Supporting structures in two particle detectors

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(1)2001:055. MASTER'S THESIS. Supporting Structures in Two Particle Detectors. Anders Angantyr. Civilingenjörsprogrammet Maskinteknik Institutionen för Maskinteknik Avdelningen för Hållfasthetslära. 2001:055 • ISSN: 1402-1617 • ISRN: LTU-EX--01/055--SE.

(2) Supporting Structures in two Particle Detectors. Preface As a compulsory part of the Master of Science program in Mechanical Engineering at Luleå University of Technology, Sweden, the student requires to perform a project during five months. The purpose of the project is that the student shall have an opportunity to practice the skills and abilities achieved during the educational period. For me, Anders Angantyr, the project has been carried out at CERN, Switzerland, from September –00 to February –01. The focus of the project was to study the mechanical behaviour of different supporting structures in two particle detectors. My enthusiastic supervisor at CERN has been Hans Danielsson and the work was carried out in close contact with Andrea Catinaccio and Antti Onnela who have given a lot of valuable input and advise. My supervisor at Luleå University of Technology has been Jan-Olov Aidanpää. I would like to thank the above mentioned people and also all the members and colleagues of the TA1 group at CERN, the group where the project was carried out. CERN, 30 January, 2001 Anders Angantyr.

(3) Supporting Structures in two Particle Detectors. Abstract CERN is an international collaboration and the European Laboratory for Particle Physics. CERN is located just outside Geneva on the French-Swiss border. The primary goal of CERN is to provide physicists from all over the world with high-energy particle beams to use in their experiments. In the experiments, high energy particles are brought to collide with other high energy particles or fixed targets. The produced particles in the collision are identified in particle detectors. To not disturb the produced particles, the matter in the detectors must be minimised. The supporting structures in the particle detectors are therefore often well optimised lightweight structures. This thesis is a study of the mechanical behaviour of two supporting structures in two different detectors. The first part is a study of the deformation of the wheels in the HARP TPC (Time Projection Chamber). The second part is a static and dynamic analysis of the barrel TRT (Transition Radiation Tracker) that is an inner part of the large ATLAS detector. HARP is an approved experiment now under construction at CERN. The aim of the project is to study hadron production for the neutrino factory and the atmospheric neutrino flux. The main detector in the project is a TPC. In the TPC there exists three consecutive wire grids: the gating grid, the cathode and the sense wire grid. The wires in each grid are tensioned onto the spokes of three similar types of wheels. The aim of this study is to determine the deformation of the wheels due to the wire tension. The result is supposed to work as a guideline for the detail design and assembly procedure. An analytical study of the problem is performed. The aim of the analytical study is to understand how the system behaves under different conditions and to understand the order of magnitude of the expected deformations. An FEMsimulation of a wheel is also performed to check the simplifications made in the analytical study and to get more accurate estimates of the displacements. The main conclusions from the analysis are that the out of plane deformation of the complete wheels is small but it may be significant during wiring of the wheels. Furthermore, from the deformation point of view there are several advantages of doing the wiring of the wheels outside in. However, for the final choice of the wiring method the practical constraints must be taken into account. The Large Hadron Collider (LHC) is a new particle accelerator now under construction at CERN. The LHC will bring protons to head-on collisions at energy never achieved before. One of the detectors used for particle identification from collisions in the LHC is the large ATLAS detector. The innermost sub detector of ATLAS is the inner detector. The aim of the inner detector is to measure the momentum of particles produced in the collision. One of the main components in the inner detector is the barrel TRT support structure. The barrel TRT support structure will position some of the detecting elements in the space. The stability in position of the precision detectors inside the barrel TRT is in the order of a few µm. Thus it is extremely strict restrictions of the allowed amplitude of possible vibrations of the barrel TRT support structure. The second part of the thesis is a static and dynamic analysis of the barrel TRT support structure. The dynamic analysis is limited to a modal analysis. Also the torsional stiffness of the barrel TRT support structure is investigated. The fundamental mode of vibration (frequency around 5 Hz) for the barrel TRT support is definitely the most dangerous mode and depending on the frequency of the possible sources of excitation it may cause problems for the detectors inside the barrel TRT. It is not possible to increase the value of the fundamental frequency a large amount without making major changes to the barrel TRT support structure. To retain the torsional stiffness of the barrel TRT support structure, it is of great importance that the connection between the upper and lower half of the outer cylindrical skin is good. If the connection is good, the design of the supporting endplates is the dominating factor of the torsional stiffness of the whole barrel TRT support structure..

(4) Supporting Structures in two Particle Detectors. Contents 1 GENERAL INTRODUCTION ................................................................................................................. 5 1.1 CERN.............................................................................................................................................. 5 1.2 BASIC PRINCIPLES OF PARTICLE ACCELERATORS AND DETECTORS................................................... 5 1.2.1 Particle accelerators...................................................................................................................... 5 1.2.2 Multiwire chamber detectors ......................................................................................................... 7 1.3 AIM OF THESIS WORK ....................................................................................................................... 8 2 THE HARP TPC........................................................................................................................................ 9 2.1 INTRODUCTION ...................................................................................................................................... 9 2.1.1 HARP and the TPC ........................................................................................................................ 9 2.1.2 Aim of this study........................................................................................................................... 10 2.1.3 Input to the analysis ..................................................................................................................... 10 2.2 ANALYTICAL CALCULATIONS .............................................................................................................. 10 2.2.1 Radial deformation ...................................................................................................................... 10 2.2.2 Out of plane deformation ............................................................................................................. 12 2.3 FEM-MODEL........................................................................................................................................ 12 2.3.1 Radial deformation ...................................................................................................................... 13 2.3.2 Out of plane deformation ............................................................................................................. 13 2.3.3 Radial stiffness of inner- and outer wheel.................................................................................... 14 2.3.4 Spoke attached to inner wheel...................................................................................................... 14 2.4 CONCLUSIONS...................................................................................................................................... 15 3 THE BARREL TRT SUPPORT STRUCTURE ................................................................................... 16 3.1 INTRODUCTION .................................................................................................................................... 16 3.1.1 LHC and ATLAS .......................................................................................................................... 16 3.1.2 The inner detector and the TRT ................................................................................................... 17 3.1.3 Background and aim of this study................................................................................................ 19 3.2 FEM MODEL ........................................................................................................................................ 20 3.2.1 Geometry...................................................................................................................................... 20 3.2.2 Elements....................................................................................................................................... 20 3.2.3 Loads............................................................................................................................................ 21 3.2.4 Boundary conditions .................................................................................................................... 22 3.2.5 Material properties ...................................................................................................................... 23 3.3 MODAL ANALYSIS................................................................................................................................ 24 3.3.1 Analytical estimation of fundamental frequency.......................................................................... 24 3.3.2 Initial study .................................................................................................................................. 25 3.3.3 Check of mesh quality .................................................................................................................. 26 3.3.4 Mode shapes ................................................................................................................................ 27 3.3.5 Limit range of fundamental frequency ......................................................................................... 27 3.3.6 Results of different lay-ups in cylindrical skins............................................................................ 28 3.3.7 Influence of variation in geometrical parameters........................................................................ 28 3.3.8 Conclusions.................................................................................................................................. 29 3.4 STATIC ANALYSIS ................................................................................................................................ 30 3.4.1 Initial study .................................................................................................................................. 30 3.4.2 Results.......................................................................................................................................... 30 3.4.3 Influence of variation in geometrical parameters........................................................................ 32 3.4.4 Conclusions.................................................................................................................................. 32 3.5 OPTIMUM LAY-UP OF THE CYLINDRICAL SKINS .................................................................................... 33 3.6 GENERAL CONCLUSIONS ...................................................................................................................... 34 4 REFERENCES......................................................................................................................................... 35.

(5) Supporting Structures in two Particle Detectors. APPENDIX A.. PRESENT DESIGN OF HARP TPC WHEELS…………………………………….. I. APPENDIX B.. ANALYTICAL CALCULATIONS HARP TPC……………………………………II. APPENDIX C.. DEFORMATION FIGURES HARP TPC………………………………………….III. APPENDIX D.. 1 DOF MODEL OF THE BARREL TRT………………………………………… IV. APPENDIX E.. FEM MODEL OF BARREL TRT…………………………………………………..V. APPENDIX F.. PRESENT DESIGN OF ENDPLATE……………………………………………...VI. APPENDIX G.. MODE SHAPES OF BARREL TRT………………………………………………VII.

(6) Supporting Structures in two Particle Detectors. 5. 1 General introduction 1.1 CERN In 1954 a collaboration started between 12 European states for fundamental particle physics. This was the birth of CERN and the beginning of a shining example of international collaboration. Today CERN has 20 member states and a large number of observer states. The laboratory is located at the foot of the Jura Mountains on the French-Swiss border just outside Geneva. CERN employs just under 3000 people, representing a wide range of skills and trades - engineers, technicians, craftsmen, administrators, secretaries and workmen. About 6500 scientists from all over the world are involved in the different types of experiments under study at CERN. One of mankind’s strongest driving forces is curiosity. The existence of CERN is motivated by the curiosity of understanding the fundamental coupling between mass and force. One of the most important aims of CERN is to verify the theoretical models of particle physics. In the Standard Model, developed in the 1960s, a particle called the Higgs Boson appears. The Higgs particle is believed to be an important factor in the explanation to the concept of mass. Today one of CERN’s most important research focus is to verify the existence of the Higgs Boson. In order to prove the existence of the Higgs Boson, higher energy at the collision is required and more advanced particle accelerators and detectors than today’s must be used. The demand for more and more advanced equipment for particle detecting leads to the fact that state of the art engineering in all areas is needed at CERN, for example, computing, electronics and mechanics. During the history of CERN many applications not directly related to particle physics have been invented and developed. One of the most famous inventions from CERN is the HTML-protocol, now used in every Web browser. Originally it was thought as a tool for physicists to share information easily between each other. CERN’s aim is to provide the scientists with high-energy particle beams to be used in their experiments. The development and maintenance of particle accelerators is supported by CERN whilst the development of new experiments and detectors are supported by universities and institutes from all over the world.. 1.2 Basic principles of particle accelerators and detectors Quite simply, accelerators increase the energy of subatomic charged particles, which then collide with fixed targets or other particles. Out of this interaction point come many other subatomic particles that pass through the detectors. From the information gathered in the detectors (charge, momentum and energy of particles) the identification of the particles is done. To create new particles in a collision energy is needed. The relation between mass and energy are described by Einstein in the well known formula. E = m ⋅ c2 .. (1.1). To create heavier particles, like the Higgs Boson for example, extremely high energy is needed in the collision. To achieve the high energy a new accelerator is being built at CERN, the Large Hadon Collider (LHC).. 1.2.1 Particle accelerators An electrically charged particle positioned in an electrical field will be affected by a force. This force will accelerate the particle to higher velocity and energy. This principle is found in for example a TV, computer monitor or x-ray equipment. This principle is also applied and repeated in a particle accelerator. In a linear accelerator a variable electrical field is applied and the velocity of the particle is increased each time it passes by the anode or the cathode (depending on the charge of the particle), see figure 1-1.. 1 General introduction.

(7) Supporting Structures in two Particle Detectors. Particle source. 6. Particle beam. e-. Figure 1-1 Principle of a linear particle accelerator.. The maximum particle energy, which possibly can be achieved in a linear accelerator, is limited by the length of the accelerator. For practical and economical reasons one cannot build as long linear accelerators as required to produce the energy which is achieved at the forefront today. Nowadays most of the highenergy accelerators are circular accelerators. A circular particle accelerator is almost the same as a curved linear accelerator with an applied magnetic field. In a circular accelerator the particles pass RF-cavities (Radio Frequency-cavities). Each time the particles pass these cavities the energy of the particles is increased. Several of these cavities are often used to increase the efficiency of the accelerator. Very high energy can be achieved in this type of accelerator. To force the particles in a closed circular path, a magnetic field perpendicular to the particle path is needed. RF-cavity Bending magnets r. Figure 1-2 Principle of a circular accelerator.. An electrically charged particle moving in a magnetic field is affected by a force, the Lorentz force, perpendicular to the velocity of the particle and perpendicular to the magnetic field. According to [1] equilibrium between the Lorentz force and the centrifugal force is achieved in the radial direction if. r=. p , B⋅q. (1.2). where r is the radius, p is the momentum of the particle, q is the charge of the particle and B is the power of the magnetic field. In a modern circular accelerator the upper limit of the particle energy is limited by the radius of the accelerator and the power of the magnetic field. Superconducting magnets are needed to create the extremely strong magnetic field that is needed to bend the particle path in the latest accelerator under development at CERN. At CERN particles are pre-accelerated in linear and circular accelerators with smaller radius before they are injected into the largest type of circular accelerator.. 1 General introduction.

(8) Supporting Structures in two Particle Detectors. 7. 1.2.2 Multiwire chamber detectors Detectors are used to measure charge, momentum, and energy of particles produced in a collision. These measurements are needed for the identification of the particles. To determine the momentum of particles often multiwire chamber detectors are used. Every type of multiwire chamber detectors are based on the same principle. When a fast moving particle, produced in the collision by other particles, passes the detector gas, it knocks out electrons. Ions and free electrons are produced. These free electrons then create a detectable signal. Since the speed of the passed particle is near the speed of light the energy lost to the ion and the free electron is small and the particle passes by almost unaffected. In this section two types of common multiwire chamber detectors, used to determine particle trajectories, will be described. The first type is a proportional wire chamber detector and the second type is a drift chamber detector. One type of proportional wire chamber detector consists of a wire surrounded by a so-called straw, see figure 1-3. The straw contains a suitable mix of different gases. Between the wire and the straw there is an electrical potential difference. The potential difference forces the produced free electrons to drift towards the wire. Near the wire, where the electrical field is strong, the free electrons knock out new electrons. Due to this amplification effect a detectable signal is achieved. This is well described in [2]. By measuring the time and knowing the drift velocity also the distance from the wire to the particle path can be determined. To detect particles at high precision (∼150 µm) in a large volume many of these wire chamber detectors are needed. In the new ATLAS TRT detector, under construction at CERN, the diameter of the straw is 4 mm and several hundred thousand of these is required to cover the detection space. Wire at + potential. Particle track. Straw at - potential. Gas. Figure 1-3 Axial view of a straw chamber detector.. A drift chamber detector, or Time Projection Chamber, is another type of multiwire detector, see figure 1-4. A large volume of gas surrounds the point of collision. Between each end of the gas volume, a uniform electrical field is applied. This field forces the free electron to drift towards the anode. When the free electrons reach the anode the same amplification effect as explained earlier is achieved and a detectable signal is produced. Since the drift speed of the free electrons is much lower than the speed of the detected particle, the drift time for the free electrons can be measured. The distance from the anode to the particle track is then calculated via the drift velocity. The other two coordinates of a point on the particle track are given by the projection of the particle track on the end of the gas chamber. The main advantage with this type of detector is that a large volume can be covered at low cost. A disadvantage is the low accuracy in the measurements of the particle tracks due to the non-uniformity in the drift field. Another disadvantage of the drift chamber detector is that it is not working properly at high particle intensity.. 1 General introduction.

(9) Supporting Structures in two Particle Detectors. 8. ~2m Particle track. Drift of electrons + potential. - potential Drift time. Detecting elements. Point of collision. Large gas volume. ~1m. Figure 1-4 Principle of a drift chamber detector.. 1.3 Aim of thesis work To detect particles produced in a collision, the particles must interact in some way with the detector matter. This interaction disturbs the particles and the optimum would be to have complete vacuum in the detectors. But with vacuum in a detector there is nothing that can register the particles. At least the detectors must be filled with suitable gas or detecting elements that fills up the volume of the detectors. The amount of other material must be minimised within the detectors. Still other material is needed in the detectors, for example, electronics needed for signal readout, detecting elements for particle registration, supporting structures to the electronics and detecting elements. The positioning of the detecting elements must often be extremely accurate. The tolerances in position stability of the detecting elements in modern particle detectors usually is in the order of a few µm. These extreme requirements in stiffness and low mass of the supporting structures often leads to well optimised light weight structures. This thesis is a study of the mechanical behaviour of the supporting structures in two types of particle detectors. The first chapter is a study of the deformation of wheels in the Time Projection Chamber of the HARP (Hadron Production Experiment) project. One of the aims with the HARP project is to study the atmospheric neutrino flux. The other part of the thesis is a static and dynamical study of the barrel support structure in the Transition Radiation Tracker (TRT) that is a inner part of the large ATLAS detector which will begin to run in 2005. Chapter 2 and 3 of this thesis can be read independently.. 1 General introduction.

(10) Supporting Structures in two Particle Detectors. 9. 2 The HARP TPC 2.1 Introduction 2.1.1 HARP and the TPC The aim of the HARP project is to study hadron production for the neutrino factory and the atmospheric neutrino flux. A beam of protons and pions with momenta in the range 2 to 15 GeV/c will be guided to a fixed target, see figure 2-1. The main detector in the HARP project is the TPC, the Time Projection Chamber. The TPC is located inside a solenoid magnet. By using the TPC it is possible to determine the path in three dimensions of the produced particles in the collision. The function of the TPC is exactly similar to the drift chamber detector described in 1.2.2. Two coordinates of a point on a particle track are known by the projection of the particle track onto the TPC end. The third coordinate is given by the drift time from the particle track to the detecting elements at the end of the TPC. The drift of the ionisation electrons in the axial direction of the TPC field cage is ensured by an electrical field. This field is created by a potential difference between each strip, running in the circumferential direction at the cylindrical surface of the TPC. The amount of secondary drift electrons, about 50 / cm particle path, is not enough to get a detectable signal. Therefore the amount of drift electrons is amplified (about 104) by an anode grid facing the detecting elements at the end of the TPC. This anode grid is a grid of thin wires (20 µm) wound onto the spokes of a wheel. At the end of the TPC there are also two similar wheels, called Gating grid, which acts as a door for the secondary drift electrons and uninteresting produced ions. The potential of the Gating grid is variable such that it can prevent the positive ions produced in the signal amplification to drift back into the field cage. Strips. Target. Particle beam Field cage. Wheels and detecting elements Figure 2-1 Side view of the TPC.. Two types of wheels are located at the left end of the TPC field cage: I) II). The anode wheel which is wired by a ∅ 20 µm Tungsten wire, 70 wires / spoke The two Gating grid wheels wired by a ∅ 70 µm Cu-Be wire, 140 wires / spoke. The wheels are made of a nonmagnetic and electrically insulating composite material.. 2 The HARP TPC.

(11) Supporting Structures in two Particle Detectors. 10. Wires. Outer wheel Spoke Inner wheel. Figure 2-2 Wheel in the TPC.. The wires are kept in position by small knobs mounted at each spoke. In the present design the spokes are free to move in the radial direction at the inner wheel. A more detailed drawing of the ∅ 20 µm wires wheel is found in Appendix A. The wiring of the wheel is in the present case assumed to start at the inner wheel. The idea is to assemble the wheels, on top of each other, on a rigid assembly table and keep the package of wheels on the table until mounting in the final structure.. 2.1.2 Aim of this study The performance of the detector is depending on the accuracy of the wire positions. The aim of this study is to determine the deformation of the wheels in the TPC and to understand the behaviour under different loading and boundary conditions. The result of this study may be used as a guideline for the design and the assembly process.. 2.1.3 Input to the analysis The material in the wheels and the spokes is Stesalite 4411W, which is a short fibre reinforced epoxy material. The in-plane material properties are isotropic. The Young’s modulus for the material is 24 GPa and the Poisson’s ratio is assumed to be 0.29. Other properties of the Stesalite 4411 W material can be found in [3]. All the data about the wires used in the analysis is summarised in table 2-1. Table 2-1 The two types of wires used in the TPC wheels.. Diameter Material Young’s modulus Nominal wire tension Number of wires / spoke. 70 µm Tungsten 375 GPa 120 g 140. 20 µm Cu-Be 130 GPa 50 g 70. 2.2 Analytical calculations Due to the tension in the wires the wheels will deform. The aim of the analytical calculations is to understand how the wheel structure behaves mechanically. The aim is also to get the order of magnitude of the displacements that will occur in reality.. 2.2.1 Radial deformation The wire tension gives, on each knob, a resultant force pointing inwards. There are 140 or 70 wires spread on a short distance (315 mm). The force on each knob is assumed as a line load with intensity N/m. Another important assumption in the calculations is that the wire tension is assumed to be constant. In a more accurate model the wires might have been treated as springs with only tension capabilities. In the. 2 The HARP TPC.

(12) Supporting Structures in two Particle Detectors. 11. analytical calculations the deformation of the outer wheel is also ignored. The calculations can be seen in detail in Appendix B. One can note that the radial deformation of the spokes in the wheel wired by the 70 µm Cu-Be wire will be larger than in the wheel wired by the 20 µm W wire. This is due to the higher tension and the double amount of wires in the 70 µm-wire wheel. Present design In the present design the spoke is free to move in the radial direction at the inner wheel. If the outer wheel is assumed to be infinitely stiff the maximum radial displacement of the spoke then occurs at the inner wheel. The maximum radial displacement is 31 µm for the 70 µm-wire wheel. This corresponds to a loss in tension of about 19% (see Appendix B). Assuming the present boundary conditions the loss in tension in the 20 µm wires will only bee 2.2% (see Appendix B). Other design solutions One possible solution to reduce the loss in tension of the wires may be to start the wiring from the outer wheel. This change decreases the maximum difference in radial displacement between radial displacement of the knob during wiring and radial displacement of knob when the wiring is completed. This change also makes the maximum radial displacement to occur at a position where the affected wire is longer. It may be important to notice that this change only affects the loss in tension and not the position of the wires when the wiring is completed. The maximum loss in tension in this case will be up to 4% in the 70 µm wires, for further details see Appendix B. Another possibility to decrease the loss in tension may be to attach the spoke to the inner wheel and let the spoke also work in compression. If the spoke is assumed to be clamped in both ends and the wiring starts from the inner wheel then the maximum loss in tension will be up to about 1.5% for the 70 µm wires, which is the worst case (see Appendix B). The radial displacement of the knobs will also be reduced if the spoke is attached to the inner ring. It would be important to examine the buckling of the spoke if the spoke also is allowed to work in compression mode. In table 2-2 the effect on the radial displacement of the spoke for different proposed design solutions can be compared. The loss in wire tension expressed as fraction of the nominal value of the tension is higher than in reality, due to the assumption of constant wire tension. Table 2-2 Comparison of maximum displacement and loss in wire tension between different design solutions.. Constraints in radial direction at spoke ends Inner end – Outer end Free – Clamped Wiring in ⇒ out Free – Clamped Wiring out ⇒ in Clamped – Clamped Wiring in ⇒ out. Maximum difference in radial displacement 70 µm wire 20 µm wire 31 µm 6.4 µm. Maximum loss in wire tension 70 µm wire 20 µm wire 19% 2.2%. 16 µm. 3 µm. 4%. 2%. 4.5 µm. 1 µm. 1.5%. 0.7%. The most important assumption in the calculations of the radial deformation of the spoke is the infinitely stiff outer- and in the last case also the inner wheel. This is of course difficult to implement in reality. An analytical estimation of the deformation of the outer wheels would be rather time consuming. The FEMmodel will give answers to the importance of this assumption.. 2 The HARP TPC.

(13) Supporting Structures in two Particle Detectors. 12. 2.2.2 Out of plane deformation The forces on the knobs are also in this case treated as a line load with uniform distribution. If this assumption is adopted it can be shown that the bending moment in the spokes always is zero if the spokes are supported in the plane at each end. In Appendix B it is shown that the bending moment is zero everywhere in the spoke in the case of assuming the spoke simply supported at the inner wheel and simply supported at the outer wheel. A result of zero bending moment is that there is no out of plane deformation. The out of plane deformation is zero regardless if the spoke is clamped or free to move in the radial direction at the inner wheel. One must keep in mind that these calculations are based on perfect uniform distribution of the line load along the spoke. This is not the case during assembly of the wires onto the wheels. The out of plane deformation may therefore be significant during the assembly process or if the wire tension not is uniform along the spokes. Also when the wiring is complete there is a small region of the spoke (about 9mm) at the inner wheel which is free of knobs. The wire free region gives not a symmetric load case which may cause a small out of plane deformation.. 2.3 FEM-model The aim with the FEM-model is to get more detailed results of the displacements and to check the assumptions made in the analytical calculations, for example the uniform line load assumption. It will also provide information about the radial stiffness of the outer and inner wheel. The FEM program used is Ansys 5.6.1 on a Unix platform. The outer wheel, inner wheel and the spoke are modelled by Shell 63 elements. This is a four-node element with bending and membrane capabilities. The interesting output from the model will be the displacement field. The model is made of 554 elements, which is enough to reach a sufficiently converged solution. This is checked by comparing the displacement field to the displacement field of a simpler model that is made of Beam 4 elements. Symmetry is used to reduce the size of the model. A 60° segment of the wheel is modelled. It would also be possible to model only a 30° segment. The mesh is shown in figure 2-3.. Figure 2-3 FEM-model of 60° segment of wheel.. The model may not be used for determining the stress field because of the coarse mesh around the holes. Still the mesh quality is enough to determine the displacement field with necessary accuracy. The load is applied to each knob (node) as a constant force and moment. In a more accurate model the wires might have been modelled by links with only tension capabilities. The wires attached to the outer wheel are also. 2 The HARP TPC.

(14) Supporting Structures in two Particle Detectors. 13. neglected in the simulation. The simulated wheel is the 70 µm wheel, which is the worst case from the deformation point of view.. 2.3.1 Radial deformation The aim has been to imitate the boundary conditions of the present design. The fixation holes in the outer wheel are locked in translation in each direction. The inner end of the spoke is free to move in the radial direction and also in all rotational directions. Symmetry boundary condition is used at the symmetry planes of the outer wheel. The radial deformation can be seen in figure 2-4.. Figure 2-4 Radial deformation in m for the present boundary conditions.. The inner end of the spoke is displaced 33 µm. This is to be compared with the analytical calculated value of 31 µm in which the outer wheel was assumed to be rigid. Since the displacement of the outer wheel is quite small (3.5 µm), the outer wheel appears to be almost rigid and thus the simple model predicts the radial displacement of the spoke very well.. 2.3.2 Out of plane deformation If the forces on the knobs are assumed to be a uniform line load the out of plane deformation is predicted to be zero. In the real case the load at the spoke is not perfectly symmetric. There is a small region at the inner wheel (about 9 mm) of the spoke that is free of knobs. This causes a small bending deformation of the spoke. If the present boundary conditions (described in 2.3.1) is used the out of plane deformation will be as in figure 2-5 and figure 2-6 depending of whether the spoke is allowed to rotate around the x-axis at the inner wheel or not.. 2 The HARP TPC.

(15) Supporting Structures in two Particle Detectors. 14. Figure 2-5 Out of plane deformation in m if the Figure 2-6 Out of plane deformation in m if the spokes are free in radial direction at the inner wheel. spokes are free in radial direction and constrained in The maximum displacement is 21 µm. x-rotation at the inner wheel. The maximum displacement is 0.8 µm.. The out of plane deformation of the spoke is small and sensitive to the boundary condition at the inner wheel. One should keep in mind that this calculation is based on the assumption that there is equal tension in each wire. If this is not true the out of plane deformation may be larger. During wiring of the wheel the load applied to the spoke is not symmetric. In figure 2-7 the deformation due to the case when the load is applied to the inner half of the spoke can be seen. The deformation in figure 2-8 corresponds to the case when the load is applied to the outer half of the spoke.. Figure 2-7 Out of plane deformation in m if the load is applied to inner half of spoke. The maximum displacement is 204 µm.. Figure 2-8 Out of plane deformation in m if the load is applied to outer half of spoke. The maximum displacement is 222 µm.. It is worth noticing that if the wiring starts from the outer wheel there will be a deflection of the spoke downwards. This deflection is in reality constrained by the assembly table.. 2.3.3 Radial stiffness of inner- and outer wheel In the analytical model the outer wheel is assumed infinitely stiff. In Appendix C a comparison of the radial stiffness between the inner- and outer wheel is performed. If a radial force of 165 N, which is the total radial force applied to each spoke, is applied in the radial direction to the outer wheel the radial deformation is 0.53 mm. If the same load is applied to the inner wheel the radial deformation is 0.018 mm. The inner wheel is about 30 times stiffer than the outer wheel in the actual load range. If the inner end of the spoke is free to move in the radial direction at the inner wheel and the outer wheel is not supported in the radial direction by the pins, the deformation of the outer wheel would cause considerable loss in wire tension.. 2.3.4 Spoke attached to inner wheel One possible solution to reduce the radial deformation and the loss in tension may be to glue the inner end of the spoke to the inner wheel. In Appendix C the radial deformation corresponding to these boundary conditions can be seen. The out of plane deformation of a completely free wheel is also shown in Appendix C.. 2 The HARP TPC.

(16) Supporting Structures in two Particle Detectors. 15. If the wheel is not constrained in translation by the fixation pins at the outer wheel and the inner ends of the spokes are attached to the inner wheel the radial deformation of the spoke would be drastically reduced. This is due to the much stiffer inner wheel. If this alternative is considered the buckling tendency of the spoke, when it is also allowed to work in compression, must be investigated. If the spoke is supported in plane at each end the alternative of gluing the spoke to the inner wheel has only a minor effect to the out of plane deformation. If the wheel is completely free this change would reduce the out of plane deformation but still the deformation would be too large to be acceptable. It is therefore recommended to always keep both ends of the spoke constrained in plane. The analysis made is only a linear static analysis. There may also be other effects as buckling if the wheel is completely unconstrained since the structure is probably not very stable.. 2.4 Conclusions During wiring of the wheels the knobs on the spokes will be displaced towards the centre. This displacement will reduce the tension in the already wired wires. It is shown that the out of plane displacement of the spokes is small if the wire tension is uniform along the spokes. Therefore, it is important to achieve as uniform wire tension as possible. One way to attain uniform wire tension is to vary the tension during wiring. If it is decided to start the wiring from the inner wheel the suggestion is to examine this alternative carefully especially for the wheels wired by the 70 µm wire. The essential results from the analysis can be summarised in the following points: • The inner and outer wheel should always be supported in plane. • If the inner ends of the spokes are free to move in the radial direction the outer wheel should be supported in the radial direction. • If the tension is equal in each wire and the spoke is supported in plane at both ends the out of plane deformation of the spokes is small, i.e. 1-20 µm depending on boundary conditions. • It is preferable to start the wiring of the wheels from the outer wheel, since this gives: - Less loss in wire tension. - No out of plane deformation during wiring because the wheel is constrained against the assembly table.. 2 The HARP TPC.

(17) Supporting Structures in two Particle Detectors. 16. 3 The barrel TRT support structure 3.1 Introduction 3.1.1 LHC and ATLAS The Large Hadron Collider (LHC) is a new circular particle accelerator under development at CERN. It will begin to run in 2005. The LHC will accelerate protons to energies higher than ever achieved before. The LHC will be situated in the same tunnel 100 m under ground level as its forerunner the Large ElectronPositron collider (LEP). Protons are produced and pre-accelerated in linear and circular accelerators, with smaller radius than the LHC, before they are injected into the two beam pipes of the LHC. The energy of a single proton is 450 GeV before injection into the LHC. The energy is increased up to 7 TeV by the LHC. As a comparison, the mass at rest of a proton is 938 MeV. Due to the relativistic effects this increase in energy only corresponds to a slight increase in speed. The speed of the protons is up to 99.9999991% of light speed in the LHC. At this speed the protons travel around the LHC 11000 times per second. To keep the protons at position on its circular path at this high speed a magnetic field of about 8 T is needed. To create the strong magnetic field superconducting magnets must be used and the LHC will be the largest superconducting installation in the world. The two counter rotating beams of protons intersect each other at different positions and the protons are brought to head on collisions. The total energy in a single collision, or event as it is called, is 14 TeV. This amount of energy approximately corresponds to the kinetic energy of a small and slowly walking spider. This surprisingly low energy is squeezed into the tiny space of the same size as a proton so the energy density is extremely high. The energy density is in the same order as 10-12 s after the Big Bang.. Figure 3-1 Principle of Large Hadron Collider at CERN. [4].. At one of the points of collision in the LHC the large ATLAS detector is situated, see figure 3-1. The most important mission of the ATLAS detector is to increase the knowledge and understanding of the fundamental concept of mass. The ATLAS detector will register the tracks of the secondary produced particles in the collision. Some particles, as for example the Higgs Boson, cannot be directly detected since the lifetime for these particles is too short and they are rapidly decayed into other particles. On the contrary, the ATLAS detector can register some of the secondary particles so that the origin position and existence of. 3 The barrel TRT support structure.

(18) Supporting Structures in two Particle Detectors. 17. the unstable particle can be determined. The rate of collisions, or events, in the LHC is about a billion per second but the interesting events are about one in ten million. One of the most challenging tasks for the ATLAS physicists and engineers is to develop algorithms and electronics that can filter the interesting events from the ordinary events. The ATLAS detector is built from many sub detectors, developed for a certain measurement or task. The innermost detector in the ATLAS detector is the inner detector, marked by yellow in figure 3-2. A superconducting Solenoid Magnet creating a magnetic field of about 2 T surrounds the inner detector. The point of collision is in the centre of the detector. The height of the ATLAS detector is about the height of a five-storey building. 1850 physicists from 150 universities and laboratories in 34 countries are participating in the ATLAS experiment.. Figure 3-2 The ATLAS detector. [5].. 3.1.2 The inner detector and the TRT Electrically charged particles, for example electrons and pions, which travel in a magnetic field, will be affected by a force perpendicular to the particle path. The superconducting solenoid will force the charged particles to travel in a path with a radius determined by the magnetic field, the electrical charge and the momentum of the particle. The purpose of the inner detector is to determine the radius of curvature of the tracks from the electrically charged particles. When the radius is known the momentum can be calculated. The accuracy in determination of the particle tracks is more stringent the closer to the point of collision the particle is. Within the inner detector there are three sub systems. These are the pixel detector, the semiconductor tracker (SCT) and the transition radiation tracker (TRT). In the pixel detector and the SCT, the detecting elements are made of thin layers of silicon. When a detectable particle passes one of these layers of silicon a measurable signal is produced. These types of detecting elements give a precise measure of the particle tracks. More far out in the detector it would become too expensive to use these types of detecting elements. In the TRT, marked by yellow in figure 3-2, therefore other types of detecting elements are used. The detecting elements in the TRT are gas filled thin tubes, called straws, with a wire in the centre. The principle of these straws is similar to the principle of a wire chamber detector described in section 1.2. Within the TRT there are about 370 000 of these straws. Between the straws thin foils of polyethylenepolypropylene are located. These foils produce the transition radiation that is used to distinguish between pions and electrons. Within the barrel TRT, which is a sub unit of the TRT, the detecting straws are located in the axial direction of the inner detector as indicated in figure 3-3. In the two end-caps of the TRT the straws are located radially.. 3 The barrel TRT support structure.

(19) Supporting Structures in two Particle Detectors. 18. Straw direction. Straw direction. End-cap TRT Barrel TRT. End-cap TRT Figure 3-3 Inner detector of ATLAS. [6].. The barrel TRT support structure The main components in the barrel TRT support structure are the inner cylindrical skin, the outer cylindrical skin and the two supporting frames, called endplates. The detecting straws in the barrel TRT are gathered into three types of modules of rhomboid shape. The main function of the barrel TRT support structure is to support these modules and also the pixel detector and the SCT. The barrel TRT modules are supported at each end by the two endplates. Figure 3-4 and figure 3-5 shows the barrel TRT support structure and the used terminology. The outer cylindrical skin is divided in the horizontal plane in two halves. The exact type of connection between the upper and lower half is not designated at the present date. The inner cylindrical skin is bonded to the endplate. The outer cylindrical skin is connected to the endplate by screws. Two horizontal rails, bolted to the structure outside the barrel TRT, the cryostat wall, support the barrel TRT. The length of the barrel TRT is 1.5 m and the outer diameter is about 2 m.. Outer cylindrical skin. Module type 3. Module type 2. Endplate. Module type 1. Inner cylindrical skin Figure 3-4 Barrel TRT support structure.. Ring 1 Ring 2 Ring 3 Ring 4 Figure 3-5 Front view of endplate and the three types of modules.. 3 The barrel TRT support structure.

(20) Supporting Structures in two Particle Detectors. 19. 3.1.3 Background and aim of this study The accuracy in the positioning of the detecting elements is in the order of 10 µm. This means that there must be strict restrictions on the stability of the supporting structures. Near the point of collision the accuracy in determining the particle tracks must be better than far out in the detector. The stability in position of the pixel detector and the SCT is therefore more stringent than the stability in position of the modules in the barrel TRT. The straws in the barrel TRT have an intrinsic resolution of ∼120 µm. According to [7] the total accuracy in the detecting elements of the SCT with respect to the nominal baseline is summarised in table 3-1. Table 3-1 Short-term alignment requirements for detecting elements in the barrel SCT.. Direction r-ϕ r z. Allowed displacement with respect to nominal baseline 12 µm 100 µm 50 µm. The values presented in table 3-1 gives a hint of the accepted amplitudes of vibration of the barrel SCT. To predict the actual amplitudes of vibration is a very difficult task to perform since there are mainly two unknowns: -. What is the damping in the system? What are the levels of excitation from possible sources?. The damping is due to material damping in cables, pipes, support structure, etc. To determine the level of damping at reasonable accuracy is more or less impossible for the barrel TRT support structure without making measurements on the final assembled structure. In [8] Lucas has presented the probable sources of vibration in the ATLAS cavern to be: 1. 2. 3. 4. 5.. Seismic sources Ventilation The cryogenic pumps Flows in the pipes Electromechanical or magnetic-mechanical coupling. For all sources except the seismic sources it is practically impossible to make a realistic quantification of the levels of excitation. To clarify the difficulties of determining the actual amplitudes of vibration of the barrel TRT the governing equation in a FEM analysis of the mechanics of a solid structure is studied. The aim is not to give a detailed explanation of the Finite Element Method. According to [9] the governing equation for analysis of a solid structure with FEM is. [M ]{D}+ [C ]{D}+ [K ]{D} = {R ext }. ••. •. (3.1). If the mass ([M]), the damping ([C]) and the stiffness matrix ([K]) are known and the exciting force ({Rext}) is assumed to vary harmonically the amplitude of vibration, given by {D}, could be calculated in a harmonic response analysis. Since [C] and {Rext} are unknowns it is not possible to determine the amplitude of vibration. Still [M] and [K] are known for the barrel TRT support structure which makes it possible to determine the mode shapes and the natural frequencies of vibration in a modal analysis. The aim of this study is therefore limited to determine the mode shapes and natural frequencies of vibration of the barrel TRT support structure. The aim is also to find the optimal design to keep the levels of vibration as low as possible. The energy needed to excite a vibration mode is related to the frequency and. 3 The barrel TRT support structure.

(21) Supporting Structures in two Particle Detectors. 20. the amplitude of the vibration. Assuming constant input energy, a higher natural frequency gives smaller amplitude. The optimum is therefore to have as high natural frequencies as possible. The primary variables for optimisation are the properties of the two cylindrical skins. A second aim with this study is to determine the static deflection and torsional stiffness of the barrel TRT support structure. The torsional stiffness is of interest when the planarity of the supporting rails is to be specified.. 3.2 FEM model In order to determine the natural frequencies, natural modes and static deflection of the barrel TRT support structure at better accuracy an FEM-model is made. The software used for the analysis is ANSYS* 5.6.1 on a Unix platform. The model is defined by parameters determining the geometry, mesh quality, loads, etc. The barrel TRT support structure has many symmetry planes. In order to get every mode in the analysis these symmetry planes are not used and the whole structure is modelled. A more detailed description of how the model is created is found in Appendix E where also the code is presented. The analyses are executed in batch mode and the results are viewed via the Graphical User Interface. The most important assumptions, for the static and dynamic analysis, made in the model are summarised in the points below. -. Barrel TRT modules applied as point masses Pixel detector and SCT applied as point masses The contribution to the stiffness and mass from service cables and pipes is ignored Perfect bounding between upper and lower part of the outer cylindrical skin. 3.2.1 Geometry The geometry of the barrel TRT support structure is defined by a few parameters. The most important parameters are found in table 3-2, see also figure 3-4 and figure 3-5. Table 3-2 Parameters defining the geometry of the barrel TRT.. Definition Radius to ring 1 Radius to ring 2 Radius to ring 3 Radius to ring 4 Thickness of inner cyl. skin Thickness of outer cyl. skin Thickness of supporting endplate Total length of barrel. Name in model radius_1 radius_2 radius_3 radius_4 in_thick ou_thick e_pl_dep length. Value 563.9 mm 701.2 mm 868.4 mm 1073.5 mm 2 mm 3 mm 21 mm 1500 mm. The radius to each ring is defined as the radius to the point where the mid-surface of the beams in the endplate intersect each other. These points (nodes) are also assumed to be the supporting points of the barrel TRT modules. The module supporting points are about 5 mm offset from the beam intersection point in reality but the error of assuming them coincident in the model is negligible. The thickness of ring 1 and ring 4 is tapered. In the FEM-model the thickness of these rings is assumed to vary linearly in the hoop direction. A detailed drawing of the supporting endplates is found in Appendix F. 3.2.2 Elements The supporting endplates are modelled by 4 nodes-Shell63 elements. This is a shell element with bending and membrane capabilities. Orthotropic material properties used as input. The different effective in plane stiffness and bending stiffness that may occur in a laminate can not be taken into account by this element.. *. ANSYS is a trademark of the Swanson Analysis System Inc.. 3 The barrel TRT support structure.

(22) Supporting Structures in two Particle Detectors. 21. The two cylindrical skins are modelled by Shell91 elements. This is an element used for modelling laminate shells. The effect of differences in the in plane stiffness and the bending stiffness is included by this element. The mass of the barrel TRT modules, the SCT and the pixel detector are modelled by the point mass element 21. The rotational inertia of the components modelled by this element is ignored.. 3.2.3 Loads The loads applied to the barrel TRT support structure are the mass of the pixel detector, the SCT, the barrel TRT modules and its own weight. The masses are summarised in table 3-3. The masses with a parameter name are implemented in the FEM-model and the total values are shown only as a comparison. The total mass of the barrel TRT support structure is the mass of the cylindrical skins and the endplates. Table 3-3 Masses applied to the barrel TRT support structure. [10].. Description Pixel detector Mass of barrel 3 SCT Mass of barrel 4 SCT Mass of barrel 5 SCT Mass of barrel 6 SCT Interlinks Thermal enclosure of SCT Total mass of pixel detector and SCT Mass of module 1 Mass of module 2 Mass of module 3 Total mass of all modules Total mass of barrel TRT support structure. Parameter name in FEM-model sct module1 module2 module3 -. Value 65 kg 24 kg 30 kg 37 kg 43 kg 11.3 kg 7.5 kg 217.8 kg 2.7 kg 3.9 kg 5.6 kg 390.4 kg 86.8 kg. Two pins at each end support the barrel TRT modules. The masses of the modules are applied as point masses to the supporting locations. The masses of the modules are split evenly between each end of the modules and also between each supporting pin at one end. The total mass of the pixel detector and the SCT are split evenly between the four supporting points of the barrel SCT at ring 1. All the applied point masses are found in figure 3-6.. Mass of SCT and pixel detector. Mass of barrel TRT modules. Figure 3-6 ISO view of applied point masses.. 3 The barrel TRT support structure.

(23) Supporting Structures in two Particle Detectors. 22. 3.2.4 Boundary conditions Two rails are bolted on the structure outside the barrel TRT, the cryostat wall. When the inner detector assembles, the barrel TRT will slide on these rails into the cryostat. To not over constrain the barrel TRT one of these rails has a v-shape while the other is flat. The barrel TRT is supported by the rails at four points. The boundary constraints conditions assumed in the analysis are shown in figure 3-7. All the nodes through the endplate thickness are constrained in translation for the specified direction at all four supporting points. Y 4. (X,Y) Z. 1. (X,Y,Z). X. 3. (Y). 2. (Y) Figure 3-7 Boundary conditions for barrel TRT model.. In the modal analysis the barrel structure is considered supported at four points as indicated in figure 3-7. In the static analysis two different cases are studied. Case 1, the nominal case, is when all the four supports are assumed to be acting. Case 2 is when support No 3 is assumed to be missing due to possible rails misalignment. The deflection, due to gravity, at the location of supports No 3 in case 2, gives an indication of the torsional stiffness of the structure. To simulate the bonded joint of the endplates to the inner cylindrical skin, all degrees of freedom for coincident nodes are coupled. This is shown in figure 3-8. The outer cylindrical skin is connected to the endplates by screw joints at 32 locations. At each location, two nodes along the end plate thickness are coupled to the corresponding nodes on the outer skins, blocking in this way the relative rotations.. Bonding. Screw joints. Figure 3-8 Connection of the endplate to the cylindrical skins.. 3 The barrel TRT support structure.

(24) Supporting Structures in two Particle Detectors. 23. 3.2.5 Material properties The endplate is a laminate made of carbon fibre reinforced epoxy. It is manufactured by milling a large solid laminate plate to the final shape of the endplate. Through the thickness of the endplate there are several layers (about 180) with unidirectional fibre orientation. For unidirectional oriented fibre composite materials, named transversally isotropic, the in-plane mechanical behaviour of one ply can be defined by four material constants. The ply properties given by the manufacturer (Technologia in Obninsk , Russia) and accepted for detailed design are summarised in table 3-4. Table 3-4 Ply properties.. Material constant E1 E2 G12 ν12 CTE 1 CTE 2. Value 150 GPa 9.8 GPa 6.1 GPa 0.26 -0.1⋅10-6 1/C° 27.5⋅10-6 1/C°. Index 1 refers to the axial direction of the fibres. The second direction is the transversal direction. E is Young’s modulus in the specified direction, G12 is the shear modulus and ν12 is the major Poisson’s ratio. CTE is the thermal expansion coefficient in the specified direction. Given the ply properties it is possible to calculate the mechanical properties of each beam composing the endplate. These calculations are done using the laminate macro-mechanics theory implemented in EsaComp* 1.5, a program developed for mechanical calculations of composite structures. The calculated properties of each bar in the endplate are found in table 3-5. Table 3-5 Calculated characteristics of the endplate bars.. Bar type. Circumferential. Lay-up of the bar. At 20 ° El, GP 92,9. Et, GP 50,9. E z, GP 9,8. Glt, GP 12,6. vlt. Within the range from 20 to 35 ° αt, αl, 10-6×1/º 10-6×1/º 1,02 3,59. 030%/-68,0910%/ 0,182 68,0910%/5,6330%/ -62,4710%/73,7210% Radial -68,0930%/ 43,8210%/ 40,7 53,2 9,8 18,8 0,343 3,15 1,47 010%/-62,4730%/ 49,4510%/5,6310% Note: l – direction along bar t – transverse direction for a bar in monolayer plane z – direction through a thickness of bar (transversely to a monolayer plane, along the TRT axis) The notation for the lay-up may be confusing. The given fraction is the total fraction of plies in the specified direction. Since the total number of layers in the laminate is large (about 180) and there is more or less a uniform distribution of every layer with the same direction through the laminate thickness, the effective bending modules are almost the same as the in-plane modules. This is also assumed in the FEMmodel. For the lay-up of the cylindrical skins there are four different types proposed by the manufacturer. The in EsaComp calculated mechanical properties of the different lay-ups are found in table 3-6.. *. EsaComp is a registered trade mark of Helsinki University of Technology. 3 The barrel TRT support structure.

(25) Supporting Structures in two Particle Detectors Table 3-6 Calculated characteristics of proposed cylindrical skins. At 20° No Lay-up variant E z, E c, Gzc, vzc GP GP GP 1 060%/9022%/±4518% 99,6 46,9 12,0 0,178 2 033.3%/±6066.6% 58,3 58,3 22,5 0,296 3 ±45100% 21,3 21,3 38,8 0,743 4 022%/±6078% 42,7 63,5 25,3 0,297 (013%/9029%/±4558%) Note: z – axial direction (along the TRT axis) c – circumferential direction. 24. Within the range from 20 to 35 ° αc, αz, 10-6×1/º 10-6×1/º 0,86 4,13 1,97 1,97 1,97 1,97 3,24 1,02. Each variant of the lay-up reflects a definite concept of cylinder design: 1 – minimal CTE and maximal stiffness along the TRT axis 2 – pseudo-isotropic properties with low shear modulus 3 – pseudo-isotropic properties with ultimately high shear modulus 4 – equal CTE in circumferential direction for the bars of the TRT frame and cylindrical skins Since the lay-up only is known as fraction of plies in specified direction compared to total skin thickness the flexural modulus are assumed to be the same as the in-plane modulus presented in table 3-6. The density of the fibres is assumed to be 1775 kg/m3 and the density of the epoxy is assumed to be 1200 kg/m3. If the fibre content is assumed to 60 % (volume fraction) the density of the composite material is 1545 kg/m3.. 3.3 Modal analysis The assumptions on which the FEM-model is based, presented in 3.3, have different impact on the modaland static analysis. A result of assuming the pixel detector and SCT as point masses is that the dynamical coupling between the pixel detector, the SCT and the barrel TRT is not considered in the analysis. A result of assuming the barrel TRT modules as point masses is that the impact of the modules on the stiffness of the barrel TRT support structure is neglected.. 3.3.1 Analytical estimation of fundamental frequency The barrel TRT support structure is very stiff in the radial direction compared to the stiffness in the axial direction. A consequence of this is that the fundamental mode is most probably when the inner cylinder oscillates in the axial direction which can be seen in figure 3-9.. Axial oscillation of inner cylinder. Endplate. Figure 3-9 Oscillation of inner cylinder in the axial direction of the barrel TRT.. 3 The barrel TRT support structure.

(26) Supporting Structures in two Particle Detectors. 25. If the endplates are assumed not to bend and to have no stiffness in the plane the cylindrical skins determines the stiffness of the barrel TRT support structure. The axial motion of the SCT can be described, at reasonable accuracy, by a simple single degree of freedom model if the assumptions below are adopted. -. Endplates assumed to have no stiffness in the plane Endplates assumed to have infinite stiffness for bending out of plane All masses (SCT, barrel TRT modules) regarded as point masses Isotropic material properties of cylindrical skins. A suitable representation of the two first assumptions is to imagine the endplate as rigid beams in the radial direction attached to the cylindrical skins as indicated in figure 3-10. The first assumption is valid for thin endplates and the second assumption is valid for thick endplates. The model can be seen as an approximation within a range of the endplate thickness.. Figure 3-10 Endplate assumed as radial beams in the analytical model.. In Appendix D the model is described in detail. If the material in the cylindrical skins is assumed to be Aluminium the natural frequency is 4.2 Hz. It can also be shown that the fundamental frequency of the barrel TRT is related to the thickness of the cylindrical skins (h) and to the elastic modulus (E) in the following manner. ω ∝ C1 ⋅ h1. 5/ 2. ⋅ E1 + C 2 ⋅ h2. 5/ 2. ⋅ E2. (3.2). Index 1 refers to the inner cylindrical skin and index 2 refers to the outer cylindrical skin. C1and C2 are constants depending on geometric parameters, as radius to the skins for example. It is clear that the most effective way to increase if the fundamental frequency is to increase the thickness of the cylindrical skins. It may also be worth noticing that the fundamental frequency depends on the square root of the Young’s modulus. This implies that it will become very difficult to affect the fundamental frequency by changing material or the lay-up of the laminate in the two cylindrical skins.. 3.3.2 Initial study The FEM-model in this study is developed in steps with increasing complexity. To implement the wrong material properties in the model is easy, therefore the material properties are assumed to be isotropic Aluminium at the early stage. The result of this assumption is presented in this section. The fundamental mode shape of the barrel TRT support structure is when the inner cylindrical skin oscillates in the axial direction. This is due to the low stiffness of the structure in this direction. This is also the most harmful direction for movements of the SCT. The natural frequency corresponding to this mode is 5.6 Hz. This is in good agreement with the result from the analytical model presented in 3.3.1.. 3 The barrel TRT support structure.

(27) Supporting Structures in two Particle Detectors. 26. The supporting endplates in the barrel TRT structure are more or less fully developed at the present date. The natural way of achieving an increase of the fundamental frequency of the system is therefore to optimise and possibly increase the thickness of the two cylindrical skins. To get a first feeling of how the thickness of the two cylindrical skins and the endplate affects the fundamental frequency a comparative analysis is made. The changes compared to the reference model and the result is found in table 3-7. Table 3-7 Influence of changes in parameters on fundamental frequency.. Values for reference model are; inner skin thickness 2 mm, outer skin thickness 3 mm, endplate thickness 20 mm Change compared to reference model Increase of the fundamental frequency Increase inner skin thickness 1 mm to 3 mm 0.6 Hz Increase outer skin thickness 1 mm to 4 mm 0.6 Hz Increase supporting endplate thickness 1 mm to 21 mm 0.2 Hz Improve connection of outer ring and outer cylindrical skin 0.7 Hz One simple way to make the structure stiffer and slightly increase the fundamental frequency is to improve the connection of the outer ring and the outer cylindrical skin. The improvement presented in table 3-7 is that six more screws are assumed applied between the current screws. One other conclusion from the analysis is that there is no major difference if the inner or the outer cylindrical skin is increased in thickness as long as there is no improvement of the connection between the outer ring and outer cylindrical skin.. 3.3.3 Check of mesh quality In an FEM-analysis there is a relation between the accuracy in the results and mesh size. The more refined the mesh is the more accurate the result is to the cost of more CPU time. It is important not to use a finer mesh than necessary. A coarse mesh will represent the real structure by a too stiff approximation. This will result in natural frequencies that are higher than the real values. In table 3-8 the CPU time and the natural frequencies from analyses with different mesh size are compared. The analyses are based on assuming isotropic material properties (Aluminium). The presented results are not supposed to agree very accurately to the real values. The aim is to have a comparison between different sizes of the mesh. Table 3-8 Comparison between different mesh size.. Elements 4612 10116 14084. DOF:s 69888 158208 228096. CPU time 54 min 43 min 78 min. Natural frequencies in Hz Mode 1 Mode 2 Mode 3 5.8 24.4 34.5 5.5 23.6 33.2 5.6 23.6 33.2. Mode 4 44.7 40.4 40.5. Mode 5 47.2 42.6 42.7. In the first model the natural frequencies are higher than in the other two models due to the stiff approximation of the barrel TRT structure. The long computing time is due to the number of iterations needed to find a sufficiently converged eigenvalue solution. The fundamental frequency is higher in the third model than in the second but the difference seems to be higher than it actually is due to round off errors. The higher natural frequencies in the third model are probably due to numerical errors. The 10116 elements model achieves a compromise between CPU time and accuracy in the result.. 3 The barrel TRT support structure.

(28) Supporting Structures in two Particle Detectors. 27. 3.3.4 Mode shapes The stiffness in the axial direction of the barrel TRT support structure is quite low. There is no doubt that the first mode of vibration for the barrel TRT support structure is when the SCT and the pixel detector oscillates in the axial direction. The frequency for this mode is around 5 Hz. The fundamental mode shape can be seen in figure 3-11. Figures of the higher modes are found in Appendix G.. Figure 3-11 Side view of fundamental mode shape for barrel TRT support structure, frame 1/10 and frame 10/10.. The second (around 20 Hz) and the third mode (around 30 Hz) assume that the barrel TRT support structure will slide on the flat rail. A rough estimation of the force needed to overcome the friction at the flat rail gives a few hundred Newton. It seems unlikely that an exciting force of this magnitude would occur in the ATLAS cavern. These modes will therefore probably not be present in reality. The higher modes (above 30 Hz) are when the supporting endplates oscillates in an umbrella-like way with different numbers of nodal diameters. These modes affect only the barrel TRT modules and not the SCT and the pixel detector. The positioning of the barrel TRT modules in the axial direction does not need to be very precise and the energy needed to excite these modes is higher than the energy needed to excite the more risky fundamental mode.. 3.3.5 Limit range of fundamental frequency In 3.4.1 it has been shown that the fundamental frequency depends on the thickness of the cylindrical skins and the thickness of the endplate. Since the design of the endplates is more or less frozen at the present date the natural way to increase the fundamental frequency is to optimise the lay-up, and possibly increases the thickness, of the cylindrical skins. Before starting optimisation of the cylindrical skins the upper possible limit to achieve is good to know. Therefore different cases with extreme assumptions of the cylindrical skins have been run. These cases and the results are found in table 3-9. The assumed material properties are those presented in 3.3.5. Table 3-9 The effect of extreme assumptions of the cylindrical skins.. Lower limit Upper limits. Thickness of endplate 21 mm 21 mm 21 mm 24 mm. Inner cylindrical skin 2 mm, lay-up 4 2 mm, lay-up 4 Infinitely rigid Infinitely rigid. Outer cylindrical skin Not present Infinitely rigid Infinitely rigid Infinitely rigid. Fundamental frequency 4.3 Hz 7.6 Hz 9.3 Hz 11.1 Hz. 3 The barrel TRT support structure.

(29) Supporting Structures in two Particle Detectors. 28. Assuming 2 mm inner cylindrical skin and lay-up 4 the fundamental frequency is 4.3 Hz -7.6 Hz depending on the properties of the outer cylindrical skin. No matter how great improvements of both the cylindrical skins the fundamental frequency will never be higher than 9.3 Hz. The case in which the endplate thickness is 24 mm is only shown as reference.. 3.3.6 Results of different lay-ups in cylindrical skins The mode shapes and natural frequencies for each type of proposed lay-up are calculated. The thicknesses of the endplates are assumed to the basic value of 21 mm. The result for 2 mm and 3 mm skin thickness is summarised in table 3-10. As a comparison a calculation also is done for 5 mm inner skin thickness and 5 mm outer skin thickness. The result can be seen in table 3-11. Table 3-10 Calculated natural frequencies for 2 mm inner cylindrical skin and 3 mm outer cylindrical skin.. Lay-up No 1 2 3 4. Natural frequencies in Hz Mode 1 Mode 2 Mode 3 5.2 19.6 27.6 5.2 19.7 27.7 4.9 19.4 27.6 5.1 19.6 27.7. Higher modes 33.1 33.1 32.4 32.9. 35.0 35.0 33.7 34.7. 35.9 35.9 35.3 35.7. 37.0 36.9 36.2 36.7. Table 3-11 Calculated natural frequencies for 5 mm inner cylindrical skin and 5 mm outer cylindrical.. Lay-up No 1 2 3 4. Natural frequencies in Hz Mode 1 Mode 2 Mode 3 6.9 20.1 27.2 6.9 20.2 27.4 6.6 19.9 27.1 6.8 20.1 27.4. Higher modes 41.7 41.7 40.1 41.2. 43.3 43.2 41.5 42.7. 43.8 43.5 42.3 43.0. 44.8 44.6 43.1 44.1. Lay-up 1 or lay-up 2 of the cylindrical skins results in the highest fundamental frequency but the difference compared to lay-up 3 and lay-up 4 is small. This implies that a change of the material properties only has a minor effect on the fundamental frequency. This is also indicated in the analytical model in section 3.2. It seems like lay-up 4 would be a good choice since this lay-up has better thermal expansion properties than the other lay-ups and the fundamental frequency for this lay-up is relatively high. Furthermore, it can be seen that the increase of the fundamental frequency is about 1.7 Hz if the skin thicknesses are increased to 5 mm. It may be worth noticing that there exists several modes, close to each other, above 30 Hz. Probably there will exist modes in the range around 50 Hz regardless of which lay-up will be chosen. It is interesting to notice that there is no difference in the fundamental frequency for lay-up 1 and lay-up 2 despite lay-up 1 has higher axial modulus. This is an effect of that only the local stiffness of the outer cylindrical skin is affecting the fundamental mode. With the present connection between the endplate and the outer cylindrical skin it appears that the optimum lay-up of the outer cylindrical skin is necessarily not the lay-up with the highest axial modulus as expected.. 3.3.7 Influence of variation in geometrical parameters It is shown that it is not possible to drastically increase the fundamental frequency by changing neither material properties nor the geometry of the barrel TRT. However it is not clear how different changes in the geometry affects the fundamental frequency. Therefore an analysis with the aim to clear these questions is carried out. A comparative analysis with respect to the basic model is done. The model used as basis is assumed to have 21 mm endplate thickness, 2 mm inner skin thickness, 3 mm outer skin thickness and lay-up 4 in the cylindrical skins. To see the effect of changes in geometry one of the parameters endplate thickness, inner. 3 The barrel TRT support structure.

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