DESIGN & FABRICATION: HAAS CNC ROTARY TABLE

Transcription

1 DESIGN & FABRICATION: HAAS CNC ROTARY TABLE PRELIMINARY DESIGN REPORT Team 5442 Patrick Walsh Craig Rothgery Steve Kumpf

2 Table of Contents: Executive Summary List of Illustrations 1.0 Project Assessment 1.1 Problem Statement Needs Assessment Level Zero: Project Mission Statement Level One: Qualifiers (Qualitative) Level Two: Winners (Qualitative) Level Three: Winners (Quantitative) Design Requirements Project Proposal Specific Requirements Goals Concept Development 2.1 Initial Concept Development Connector Design Material Design Concept Development After Re-evaluation Table Design Feasibility Assessment 3.1 Initial Concept Feasibility Main Concept Feasibility Weighted Method Attribute Weights Pairwise Comparison Breakdown Concept Scoring Scoring Breakdown Design Specifications and Drawings 4.1 Specifications and Material Properties Drawings Design Analysis 5.1 Stress Analysis Maximum Force Produced From Machining Overview Actual Calculations Deflections: Torsion and Bending Semi-Circle Table Triangular Table Current Table (analyzed as rectangular beam) Common Equations Deflection Due to Torque Deflection Due to Bending Conclusions FE Stress Analysis Bending in the X Direction Bending in the Z Direction Combined Loading 30

3 5.2 Vibration Analysis Triangular Aluminum Table FE Harmonic Analysis Triangular Cast Iron Table FE Harmonic Analysis Semi-Circular Aluminum Table FE Harmonic Analysis Semi-Circular Cast Iron Table FE Harmonic Analysis Analysis Verification Quarter Model Boundary Value Verification Overall I-deas FE Harmonic Analysis Verification Future Project Planning Conclusion / Summary 43

4 Executive Summary The sponsor for our senior design project is Lockheed Martin, Missiles and Fire Control stationed in Grand Prairie, Texas. The manufacturing division came to us with a problem concerning their HAAS CNC machine. Lockheed machining operations maintain very small tight tolerances as small as.001 in. In order to accommodate these tolerances, the table that the parts are machined on must be able to hold the part in its original place despite any outside factors. The current table has been having difficulty holding these tolerances due to vibrations, wear, and other minute factors. The goal for this project is to design and produce a table that will hold tight tolerances during any machining process and continue to do so time and again. After establishing the requirements of the table we began our concept development stage. This stage consisted of two phases: Connector Design and Geometry Design. Connector Design dealt with the way in which the part itself was mounted to the table. Current methods allowed tolerances to fall out of specification during necessary machining operations. Two different solutions were proposed to solve this problem. The first solution used a shoulder bolt and chamfered insert which slid into a counter sink in the table geometry to locate the part. The second solution also involved an insert; however, this insert was not chamfered and instead located itself on a bushing placed in the surface of the table. Both methods proved to be better than the current design. Unfortunately, both proved to be infeasible. In order to mount the part to the table some degree of motion is necessary to get all four bolts into the part. This concern was later shown to be ill conceived. Focus was then changed to deflections and vibrations. Deflection concerns were able to be solved through material selection and table geometry. Two geometries were proposed after some research into the stiffness and rigidity of different shapes. The geometries chosen were a triangular style geometry and a semi-circular geometry. After concept generation a feasibility assessment was done to solidify which concept should be used. The major criteria involved in the assessment were Weight, Harmonics, Cost of Materials, Cost of Production, Ease of Design, Ease of Production, Resistance to Wear, and Stiffness. Each criterion was weighted and applied to our needs. The feasibility assessment showed that the best choice was that of a semi-circular aluminum table with hardened steel bushings in the bolt holes. With the feasibility complete we began our analysis. Not only did we choose to analyze the feasible choice, we also chose to analyze all of the proposed tables in order to validate out feasibility assessment. We examined all of the criteria involved in the feasibility assessment while maintaining significant focus on the reaction of the table to applied loads and vibration sensitive scenarios. In conclusion we found that our feasibility assessment matched our analysis and that the semi-circular aluminum table was the proper choice. At this time we do not have all the data necessary to complete our analysis to the degree we would like. Before the final product is produced and tested, more analysis is to be done as soon as the data is received. Any further evaluation will most likely involve the optimization of weight versus performance and the production of the table in the most cost effective manner possible.

5 List of Illustrations Figure 1.1.1: Original Table Figure 2.1.1: 2-D assembled counter bore insert concept design. Figure 2.1.2: 3-D exploded counter bore concept design. Figure 2.1.3: 2-D assembled countersink insert concept design. Figure 2.1.4: Aluminum table concept with steel plate and bushings. Figure 2.2.1: Semi-circular concept table design. Figure 2.2.2: Triangular concept table. Figure 3.2.1: Feasibility assessment attributes weights. Figure 3.2.2: Feasibility assessment concept score. Figure 4.2.1: Semi-circular table (actual model). Figure 4.2.2: Semi-circular table drawing. Figure 4.2.3: Triangular table (actual model). Figure 4.2.4: Triangular table drawing. Figure : Example of table under torque. Figure : Torsional deflection (Graph: hand calculations). Figure : Bending in the Z-direction (Graph: hand calculations) Figure : FE analysis Triangular table bending in the X direction. Figure : FE analysis Triangular table bending in the X direction (Slice). Figure : FE analysis Semi -circular table bending in the X direction. Figure : FE analysis Semi-circular table bending in the X direction (Slice). Figure : FE analysis Triangular table bending in the Z direction. Figure : FE analysis Semi-circular table bending in the Z direction. Figure : FE analysis Triangular table combined loading. Figure : FE analysis Semi-circular table combined loading.

6 Figure : Oil-lite bearing on original table on HAAS machine. Figure : New air break bearing for Mazak machines Figure : FE harmonic analysis Triangular aluminum table (side view). Figure : FE harmonic analysis Triangular aluminum table (orthogonal view). Figure : FE harmonic analysis Triangular cast iron table (side view). Figure : FE harmonic analysis Triangular cast iron table (orthogonal view). Figure : FE harmonic analysis Semi-circular aluminum table (side view). Figure : FE harmonic analysis Semi-circular aluminum table (orthogonal view). Figure : FE harmonic analysis Semi-circular cast iron table (side view). Figure : FE harmonic analysis Semi-circular aluminum table (orthogonal view). Figure : Quarter model verification aluminum table. Figure : Quarter model verification cast iron table. Figure : Overall FE harmonic verification simple cantilevered beam.

7 1.0 Project Assessment The rotary tables are a custom design for Lockheed Martin Missiles and Fire Control and they are to be used on their HAAS and Mazak CNC machines. This division of Missile and Fire Control in Grand Prairie, Tx, is responsible for manufacturing parts for missiles such as the ATACMS, PAC-3, and LOSAT. Government specifications require them to machine features of parts to an extremely tight tolerance.001 inches. The current tables used in the HAAS machines make it difficult to hold these tolerances because they twist, vibrate, and wear out in the bolt hole locations. The purpose of this project is to design a new table that will eliminate these problems. 1.1 Problem Statement 1. Hole Size and Location a. Cause On the existing table, constant wear from the steel bolts on the aluminum tables holes is causing the hole size and true location to fall out of tolerance. b. Effect When a part is pivoted 90 degrees on one hole location for a secondary machining operation, the part moves 3 to 5 thousands out of tolerance. 2. Surface Wear a. Cause On the existing table, constant wear from a steal part vice is causing the aluminum surface to loose a true flat surface. b. Effect When the part is machined it may be out of tolerance because the surface datum of the table may be distorted. 3. Vibration a. Cause On the existing table, vibration is caused by improper constraint at the bearing end, tool chatter, and a low natural frequency of the table. b. Effect This may halt the machining or cause distortions resulting in a scraped part. 4. Twist a. Cause On the existing table twist occurs when the table is put under high loads, which is usually caused by operator error. b. Effect This will cause the surface datum to rotate and put the part out of tolerance. 1

8 Figure 1.1.1: Original Table 1.2 Needs Assessment Level Zero Project Mission Statement Design a new Rotary Table that will not wear on the surface and in the location holes to maintain a consistent hole size. The table should have a natural frequency higher than that produced by the machine, resist twisting, and be cost effective in the production of 3 tables Level One Qualifiers (Qualitative) Performance Attributes o Table should withstand wear. o Table should not vibrate during machining o Table should resist twisting Schedule Attributes o Table should be ready for use by summer 2005 Technological Attributes o Table should be made of a material that withstands wear. o Table should be made of a material that will not vibrate during operation. o Table should use a geometry that resists twist. Economic Attributes o Table should have a reasonable cost to produce 2

9 1.2.3 Level Two Winners (Qualitative) Performance Attributes o Table should be able to hold tolerance on surface and hole locations after constant wear. o The table should not vibrate when parts are machined. o The table should not twist when the parts are machined. o The table should have a reasonable weight. Schedule Attributes o Table should be completed by the end of May 2005 Technological Attributes o The table material should withstand consistent wear. o The table material should have a resonance frequency above the frequency produced by the machine. o The table geometry should have a high strength in twist. Economic Attributes o Table should be cost effective to produce, either in house or out of house Level Three Winners (Quantitative) Performance Attributes o The table must a hold a.001 in tolerance on the surface and hole locations. o Any hole in the table should be with in.001 of any other hole. o The table must not vibrate when parts are machined o The table must not twist more than.001 in. o The table must not weigh more than 300 lbs. Schedule Attributes o Table must be completed by the end of May 2005 Technological Attributes o The table bulk material should have a hardness high enough to withstand wear and all holes must have steel bushings. o The table material must have a resonance frequency above that produce by the machine. o The table must use a unique geometry to resist twist, such as a triangle or semi circle. Economic Attributes o Table must be cost effective to produce, either in house or out of house. 3

10 1.3 Design Requirements Project Proposal PROJECT NAME: Design and Fabrication of Rotary Tables for HAAS CNC Machines SPONSOR: Lockheed Martin Missiles and Fire Control, Dallas Texas DATE: 9/9/04 SPONSOR CONTACT: Thomas Carrubba PHONE: PROJECT CONTACT: Jeffrey Morgan PHONE: RIT CONTACT: Patrick Walsh PHONE: Introduction The HAAS CNC Machines are three axis machines that can be converted to four axis machines with the addition of a rotary. The rotary requires the build up of a table to clamp hardware. This table needs to include hold down holes as well as bushed holes that are used for collection of SPC data. The following should be considered when working this project: 1. The scope of the project is to design three tables and produce one table to test concept. 2. The tables will have standard locations for hold down holes consistent across three tables. 3. Evaluate design of the tables and eliminate any harmonic distortion. 4. All tables will require bushed holes for checking volumetric accuracy and gathering SPC data. The project team will be provided with the following: 1. A point of contact in the Production Engineering department. 2. Necessary equipment, materials, and supplies. 3. Support from Tool Design and Production Engineering as necessary. Desired Outcomes: 1. Standardized Rotary Table designs and one working model. 2. Cost analysis for producing the tables in house or at a vendor. 3. Harmonic evaluation of the table in relation to the HAAS CNC machining process. Disciplines Involved: 1. Mechanical Engineering 2. Industrial Engineering Funding Consideration: 1. Materials will be provided by Lockheed Martin. Planned Period of Performance: The Design and analysis is to take place in Fall Semester 04 and 1 st unit fabrication is to be developed in Winter/Spring Semester 05. 4

11 1.3.2 Specific Requirements For NC programming reasons, the hole grid size and SPC bushings need to be the same size and in the same location as the original table. The holes in the grid must be within.001 of their true position. Table geometry design has no limits except for the fact that it needs to have the same center line and table height. The table must weigh less than 300lbs, preferably less than 100lbs. Deflections: 1. Twist must be under.001 in. 2. Bending must be under.001 in. Cost: At this point, cost has been placed at low priority. The table performance is more important at this time and cost optimization will occur when all outstanding data has been received. 1.4 Goals Our goals for this project are to design and produce a rotary table that best satisfies our sponsor s needs while learning to successfully initiate and navigate the steps of a detailed design. 5

12 2.0 Concept Development Our concept development is broken in two separate phases. The first phase stemmed from a concern raised regarding the current table. We were told by the sponsor that they had a problem with the part falling out of tolerance after a second machining operation. They felt this was caused by wear of the aluminum holes. When the part is rotated 90 degrees around one bolt location for the second operation, the wear causes the part to fall out of location. We then expanded on that problem and figured that if they were locating off the shoulder of a bolt, tolerances would be nearly impossible to maintain. This resulted in the insert concept designs for maintaining hole tolerance shown below. Unfortunately, these designs were not feasible. This is explained in feasibility assessment. After our initial concepts, we moved on from connector design and focused on vibration and twisting problems. To do this we focused on table geometry and material, which started the second phase of our concept development. To solve the torsion rigidity problems we explored triangle and semicircle geometries. After looking through a mechanics of materials book at torsional stress equations, we decided that these shapes would optimize the table s strength in torsion. 2.1 Initial Concept Development Concepts are branched into two areas, connector design and table material Connector Design 1. Round steal insert with a matching table counter bore. a. This design utilizes a round steal insert that will be placed in the aluminum stock of the part and aligns with a counter bore in the table. The bolt will then fasten the part to the table through the insert. (Refer to figure ) b. The advantage of this design is that the part locates to the table by the insert and the counter bore, not by the bolt and the table. Also, it reduces wear because the motion is straight in and out without the rotation. c. The bolt will attach to the insert by some sort of bearing surface and a c- clip. This will utilize the mechanical advantage of the bolt to place and remove the round steal insert in the counter bore. 6

13 Figure 2.1.1: 2-D assembled counter bore insert concept design. Figure 2.1.2: 3-D exploded counter bore concept design. 2. Round countersunk steal insert with matching table countersink. d. This concept is almost identical to the previous concept, but is different by the fact that is does not need a steel bushing in the aluminum table. (This will be retouched in the material concepts.) 7

14 2.1.2 Material Design Figure 2.1.3: 2-D assembled countersink insert concept design. 1. Composite Table a. This concept uses a carbon composite for the bulk of the table with a harden steal plate on the top surface. Also, it will have steal bushings in the hole locations with either a counter bore or countersink for the connectors. b. The advantage of this design is that it is lightweight and rigid. c. The disadvantage is that it will be difficult and expensive to produce due to the grid of holes in the table. 2. Aluminum Table a. This concept uses aluminum for the bulk of the table with a harden steal plate on the top surface. It will require steal bushings in the counter bores to prevent wear. If countersinks are used it will not need bushings because the cone geometry will help prevent wear. Steal Helicoils will need to be inserted into all the threads to prevent wearing due to the threads of the bolt. b. The advantage of this design is that it will be lightweight and cheap to produce. c. The disadvantage of this table is that it is constructed out of multiple materials which could to complications. Hardened Steel Plate Holes w/ Steel Bushings Bulk Table Aluminum/Composite Figure 2.1.4: Aluminum table concept with steel plate and bushings. 8

15 3. Cast Iron Table with Machined Holes a. This concept table will be cast out of cast iron with machined counter bores/sinks and threads. b. The advantage of this design is that it is strong, wear resistant and moderately easy to manufacture. c. The disadvantage is that it is heavy and expensive to produce. 2.2 Concept Development After Revaluation Table Design 1. Semi-Circle Table with Steel Bushings. a. This concept will use either aluminum or cast iron for the bulk of the table with hardened steel bushings. b. The advantage of this design is that it is very rigid (the semi-circle geometry allows the table to take high stresses) and resilient to vibrations. c. The disadvantage of this design is that it contains a large amount of material which causes the weight to be somewhat excessive, when using cast iron. This problem can be avoided through geometric manipulation removal of non-stress bearing material. Figure 2.2.1: Semicircular concept table design 2. Triangular Table with Steel Bushings. a. This concept will use either aluminum or cast iron for the bulk of the table with hardened steel bushings. b. The advantage of this design is that it is very rigid and doesn t contain as much material as the semi-circle design (weight saving). 9

16 c. The disadvantage of this design is that because the amount of material is less than semi-circle design, the table is more prone to vibrations. Figure 2.2.2: Triangular Concept Table 10

17 3.0 Feasibility Assessment 3.1 Initial Concept Feasibility After reviewing our initial concept designs with our sponsor, we discovered that the insert design would not be feasible in their application. The purpose of our design was to tighten the tolerance in the way the part was attached to the table. We intended to do this by using an insert that would align the part with the outer diameter of the insert and the inner diameter of the bushing. Lockheed told us this was not feasible because they could not machine the part bolt-down holes with enough accuracy. Therefore they would not be able to get all four of the inserts in the holes. They need a.002 tolerance between the shoulder of the bolt and the table holes to allow them to get all four bolts in the holes. As a result, we had to scrap these concept designs. Also, the steel plate would not be preferred by Lockheed because of the multiple part issues. If the aluminum is feasible for vibrations, it would be cheaper for them to resurface the table when it had seen too much wear. 3.2 Main Concept Feasibility The feasibility of the concepts was calculated using the weighted method feasibility tool. The scoring for attributes such as costs of material and production, and ease of production were estimated because those actual values have not yet been confirmed Weighted Method To perform our primary feasibility assessment on our concept designs we used the weighted method. 11

18 Attribute Weights Pairwise Comparison: Place an "R" if the row is more important. Place a "C" if the column is more important Weight Harmonics Cost of Materials Cost of Production Weight c r r c % Harmonics r r r r r r % Cost of Materials r % Cost of Production c c % Ease of Design c c c % Ease of Production c c % Resists Wear % Stiffness (Meets Twist Requirment) % Additional 1 (Future Use) % Additional 2 (Future Use) % Column Total % Figure 3.2.1: Feasibility assessment attributes weights Pairwise Comparison Breakdown 1. Harmonics over all was rated the most important attribute, because it was a main requirement and also because it was more logical to design the table around harmonics rather than design harmonics around any other attribute. 2. Wear and stiffness also stand out because they are main requirements and key features to the design. 3. Weight is important because it is one of the main requirements. 4. The rest of the attributes went hand in hand and were almost equal in their importance. Ease of Design Ease of Production Resists Wear Stiffness (Meets Twist Requirment) Additional 1 (Future Use) Additional 2 (Future Use) Row Total Column Total Row + Column Total Relative Weight 12

19 Concept Scoring Evaluate each additional concept against the baseline, score each attribute as: 1 = much worse than baseline concept 2 = worse than baseline 3 = same as baseline 4 = better than baseline 5= much better than baseline Weight % Harmonics % Cost of Materials % Cost of Production % Ease of Design % Ease of Production % Resists Wear % Stiffness (Meets Twist Requirment) % Additional 1 (Future Use) 3.0 0% Additional 2 (Future Use) 3.0 0% Weighted Score Normalized Score 97.1% 90.8% 100.0% 90.8% Figure 3.2.2: Feasibility assessment concept score Scoring Breakdown The Aluminum triangular table was set as the baseline for the scoring. The aluminum tables scored the highest because alternative cast iron is expensive and heavy. Its advantage is wear resistance. There is some speculation in the cost, because it has not been determined. After talking with our sponsor we agreed the cast iron would be more expensive. At this point the semi-circular table scores the highest because it is lightweight and resists deflection. This table will not be chosen for production until the vibration experiments are done. Triangular Aluminum Triangular Cast Iron Semi-circle Aluminum Semi-circle Cast Iron Relative Weight 13

20 4.0 Design Specifications and Drawings The table material properties, specifications, actual models, and drawings are shown in this section. 4.1 Specifications and Material Properties Cast Iron Aluminum Modulus of Elasticity (Psi) 1.00E E+07 Modulus of Rigidity (Psi) 4.10E E+06 Density (lbs/in^3) Poisson's Ratio Overall Weights (lbs.) Cast Iron Semi-circle Cast Iron Triangular Aluminum Semi-circle Aluminum Triangular Note: Possible concerns for the machinability of the table may be raised. A proposed assembly could perhaps be a solution to this problem. The ends of the table could be constructed as separate plates which are later attached to the table. Not only does this make machining a bit simpler, it also allows for a degree of versatility in reference to the method of connection to the supporting components of the table. 14

21 4.2 Drawings Figure 4.2.1: Semi-circular table (actual model). Figure 4.2.2: Semi-circular table drawing. 15

22 Figure 4.2.3: Triangular table (actual model). Figure 4.2.4: Triangular table drawing 16

23 5.0 Design Analysis Our design analysis includes both stress and harmonic analysis. We performed basic hand calculations on solid bodies to find preliminary torsional stresses and deflections, and bending stresses and deflections. I-deas FE analysis was used to calculated natural frequencies, modes shapes, and bending deflections. Analysis was done on all four concepts to predict actual feasibility. 5.1 Stress Analysis Maximum Force Produced From Machining Overview The maximum force produced by the cutter was analyzed using power and energy relationships in machining. The analysis was not performed using force relationships and the merchant equation because none of the required angles were known - the angle between the resultant cutter force and the normal force, the angle of the shear plane with the surface of the part, or the angle between the cutter face and perpendicular axis to the part. The following equations were utilized. 1) P c = F c ν P c = cutting power (ft-lb/min) F c = cutting force (lb) ν = cutting speed (ft/min) 2) P g = Pc E P g = gross power of the machine tool motor (W) 3) Combining equations 1 and 2 F c = P E g ν E = efficiency of tool 4) V = ω * D 2 V = surface velocity of tool (ft/min) 5) ω = rpm * 2π 17

24 Actual Calculations The following calculations were done at a worst case scenario to obtain the highest possible forces that the table will ever experience. ν = 500 rpm (lowest the HAAS is ever ran at) E = 90% P g = 20 HP (the greatest HP machine) D =.0833 ft 2 ω = 500rpm * π rev = rad/s ( )(.0833) ν = 2 = ft/min 33,000( ft lb / min) P g = 20HP * 1HP = 660,000 ft-lb/min F c 660,000( ft lb / min)*(.9) = 130.9( ft / min) = lbf This max force of lbs is the absolute worst case obtained by running the machine at lowest speed and highest horse power. The machine is never run at the greatest horsepower, so in this kind of scenario the machine would probably stall out. Since every part is bolted in 4 corners when being machined, the actual force seen at one hole of the table is lbs ( /4). 18

25 5.1.2 Deflections: Torsion and Bending After determining the max cutter forces from the power and energy relationships in machining, we had a range of forces to examine in both torsion and bending. The following equations were used to generate the tables and figures on the next pages Semi Circle Table 4* T 1) τ max = 3 π * R T = torque produced from induced load times the moment arm (3.5 in) R = radius of semi-circle 2) I =. 1098* R 4 I = moment of inertia Triangular Table 20* T 1) τ max = 3 b b = base of triangle (11.5 in) 2) b * h 3 I = 36 h = height of triangle (5.75 in) Current Table (analyzed as rectangular beam) a ) = = b 3.5 2) C 1 =.2713 C 2 =.2681 ** C 1 and C 2 are interpolated from Table 3.1 (pg. 187) Mechanics of Materials Beer, Johnston, DeWolf 3) T φ * C * a = L 2 * b 3 φ = angle of deflection (radians) 19

26 L = 21.5 in 1 2 4) φ = Tan a = deflection (greatest seen in table was.003 in) **.003 deflection equates to an angular deflection of.0299, or rads. ( )(.2681)(11.5)(3.5) T = 21.5 = 11,869 lb-in 5) Combining equations 3 and 4 a T * L * 2 = Tan 3 C * a * b * G Common Equations 3 (3.7E06) τ max 1) d θ = * dx (Semi-Circle & Triangular) a * G dθ = deflection from torque (rads) G = Modulus of Rigidity dx = length along table (assumed worst case at 21.5 in) 2) P * L 3 y = (All) 192* E * I P = Force (lbs) L = 21.5 in E = Modulus of Elasticity (material dependent) I = Moment of Inertia (dependent on previous equations) ** All equations and material properties used for analysis were obtained from Mechanics of Materials Beer, Johnston, DeWolf 20

27 Deflection Due to Torque Maximum Torque Deflection values are assumed to be at the furthest distance from the centerline of the table. This implies that the edges of the table half way down the length must endure these torques without falling out of tolerance. Table Twisting Under Torque Maximum Torque Deflection Figure : Example of table under torque Modulus of Rigidity Cast Iron 4.10E+06 psi Aluminum 3.92E+06 psi Modulus of Elasticity Cast Iron 1.00E+07 psi Aluminum 1.03E+07 psi Moment Arm 3.5 in Semi circle with 5.75 in radius Torsion Applied Stress Force(lbs.) Triangle with 11.5 in sides Torsion Applied Force(lbs.) Stress

28 Semi Circle Deflection (Cast Iron) Triangle Deflection (Cast Iron) Torque (lb-in) Deflection (inches) Torque (lb-in) Deflection (inches) E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Semi Circle Deflection (Aluminum) Triangle Deflection (Aluminum) Torque (lb-in) Deflection (inches) Torque (lb-in) Deflection (inches) E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Current Table (Aluminum) Torque (lb-in) Deflection (inches) E E E E E E E E E E E E E-03 22

29 Torsional Deflection New Tables 2.50E E-03 Semi Circle Deflection (Cast Iron) Triangle Deflection (Cast Iron) Semi Circle Deflection (Aluminum) Triangle Deflection (Aluminum) Current Table (Aluminum) Deflection (in) 1.50E E E E Torque (lb-in) Figure : Torisonal deflection (Graph: hand calculations) Deflection Due to Bending Maximum deflections due to pure bending are assumed to be seen when the table must withstand forces from machining at the center of the table. The following tables show calculations done to quantify this deflection. Modulus of Elasticity Cast Iron 1.00E+07 psi Aluminium 1.03E+07 psi Moment of Inertia Semi-circle in^4 Triangle in^4 Rectangle in^4 23

30 Semi Circle Deflection (Cast Iron) Applied Bending (inches) Force(lbs.) Triangle Deflection (Cast Iron) Applied Force(lbs.) Bending (inches) E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Semi Circle Deflection (Aluminum) Triangle Deflection (Aluminum) Applied Applied Bending (inches) Force(lbs.) Force(lbs.) Bending (inches) E E E E E E E E E E E E E E E E E E E E E E E E E E-04 Current Table (Aluminum) Applied Bending (inches) Force(lbs.) E E E E E E E E E E E E E-04 24

31 Bending (Z-direction) Deflection (in) 7.00E E E E E-04 Semi Circle Deflection (Cast Iron) Triangle Deflection (Cast Iron) Semi Circle Deflection (Aluminum) Triangle Deflection (Aluminum) Current Table (Aluminum) 2.00E E E Applied Force (lbs) Figure : Bending in the Z-direction (Graph: hand calculations) Conclusions After analyzing all the tables with both a torque and bending load applied, several conclusions can be drawn. For torque, cast iron is a better choice since the modulus of rigidity is higher, thus deflecting less. The semi-circle geometry constructed out of cast iron proved to be the best choice, with the triangular cast iron being second best. With the customer requirements stipulating that the table can deflect no more than.001 in any direction, the maximum torque was calculated that would produce an equivalent deflection at the edge of the table where deflection is assumed to be at a maximum. A factor of safety of 2 was used to compensate for the addition of the holes in the table. The results are shown below: Max Torque Required to Deflect.001 in Max Moment Arm Max Torque (FS 2) Safe Moment Arm Max Torque Semi-Circle Aluminum Semi-Circle Cast Iron Triangle Aluminum Triangle Cast Iron

32 It can clearly be seen that the semi-circle cast iron table can take the highest torque (56,975.2 lb-in). At the maximum torques calculated above, the maximum moment arms were determined using the maximum force calculated from the cutter ( lbs). These maximum moment arms are the distance from the surface of the table that the cutter can engage the part, while maintaining the specified torques. Again, the semicircle cast iron table has the greatest moment arm of In bending, the semi-circle geometry again proved to be the best design. The best material proved to be aluminum. Aluminum is the better choice in bending because the equation relies on the modulus of elasticity, which is greater in aluminum than in cast iron (the lowest modulus for cast iron was chosen). The maximum forces were calculated for each table under a.001 deflection. The results are shown below: Max Force Required to Deflect.001 in Max Force Max Force (FS 2) Semi-Circle Aluminum Semi-Circle Cast Iron Triangle Aluminum Triangle Cast Iron FE Stress Analysis Our hand calculations were done using solid bodies. To get more accurate bending deflections we used I-deas Finite Element analysis. Meshing restrictions required all holes modeled to be rectangular, and fillets were removed. The analysis used the maximum lb force that is produced by the machine and it was divided among four holes in the middle of the table for a worst case scenario. The deflections will be reasonable, however not entirely accurate, because the forces are concentrated on the edges of the square holes. In realty the deflection will be less. Only the aluminum tables were analyzed because the deflections of the cast iron table will be scaled by the modulus of elasticity. The corresponding difference is only a few hundredths of an inch. 26

33 Bending in the X Direction Triangular Table Figure : FE analysis Triangular table bending in the X direction. Figure : FE analysis Triangular table bending in the X direction (Slice) The maximum table deflection is in. 27

34 Semi-Circular Table Figure : FE analysis Semi - Circular table bending in the X direction. Figure : FE analysis Semi - Circular table bending in the X direction. The maximum table deflection is in. 28

35 Bending in the Z Direction Triangular Table Figure : FE analysis Triangular table bending in the Z direction. The maximum table deflection is.0011 in. Semi-Circular Table Figure : FE analysis Semi - Circular table bending in the Z direction. The maximum table deflection is in. 29

36 Combined Loading Combined loading analysis involved both torque and bending. To compensate we used a factor of safety of 2 in both the moment arm and force that were calculated using solid bodies. The maximum deflection shown is at the concentrated force and not theoretically accurate. The actual deflection of the table should be around.001 in. Triangular Table Figure : FE analysis Triangular table combined loading. The maximum table deflection is in. 30

37 Semi-Circular Table Figure : FE analysis Semi - Circular table combined loading. The maximum table deflection is in. 5.2 Vibration Analysis There are currently 3 variables in the vibration analysis: the bearing end, the table, and the tool. We feel that the slop in the oil-lite bearing on the tail-end of the current table in the HAAS machines is probably causing most of the vibration problems. However, that variable should be eliminated by the recently acquired brake bearing that came with the new Mazak machines. The second problem is tool chatter. This is caused when the natural frequency of the tool is out of phase with the spindle RPM frequency. According to the sponsor, they would need a harmonizer to measure the natural frequency of the tool in the spindle. For this reason the tool at times could be run at an incorrect rpm causing vibration. Due to these other variables, it is difficult to accurately quantify vibration problems involved with the current aluminum table. Our goal in the finite element vibration analysis is to obtain a general idea of the natural frequencies in each table geometry and material. We then plan to perform a vibration analysis experiment on the current table to obtain the actual frequencies it is experiencing. Once we have obtained that experimental data, we will use the information to optimize our concept design. This will allow us to accurately design the table to meet the sponsor s harmonic specifications. The FE analysis was done using I-deas and the tables were constrained by 2 holes on each end. Because the new tables are to be eventually used on the new Mazak machines, 31

38 the way the table is attached to the bearing and motor is subject to change. Due to time limitations we analyzed the tables using the current table constraints. Also, all holes were modeled as rectangular holes for meshing reasons. Figure : Oil-lite bearing on original table on HAAS machine. Figure : New air break bearing for Mazak machines. 32

39 5.2.1 Triangular Aluminum Table FE Harmonic Analysis Figure : FE harmonic analysis Triangular aluminum table (side view). Figure : FE harmonic analysis Triangular aluminum table (orthogonal view). The analysis above shows the triangular aluminum table s first mode shape and lowest natural frequency of HZ. 33

40 5.2.2 Triangular Cast Iron Table FE Harmonic Analysis Figure : FE harmonic analysis Triangular cast iron table (side view). Figure : FE harmonic analysis Triangular cast iron table (orthogonal view). The analysis above shows the triangular cast iron table s first mode shape and lowest natural frequency of 662 HZ. 34

41 5.2.3 Semi-Circular Aluminum Table FE Harmonic Analysis Semi-Circular tables were cut into quarters and analyzed using symmetry because the geometry was to complex to be modeled as a whole. Figure : FE harmonic analysis Semi-circular aluminum table (side view). Figure : FE harmonic analysis Semi-circular aluminum table (orthogonal view). The analysis above shows the semi-circular aluminum table s first mode shape and lowest natural frequency of 1180 HZ. 35

42 5.2.4 Semi-Circular Cast Iron Table FE Harmonic Analysis Figure : FE harmonic analysis Semi-circular cast iron table (side view). Figure : FE harmonic analysis Semi-circular aluminum table (orthogonal view). The analysis above shows the semi-circular cast iron table s first mode shape and lowest natural frequency of 711 HZ. 36

43 5.2.5 Analysis Verification Quarter Model Boundary Value Verification The analysis on the quarter models was done using symmetry and the boundaries were setup as shown in the table below. Plane #1 (along the length) and Plane #2 (along the width) are along the symmetrical planes of the part. Plane #1 Plane #2 Fixed Free Fixed Free X Y Z Y Rot. about Z Z Rot. about X X Rot. about Y Rot. about X Rot. about Y Rot. about Z To verify these boundary conditions we analyzed the triangular table as quarter models with symmetry and compared the results with that of the full table. Figure : Quarter model verification aluminum table. 37

44 Figure : Quarter model verification cast iron table. Symmetric Analysis Verification Results Full Table Quarter Table Aluminum Cast Iron The figures and table above verify that the symmetric analysis boundary conditions used on the quarter tables are correct Overall I-deas FE Harmonic Analysis Verification In order to ensure functionality of I-deas as a viable tool for vibration analysis, a test was preformed with a simplistic model of a cantilevered beam. Theoretical equations for a cantilevered beam were used to calculate the first mode shape of the beam. ω = 3.52 n EI ρl 4 Where ω n is the natural frequency, E is the modulus of elasticity, I is the moment of inertia, ρ is the mass per unit length of the material, and L is the length. For a cantilevered beam, 1 I = bh 12 3 Where b is the length of the base of the beam and h is the height of the beam. 38

45 For a Cast Iron beam with a Length of 12 in, a width of 1 in, and a height of 0.25 in the analysis is as follows. Ρ = 12in *1in *.25in *.258lb in 386*12in 3 = 1.67 *10 4 lb / in I = *1*(.25) = 1.3*10 in *10 *(1.3*10 ) ω n = 3.52 = rad / s = Hz *10 *(12) Modeling the same cantilevered beam in I-deas with a relatively coarse mesh of.5 returned a value of Hz for the first mode shape. An error of 0.38% between the two shows a very tight correlation and confirms the functionality of I-deas as a vibration testing tool. Figure : Overall FE harmonic verification simple cantilevered beam. Yet another check was done in order to confirm the quality of the results. Theory states that the ratio of the natural frequencies can be determined by an expression involving the modulus of elasticity and the density of both materials. The equation is as follows: 39

46 E * ω alu min um = al ρci ω CastIron ECI * ρ al For our materials the ratio above is equal to Results from I-deas for the Triangle Table gave a natural frequency for the aluminum table and the cast iron table of 1085 Hz and 662 Hz, respectively. Therefore, ω ω alu min um CastIron 1085 = = This is surprisingly accurate and once again confirms the quality of the results obtained using I-deas. In conclusion, each table was evaluated to find the lowest frequency at which the table may encounter significant vibration induced deflections. Although up to ten different mode shapes were calculated for each table, our concern lay within the first mode shape. During the machining process the vibrations that the table may undergo will most likely not reach the frequency of the second or greater mode. A full model of the triangular table produced results for both aluminum and cast iron (see chart below for values). Unfortunately the capabilities of I-deas began to dwindle when we tried to model a full semi-circle table. Meshing the full table caused I-deas to create a mesh that it was unable to use without encountering errors. As a result, a quarter model was produced and the proper constraints were applied. Additional analysis (alternate constraint sets) was performed in order to ensure the proper constraints were used. The quarter semi-circle model was used with both aluminum and cast iron (see chart below for values). Material Size Geometry Natural Frequency (Hz) Aluminum Full Triangular Cast Iron Full Triangular 662 Aluminum Quarter Semi-circular 1180 Cast Iron Quarter Semi-circular

47 6.0 Future Project Planning This winter we plan to take the next step in our project. An experiment on the current table must be done to obtain the actual input frequencies the tables are experiencing. The first two weeks of senior design II, during the spring, we plan to use this data to optimize our design. Through the optimization process, we plan to remove any unnecessary material, reconfigure constraints, and adjust any other attributes to ensure maximum performance while still meeting all requirements. This winter we also plan to order the material and make arrangements with a casting house if needed, and a machine shop to apply the finishing details on the table. A cost vs. performance analysis will be done once outstanding data is obtained to determine most effective way to produce the table. After we optimize the design, we will then start to produce the table. If the table is to be cast, then the design will be sent to the casting house. If not, it will be roughed from stock material. We plan to do all roughing operations ourselves with the help of a machinist. Due to the tight tolerances required, we will send the table finishing operations. Our next step is to test the table at Lockheed, and do a financial analysis to find out whether or not it is more financially feasible to produce the tables in or out of house. The PERT chart for the rest of the project is shown on the next page. 41

48 ID Task Name ov 7, '04 Nov 14, '04 Nov 21, '04 Nov 28, '04 Dec 5, '04 Dec 12, '04 Dec 19, '04 Dec 26, '04 Jan 2, '05 Jan 9, '05 Jan 16, '05 Jan 23, '05 Jan 30, '05 Feb 6, '05 Feb 13, '05 Feb 20, '05 Feb 27, '05 Mar 6, '05 Mar 13, '05 Mar 20, '05 Mar 27, '05 Apr 3, '05 Apr 10, '05 Apr 17, '05 Apr 24, '05 May 1, '05 May 8, '05 May 15, '05 M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F S S M T W T F 1 Review Preliminary Design With Sponsor and Decide on Concept 2 Perform Vibration Experiment 3 Order Materials 4 Find Vendor to Perform Finish Operations 5 Optimize Design to Harmonic Experimental Data 6 Update Models and Drawings 7 Rough Out Table in Machine Shop 8 Send Table Out to be Finished 9 Send Table to Sponsor to be Tested 10 Start CDR Report 11 Finish CDR Report Project: SD Date: Tue 11/9/04 Task Split Progress Milestone Summary Project Summary External Tasks External Milestone Deadline Page 1

49 7.0 Conclusion / Summary As expected, our initial feasibility results were confirmed through analysis. Although the calculation of stresses in I-deas may contain a significant amount of error due to the geometry of the holes in the part, we feel as though the worst case scenario was covered with our analytical approach. Despite the completion of our preliminary design, the addition of new data may cause design changes leading to a final product containing significant changes. Some immediate changes that will occur upon acquisition of outstanding data will undoubtedly deal with weight vs. performance optimization in order to meet our sponsor s criteria more securely. The method in which the table will join to surrounding parts may also have a large impact on table constraints, leading to possible variations in vibration analysis and stress analysis. Reductions in weight may have a significant impact on vibration analysis; however, the required testing necessary to obtain the actual vibration specifications has yet to be performed. Based on our analysis, at this point we recommend using the aluminum semicircular table. This design geometry has the lowest deflections in both torsion and bending, and the material has the highest natural frequency. 43