ACTIVE BRAKE COOLING 89

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1 ACTIVE BRAKE COOLING 89 Appendix M: Finite Element Analysis ABSTRACT The Purpose of this report is to show how finite element analysis is a method and technique used to solve a variety of engineering design application problems through the utilization of the powerful Lisa software. The introduction to the engineering design focus is given on pages 3-5 of this technical report where the mechanical engineering design is an active cooling conditioning and monitoring system for heavy transportation vehicles. The demand for this system is such that will aid and abide in the shipping and distribution industry offering a safer means of transporting goods on commercial highways where accidents due occur from a scientific phenome called brake fade. The thermal analysis of a radial cross section plate Is approximated as a flat plate or plane wall that is subjected to boundary conditions having a temperature of 560 degrees Celsius on the interior surface and a temperature of 20 degrees Celsius on the external surface. The analytical analysis will be performed by conducting sequential integration of the second order linear homogenous differential equation by solving for the integration constants and formulating a general solution this detail is modeled on pages 6-8. The finite element analysis will be conducted utilizing Lisa software and boundary conditions at the 2dimensional solid 4 element 5 node body. Where the known temperatures at the nodes on the y=o axis are 560 degrees Celsius and the temperatures at the y=l axis are 20 degrees. The mechanical properties of the grey cast iron h250/g3000 plate are given in table 1 on page 5. The actual conditions that a brake drum experiences at critical temperatures are give in table 2 located on page 5. The full analysis of the drum and the purpose of offering forced convection through the design of an active cooling conditioning and monitoring brake system with air as a fluid medium are beyond the scope of this report. The convergence test is shown in table 7 located on page 10 of this technical

2 ACTIVE BRAKE COOLING 90 report. TABLE OF CONTENTS ABSTRACT.. Page1 TABLE OF CONTENTS...Page2 INTRODUCTION. Page3-5 ANALYTICAL ANALYSIS.Page6-8 FINITE ELEMENT ANALYSIS...Page8-9 CONCLUSION Page10 REFERENCES..Page11 DOCUMENTS...Page12

3 ACTIVE BRAKE COOLING 91 Figure 1 Race Car Application Page 3 Figure 2 Air Plane Application Page 4 Figure 3 Figure 4 Transport Truck Application Temperature Distribution Page 4 Page 8 Table 1 Mechanical Properties of grey cast iron H250/g3000 Page 5 Table 2 Loading Conditions Page 5 Table 3 Temperature Distribution Page 7 Table 4 Node ID Page 8 Table 5 Element ID Page 8 Table 6 Results Page 9 Table 7 Convergence Page 10 INTRODUCTION Heavy Transportation vehicles are requested in industry to transport a variety of goods to a variety of locations. Some of these goods are simple goods that individuals encounter everyday such as products from the grocery that have been processed and packaged or goods such as stationary items that are used in professional office settings. On the other end of the spectrum with respect to the variety of goods that are requested to be shipped from location to location by heavy transportation vehicles, some of these goods can be of a significant amount of weight increasing the loading of the heavy

4 ACTIVE BRAKE COOLING 92 transportation vehicles which of course increases the demand of the engine and other mechanical related components and attributes on these vehicles. Such as lubrication, fuel, and braking power. Brake Fade is a Phenomena that occurs in various types of vehicles, such as race cars, air planes, and transport trucks. Brake fade occurs when the temperature of the braking element disc or drumreaches a temperature that causes a volume increase due to thermal expansion requesting more work from the braking piston. Brake fade occurs when the brake pad combusts from the release of a gaseous substance degenerating the quality of braking performance. Brake fade occurs when the braking effort is not equally distributed requesting more work to be done by the braking piston. A general misconception for brake fade occurs when the braking fluid reaches a temperature that causes a thermodynamic state transformation from liquid to vapor again degenerating the quality of braking; however, for terms of this technical finite element analysis project report, Vapor Brake fade is not a primary focus. Race Cars Figure One Brakes: 6-piston (front and rear) carbon calipers, carbon discs and pads Brake disc size: 278 x 28 mm (front and rear) Weight 642 kg Figure One shows a Formula One race car making a sharp turn around the competitive race track. Formula One race cars like the one depicted in figure one reach top speeds up to 360 Km/h. These speed request heavy quality braking that avoids the brake phenome brake fade. Air Planes

5 ACTIVE BRAKE COOLING 93 Figure Two Figure Two shows a plane running off the landing strip. Landing speeds for typical airplanes are miles per hour with a weight of kg, the request is for quality braking without the occurrence of the mechanical phenome brake fade. Transport Trucks Figure Three Figure three is shows a heavy transportation vehicle transporting an over-sized load that is vulnerable to suffering brake fade at quick braking such as when travelling through a steep decline through a gravitational field The focus of the capstone mechanical engineering design project is to design an active conditioning and monitoring cooling system for heavy transportation vehicles. Finite Element Analysis from the software Lisa will show the stresses that the brake drum is subjected to at high stress levels. Table 1

6 ACTIVE BRAKE COOLING 94 Modulus of Elasticity 150 Gpa density 7100 kg/m^3 Poisson ratio 0.26 thermal conductivity 53 W/m K specific heat 0.46 kj/kg*k Thermal Expansion coefficient 1.1*10^-5 ⁰C^-1 Convection Heat Transfer Coefficient of 800 W/m^2⁰C Heat Flux Acting on the inner surface 1607 Kw/m^2 Tabulated in table 1 are the mechanical properties of the grey cast iron ht250/g3000 drum where the Modulus of Elasticity is 150 Gpa, the density is 7100 kg/m^3, the poisons ratio is 0.26, the thermal conductivity is 53 W/mK and the specific heat is 0.46 kj/kg K, the thermal expansion coefficient is 1.1*10^5 /⁰C. Table 2 Parameter Quantity Detail Calculations Centrifugal force N density * outer radius of drum *(w^2) Speed (rotation) (z axis) rad/s Velocity / inner radius = 120km *(1000/3600)/ (0.2032) Internal Temperature 560⁰C due to friction Temperature of air 20⁰C close to room temperature

7 ACTIVE BRAKE COOLING 95 Gravity (-y direction) 9.81 m/s^2 Gravitational force due to acceleration

8 ACTIVE BRAKE COOLING 89 Braking Pressure Pa Applied Braking Pressure Inner Surface Area of drum m^2 To Scale inner surface area of the drum Surface Force N Corresponding Surface Force inner radius of drum m To Scale inner surface area of the drum outer radius of drum m To Scale outer surface area of the drum Tabulated in table two are conditions that a brake drum experiences at the critical temperature 560⁰C along with the geometry layout.

9 ACTIVE BRAKE COOLING 97 Analytical Analysis Modelling a thick plate cross section as a plane wall to simplify the analysis and to test convergence using an Analytical Method. Free Body Diagram Surface Area = Projected length of the Z axis * L = * = m^2 The quantities of interest to be determined are the heat flux acting on the surface generated by the friction braking pressure of the brake pad relative to the drum surface where x=0m, as well as the temperature distribution throughout the cross section of the drum in the lateral direction. The Thermal Properties are given in Table 1. Assumptions: Steady State Heat Conduction One Dimensional Heat Conduction Thermal conductivity is constant No heat is generated

10 ACTIVE BRAKE COOLING 98 The second order linear homogenous differential equation The corresponding boundary conditions Performing sequential integration The general solution is the correspond linear straight line linear combination Applying Boundary Condition solving for the constants of integration Substituting into the general equation Leads to the temperature distribution profile

11 ACTIVE BRAKE COOLING 99 Table 3 Tabulated in table 3 are the temperature at each position of x (m) using a step size of

12 ACTIVE BRAKE COOLING 100 Figure 4 is a visualization of the temperature distribution through the Cross- Section Plate. Now determining the rate of heat conduction from Fourier s Law

13 ACTIVE BRAKE COOLING 101 Finite Element Analysis Modelling the thick plate cross section as a plane wall to simplify the analysis and to test convergence using a Finite Element Method software Lisa. Table 4 Table 5 2-Dimensional Analysis of a thick plate in a spatial reference frame to be analyzed under the nodal temperature conditions using. Table 4 and Table 5 represent the location of the 5 nodes for the 4 tri3 elements.

14 ACTIVE BRAKE COOLING 102 Table 6 Tabulated in table 6 are the corresponding temperatures at node1, node2, node3, node4, and node5 With the corresponding heat flux at each node in the x direction and the corresponding heat flux in the y direction. The Temperature distribution is shown in color coding representing the various temperatures as a function of location in the y direction

15 ACTIVE BRAKE COOLING 103 Conclusion Temperature at x=l/2 (⁰C) Heat flux at Surface of the plate (W/m^2) Finite Element Method Analytical Method Relative Error Table 7 Tabulated in Table 7 are the results of both the finite element method using Lisa software, and the analytical method. The relative error for the temperature at location X=L/2 is 0, and the relative error of the heat flux at the surface of the plate is Another interesting observation is that the assumption that heat transfer is only is one direction is a very good assumption and is scientifically verified as results indicate in column three of table 6 because the heat flux is significantly small that it can be disregarded completely. Lisa Software is a powerful tool that can aid in the mechanical engineering design applications

16 ACTIVE BRAKE COOLING 97 REFERENECES Daryl Logan a First Course in Finite Element Using Algor Dr. Bai s ENGI-0450-WA Lecture Notes Wikipedia Engineering Tool Box Yunus Cengal & Ghajar Heat and Mass Transfer Fundamentals and Applications e_manufacturer=&start=15&field=&order=asc&orderby=application&lang=en

17 ACTIVE BRAKE COOLING 105 DOCUMENTATION The purpose of this section is to show the drum illustrated in the figure below to be modelled and analysed using ANSYS WORKBENCH. Under the loading mentioned similar to table two with mechanical properties of structural steal again which is similar to that mentioned in table 1. Generating the Mesh Selecting appropriate elements for specified regions to match the physical behavior of the system is an important aspect of modelling in engineering applications. Finer Elements should be used closer to geometric discontinuities such as abrupt changes in cross section or around sensitive areas. The closer the mesh models the physical system the more accurate the solution will be. The Aspect Ratio is optimal when equality is 1. This is because of the more precise configuration of the element. This Figure shows a very good resolution of fine mesh that has been generated. The top left corner displays the Aspect Ratio which can be shown that the majority of the mesh is less than 4. The bottom right hand corner shows the scale in units of m.

18 ACTIVE BRAKE COOLING 106 This Figure Illustrates the meshing that was configured utilizing the software LISA. The Figure above is the same Drum with a mesh that has been generated however the coarse is mesh. Notice the increase in the Aspect Ratio. AN are the solutions to the problem where fixed supports are located at each of the 10 holes as well as the axel entry. The results show the detail of the stress and deformation, and temperature distribution The accuracy of these values are dependent on the accuracy of the geometry configuration, the mesh, and the in-service loading conditions. Appendix N: Lumped System Analysis Objective

19 ACTIVE BRAKE COOLING 107 Determine the velocity required to keep the surface of the inner surface of the drum at safe temperatures Analysis Prevention through Design with lumped system analysis which requests that the temperature of a lumped body is a function of time. T(t), such as an egg that is being boiled or cooled for consumption. The brake drum is required to have a maximum in service condition of 427⁰C Assume braking starts at 120 km/h and decreases to 0 Conclusion Once the velocity is known that will maintain the temperature at safe limits, sizing of outlets of piping can be determined and the corresponding volume flow rate can be determined and the corresponding power can be determined for an accurate blower. Lumped System Analysis is not a valid technique for this analysis because it violated the condition of keeping the Biot number less than <0.1 even with significant adjustments such as the rotations of the braking wheel, the linear velocity of the wheel. Reference Page 243 chapter 4 Heat and Mass Transfer Fundamentals Applications Excel Work

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21 ACTIVE BRAKE COOLING 109 Appendix O: Bill of Materials

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23 ACTIVE BRAKE COOLING 111 Appendix P: Final Gantt Chart

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28 ACTIVE BRAKE COOLING 116 Appendix Q: Work Breakdown Structure April Involved TASKS STU ZACH JOHN -ALLAN STATUS MIDTERM PROGRESS REPORT x x x COMPLETE PRELIMINARY DESIGN x x x COMPLETE PROTOTYPE/ APPARTUS CONSTRUCTION x x x COMPLETE ID. KEY PERFORMANCE INDICATORS x x x COMPLETE List Constraints/Limitations of Applications AHP ANALYSIS FOR COOLING MEDIUM x x x COMPLETE x x x CANCELLED CON. LABORATORY EXPERIEMENTS x x x CANCELLED BILL OF MATERIAL x x x COMPLETE MAKE CONTACT WITH FIN.SPONSOR (CLIENT IS FIN SPONSOR) COMPLETE WHIMIS SAFETY TRAINING x x x COMPLETE x x x COMPLETE COST/BUDGET ANALYSIS x x x COMPLETE WEEKLY TEAM MEETINGS x x x COMPLETE DRAFT REPORT x x x COMPLETE LOG BOOK KEEPING x x x COMPLETE WORD FORMATTING x x x COMPLETE PENDING TREASURING DUTIES x x x CANCLLED I.P RESEARCH DATA BASE x x x COMPLETE BOOK LAB TIMES MAKE CONTACT WITH Mr.Keilash COMMUNICATE THROUGH WITH SUPERVISOR LIST ADVANTAGES DISADVANTES OF CURRENT MODELS FOR PRESENTATION AND REPORT IDENTIFY WAYS TO GATHER PHYSICAL RESOURCES (OBTAIN COMPONENTS) x x x COMPLETE x COMPLETE x x x COMPLETE x x x COMPLETE

29 ACTIVE BRAKE COOLING 117 PUMP ASSEMBLY ANALYSIS x COMPLETE QUENCHING ANALYSIS x COMPLETE CONDITIONING AND MONITORING ANALYSIS x COMPLETE MECHATRONICS DESIGN x COMPLETE PUMP ASSEBMLY DESIGN x COMPLETE PROJECT MANAGEMENT /FLUID MEDIUM/ APPLICATIONS x COMPLETE THE MAJOR PHASES OF THE PROJECT ARE: COMPLETING THE PRELIMINARY DESIGN Of AN EXPERIMNTAL APPARATUS WILL CAUSE A TRANSITION INTO THE AREA OF THE PROJECT WHERE WE CAN FOCUS NOT ONLY AS A TEAM ON THE FINAL DESIGN BUT ON OUR INDIVIDUAL CONTRIBUTIONS RECEIVING FEEDBACK FROM OUR SPONSOR REGARDING THE PROPE+OSAL AND THE PROJECT OUTLINE WILL ASSIST IN NARROWING DOWN THE SCOPE OF THE PROJECT MAKING CONTACT WITH A FINANICAIL SPONSOR WILL ALLOW US TO DO A PROPER COST ANALYSES AND GIVE US A SENSE OF SECURITY BY RAISING TEAM MORAL CLIENT IS ACTING AS FIN SPONSOR CONDUCTING LABORATORY EXPERIMENTS WILL PROVIDE US WITH OPTIMAL PERFORMANCE INDICATORS AND PRESENT ADDITIONAL INFORMATION THAT WILL BE APPLIED DIRECTLY TO DESIGN APPLICATIONS COMPLETE ACTIVE COMPLETE CANCELLED

30 ACTIVE BRAKE COOLING 118 AS WEEKLY TEAM MEETINGS PROGRESS OUR TEAM WILL DEVELOP CONFIDENCE WITH OUR OWN STRENGTHS AND TRUST WILL BE GENERATED TO ENSURE QUALITY WORK ACTIVE