristic equation, the roots are:
, (4.2)
The ratio of the actual system damping to the critical system damping gives the damping ratio .
0 (4.3)
Ω (4.4)
(4.5)
, 1 Ω (4.6)
Since the system here is an under damped system which means 1 it is possible to write the upper equation as follow:
, (4.7)
By using the equation (6) it can be drive:
√ (4.8)
Ω (4.9)
Ω √ (4.10)
And get the transfer function:
(4.11)
Where and are the poles of the transfer function and are conjugates of each other.
(4.12)
(4.13)
(4.14)
Assuming ) we can drive:
(4.15)
(4.16)
Finally the modal model can be generally written as:
∑ (4.17)
A is the residue matrix for mode r and can be calculated as a product of eigenvector by its transposed matrix, multiplying a scaling constant.
(4.18)
Sometimes it happens that computational poles exist in the system so it is not possible to assume them as complex conjugate pairs and the following formula should be used, which is time domain [6].
∑ (4.19)
4.2.4 Power spectral density (PSD)
In every signal which can be from a random process, acoustic wave, electromagnetic wave and so on, there is some energy. If multiply this by an appropriate factors the power which is carried by the wave will be given.
Power spectral density shows the strength of the energy and the magnitude in specific frequencies and tells where these variations are bigger [7].
The benefit of using this tool is that power spectral density can gives information about the energy in the system. For example if a device is running by a motor there may be some unwanted vibrations in the system, by this way we can look at the PSD plot and from the power distribution in a range of frequencies, detect at which frequency and by what magnitude it happens [7].
4.3 Introduction to ABAQUS
ABAQUS is a computer aided engineering software application which mainly uses for analysing the simulated parts and also for drawing some simple parts. The program can analyse parts by using some numerical
methods like FEM and gives the approximate stress due to the force and show deflection in different places and also specifying the weak points of the structure. The result is also dependent on how and how many elements are introduced; it is possible to mesh a part in different ways. It is possible also to import designed file of other programs into ABAQUS to do stress analysis and do both statistical and dynamic analysis. One of the benefits of having software programs is that it can be really helpful for engineers to save time and money for experiments which need some basic knowledge to be able to start a useful and accurate experiment. For example for doing Modal analysis one of the most important things is to know which points should be selected to motivate the mode shapes. If the points that are selected are located on the nodes of the structure then the experiment wouldn’t be accurate enough to be able to rely on the results. Using this kind of software can save a lot of time since finding out the information by just doing try and error can be demanding and difficult [8].
On the other hand it is possible to use ABAQUS to get the natural frequencies and plotting Frequency response function (FRF) of the structure. This can be very helpful if done correctly before running the experiment because an approximation of results which should be obtained during the experiment is available in forehand.
4.4 Ring test
This test is common for grinding wheels and parts which doesn’t have complicated shapes, it is usually used to check if there is any crack on the part or not but it is not a very accurate way of investigating cracks and is said to be good for testing the parts just before using them. The reason that is good for grinding wheel is that by having more complicated shape the sound will be different and it is more difficult to check if the sound is good or there is something wrong with the part. Ring testing also depends on the damping characteristics of a cracked part to alter the sound emitted when the part is tapped slightly and is highly depended to the inspector’s ability of the assessment on the sound and this needs lot of experience and also a good hearing ability. To perform the ring test, part should be tapped gently with a light nonmetallic device, such as the handle of a screw driver, since the part is not very big and complicated. What we need to bear in mind while testing is that:
1. It is needed to tap the part in different parts like each 45 degree.
2. The part should be clear and dry; otherwise the sound may be deadened.
3. An undamaged part should give us clear tone. A dead sound usually means crack [9, 10].
The problem is that according to the material used for the production the sound differ from part to part so for each product at first you need to have a source sound from an intact part to be able to compare the other sounds with and be sure about the precision.
In order to solve this problem a microphone is used to record the ring sound and then it has been processed using MATLAB to plot it and see how much similarity exist between different parts.
4.5 Hardness Testing
In order to increase the efficiency of the metal objects like ductile cast iron sometimes the working condition needs a harder part to be used and for this purpose usually hardening is done on the part. After this procedure and before using the hardened part it is needed to be sure about the accuracy of the process, Indentation hardness tests shows the hardness of a material to deformation. One of the advantages of this test is that it is a nondestructive test and has an economically importance.
Some of the common hardness tests are Vickers hardness test, Brinell hardness test and Rockwell hardness test.
The general procedure of the test is that by applying force, resistance to indentation is checked. Considering the magnitude of the load it is a micro indentation or macro indentation tests which the first one has usually forces less than 2N. The Hardness number can be achieved regarding the test, for example in the Rockwell test it can be read directly from the indicator on the device but for the Brinell test it is needed to have the diameter of the ball penetrator and diameter of the impression. Hardness test can only give us relative idea of material properties and to somehow resistance of the material to plastic deformation and is not fundamental material property [11].
5 Investigations
According to cited potential errors, part design and casting were among the first prioritized potential problems. To check if there is any major problem in some specific parts, ringing test, a quick and easy test was chosen.
Further in order to make the investigation more accurate and find out more information modal testing was done and the power spectral density of working condition was recorded and plotted. The other possibility which may cause failure of the parts was hardness and this was investigated by a liable company and results were delivered. The other test was destructive test which was tried to break a part which was failed during the work and customer had send it back to the company and this test was to somehow important for MRT System International AB, which tried to break the part and this effort was not successful.
5.1 Ring test
The ring test is run usually by tapping the object and listening to the sound in order to find out if there is crack in the part or not and it depends to the person’s experiences who run the test knowing about the correct sound and by this way it is not possible to document the test. In order to be able to make the test more accurate the sound is recorded by microphone and the signal is plotted in MATLAB [12].
Four different points have been chosen for the ring test as follow:
Figure 5.1. Selected points for Ringing test.
5.1.1 Results
The following plots compare the response of four different points tapped on one of the parts which is taken randomly from the same production batch.
There are five more parts that has been studied that the results are nearly the same and to avoid using lots of figures these plots and results can be found in appendix.
Figure 5.2. Ringing test on point 1.
The frequency range that is shown here is up to 8000 Hz but in further works with modal analysis the frequency range is up to 4500 because of the accuracy limitation of devices which have been used.
Figure 5.3. Ringing test on point 2.
The amplitude of the force is slightly different in each experiment and this is because the experiment was done manually and it is difficult to adjust the force accurately.
Figure 5.4. Ringing test on point 3
Still we can see the same resonance frequency although the amplitude of the force is different.
Figure 5.5. Ringing test on point 4
5.1.2 Discussion and Conclusion
Comparing all six different parts, It can be seen that the results are nearly the same, although little different can be seen but in all tests the first resonance frequency is around 2000 Hz and the other three resonance frequencies are between 3500 and 4000 Hz. This can be also perceived later in Modal testing and because the accuracy of the Modal testing is up to 4500 Hz. The reason for checking the resonance frequencies is to see if the resonance frequency of the motor could affect the part or not and as far as in the faster motor rotate at 950 RPM produce frequency around 16Hz which means that the accuracy of 4500Hz is enough for the experiment.
5.2 Modal testing
To run the test as it has been described before it is needed to prepare proper test condition. Points that are needed to be tapped should be indicated and accelerometer should be accurately mounted on a chosen reference point which is not a nod to record the information. For the experiment the following equipment’s are needed. Impulse hammer, Accelerometer national instrument to transfer data to computer and MATLAB to record and save the data.
The boundary condition and how to keep the part can extremely affect the results. Although the natural frequency of the part is different while it is mounted on real working condition but it still gives us useful information to compare parts by just hanging them and run the test considering the same condition for all parts.
Figure 5.6. Position of the disk and accelerometer for test.
5.2.1 Results
The result of the experiment will be shown in the following plots comparing each point with the plot obtained from ABAQUS by applying the force in the same place as the real test.
The points have been chosen as follow:
Figure 5.7. Chosen points for tapping by impulse hammer.
The dimensio impulse hamm whole in the m In order to ha ABAQUS an calculated to seems the se resonance fre FRFs.
Figure 5.
Figure 5.2
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5.6.FRF at firs nce point whic
7.FRF at secon y is identical w is not possible
ce limitation an Hz and the A
st point.
ch accelerome
nd point.
with ABAQUS e to make a dis
nd increasing ABAQUS FRF
eter is attached
S but because stinction betwe
the F is
d
the een
Figu
Figur
Figu
ure 5.8.FRF at
re 5.9.FRF at f
ure 5.9.FRF a
t third point.
fourth point.
t point five.
Figure 5
Figure 5.1
Figure 5.1
5.10.FRF at po
11. FRF at poi
12. FRF at po
oint six.
int seven.
int eight.
Figur
Figu
Figure
re 5.13. FRF a
ure 5.14. FRF a
e 5.15. FRF at
at point nine.
at point ten.
t point eleven.
5.2.2 It c betw natu diffe issu freq Part has spec was On resu freq state the prop
2 Discussion a can be seen th ween 1935 to ural frequency ference betwee ue is the weigh quencies of the t number 4 sho
higher natural ctral density o
working in th the other hand ults from exp quencies in rea ed as attaching natural freque portional in all
Figure 5.1
and Conclusi hat the first 2000 Hz and y obtained from en the real pa ht of the accele
e part.
ows little diffe l frequency. T f the whole de he real conditio d the results fr periment but
al experiment g the accelerom encies of the d l different natu
16. FRF at poin
on
natural freque has approxim m the ABAQU art and the sim erometer that c
erent character This part was u
evice while the on by feeding rom ABAQUS
as far as lo and one of t meter on the r disk [4] it can ural frequencie
nt twelve.
ency of five mately 300 Hz US and this ca mulation. The can affect and
ristics from th used in order e rotary disk w different kind S is not exactly
ots of factor the most effec rotary disk wh n be seen that es.
parts are nea z difference w an be due to lit other import damp the natu e other parts a to get the pow was mounted a
of materials.
y identical to rs affect natu
ctive one can hich can decrea t this decrease
arly with ttle tant ural and wer and the ural be ase e is
5.3 Curve fitting
It is possible to animate the mode shapes by the help of MATLAB and also check the accuracy of the experiment by using the curve fitting method [13]
which shows the difference between the analytical solution and experiment.
First it is needed to change the FRFs from Accelerance to mobility in order to create the appropriate matrix as follow.
… …
…
…
…
…
…
5.3.1 Results
By plotting the stability diagram there will be some green stars as poles which the stable one on resonance frequencies is needed to be picked to be able to run the curve fitting.
Figure 5.17. Stability diagram.
There is some noise 2500 Hz but still we can see the resonance frequencies and by clicking on the 5 resonance frequency in this area we get 12 plots for 12 point which has nearly good accuracy.
The last one is added to show the accuracy of measurement.
Figure 5.18. Curve fitting plot.
The dimension of the points that has been taped by impulse hammer and displacement which has been calculated are shown in the following table.
Table 5.9. Dimension chosed to tap by hammer.
Point number X Y
1 60.8112 60.8112
2 60.8112 -60.8112
3 -60.8112 -60.8112
4 -60.8112 60.8112
5 86 0
6 0 -86
7 -86 0 8 0 86
9 15.9099 15.9099
10 15.9099 -15.9099
11 -15.9099 -15.9099
12 -15.9099 15.9099
There is no possibility to show the animation in word document, so only one view of vibration is shown here. The star nearly shows the reference point.
Figure 5.19. Mode shape from first natural frequency by MATLAB.
The black line is the stable condition of the disk and the red line shows mode shape at first resonance frequency.
5.3.2 Discussion and Conclusion
The mode shape derived from modal testing is not identical to the first mode shape of ABAQUS although both are from the first resonance frequency, the reason is because in the reality the two first resonance frequency which one is probably repeated resonance frequency cannot be seen so the mode shape is a little different from ABAQUS but as far as the data is not going to be used for improving the part design and it is only used
for a comparison between the different parts and also checking the accuracy of the experiment it is reliable.
5.4 Running the machine
It is useful to check the characteristic of the rotary disk while it is working.
This can be compared while different materials are fed for crushing in the machine. According to the position of the part and its working condition there is no possibility to mount the accelerometer on the crusher because all parts of the rotary disk is in touch with the fed materials with lots of energy which can easily break the accelerometer. So the accelerometer should be mounted outside where there is no extra material to hit it and this cause another problem which means that there is a new system with new natural frequencies and new characteristics which is not the same as information obtained from rotary disk. The useful experiment which can be done is recording the signals of the machine while working in different conditions by feeding glasses, end cap aluminium, and hard metal to compare the response and plotting the power spectral density (PSD) of the system which can tell us about the magnitude of the power produced during the work.
At first the same accelerometer which had been used for impact testing on rotary disks was attached on the outer side of the housing on the machine which rotary disk is placed inside and crushes the material and it was kept in the same place while different materials were fed into machine. The machine was started and the given signal for rotation of the empty machine was recorded. This was done for three other feeding materials and information was recorded which will be shown in the following figures.
Figure 5.20. Accelerometer attached on outer side of housing.
5.4.1 Results
The following figure and plots are results of the experiment while the disk was mounted and worked in real condition.
Figure 5.21. Data recorded from accelerometer attached on crusher
assembly.
The PSD of the system after calculating by the help of MATLB is as follow.
Figure 5.22. PSD calculated in different working condition.
5.4.2 Discussion and Conclusion
Figure 5.21 shows the effect of three different materials. At first the device was run empty and without any load for 30 seconds which the black line is showing it. Two different experiments performed feeding glass into crusher and it is obvious that at the time of feeding there is a sudden shock in magnitude and gradually decreases until the new material are fed to again but two different experiments show nearly the same magnitude, little difference is because of the quantity of the material fed to the crusher.
Comparing these data to the data recorded while the crusher was running empty it can be seen that difference of the magnitude is not that much remarkable.
There are two other information in the plot which related to the aluminium end caps and some hard metals and bolts which was fed to the device to check the response of the crusher and also checking if feeding wrong material among the other original material can cause failure of disk or does it have any other effects or not.
Logically it seems that hard material should be more dangerous for the device while it is working but as it can be seen in the above figure, this is the aluminium end caps which produce bigger magnitude. The experiment
for aluminium caps was 15 seconds and the crusher was operating with hard metal and bolts for nearly 1 min.
Figure 5.22 shows that largest amount magnitude belongs to aluminium end caps and bolts and also the aluminium has bigger magnitude in compare to bolts. It is plotted up to 2500 Hz because after that there is no remarkable picks, by calculating the root mean square value and standard deviation of the data it can be calculated that nearly 90% of the power is in this frequency range.
According to figure 5.23 most of the power for bolts is accumulated in three different parts 300-900HZ, 1450-1600 Hz, 2250-2400Hz.
If we find out the RMS value of a frequency range and by having the standard deviation it can be seen that nearly 60% of the power is between 1450-1600 Hz.
For the bolts we have approximately 87% of the power in the range of 20- 2500 Hz. Nearly 66% of the power is between 300-800Hz, 20% of the power is in the range of 1140-1240 Hz, 34% is between 1450-1600 Hz and 28% is between 2210-2310 Hz.
This tells that there is not a lot of power accumulated in the range of first natural frequency of the part.
5.5 Hardness test
5.5.1 Results
The hardness process has been tested on four different parts as well as the one which was broken during the work and the result was 52 to 55.5 but the direct conversion to Brinell hardness number is not possible because the applied force and conditions for Brinell and Rockwell hardness test are different.
5.5.2 Discussion and Conclusion
This means that the accuracy of the hardening process is also acceptable but as far as there is not a specific way of converting Rockwell to Brinell hardness number it is still needed to investigate if this is exactly the same as what decided for the part material or not.
5.6 Destructive test
The last part of the experiments is destructive test on a broken part which had been used by customer for a while, but there is not enough information about the working hours of the part. The form of breakage shows that the part has been broken due to a huge and sudden force and no fatigue or fracture has occurred.
Figure 5.23. Broken part during work.
This is what can be seen by naked eyes, but still more accurate investigation should be done on the part. By assuming that this has happened by a sudden force the part was analyzed by the help of ABAQUS to find out how much force is needed and in which direction to pass the yield stress of the material that part has been made of. Different places, magnitude and direction has been checked by the help of ABAQUS and the place and force that will be shown in the following figures are the most
likely ones th real work.
Fi The boundary and also the build-up force in figure 5.26
hat can break th
igure 5.24.Sim y condition has
experiment. A e inside the as
a force can be
he part in a w
mulated conditi s been chosen Assuming that ssembly becau
e produced in
ay that has be
ion for maximu n in a way mos
t during the w use of the inpu
a way shown i
en broken dur
um stress.
st likely to the work there ca ut materials as in the figure 5
ring the
e reality an be a shown .25.
Figure 5.25.Assembly of disk and rings.
In order to be able to simulate the condition near to the reality it is needed to use pressure in ABAQUS. Giving 215 (nearly 65000 N force), the stress is nearly 509 which is more than yield stress and tensile stress of the part, by giving 50000 N force also the magnitude of stress is 393 which pass the yield stress. The part deformation for first force is like bellow although the maximum stress happens in the same place for second force as well; the maximum stress has been marked red.
Figur In order be a diameter of th condition. Th as it has been manually in direction and
re 5.26.Stress a able to run d he disk whole he next problem
n simulated in the laboratory place.
analysis by app destructive tes
e to keep it st m is giving the n ABAQUS. F
y for applying
pplied force fro st a shaft was table and hav e force to part For this purpos g appropriate
om figure 25.
s needed with e a proper bo t in specific di se a part was force in the
h same oundary
irection created aimed
5.6.1 Results
Figure 5-27, Handmade part used for experiment.
The part was placed in a good and stable position in order to start giving force.
Figure 5.28. Position of the disk and boundary condition.
The force needed to break the part is nearly 7 tons or a little more.
Figure 5.29. Applying force by hydraulic press.
The hydraulic press that was used in the experiment is 30 tons, so we need to read the blue line of the gage.
Figure 5.30. The pressure gate just before part break.
The result of the test is not identical to what has happened during the real work but it has nearly the same pattern. In the following picture it can be seen how the part has broken and it also shows that the ABAQUS simulation is quite accurate because the break happened at the same place that there is more stress.
Figure 5.10. Broken part similar to one which had break during the work.
The test was repeated three times for all three pins that were remained unbroken and the needed force was nearly the same.
It is required to consider that there can be leakage of hydraulic in the press and also there are some other factors that is not possible to be omitted during a real test.
It can be seen maximum stre the exact pla completely ra some pictures
F In the above pins and the s
n that the same ess in differen ace which ma andom and the s from ABAQU
Figure 5.31. Ap picture one fo stress is like.
e force in diffe nt places. This ay break durin
ere is no way US are shown
pplying force i orce with sam
erent positions means that it ng the work to guess it. F below.
in two differen me magnitude
s of the disk ca is difficult to because the or more clarif
nt places.
is given to th
an have predict load is fication
he other
Her yiel
By dire max
Figu
e the maximu d stress.
Figure 5.3 changing the ection and kee
ximum stress c
ure 5.32. Stress
um stress is ne
33. Same load place of forc eping the othe changes as foll
s analysis of th
ear the key and
as figure 5.32 ce which is in r one in the s low.
he previous for
d still the stre
on two other p ntroduced to d same position
rce.
ess is bigger th
positions.
disk nearly in the place of
han
n Z the
5.6.2 Discuss By having the been hardene passing the m Different kind simulated in t breaks. Apply place of the m possible to pr possible to be crusher assem cause this pro which have be than damagin like aluminium between the r
Figure 5.34.
ion and Conc e yield’s stres d we know th maximum yie
d of forces h the laboratory ying different l
maximum stre redict the part e built up easil mbly to create
oblem. The ex een fed to the ng the disk. On m end caps an ings teeth and
Stress analysi
clusion
ss of the mater hat the part is ld’s stress the as been used y to see the pa
loads to differ ess changes ac t behaviour. O
ly and needs l this amount o xperiment show
machine coul ne of more pow
nd lamps filam increase the s
is of the figure
rial and know not flexible t e possibility o
and one of t art reaction to rent parts of th ccording to the On the other h
lots of materia of force and it ws also that h d hurt more lik werful options ments which m stress and caus
e 5.34.
wing that the p to deformation of breaking i these conditio the force and he disk shows t e loading so it hand this force al to gather ins is unlikely tha hard metals an
kely the motor s can be softer may press and se a sudden bre
part has n so by s high.
ns was how it that the t is not e is not side the at glass nd bolts r rather metals d gather
eak.
6 Conclusion
In summary, in order to explore the reason of the fracture failure work was primarily focused on the rotary disk itself, the design, casting, and hardening was investigated.
From modal analysis it could be understood that the investigated parts which the production company had provided from a similar batch were nearly identical and there were no significant differences or specific problems that modal analysis could show. Although fatigue and fracture analysis has not been the major focus of this study, it is important to note that future new parts need to be studied specifically in terms of the aforementioned cases.
The destructive test showed that by applying a specific force, it was possible to simulate the break pattern which had happened during the work.
This meant that crack and fatigue was not always required to dismantle the part as it could happen suddenly. But the force will not be created easily and needs extra material to accumulate in the assembly part so as to build up enough energy to cause breakage. This is more probable by feeding the crusher soft metal and the reason considering the part design could probably be the brims' angle which may have caused this problem. All things considered, it is not possible to state that the reason of the problem is understood by this work yet the experiment brings forth clarifications and guidelines to pave the way for better and more accurate future studies.
6.1 Further works
The total work in this thesis focuses on stress analysis and natural frequencies of the rotary disk. The modal testing shows that the quality and similarity of the parts are acceptable but still this not for sure for all the parts because the parts available for all analysis was from a same batch that producer company had provided before so further investigation on new parts from new batches can still be studied. One of the probable causes that may lead to disk failure is wedging of the ring which is due to build up force from gather materials, these materials are most likely metals and it cannot be hard material because the experiment showed that very hard
material can damage the motor also as increasing the temperature of the motor was observed while feeding crusher with bolts and metals. So a poor assembly with feeding soft metals like aluminium end caps and lamp’s filaments to make condition for gathering and compressing material to see how much force they can produce and if it is possible to brake the part in this condition or not.
The other possibilities that has been mentioned in the beginning can be consider and of course there can be some more reason that has been neglected or forgotten to be mention in this thesis and can be investigated later.
• There is no obvious crack in studied parts produced from a same batch considering the casting process.
• The excitation frequecy of the system does not reach the natural frequency of the part.
• Build up force can be considered as an important reason of product failure.
• The breakage occurs usually suddenly due to accumulated energy rather than expansion of a crack or fatigue.
• Due to the random force, there is no possibilty to guess the crack pattern all through the work.
7 References
1. Material properties:
http://www.substech.com/dokuwiki/doku.php?id=ductile_cast_iron_ast m_a536
2. Göran Broman, Computational Engineering, (2003), Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden.
3. D.J.Ewins, second edition, Modal Testing: Theory, Practice and Application, (2000), Baldock, Hertfordshire, England.
4. Kjell Ahlin and Anders Brandt, Experimental Modal Analysis in Practice, (2001), Sasven EduTech AB, Sweden.
5. Jimin He and Zhi-Fang Fu, Modal analysis, (2001), Butterworth- Heinemann, Oxford.
6. Dr. Randall J. Allemang, Vibrations: ANALYTICAL AND EXPERIMENTAL MODAL ANALYSIS, (1994), UC-SDRL-CN-20- 263-662.
7. Anders Brandt, Introductory Noise & Vibration Analysis, (2001), Sasven EduTech AB and The Department of Telecommunications and Signal processing, Blekinge Institute of Technology
8. ABAQUS 6.9 DOCUMENTATION.
9. SAINT-GOBIAN, ABRASIVES, How to perform a Ring Test on a Grinding Wheel.
10. Ring test: www.lni.wa.gov/wisha/Rules/portablepowertools/PDFs/HT2- PPT.pdf
11. Hardness test: http://www.worldoftest.com/pdf/hardnesstesters.pdf 12. Jesse Hansen, Record.m, (12-1-01),MATLAB code
13. L. Håkansson, Signal Analysis: Power Spectra and Power Spectral Density of Time Limit signal records, and stationary test methods, (2008), Department of signal processing, Blekinge Institute of Technology.
14. Autodesk Help: http://wikihelp.autodesk.com/Inventor/enu/2011.
A. Plots of the ring test
The first point
Figure 7.1. Ring test for part one, point one.
Figure 7.2. Ring test for part three, point one.
Figure A.3. Ring test for part four, point one.
Figure 7.4. Ring test for part five, point one.
Figure A.5. Ring test for part six, point one.
The second point:
Figure 7A.6. Ring test for part one, point two.
Figure 7.7. Ring test for part three, point two.
Figure 7.8. Ring test for part four, point two.
Figure 7.9. Ring test for part five, point two.
Figure 7.10. Ring test for part six, point two.
The third point:
Figure 7.11. Ring test for part one, point three.
Figure A.12. Ring test for part three, point three.
Figure 7.13. Ring test for part four, point three.
Figure 7.14. Ring test for part five, point three.
Figure 7.15. Ring test for part six, point three.
The fourth point:
Figure 7.16. Ring test for part one, point four.
Figure 7.17. Ring test for part three, point four.
Figure A.18. Ring test for part four, point four.
Fig
Fig
gure 7.19. Ring
gure 7.20. Rin
g test for part f
ng test for part
five, point fou
t six, point four
ur.
r.
B. Coherence function from Modal testing
Coherence functions at twelve points of six different parts:
Figure A.21.Coherence function of modal testing at point one.
Figure A.22.Coherence function of modal testing at point two.
Figure 7.23. Coherence function of modal testing at point three.
Figure 7.24. Coherence function of modal testing at point four.
Figure 7.25. Coherence function of modal testing at point five.
Figure A.26.Coherence function of modal testing at point six.
Figure A.27.Coherence function of modal testing at point seven.
Figure A.28.Coherence function of modal testing at point eight.
Figure A.29.Coherence function of modal testing at point nine.
Figure A.30.Coherence function of modal testing at point ten.
Figure 7.31.Coherence function of modal testing at point eleven.
Figure 7.32.Coherence function of modal testing at point twelve.
School of Engineering, Department of Mechanical Engineering Blekinge Institute of Technology
Telephone:
E-mail:
+46 455-38 50 00 info@bth.se
