DESIGN AND FABRICATION: HAAS CNC ROTARY TABLES

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Proceedings of the 004/005 Spring Multi-Disciplinary Engineering Design Conference Kate Gleason College of Engineering Rochester Institute of Technology Rochester, New York 146 May 1, 005 Project

Rothgery / Mechanical Engineer ABSTRACT The objective of this paper is to give an overview of our CNC Rotary Table Design.

1 Proceedings of the 004/005 Spring Multi-Disciplinary Engineering Design Conference Kate Gleason College of Engineering Rochester Institute of Technology Rochester, New York 146 May 1, 005 Project Number: 054 DESIGN AND FABRICATION: HAAS CNC ROTARY TABLES Patrick J. Walsh / Mechanical Engineer Steven J. Kumpf / Mechanical Engineer Craig J. Rothgery / Mechanical Engineer ABSTRACT The objective of this paper is to give an overview of our CNC Rotary Table Design. This paper discusses our preliminary design and analysis, which includes finite element analysis for bending, torsion, and harmonic response, as well as hand computations. The paper also discusses our final recommendation, featuring the final design and analysis that followed. As a result, this paper gives insight into the performance of various materials and geometries that can be used in a design of a CNC Rotary Table. and LOSAT. Government specifications require them to machine features of parts to an extremely tight tolerance of.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. INTRODUCTION This Design Project was a result of the Rochester Institute of Technology s senior design program for undergraduate engineering seniors. The project was sponsored by Lockheed Martin, Missiles and Fire Controls, located in Grand Prairie, Texas. The objective of this project was to design a CNC rotary table that would minimize table deflection and harmonic disruption, to prevent out of tolerance machining. The scope of the project was to prepare a standardized design for three tables, and oversee the production of one table for proof of concept. Lockheed s motivation for sponsoring this project was that this specific division is responsible for producing high tolerance missile components, and the poor design of their current table had resulted in machining failures and out of tolerance parts. 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 Missiles and Fire Control in Grand Prairie, TX, is responsible for manufacturing parts for missiles such as the ATACMS, PAC-, Figure 1: Original Table 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 00 lbs, preferably less than 100 lbs. Deflections: 1. Twist must be under.001 in.. Bending must be under.001 in Cost: Cost is a low priority compared to performance, but the final table design should be made in the most cost efficient way. 005 Rochester Institute of Technology

Proceedings of KGCOE 005 Multi-Disciplinary Engineering Design Conference Page CONCEPT DEVELOPMENT Our concept development focused on table geometry and material.

After referencing torsional stress equations from mechanics of materials documentation; we decided that semi-circular and triangular geometries would optimize the table s strength in torsion.

2 Proceedings of KGCOE 005 Multi-Disciplinary Engineering Design Conference Page CONCEPT DEVELOPMENT Our concept development focused on table geometry and material. To solve the torsional rigidity problems we explored various geometries. After referencing torsional stress equations from mechanics of materials documentation; we decided that semi-circular and triangular geometries would optimize the table s strength in torsion. PRELIMINARY DESIGN SPECIFICATIONS AND MODELS Specifications and Material Properties Models Cast Iron Aluminum Modulus of Elasticity (Psi) 1.00E E+07 Modulus of Rigidity (Psi) 4.10E+06.9E+06 Density (lbs/in^) Poisson's Ratio Weights (lbs.) Cast Iron Semi-circle 5.46 Cast Iron Triangular Aluminum Semi-circle Aluminum Triangular 61.0 P c cutting power (ft-lb/min) F c cutting force (lb) cutting speed (ft/min) P () P c g E P g gross power of the machine tool motor (W) () Combining equations 1 and Pg E F c ν E efficiency of tool (4) V * D V surface velocity of tool (ft/min) (5) rpm * π 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 0 HP (the greatest HP machine) D.08 ft 500rpm * π rev rad/s (141.59)(.08) ν 10.9 ft/min Figure : Semi-circular table (left). Triangular table (right). PRELIMINARY 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 calculate natural frequencies, modes shapes, and bending deflections. Analysis was done on all four concepts to predict actual feasibility. 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 following equations were utilized: (1) P c F c ν,000( ft lb / min) P g 0HP * 1HP F c 660,000 ft-lb/min 660,000( ft lb / min)*(.9) 10.9( 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 (457.8/4). 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 Paper Number 054

3 Proceedings of the Winter KGCOE Multi-Disciplinary Engineering Design Conference Page were used to generate the figures for torsional and bending deflections. Semi Circle Table (6) 4* T τ max π * R T torque produced from induced load times the moment arm (.5 in) R radius of semi-circle I. 1098* R (7) I moment of inertia Triangular Table (8) (9) τ max 0* T b b base of triangle (11.5 in) * b h I 6 h height of triangle (5.75 in) 4 Current Table (analyzed as rectangular beam) a b (10). 86 (11) C 1.71 C.681 ** C 1 and C are interpolated from Table.1 (pg. 187) Mechanics of Materials Beer, Johnston, DeWolf (1) T φ * C * a L * φ angle of deflection (radians) L 1.5 in 1 (1) φ Tan b a deflection (greatest seen in table was.00 in) **.00 deflection equates to an angular deflection of.099, or.0005 rads. (.0005)(.681)(11.5)(.5) T ,869 lb-in (14) Combining equations and 4 a T * L * Tan C * a * b * G (.7E06) τ max (15) d θ * dx (Semi-Circle & Triangular) a * G d deflection from torque (rads) G Modulus of Rigidity dx length along table (assumed worst case at 1.5 in) P * L (16) y (All) 48* E * I P Force (lbs) L 1.5 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 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. Maximum Torque Deflection Table Twisting Under Torque Figure : Example of table under torque.50e-0.00e E E E E+00 T or si onal Def l ecti on New Tables Semi Circle Def lect ion (Cast Iron) Triangle Def lect ion (Cast Iron) Semi Circle Def lect ion (Aluminum) Triangle Def lect ion (Aluminum) Current Table (Aluminum) T or que (l b-i n) Figure 4: Torisonal deflection (Graph: hand calculations) Deflection Due to Bending Common Equations Copyright 005 by Rochester Institute of Technology

Proceedings of KGCOE 005 Multi-Disciplinary Engineering Design Conference Page 4.50E-0.00E-0 1. 5 0 E-0 1. 0 0 E-0 5.00E-04 0.

1000 1500 000 500 000 500 4000 4500 5000 Appl i ed For ce (l bs) FE Results Combined Torque and Bending Deflections (in) Triangular 0.00117 Semi-Circular 0.

4 Proceedings of KGCOE 005 Multi-Disciplinary Engineering Design Conference Page 4.50E-0.00E E E E E+00 Bendi ng (Z-di r ecti on) Semi Circle Deflection (Cast Iron) Triangle Deflection (Cast Iron) Semi Circle Deflection (Aluminum) Triangle Deflection (Aluminum) Current Table (Aluminum) Appl i ed For ce (l bs) FE Results Combined Torque and Bending Deflections (in) Triangular Semi-Circular Vibration Analysis: There are currently 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. Figure 5: 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. 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). 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 square, and fillets were removed. The analysis used the maximum lb force that is produced by the machine and divided it 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 reality 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. Bending in the X & Z directions FE Results Bending Deflections (in) x z Triangular Semi-Circular Combined Loading: Combined loading analysis involved both torque and bending. To compensate we used a factor of safety of 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. Figure 6: Oil-lite bearing on original table on HAAS machine (left). New air break bearing for Mazak machines (right). 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. The FE analysis was done using I-deas and the tables were constrained by holes on each end. Because the new tables are to be eventually used on the new Mazak machines, 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. 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. EI (17) n.5 4 L ρ Paper Number 054

Proceedings of the Winter KGCOE Multi-Disciplinary Engineering Design Conference Page 5 Where n is the natural frequency, E is the modulus of elasticity, I is the moment of inertia, is the mass per

5 Proceedings of the Winter KGCOE Multi-Disciplinary Engineering Design Conference Page 5 Where n is the natural frequency, E is the modulus of elasticity, I is the moment of inertia, is the mass per unit length of the material, and L is the length. For a cantilevered beam, 1 (18) I bh 1 Where b is the length of the base of the beam and h is the height of the beam. For a Cast Iron beam with a Length of 1 in, a width of 1 in, and a height of 0.5 in the analysis is as follows. 1in*1in*.5in*.58lb in 4 ρ 1.67*10 lb/ in 86*1in 1 4 I *1*(.5) 1.*10 in *10 *(1.*10 ) n rad/ s 4. 1Hz *10 *(1) Modeling the same cantilevered beam in I-deas with a relatively coarse mesh of.5 returned a value of 4.44 Hz for the first mode shape. An error of 0.8% between the two shows a very tight correlation and confirms the functionality of I-deas as a vibration testing tool. alu min um CastIron 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 semicircle 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 66 Aluminum Quarter Semi-circular 1180 Cast Iron Quarter Semi-circular 771 Aluminum Full Original (rectangular) 704 RECOMMENDATION Figure 7: 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: alu um (19) min Eal * ρci CastIron ECI * ρ al For our materials the ratio above is equal to Based on our analysis, we recommend that the customer use the aluminum semi-circular table as their rotary table. This design geometry has the lowest deflections in both torsion and bending, and the material has the highest natural frequency. FINAL DESIGN Our decision on the final design is based off analytical analysis of the preliminary designs. We choose to use the semi-circular geometry and aluminum material. The table has steel endplates designed for the Mazak Nexus Machines. Models: 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 66 Hz, respectively. Therefore, Copyright 005 by Rochester Institute of Technology

Proceedings of KGCOE 005 Multi-Disciplinary Engineering Design Conference Page 6 Our FE analysis found the table s lowest natural frequency to be 1050 hertz.

hertz. This is highly unlikely because the machines maximum speed is 15,000 rpm.

make it with Lockheed s own machines in house.

We then performed a finite element analysis on the model of that table, to allow us to measure the difference between the analytical and experimental data.

This correlation factor allowed us to accurately estimate the true natural frequency of our table.

Design Specifications: Table End Plates Material MIC-6 Aluminum 4140 H. T. Steel Density (lb/in ) 0.101 0.84 Weight (lbs) 91.7 95.4 Modulus of Elasticity (psi) 1.0E+07.

6 Proceedings of KGCOE 005 Multi-Disciplinary Engineering Design Conference Page 6 Our FE analysis found the table s lowest natural frequency to be 1050 hertz. Using the equation below: RPM N (0) N Number of Cutter Teeth 60 We figured the machine would have to run at 15,750 rpm with a 4 tooth cutter, in order create an input frequency of 1050 hertz. This is highly unlikely because the machines maximum speed is 15,000 rpm. Figure 8: Final Table Design (Isentropic) Figure 9: Final Table Design (Side) Cost: A cost analysis proved it was 0% cheaper to build the table from an outside vendor rather than to make it with Lockheed s own machines in house. Harmonic Experimental Testing: To prove the validity of our Finite Element Harmonic Analysis we had our sponsor do a harmonic experiment on a similar table with the same constraints. We then performed a finite element analysis on the model of that table, to allow us to measure the difference between the analytical and experimental data. This experiment allowed us to create a correlation factor between the theoretical natural frequency and the experimental natural frequency of the table. This correlation factor allowed us to accurately estimate the true natural frequency of our table. The correlation factor for the rotary table is %, meaning the actual natural frequency of our rotary table design should be Hertz. Design Specifications: Table End Plates Material MIC-6 Aluminum 4140 H. T. Steel Density (lb/in ) Weight (lbs) Modulus of Elasticity (psi) 1.0E+07.97E+07 Poisson's Ration Analysis: Figure 11: Harmonic Testing Experimental Setup Finite Element Harmonic Analysis: In order to verify the harmonic response of final design, we performed another Finite Element Analysis to find it is lowest natural frequency. Figure 11: First Experimental Mode Shape (Left), First FE Mode Shape (Right) CONCLUSION Figure 10: Final Table Design FE Harmonic Analysis (Quarter Model) Our Rotary Design should meet all of Lockheed Martin s expectations. We are confident we have met all our design goals, and that the performance of our rotary table design will far exceed that of the original rotary table. ACKNOWLEDGEMENTS Paper Number 054

7 Proceedings of the Winter KGCOE Multi-Disciplinary Engineering Design Conference Page 7 Our senior design team would like to thank Thomas J. Carrubba, Lockheed Martin Dallas Operations Manager, for helping to put together and sponsor our design project, as well as give us his full support. We would like to thank everyone from the Dallas Missiles and Fire Controls team who supported our projects efforts, especially the direct support from Jeffrey S. Morgan and Aaron Kirkpatrick. Last but not least, we would like to thank our faculty mentor Dr. Kevin Kochersberger, for his guidance and support. REFERENCES 1. Beer, Johnston, & DeWolf (001). Mechanics of Materials E. McGraw-Hill Education. Europe.. Automation Creations, Inc. (005, April 0). Matweb The Online Materials Information Resource. Retrieved May 5, 005, from Alcoa, Inc. (005). Product Catalog Mic 6 Aluminum Cast Plate. Retrieved May 5, 005, from p?prod_id619&business&product&region Copyright 005 by Rochester Institute of Technology

DESIGN AND FABRICATION: HAAS CNC ROTARY TABLES

DESIGN AND FABRICATION: HAAS CNC ROTARY TABLES Proceedings of the 004/005 Spring Multi-Disciplinary Engineering Design Conference Kate Gleason College of Engineering Rochester Institute of Technology Rochester, New York 146 May 1, 005 Project Number: