DESIGN & FABRICATION: HAAS & MAZAK CNC ROTARY TABLEedge.rit.edu/edge/OldEDGE/public/Archives/P05422/05422... · Steve Kumpf . i Table of Contents ... 5.1.2.3 Current Table (analyzed

DESIGN & FABRICATION:

HAAS & MAZAK CNC ROTARY TABLE

CRITICAL DESIGN REPORT

Team 05422 Patrick Walsh

Craig Rothgery Steve Kumpf

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Table of Contents Executive Summary ........................................................................................................... iii List of Illustrations............................................................................................................. iv 1.0 Project Assessment ....................................................................................................... 1

1.1 Problem Statement .................................................................................................... 1 1.2 Needs Assessment..................................................................................................... 2

1.2.1 Level Zero – Project Mission Statement............................................................ 2 1.2.2 Level One – Qualifiers (Qualitative) ................................................................. 2 1.2.3 Level Two – Winners (Qualitative) ................................................................... 3 1.2.4 Level Three – Winners (Quantitative) ............................................................... 3

1.3 Design Requirements ................................................................................................ 4 1.3.1 Project Proposal ................................................................................................. 4 1.3.2 Specific Requirements ....................................................................................... 5

1.4 Goals ......................................................................................................................... 5 2.0 Concept Development................................................................................................... 6

2.1 Initial Concept Development .................................................................................... 6 2.1.1 Connector Design............................................................................................... 6 2.1.2 Material Design.................................................................................................. 8

2.2 Concept Development After Re-evaluation.............................................................. 9 2.2.1 Table Design ...................................................................................................... 9

3.0 Feasibility Assessment................................................................................................ 11 3.1 Initial Concept Feasibility....................................................................................... 11 3.2 Main Concept Feasibility........................................................................................ 11

3.2.1 Weighted Method............................................................................................. 11 3.2.1.1 Attribute Weights ...................................................................................... 12 3.2.1.2 Pairwise Comparison Breakdown ............................................................ 12 3.2.1.3 Concept Scoring........................................................................................ 13 3.2.1.4 Scoring Breakdown ................................................................................... 13

4.0 Design Specifications and Drawings .......................................................................... 14 4.1 Specifications and Material Properties ................................................................... 14 4.2 Preliminary Drawings ............................................................................................. 15

5.0 Design Analysis .......................................................................................................... 17 5.1 Stress Analysis ........................................................................................................ 17

5.1.1 Maximum Force Produced From Machining................................................... 17 5.1.1.1 Overview ................................................................................................... 17 5.1.1.2 Actual Calculations................................................................................... 18

5.1.2 Deflections: Torsion and Bending ................................................................... 19 5.1.2.1 Semi – Circle Table................................................................................... 19 5.1.2.2 Triangular Table ....................................................................................... 19 5.1.2.3 Current Table (analyzed as rectangular beam ......................................... 19 5.1.2.4 Common Equations ................................................................................... 20 5.2.1.5 Deflection Due to Torque.......................................................................... 21 5.1.2.6 Deflection Due to Bending........................................................................ 23 5.1.2.7 Conclusions............................................................................................... 25

5.1.3 FE Stress Analysis ........................................................................................... 26 5.1.3.1 Bending in the X – Direction .................................................................... 27 5.1.3.2 Bending in the Z – Direction..................................................................... 29 5.1.3.3 Combined Loading.................................................................................... 30

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5.2 Vibration Analysis .................................................................................................. 31 5.2.1 Original Rectangular Aluminum Table FE Harmonic Analysis...................... 33 5.2.2 Triangular Aluminum Table FE Harmonic Analysis....................................... 34 5.2.3 Triangular Cast Iron Table FE Harmonic Analysis ......................................... 35 5.2.4 Semi-Circular Aluminum Table FE Harmonic Analysis................................. 36 5.2.5 Semi-Circular Cast Iron Table FE Harmonic Analysis ................................... 37 5.2.6 Analysis Verification ....................................................................................... 38

5.2.6.1 Quarter Model Boundary Value Verification ........................................... 38 5.2.6.2 Overall I-deas FE Harmonic Analysis Verification.................................. 39

6.0 Preliminary Design Conclusion / Summary ............................................................... 42 7.0 Final Design ................................................................................................................ 43

7.1 Design Changes & Justification.............................................................................. 43 7.2 Final Drawings and Assembly ................................................................................ 44 7.3 Design Specifications.............................................................................................. 48

8.0 Final Design Analysis ................................................................................................. 49 8.1 Finite Element Harmonic Analysis......................................................................... 49 8.2 Machine RPM Input Frequency Verification ......................................................... 50 8.3 Experimental Harmonic Verification...................................................................... 51

8.3.1 Proposed Experimental Test Procedure ........................................................... 51 8.3.2 Actual Experimental Test Procedure ............................................................... 52 8.3.3 Experimental Results ....................................................................................... 53 8.3.4 Finite Element Simulation ............................................................................... 55 8.3.5 Experimental Harmonic Verification Conclusion ........................................... 59

9.0 Manufacturing............................................................................................................. 60 9.1 Cost Analysis .......................................................................................................... 60

9.1.1 Lockheed Martin in House Cost Analysis ....................................................... 60 9.1.2 Out of House Cost Analysis............................................................................. 61 9.1.3 Cost Analysis Conclusion................................................................................ 61

9.2 Manufacturing Challenges ...................................................................................... 62 9.3 Vendor Selection..................................................................................................... 62

10.0 Conclusion ................................................................................................................ 63 Acknowledgements........................................................................................................... 64 References......................................................................................................................... 66

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Executive Summary

The Lockheed Martin, Missiles and Fire Control Division, stationed in Grand Prairie, Texas, is the senior design project Sponsor. The project centered on the Sponsor’s machining operations, which must maintain very tight tolerances as small as .001 inches. 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 difficulty the Sponsor was having with the existing table was the inability to maintain the required tolerances due to influences such as vibrations, wear, and other minute factors. The design team’s goal was 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 with the Sponsor, the concept development stage began. 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 into the surface of the table. Both methods appeared 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 concept was later shown to be ill conceived. Focus was then changed to minimize deflections and vibrations, hence the Geometry Design phase. The deflection concern was 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 geometry and a semi-circular geometry.

After concept generation, a feasibility assessment was done to solidify and select which concept should be used. The major factors 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 factor was weighted and applied to the design 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 study complete, the preliminary analysis phase began. It was decided by the team that all proposed tables would be analyzed in order to validate the feasibility assessment. All of the factors involved in the feasibility assessment were analyzed, while maintaining significant focus on the reaction of the table to applied loads and vibration sensitive scenarios.

The semi-circular aluminum table was chosen as the preferred table design once it was determined that the feasibility assessment matched the preliminary analysis. As more information became available, small changes were made to the table geometry and the method in which the table is mounted to the machine. These small changes required additional vibrational analysis to be done. In addition, the Sponsor was able to obtain experimental data on its current table assembly. In order to forecast expected results with the actual implementation of the final design, the additional data was then used to verify the final analysis and determine a correlation between the analytical and experimental data. At the conclusion of the various phases of design and analysis, the project team is confident that the proposed final table design will significantly improve the current process that the Sponsor is using to machine critical components.

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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 5.2.1.5.1: Example of table under torque. Figure 5.1.2.5.2: Torsional deflection (Graph: hand calculations). Figure 5.1.2.6.2: Bending in the Z-direction (Graph: hand calculations) Figure 5.1.3.1.1: FE analysis – Triangular table bending in the X – direction. Figure 5.1.3.1.2: FE analysis – Triangular table bending in the X – direction (Slice). Figure 5.1.3.1.3: FE analysis – Semi -circular table bending in the X – direction. Figure 5.1.3.1.4: FE analysis – Semi-circular table bending in the X – direction (Slice). Figure 5.1.3.2.1: FE analysis – Triangular table bending in the Z – direction. Figure 5.1.3.2.2: FE analysis – Semi-circular table bending in the Z – direction. Figure 5.1.3.3.1: FE analysis – Triangular table combined loading.

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Figure 5.1.3.3.2: FE analysis – Semi-circular table combined loading. Figure 5.2.0.1: Oil-lite bearing on original table on HAAS machine. Figure 5.2.0.2: New air break bearing for Mazak machines Figure 5.2.1.1: FE harmonic analysis – Rectangular aluminum table (side view). Figure 5.2.1.2: FE harmonic analysis – Rectangular aluminum table (orthogonal view). Figure 5.2.2.1: FE harmonic analysis – Triangular aluminum table (side view). Figure 5.2.2.2: FE harmonic analysis – Triangular aluminum table (orthogonal view). Figure 5.2.3.1: FE harmonic analysis – Triangular cast iron table (side view). Figure 5.2.3.2: FE harmonic analysis – Triangular cast iron table (orthogonal view). Figure 5.2.4.1: FE harmonic analysis – Semi-circular aluminum table (side view). Figure 5.2.4.2: FE harmonic analysis – Semi-circular aluminum table (orthogonal view). Figure 5.2.5.1: FE harmonic analysis – Semi-circular cast iron table (side view). Figure 5.2.5.2: FE harmonic analysis – Semi-circular aluminum table (orthogonal view). Figure 5.2.6.1.1: Quarter model verification – aluminum table. Figure 5.2.6.1.2: Quarter model verification – cast iron table. Figure 5.2.6.2.1: Overall FE harmonic verification – simple cantilevered beam. Figure 7.0.1: Mazak Nexus CNC Machine Figure 7.2.1: Tail Support End Plate (Solid Model) Figure 7.2.2: Tail Support End Plate (Drawing) Figure 7.2.3: Indexer Adapter Plate (Solid Model) Figure 7.2.4: Indexer Adapter Plate (Drawing) Figure 7.2.5: Semi Circle Table (Solid Model) Figure 7.2.6: Semi Circle Table (Drawing) Figure 7.2.7: Table Assembly (Solid Model – Orthogonal

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Figure 7.2.8: Table Assembly (Solid Model - Side) Figure 8.2.1.1: FE harmonic analysis – Semi-circular aluminum final design (side view) Figure 8.2.1.2: FE harmonic analysis – Semi-circular aluminum final design (orthogonal view) Figure 8.2.1: Cutter Frequency Figure 8.3.2.1: Experimental Analysis Setup (Zoomed Out) Figure 8.3.2.2: Experimental Analysis Setup (Zoomed In) Figure 8.3.3.1: Rotary Table Modal Survey, Response: 1, Reference: 3 Figure 8.3.3.2: Rotary Table Modal Survey, Response: 3, Reference: 3 Figure 8.3.3.3: Rotary Table Modal Survey, Response: 22, Reference: 3 Figure 8.3.3.4: Rotary Table Modal Survey, Response: 24, Reference: 3 Figure 8.3.4.1: Mode 1 (Experimental 976 Hz vs. Analytical 931 Hz) Figure 8.3.4.2: Mode 2 (Experimental 1202 Hz vs. Analytical 1487 Hz) Figure 8.3.4.3: Mode 3 (Experimental 2424 Hz vs. Analytical 3150 Hz) Figure 8.3.4.4: Mode 4 (Experimental 2456 Hz vs. Analytical 1840 Hz) Figure 8.3.4.5: Mode 5 (Experimental 3835 Hz vs. Analytical 4019 Hz) Figure 8.3.4.6: Mode 6 (Experimental 4139 Hz vs. Analytical 3951 Hz) Figure 8.3.4.7: Mode 7 (Experimental 4650 Hz vs. Analytical 4303 Hz) Figure 8.3.4.8: Mode 8 (Experimental 4785 Hz vs. Analytical 5254 Hz) Figure 8.3.4.9: Analytical (Constraint 1) Mode 3 - 3290 Hz Figure 8.3.4.10: Analytical (Constraint 2) Mode 4 - 1609 Hz (left) / Mode 5 – 3433 Hz (right) Figure 8.3.4.11: Analytical (Constraint 3) Mode 3 – 4460 Hz Figure 8.3.4.12: Analytical (Constraint 4) Mode 3 - 4230 Hz (left) / Mode 4 – 4670 Hz (middle) / Mode 5 – 5050 Hz (right)

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1.0 Project Assessment The rotary tables are a custom design for the Lockheed Martin Missiles and Fire Control Division and they are to be used on their HAAS and Mazak CNC machines. The Missile and Fire Control Division in Grand Prairie, TX, is responsible for manufacturing parts for missiles, such as the ATACMS, PAC-3, and LOSAT. Government specifications require it to machine features of parts to an extremely tight tolerance of .001 inches. The tables now used in the HAAS machines make it difficult to maintain 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 being

inserted into 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 of an inch 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 a part is machined on a table that is not flat, 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 that result 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.

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Figure 1.1.1: Original Table

1.2 Needs Assessment

1.2.1 Level Zero – Project Mission Statement Design a new Rotary Table that will have minimal surface wear when used and will maintain a consistent hole size during continual use. The table should have a natural frequency higher than that produced by the machine, resist twisting, and be cost effective in the production of three tables.

1.2.2 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

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1.2.3 Level Two – Winners (Qualitative)

• Performance Attributes o The table should be able to hold tolerance requirements for surface

specifications and hole locations after constant wear. o The table should not vibrate when parts are machined. o The table should not twist when 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 to prevent twist.

• Economic Attributes o Table should be cost effective to produce, either in-house or out–of-house.

1.2.4 Level Three – Winners (Quantitative)

• Performance Attributes o The table must a hold a .001 inch 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. All holes must have steel bushings. o The table material must have a resonance frequency above that produced

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.

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1.3 Design Requirements

1.3.1 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: 972-603-3629

EMAIL: [email protected] PROJECT CONTACT: Jeffrey Morgan PHONE: 972-603-7274

EMAIL: [email protected]

RIT CONTACT: Patrick Walsh PHONE: 716-572-9930 EMAIL: [email protected] 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 1st unit fabrication is to be developed in Winter/Spring Semester ‘05.

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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 inch 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 is deemed a low priority. The table performance is more important at this time and cost optimization will occur when all outstanding data has been received. Although once the performance requirements have been made, the table production must be cost effective.

1.4 Goals The goals for this project are to design and produce a rotary table that best satisfies the Sponsor’s needs while learning to successfully initiate and navigate the steps of a detailed design. The Lockheed Martin Missiles and Fire Control Division will produce a preliminary table based on one of the initial designs. This table will provide a basis for harmonic testing and proof of concept. After data on this initial testing has been received, the final design can be modified as needed. The main goal is to produce a reliable table, in the most cost effective manner. By building a quality table, the Lockheed Martin Missiles and Fire Control Division will be able to produce a better product, have fewer scrapped parts, and ultimately save money.

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2.0 Concept Development Concept development is broken in two separate phases. The first phase stemmed from a concern raised regarding the current table. The Sponsor’s primary concern was that it had a problem with a part falling out of tolerance after a second machining operation was conducted on the same table. It was suspected that wear of the aluminum holes causes movement. When a part is rotated 90 degrees around one bolt location for the second operation, the wear causes the part to fall out of tolerance. As part of the concept trouble shooting, it was suspected that a machining process that relied upon locating off the shoulder of a bolt, tolerances would be nearly impossible to maintain. Concept designs were developed for maintaining hole tolerance, as shown below. Unfortunately, these designs were not feasible. This is explained in the feasibility assessment. After development of the initial concepts, focus shifted from connector design to vibration and twisting problems. Table geometry and material types were reviewed, which started the second phase of the concept development. To solve the torsion rigidity problems, triangle and semicircle geometries were explored. After analyzing a mechanics of materials book and torsional stress equations, shapes were chosen that would optimize the table’s strength in torsion.

2.1 Initial Concept Development Concepts are branched into two areas, connector design and table material.

2.1.1 Connector Design

1. Round steel insert with a matching table counterbore. a. This design utilizes a round steal insert that will be placed in the

aluminum stock of the part and aligned with a counter bore in the table. The bolt will then fasten the part to the table through the insert. (Refer to figure 2.1.1.)

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.

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Figure 2.1.1: 2-D assembled counterbore insert concept design.

Figure 2.1.2: 3-D exploded counter bore concept design.

2. Round countersunk steal insert with matching table countersink.

a. This concept is almost identical to the previous concept; however a steel bushing in the aluminum table is not needed. (This will be explained in the material concepts section.)

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Figure 2.1.3: 2-D assembled countersink insert concept design.

2.1.2 Material 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, there will be steel bushings in the hole locations with either a counterbore 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 steel 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. Steel 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 lead to complications.

Hardened Steel PlateBulk Table –

Aluminum/CompositeHoles w/ Steel

Bushings Figure 2.1.4: Aluminum table concept with steel plate and bushings.

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3. Cast Iron Table with Machined Holes a. This concept table will be made 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 Re-evaluation

2.2.1 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 resistant 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

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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 does not contain as

much material as the semi-circle design (weight saving). In addition, the table will be easier to machine than the semi-circle geometry.

c. The disadvantage of this design is that it contains less material than the semi-circle design, therefore making the table more prone to vibrations.

Figure 2.2.2: Triangular Concept Table

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3.0 Feasibility Assessment

3.1 Initial Concept Feasibility After reviewing the initial concept designs with the Sponsor, it was discovered that the insert design would not be feasible in its application. The design was intended to tighten the tolerance in the way the part was attached to the table. An insert was to be used to align the part with the outer diameter of the insert and the inner diameter of the bushing. Lockheed determined this was not feasible because it could not machine the part bolt-down holes with enough accuracy. Therefore, it would not be able to get all four of the inserts in the holes. Lockheed required a .002” tolerance between the shoulder of the bolt and the table holes to allow it to get all four bolts in the holes. As a result, the initial concept designs had to be revised. Also, Lockheed did not want to use the steel plate because of the multiple parts 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.

3.2.1 Weighted Method To perform the primary feasibility assessment on the concept designs, a weighted method was used.

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3.2.1.1 Attribute Weights

Pairwise Comparison: Place an "R" if the row is more important. Place a "C" if

the column is more important

Wei

ght

Har

mon

ics

Cost

of

Mat

eria

ls

Cost

of

Prod

ucti

on

Ease

of

Des

ign

Ease

of

Prod

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Resi

sts

Wea

r

Stif

fnes

s (M

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Twi

st R

equi

rmen

t)

Add

itio

nal 1

(Fut

ure

Use

)

Add

itio

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(Fut

ure

Use

)

Row

Tota

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Colu

mn

Tota

l

Row

+ Co

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n To

tal

Rela

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Wei

ght

Weight c r r c 2 0 2 11%Harmonics r r r r r r 6 1 7 39%Cost of Materials r 1 0 1 6%Cost of Production c c 0 0 0 0%Ease of Design c c c 0 0 0 0%Ease of Production c c 0 1 1 6%Resists Wear 0 3 3 17%Stiffness (Meets Twist Requirment) 0 4 4 22%Additional 1 (Future Use) 0 0 0 0%Additional 2 (Future Use) 0 0 0 0%

Column Total 0 1 0 0 0 1 3 4 0 0 18 100% Figure 3.2.1: Feasibility assessment attributes weights.

3.2.1.2 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.

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3.2.1.3 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

Tria

ngul

ar A

lum

inum

Tria

ngul

ar C

ast

Iron

Sem

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cle

Alu

min

um

Sem

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Cast

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n

Rela

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Wei

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Weight 3.0 2 2.8 1 11%Harmonics 3.0 2.5 3 2.5 39%Cost of Materials 3.0 1 3 1 6%Cost of Production 3.0 1 2 1 0%Ease of Design 3.0 3 3 3 0%Ease of Production 3.0 1 3 1 6%Resists Wear 3.0 5 3 5 17%Stiffness (Meets Twist Requirment) 3.0 3 3.5 3.5 22%Additional 1 (Future Use) 3.0 0%Additional 2 (Future Use) 3.0 0%

Weighted Score 3.0 2.8 3.1 2.8

Normalized Score 97.1% 90.8% 100.0% 90.8% Figure 3.2.2: Feasibility assessment concept score.

3.2.1.4 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. However, cast iron’s advantage is wear resistance. There is some speculation in the cost, because it has not been determined. The Sponsor agreed that the cast iron concept would be more expensive. The semi-circular table scored the highest rating because it is lightweight and resists deflection. Although, this table will not be chosen for production until the vibration experiments are done.

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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+07 1.03E+07 Modulus of Rigidity (Psi) 4.10E+06 3.92E+06 Density (lbs/in^3) 0.258 0.0975 Poisson's Ratio 0.29 0.33 Overall Weights (lbs.) Cast Iron Semi-circle 252.46 Cast Iron Triangular 161.88 Aluminum Semi-circle 95.16 Aluminum Triangular 61.02

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.

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4.2 Preliminary Drawings

Figure 4.2.1: Semi-circular table (actual model).

Figure 4.2.2: Semi-circular table drawing.

16

Figure 4.2.3: Triangular table (actual model).

Figure 4.2.4: Triangular table drawing

17

5.0 Design Analysis The design analysis includes both stress and harmonic analysis. Basic hand calculations were performed on solid bodies to find preliminary torsional stresses and deflections, and bending stresses and deflections. I-deas FE analysis was used to calculate natural frequencies, mode shapes, and bending deflections. Analysis was done on all four concepts to predict actual feasibility.

5.1 Stress Analysis

5.1.1 Maximum Force Produced From Machining

5.1.1.1 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) νcc FP = Pc = cutting power (ft-lb/min) Fc = cutting force (lb) ν = cutting speed (ft/min)

2) EP

P cg =

Pg = gross power of the machine tool motor (W) 3) Combining equations 1 and 2

ν

EPF gc =

E = efficiency of tool

4) 2

* DV ω=

V = surface velocity of tool (ft/min) 5) πω 2*rpm=

18

5.1.1.2 Actual Calculations The following calculations were done as a worst case scenario to obtain the highest possible forces that the table will experience. ν = 500 rpm (lowest the HAAS is ever ran at) E = 90% Pg = 20 HP (the greatest HP machine) D = .0833 ft

revrpm πω 2*500=

= 3141.59 rad/s

2)0833)(.59.3141(

=ν

= 130.9 ft/min

HPlbftHPPg 1

min)/(000,33*20 −=

= 660,000 ft-lb/min

min)/(9.130)9(.*min)/(000,660

ftlbftFc

−=

= 4537.82 lbf This max force of 4537.82 lbs is the absolute worst case scenario 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 1134.45 lbs (4537.82/4).

19

5.1.2 Deflections: Torsion and Bending After determining the max cutter forces from the power and energy relationships in machining, a range of forces were available to examine in both torsion and bending. The following equations were used to generate the tables and figures on the next pages.

5.1.2.1 Semi – Circle Table

1) 3max **4RT

πτ =

T = torque produced from induced load times the moment arm (3.5 in) R = radius of semi-circle 2) 4*1098. RI = I = moment of inertia

5.1.2.2 Triangular Table

1) 3max*20

bT

=τ

b = base of triangle (11.5 in)

2) 36* 3hbI =

h = height of triangle (5.75 in) 5.1.2.3 Current Table (analyzed as rectangular beam)

1) 286.35.35.11

==ba

2) C1 = .2713

C2 = .2681 ** C1 and C2 are interpolated from Table 3.1 (pg. 187) Mechanics of Materials – Beer, Johnston, DeWolf

3) L

baCT3

2 ***φ=

φ = angle of deflection (radians) L = 21.5 in

20

4) ⎟⎠⎞

⎜⎝⎛ ∆= −

aTan 21φ

∆ = deflection (greatest seen in table was .003 in) ** .003 deflection equates to an angular deflection of .0299°, or .000522 rads.

5.21)067.3()5.3)(5.11)(2681)(.000522(. 3 ET =

= 11,869 lb-in 5) Combining equations 3 and 4…

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛⎟⎠⎞

⎜⎝⎛

=∆GbaC

aLTTan

***2

**

32

5.1.2.4 Common Equations

1) dxGa

d **maxτθ = (Semi-Circle & Triangular)

dθ = deflection from torque (rads) G = Modulus of Rigidity dx = length along table (assumed worst case at 21.5 in)

2) IE

LPy**48

* 3= (All)

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

21

5.2.1.5 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.

Figure 5.2.1.5.1: 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 Triangle with 11.5 in sides

Torsion Torsion Applied

Force(lbs.) Stress

Applied

Force(lbs.) Stress

0 0.00 0 0.00 400 9.38 400 18.41 800 18.75 800 36.82

1200 28.13 1200 55.23 1600 37.51 1600 73.64 2000 46.88 2000 92.05 2400 56.26 2400 110.46 2800 65.63 2800 128.87 3200 75.01 3200 147.28 3600 84.39 3600 165.69 4000 93.76 4000 184.10 4400 103.14 4400 202.51 4800 112.52 4800 220.93

Maximum Torque Deflection

Table Twisting Under Torque

22

Semi Circle Deflection (Cast Iron)

Triangle Deflection (Cast Iron)

Torque (lb-in) Deflection (inches)


0 0.00E+00 0 0.00E+00 1400 2.46E-05 1400 4.83E-05 2800 4.92E-05 2800 9.65E-05 4200 7.38E-05 4200 1.45E-04 5600 9.83E-05 5600 1.93E-04 7000 1.23E-04 7000 2.41E-04 8400 1.48E-04 8400 2.90E-04 9800 1.72E-04 9800 3.38E-04 11200 1.97E-04 11200 3.86E-04 12600 2.21E-04 12600 4.34E-04 14000 2.46E-04 14000 4.83E-04 15400 2.70E-04 15400 5.31E-04 16800 2.95E-04 16800 5.79E-04

Semi Circle Deflection (Aluminum) Triangle Deflection (Aluminum)




Current Table (Aluminum)

Torque (lb-in) Deflection (inches) 0 0.00E+00

1400 1.67E-04 2800 3.34E-04 4200 5.02E-04 5600 6.69E-04 7000 8.36E-04 8400 1.00E-03 9800 1.17E-03 11200 1.34E-03 12600 1.50E-03 14000 1.67E-03 15400 1.84E-03 16800 2.01E-03

23

Torsional Deflection New Tables

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Torque (lb-in)

Def

lect

ion

(in)

Semi Circle Deflection (Cast Iron)Triangle Deflection (Cast Iron)Semi Circle Deflection (Aluminum)Triangle Deflection (Aluminum)Current Table (Aluminum)

Figure 5.1.2.5.2: Torisonal deflection (Graph: hand calculations)

5.1.2.6 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 120.025554 in^4Triangle 60.7293837 in^4Rectangle 41.0885417 in^4

24

Semi Circle Deflection (Cast Iron) Triangle Deflection (Cast Iron)

Applied Force(lbs.) Bending (inches)

Applied Force(lbs.)

Bending (inches)


Semi Circle Deflection (Aluminum) Triangle Deflection (Aluminum)

Applied Force(lbs.)

Bending (inches)





0 0.00E+00 400 1.96E-04 800 3.91E-04 1200 5.87E-04 1600 7.83E-04 2000 9.78E-04 2400 1.17E-03 2800 1.37E-03 3200 1.57E-03 3600 1.76E-03 4000 1.96E-03 4400 2.15E-03 4800 2.35E-03

25

Bending (Z-direction)

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 1000 2000 3000 4000 5000 6000

Applied Force (lbs)

Def

lect

ion

(in)

Semi Circle Deflection (Cast Iron)

Triangle Deflection (Cast Iron)

Semi Circle Deflection (Aluminum)

Triangle Deflection (Aluminum)


Figure 5.1.2.6.1: Bending in the Z-direction (Graph: hand calculations)

5.1.2.7 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 Torque Max Moment

Arm Max Torque

(FS 2) Safe

Moment ArmSemi-Circle Aluminum 54418.3 12.0 27209.1 6.0 Semi-Circle Cast Iron 56975.2 12.6 28487.6 6.3 Triangle Aluminum 27715.0 6.1 13857.5 3.1 Triangle Cast Iron 29017.2 6.4 14508.6 3.2

26

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 (4537.82 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 semi-circle cast iron table has the greatest moment arm of 12.56’’. 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 5970.859 2985.430 Semi-Circle Cast Iron 5796.950 2898.475 Triangle Aluminum 3021.078 1510.539 Triangle Cast Iron 2933.086 1466.543

5.1.3 FE Stress Analysis Hand calculations were done using solid bodies. To get more accurate bending deflections, I-deas Finite Element analysis was used. Meshing restrictions required all holes modeled to be rectangular, and fillets were removed. The analysis used the maximum 4537.82 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.

27

5.1.3.1 Bending in the X – Direction Triangular Table

Figure 5.1.3.1.1: FE analysis – Triangular table bending in the X – direction.

Figure 5.1.3.1.2: FE analysis – Triangular table bending in the X – direction (Slice)

The maximum table deflection is .00172 in.

28

Semi-Circular Table

Figure 5.1.3.1.3: FE analysis – Semi - Circular table bending in the X – direction.

Figure 5.1.3.1.4: FE analysis – Semi - Circular table bending in the X – direction.


29

5.1.3.2 Bending in the Z – Direction Triangular Table

Figure 5.1.3.2.1: FE analysis – Triangular table bending in the Z – direction.

The maximum table deflection is .0011 in. Semi-Circular Table

Figure 5.1.3.2.2: FE analysis – Semi - Circular table bending in the Z – direction.


30

5.1.3.3 Combined Loading Combined loading analysis involved both torque and bending. To compensate, a factor of safety of 2 was used 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 5.1.3.3.1: FE analysis – Triangular table combined loading.


31

Semi-Circular Table

Figure 5.1.3.3.2: FE analysis – Semi - Circular table combined loading.


5.2 Vibration Analysis There are currently three variables in the vibration analysis: the bearing end, the table, and the tool. 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. The goal in the finite element vibration analysis is to obtain a general idea of the natural frequencies in each table geometry and material. A vibration analysis experiment will then be performed on the current table to obtain the actual frequencies it is experiencing. Once that experimental data is obtained, that information will be used to optimize the concept design. This will allow an accurate design of 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,

32

the way the table is attached to the bearing and motor is subject to change. Due to time limitations, the tables were analyzed using the current table constraints. Also, all holes were modeled as rectangular holes for meshing reasons.

Figure 5.2.0.1: Oil-lite bearing on original table on HAAS machine.

Figure 5.2.0.2: New air break bearing for Mazak machines.

33

5.2.1 Original Rectangular Aluminum Table FE Harmonic Analysis Lockheed Martin’s original table was analyzed to determine the natural frequency of the table. This data could be used at a later time for comparison purposes as well as verification.

Figure 5.2.1.1: FE harmonic analysis – Rectangular aluminum table (side view).

Figure 5.2.1.2: FE harmonic analysis – Rectangular aluminum table (orthogonal view).

The analysis above shows the rectangular aluminum table’s first mode shape and lowest natural frequency of 704 HZ.

34

5.2.2 Triangular Aluminum Table FE Harmonic Analysis

Figure 5.2.2.1: FE harmonic analysis – Triangular aluminum table (side view).

Figure 5.2.2.2: 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 1085.11 HZ.

35

5.2.3 Triangular Cast Iron Table FE Harmonic Analysis

Figure 5.2.3.1: FE harmonic analysis – Triangular cast iron table (side view).

Figure 5.2.3.2: 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.

36

5.2.4 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 5.2.4.1: FE harmonic analysis – Semi-circular aluminum table (side view).

Figure 5.2.4.2: 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.

37

5.2.5 Semi-Circular Cast Iron Table FE Harmonic Analysis

Figure 5.2.5.1: FE harmonic analysis – Semi-circular cast iron table (side view).

Figure 5.2.5.2: 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.

38

5.2.6 Analysis Verification

5.2.6.1 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 5.2.6.1.1: Quarter model verification – aluminum table.

39

Figure 5.2.6.1.2: Quarter model verification – cast iron table.

Symmetric Analysis Verification Results

Full Table Quarter Table Aluminum 1085.11 1090 Cast Iron 662 659

The figures and table above verify that the symmetric analysis boundary conditions used on the quarter tables are correct.

5.2.6.2 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.

452.3 LEI

n ρω =

Where nω 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,

3

121 bhI =

Where b is the length of the base of the beam and h is the height of the beam.

40

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 = inlbin

inlbininin

/10*67.112*386

258.*25.*1*124

3−=

433 10*3.1)25(.*1*

121 −−== inI

Hzsradn 31.34/67.215)12(*10*67.1)10*3.1(*10*1052.3 44

36

=== −−

ω

Modeling the same cantilevered beam in I-deas with a relatively coarse mesh of .5 returned a value of 34.44 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 5.2.6.2.1: 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:

41

CastIron

umalu

ωω min =

alCI

CIal

EE

ρρ

**

For our materials the ratio above is equal to 1.64. 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,

64.1662

1085min ==CastIron

umalu

ωω

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, a 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 a model of the full semi-circle table was tried. 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 1085 Cast Iron Full Triangular 662 Aluminum Quarter Semi-circular 1180 Cast Iron Quarter Semi-circular 771 Aluminum Full Rectangular (Original) 704

42

6.0 Preliminary Design Conclusion / Summary As expected, the 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, the worst case scenario was covered with the analytical approach used. Despite the completion of the 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 the 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 the analysis, at this point, the aluminum semi-circular table is recommended. This design geometry has the lowest deflections in both torsion and bending, and the material has the highest natural frequency.

43

7.0 Final Design The semi-circular design was proven to be the best geometry to withstand torque, bending, and vibrations. This design was upgraded and improved for the final product. A great deal of information was provide that allowed for verification of the design, which enabled required changes to be made to ensure compatibility with the new Mazak Nexus machines.

Figure 7.0.1: Mazak Nexus CNC Machine

7.1 Design Changes & Justification The new endplate design developed by the Sponsor required a slight modification to the table end constraints. The endplates have a ledge on which 1.56” of the table’s edge rests on. Four .375” bolts, in each plate, are used to fix the table to the plates. The bolts are installed from the underside of the endplates and thread into the bottom of the table. In addition there is a 0.5” dowel hole used in each endplate, which provides a tight tolerance positioning guide when attaching the endplates to the table. Then the endplates are then bolted into the air brake and motor end mount. These design changes were incorporated to allow corrections to be made and to extend life of the table. During the machining process, daily wear and tear is unavoidable and it affects surface flatness. This results in scrapped parts being produced due to unacceptable tolerances. This endplate configuration allows the sponsor to raise the center line of the table using shims, thereby allowing the table to be resurfaced to the proper flatness. Lastly, 0.5” was removed from the bottom of the table. This provided a flat surface to improve ease of machining and decrease cost. The removal of the material did not significantly affect vibrational analysis and made the table lighter by 2.6 lbs.

44

7.2 Final Drawings and Assembly

Figure 7.2.1: Tail Support End Plate (Solid Model)

Figure 7.2.2: Tail Support End Plate (Drawing)

45

Figure 7.2.3: Indexer Adapter Plate (Solid Model)

Figure 7.2.4: Indexer Adapter Plate (Drawing)

46

Figure 7.2.5: Semi Circle Table (Solid Model)

Figure 7.2.6: Semi Circle Table (Drawing)

47

Figure 7.2.7: Table Assembly (Solid Model - Orthogonal)

Figure 7.2.8: Table Assembly (Solid Model - Side)

48

7.3 Design Specifications The bulk of the table was made using MIC-6 Aluminum. MIC-6 is a cast aluminum that is stressed relieved to create the highest possible surface flatness qualities. The endplates were made with 4140 High Tempered Steel upon the Sponsor’s request. The table also has Car lane Steel Bushings in each hole. The table below gives the material properties and weights.

Table End Plates

Material MIC-6 Aluminum 4140 H. T. Steel

Density (lb/in3) 0.101 0.284

Weight (lbs) 89.6 95.43

Modulus of Elasticity (psi) 1.03E+07 2.97E+07

Poisson's Ration 0.33 0.29

49

8.0 Final Design Analysis

8.1 Finite Element Harmonic Analysis The introduction of the endplates changed initial constraints, which required additional vibrational analysis and testing to be performed. The same boundary conditions that were implemented in the previous quarter model analysis were used (See section 5.2).

Figure 8.2.1.1: FE harmonic analysis – Semi-circular aluminum final design (side view)

Figure 8.2.1.2: FE harmonic analysis – Semi-circular aluminum final design (orthogonal view) The analysis above shows the semi-circular aluminum table’s first mode shape and lowest natural frequency of 1050 HZ.

50

The table’s natural frequency was slightly lower than the preliminary semi-circular design we analyzed. This is due to the fact that the endplates changed, thus changing the constraints. Unfortunately, these pre-designed endplates used by Lockheed to fix the table have a negative affect on the natural frequency of the table.

Material Size Geometry Natural Frequency (Hz) Aluminum Quarter Semi-circular (Final Design) 1050 Aluminum Quarter Semi-circular (Preliminary) 1180 Aluminum Full Rectangular (Original) 704

8.2 Machine RPM Input Frequency Verification To theoretically estimate the input frequency of the cutter in the CNC machine the equation below was used:

60NRPM ×

=ω N = Number of Teeth

Cutter Frequency

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00 1400.00

Frequency (Hz)

RPM

Cutter Frequency

Semi-Circ Final Design

Semi-Circ Prelim Design

10560 RPM at 704 Hz

15750 RPM at 1050 Hz

17700 RPM at 1180

Figure 8.2.1: Cutter Frequency

The new Mazak machines that Lockheed Martin Missiles and Fire Control has acquired are capable of running at 15000 rpm. In actuality, the machines are never run higher than 12000 rpm. The modified, rectangular table that the Sponsor is using now has a natural frequency of 704 Hz, which could theoretically be reached if the machine is run at 10560 rpm. The preliminary semi-circular design has a natural frequency of 1180 Hz, which would require the Mazak to run at 17700 rpm. The final semi-circular design has a natural frequency of 1050 Hz, would require the Mazak to run at 15750 rpm. Since this can never happen, there is a factor of safety of 1.3 in the final design.

51

8.3 Experimental Harmonic Verification In order to prove the validity of the finite element harmonic analysis, Lockheed Environmental Test Engineers performed an unconstrained experimental harmonic analysis on a rotary table they had that was similar to the rotary table design as far as constraints and material. The following section shows the test procedure test that was sent to the Sponsor.

8.3.1 Proposed Experimental Test Procedure Rotary Table Experimental Harmonic Analysis Scope: Find the first four natural frequencies and modal shapes of the rotary table. Purpose: Evaluate the accuracy of the Finite Element Harmonic analysis. Equipment Needed:

1. Accelerometer 2. Hammer with force transducer

a. Example on the bottom of webpage - http://www.acsoft.co.uk/page14.htm 3. FFT (Fast Fourier Transform) Analyzing – This can be done one of two ways.

a. (Hardware) FFT Spectrum Analyzer – click on link below for an example. i. http://www.thinksrs.com/products/SR760770.htm

b. (Software – Hardware Combination) i. Software – Lab View or Matlab

ii. Hardware – National Instruments Board Procedure:

1. Place the table on a piece of foam. (At least 2” thick) 2. Attach accelerometer to the corner of the table. 3. Connect the accelerometer and hammer outputs to the inputs of the FFT Analyzer. 4. Strike the table with hammer in the other corners and recorded the first four

natural frequencies and modal shapes. 5. Move the accelerometer to the next corner and repeat the process until all the

output/input data is recorded for each of the corners (real and imaginary terms). Contact Information: Patrick J. Walsh Senior Design Project Leader [email protected] 716-572-9930 Dr. Kevin Kochersberger Faculty Advisor [email protected] 585-475-6775

52

8.3.2 Actual Experimental Test Procedure The actual procedure that the Lockheed Engineer followed was slightly different than that of the proposed procedure. Instead of a 2” piece of foam, the Lockheed Engineer hung the table from a bungee cord. Instead of using one accelerometer, the engineer used six accelerometers to analyze the table. See pictures below:

Figure 8.3.2.1: Experimental Analysis Setup (Zoomed Out)

Figure 8.3.2.2: Experimental Analysis Setup (Zoomed In)

Point 1

Point 3

Point 24

Point 22

53

8.3.3 Experimental Results

100.0e-6

100.000 Lo

g( g

/lbf)

100 5000 1000 200 300 400 500 600 700 800 2000 3000 4000

Hz

-180

180

Phas

e°

Figure 8.3.3.1: Rotary Table Modal Survey, Response: 1, Reference: 3

100.0e-6

100.000

Log

( g/lb

f)

100 5000 1000 200 300 400 500 600 700 800 2000 3000 4000

Hz

-180

180

Phas

e°


54

100.0e-6

100.000

Log

( g/lb

f)

100 5000 1000 200 300 400 500 600 700 800 2000 3000 4000

Hz

-180

180

Phas

e°


100.0e-6

100.000

Log

( g/lb

f)

100 5000 1000 200 300 400 500 600 700 800 2000 3000 4000

Hz

-180

180

Phas

e°


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8.3.4 Finite Element Simulation The I-deas finite element harmonic analysis was cross referenced with the experimental data from the harmonic test to gage the accuracy. The test table was modeled in I-deas and a quarter model unconstrained FE harmonic analysis was performed. There were four types of boundary conditions used on the quarter model. Analyzing the model with each of these boundary conditions provided different modal shapes that the table could theoretically see. The table of the constraints is listed below.

Plane #1 Plane #2 Fixed Free Fixed Free Constraint # 1 X Y Z Y Rot. about Z Z Rot. about X X Rot. about Y Rot. about X Rot. about Y Rot. about Z Plane #1 Plane #2 Fixed Free Fixed Free Constraint # 2 Z Y X Y Rot. about X X Rot. about Z Z Rot. about Y Rot. about Z Rot. about Y Rot. about X Plane #1 Plane #2 Fixed Free Fixed Free Constraint # 3 X Y X Y Rot. about Z Z Rot. about Z Z Rot. about Y Rot. about X Rot. about Y Rot. about X Plane #1 Plane #2 Fixed Free Fixed Free Constraint # 4 X Y Z Y Z Rot. about X Rot. about X X Rot. about Y Rot. about Z Rot. about Y Rot. about Z

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Running the quarter model in I-deas provided 10 different modal shapes for each of the 4 boundary conditions. Certain modal shapes corresponded to the experimental results obtained by Lockheed Martin Missiles and Fire Control. The table below shows corresponding modal shapes by color coding. In addition, the percent difference between experimental and analytical results has been calculated.

Mode Experimental Analytical (Boundary

Condition 1)

Analytical (Boundary

Condition 2)


Condition 3)


Condition 4)

Percent Difference

1 976 0 0 0 0 5% 2 1202 931 0 0 1840 24% 3 2424 3290 1487 0 4230 30% 4 2456 3951 1609 3150 4670 25% 5 3835 4303 3433 4460 5050 5% 6 4139 5254 4019 5650 5430 5% 7 4650 6784 4413 6260 7920 7% 8 4785 7561 5017 6850 8030 10% 9 - 7694 7004 6930 8150 - 10 - 7863 7229 7620 8230 -

Average 14%

Figure 8.3.4.1: Mode 1 (Experimental 976 Hz vs. Analytical 931 Hz)


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Analytical Mode Shapes Not Matching Experimental Data (up to 5000 Hz)

Figure 8.3.4.9: Analytical (Constraint 1) Mode 3 - 3290 Hz

Figure 8.3.4.10: Analytical (Constraint 2) Mode 4 - 1609 Hz (left) /

Mode 5 – 3433 Hz (right)

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Figure 8.3.4.11: Analytical (Constraint 3) Mode 3 – 4460 Hz

Figure 8.3.4.12: Analytical (Constraint 4) Mode 3 - 4230 Hz (left) /

Mode 4 – 4670 Hz (middle) / Mode 5 – 5050 Hz (right) Due to the relatively low input frequencies created by the cutter, the analysis focused mainly on the first mode shape and natural frequency of table. From the results between the experimental and FE analysis, a correction factor could then be calculated to compensate for the difference in natural frequencies of the first mode shape. Correction Factor Calculation Mode 1 (976.38 Hz – 931 Hz) / 976.38 Hz = 5% Final Table Design Natural Frequency Adjustment 1050 Hz +/- (1050 Hz * 5%) = 1102.5 Hz / 997.5 Hz Therefore by using the correction factor of 5% (calculated above), it can be estimated that the actual constrained natural frequency of the table design will be within a range of 997.5 to 1102.5 hertz.

8.3.5 Experimental Harmonic Verification Conclusion As it has been shown, the results from Experimental and FE comparison are extremely satisfying in proving the accuracy of the FE analysis. The average difference between the matching eight modes shapes was only 14%. The first mode shape, which is the primary focus, deviated by only 5%. From this study, it can be confidently said that I-deas FE Harmonic Analysis is an accurate tool for predicting the harmonic performance of the designed table. The design team is confident that if the Sponsor requires similar analysis at a later time, accurate results using FE analysis can be easily obtained.

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9.0 Manufacturing Cost was not a priority compared to performance, however, it was required that the table be produced in the most cost effective way. To minimize the cost of producing the table, manufacturing costs were estimated from both an in-house and out of house perspective. Unfortunately, the table could not be produced by the design team at RIT due to the high tolerances requirements. RIT does not have the proper equipment and personnel to produce the table.

9.1 Cost Analysis

9.1.1 Lockheed Martin in House Cost Analysis Ground Rules and Assumptions 1. Estimates based on end plates to be fabricated from alloy steel, semi circle table to be aluminum. 2. Estimate does not include fabrication of special hardware or base plate for quick loading machine. 3. Estimates are based on following price rates, total for touch labor effort is Hourly/$85.00 N/C Programming/$102.00 $6,290 $14,688 Total: $20,978 Surface Jig N/C N/C N/C Task/Description Qty Grinder Bore NEXUS VARIAX S/A Tapes Total

Steel End Plate 1 14.0 45.0 59.0

Motor End Plate 1 14.0 45.0 59.0 Semi Circle Table 1 22.0 54.0 76.0

Assembly 1 8.0 16.0 24.0 GRAND TOTAL 8.0 16.0 28.0 22.0 144.0 218.0

In house cost analysis (hours of work required)

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9.1.2 Out of House Cost Analysis

Niagara Punch & Die Corp. Quotation A Precision Machine Shop Facility DATE May 12, 2005 176 Gruner Road Quotation # RIT-02 Buffalo, NY 14227-1090 Customer ID RIT Phone (716) 896-7619 Fax (716) 896-8958 E-Mail [email protected] Bill To: Quotation valid until: June 11, 2005 Patrick Walsh Prepared by: Hal Harter RIT 1 Lomb Memorial Drive Rochester ,NY Cell Phone: (716) 572-4930 Comments or special instructions:

Description AMOUNT Supply 1 complete Semi Circle Table as per prints. $10,695.00 Note: Lockheed Martin to supply material for table Note: Lockheed Martin to supply bushings for table Terms: 1/3 Down with receipt of PO 1/3 Upon Delivery. 1/3 Net 30 after Delivery. Delivery: 8-10 Weeks after receipt of PO TOTAL $10,695.00 If you have any questions concerning this quotation, contact Hal Harter THANK YOU FOR YOUR BUSINESS!

9.1.3 Cost Analysis Conclusion From the cost analysis, it was determined to be $10,283 cheaper to produce the table from an outside source. Therefore, it is 49% more cost effective to produce the table out of house than to produce the table in-house using Lockheed’s resources.

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9.2 Manufacturing Challenges The tolerance requirements of the table were extremely high, thus making the table very difficult to produce. The flatness, parallelism, hole location, and perpendicularity relative to the endplates all had to be within 0.0005 inches to 0.001 inches. These types of tolerances require precision machining.

9.3 Vendor Selection The design team mentor, Dr. Kochersberger, advised the team to contact Peter Lidden, a consulting engineer, to discuss manufacturing the table. After speaking with Mr. Lidden, it was recommended that we contact Niagara Punch and Die, an ISO 900 certified corporation. The team contacted Niagara and the company agreed to produce the table upon Lockheed’s request.

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10.0 Conclusion In conclusion the overall design project was a success. The design team feels that all goals and requirements were met and that the rotary table’s actual performance should be close to the estimated performance generated by the analytical analysis. The various verification methods, including experimental verification, have proven I-deas Finite Element harmonic analysis to be a viable tool in estimating harmonic response. Therefore, from all information gained from the numerous stages of design and analysis, the project team is confident that the proposed final table design will significantly improve the current process that the Sponsor is using to machine critical components. Overall this project proved to be a valuable educational experience in both detailed design and project management. At this point it is recommended that Lockheed Martin, Missiles and Fire Control Division, produce the final rotary table design. An experimental analysis (constrained and unconstrained) should also be conducted on the newly produced semi-circular table to verify its performance. After experimental analysis has proven that the new table meets performance specifications, as it should, the sponsor may then continue to produce the remaining two tables needed.

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Acknowledgements Sponsor: Thomas J. Carrubba The senior design team would like to thank Thomas J. Carrubba, Lockheed Martin Dallas Operations Manager, for helping to put together and sponsor the design project, as well as giving us his full direct support. Jeffery S. Morgan The senior design team would like to thank Jeffery S. Morgan, Lockheed Martin Process Engineer, for his direct day to day support and design advice for the project. Aaron Kirkpatrick The senior design team would like to thank Aaron Kirkpatrick, Lockheed Martin Process Engineering Team Leader, for his direct support and project coordination. Charles R. Moore The senior design team would like to than Charles R. Moore, Lockheed Martin PDRR Production Manager, for his support in calculating in-house production costs. Jeff Kirk The senior design team would like to thank Jeff Kirk, Lockheed Martin Environmental Test Engineer, for his support in performing the experimental harmonic analysis. Lockheed Martin Corporation The senior design team would like to thank everyone in the Lockheed Martin Corporation who contributed and aided in our projects efforts. RIT: Dr. Kevin Kochersberger The senior design team would like to thank Dr. Kevin Kochersberger, the design team faculty mentor, for support and guidance through all design project efforts, especially with his expertise in harmonic analysis. Dr. Allen Nye The senior design team would like to thank Dr. Allen Nye, the design team project coordinator, for his help and support.

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Prof. Paul Stiebitz The senior design team would like to thank Prof. Paul Stiebitz, Senior Design Program Director for his help in setting up the project. Other: Peter Lidden The senior design team would like to thank Peter Lidden, consultant engineer, for recommending an ISO 900 certified vender to produce the table. Robert G. Walsh The senior design team would like to thank Robert G. Walsh, for editing and revising the CDR final report.

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References

1. Beer, Johnston, & DeWolf (2001). Mechanics of Materials 3E. McGraw-Hill Education. Europe.

2. Automation Creations, Inc. (2005, April 20). Matweb – The Online Materials Information Resource. Retrieved May 5, 2005, from http://www.matweb.com

3. Alcoa, Inc. (2005). Product Catalog – Mic 6 Aluminum Cast Plate. Retrieved May 5, 2005, from http://www.alcoa.com/global/en/products/product.asp?prod_id=619&Business=&Product=&Region= 4. Groover, Mikell (2002). Fundamentals of Modern Manufacturing: Materials, Processes, and Systems, 2nd Edition. John Wiley and Sons Corp, New York, NY.

Documents

DESIGN & FABRICATION: HAAS & MAZAK CNC ROTARY TABLEedge.rit.edu/edge/OldEDGE/public/Archives/P05422/05422... · Steve Kumpf . i Table of Contents ... 5.1.2.3 Current Table (analyzed