Thesis: Ultrasonic die system for metal forming

Design and optimisation of an ultrasonic die system for forming metal cans

A doctoral thesis submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of the Loughborough University of Technology

June 1995

©C F Cheers, 1995

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To my father

"It is an important and popular fact that things are not always as they seem. For instance, on the planet Earth, man had always assumed he was more intelligent than dolphins because he had achieved so much - the wheel, New York, wars and so on - whilst all the dolphins had ever done was muck about in the water having a good time. But conversely, the dolphins had always believed they were far more intelligent than man - for precisely the same reasons."

Douglas Adams
The Hitch Hiker's Guide to the Galaxy
1979

ABSTRACT

A new manufacturing process has been developed for reducing the diameter of one end of a tinplate can by over 30%. Conventional processes are limited to a maximum of 10% reduction and typically operate at less than 5%. The improvement was achieved by using special tooling and ultrasonic excitation of the die to reduce the forming force.

Ultrasonics have been used in this way before but without a full understanding of the numerous modes of vibration of the die, and how they interact, the efficiency of earlier systems was low. Finite element analysis has been used to characterize the natural modes and frequencies of radial-mode ultrasonic dies and this has led to the development of highly efficient systems. In special cases a non-round die has been required to overcome undesirable modal characteristics; optimum shapes have been developed. A completely new method of mounting the ultrasonic dies was designed and its geometry optimized (again using finite element analysis) to further improve the efficiency of the system.

The new system operates at an amplitude under load approximately three times greater than the earlier equipment. The reduction in forming force (between 30 and 60%) makes the difference between success and failure for the manufacturing process.

ACKNOWLEDGEMENTS

The work has been carried out at CarnaudMetalbox Technology, Wantage and in the department of Mechanical Engineering, Loughborough University of Technology between January 1987 and June 1995. The work was supervised by Professor Graham Chapman and Professor Mike Preston, and directed successively by Professor Jim Hewit, Professor Ray Vitols and Dr John Tyrer, whose support and advice have been much appreciated. The work was undertaken as part of a research project funded by the Science and Engineering Research Council and CarnaudMetalbox Technology.

The author would like to thank colleagues in the Optics group (Dr Mike Shellabear) and the Dynamics group (Dr Margaret Lucas) of the Mechanical Engineering Department for their help and advice during the course of the project. Thanks are also due to the management at CarnaudMetalbox (Fred Price, Bob Barr, Sid Nayar, Mike Alderson) for providing time, support and facilities for the work and during the long writing-up period. Thanks also to the library staff for finding many obscure references. Special thanks to Paul Porucznik for starting the whole project and for numerous stimulating discussions throughout.

Principles and results of ESPI analysis described in section 6.3, including figures 6.08 to 6.16 are reproduced courtesy of Dr John Tyrer and Dr Mike Shellabear.

CONTENTS

1. INTRODUCTION
1.1 BACKGROUND
1.1.1 Background - Aerosol Cans
1.1.2 Analysis of can body strength
1.1.3 Background - Ultrasonics
1.1.4 Application of high power ultrasound to metal forming.
1.1.5 Methods of generating high power ultrasonic vibrations
1.2 ULTRASONIC SYSTEM FOR FORMING AEROSOL CANS
1.2.1 Proposed mechanisms of force reduction from earlier work
1.2.2 'Most likely' mechanisms in this application
1.2.3 Ultrasonic system for forming aerosol cans
1.3 LITERATURE REVIEW
1.3.1 Application of high power ultrasound to metal forming.
1.3.2 Other industrial applications of high power ultrasonics
1.3.3 Methods of generating high power ultrasonic vibrations
1.3.4 Analysis of vibration characteristics
1.3.5 Materials for ultrasonic tools
1.4 SAFETY OF HIGH POWER ULTRASONICS
1.5 SUMMARY

2. FINITE ELEMENT ANALYSIS (details not available here)
2.1 FUNDAMENTALS
2.1.1 Pre-processing
2.1.2 Solution
2.1.3 Post-processing
2.2 ANALYSIS TYPES
2.2.1 Static analysis
2.2.2 Modal Analysis
2.2.3 Harmonic analysis
2.3 REDUCED DYNAMIC ANALYSIS
2.4 ELEMENT TYPES
2.4.1 Three-Dimensional Elements
2.4.2 2-D Plane Stress elements
2.4.3 2-D Axi-symmetric elements
2.4.4 Elements with Mid-side Nodes
2.5 APPLICATIONS OF ANALYSIS & ELEMENT TYPES
2.5.1 Static die analysis
2.5.2 Dynamic die analysis
2.5.3 Dynamic mounting analysis
2.5.4 Summary of Applications
2.6 PARAMETRIC ANALYSIS
2.6.1 Use of Parameters in Ansys
2.7 EXAMPLES
2.8 ACCURACY
2.8.1 Comparison with real measurements
2.8.2 Comparison of FE results with "exact" solutions
2.8.3 Comparison with series solution
2.8.4 Comparison with plane stress / axisymmetric solution
2.8.5 Comparison with other finite element results
2.8.6 Accuracy recommendations

3. ULTRASONIC DIE DESIGN (details not available here)
3.1 MODE NOMENCLATURE
3.1.1 Mode Type
3.1.2 Harmonic Number
3.1.3 Mode Families
3.1.4 Selection of Working Mode
3.1.5 Summary
3.2 FREQUENCY BEHAVIOUR
3.2.1 Mode coupling
3.2.2 Mode switching
3.3 FREQUENCY ANALYSIS
3.4 OPTIMISATION OF DIE DIAMETER
3.5 SHAPED DIES
3.5.1 Evaluating die shapes
3.5.2 Two-flat design
3.5.3 Three-flat design
3.5.4 Slotted design
3.6 DIE MATERIALS
3.7 STRESS ANALYSIS
3.8 DIE MANUFACTURE AND TUNING
3.8.1 Manufacturing
3.8.2 Assembly
3.8.3 Tuning

4. SIMPLIFIED DIE DESIGN PROCEDURE (details not available here)
4.1 PRINCIPLES
4.1.1 Design Requirements
4.1.2 Principles of Simplified Design Procedure
4.1.3 Summary of Theory
4.2 INSTRUCTIONS FOR DESIGNING A NEW ULTRASONIC DIE
4.2.1 Determine the Design Variables
4.2.2 Choose the Materials
4.2.3 Check the Outside Radius
4.2.4 Check Radial Modes
4.2.5 Check the Torsional Modes
4.2.6 Revise and Recheck
4.2.7 Accurate FE Analysis
4.3 EXAMPLES
4.3.1 Design of a Die for 45 mm Aerosol Necking
4.3.2 Design of a Die for 211 Beverage Can Necking
4.4 PROGRAMS
4.5 ENHANCEMENTS
4.5.1 New Material Combinations
4.5.3 Shaped Dies
4.5.4 High Radial Mode Dies
4.6 CONCLUSIONS

5. MOUNTING DESIGN AND OPTIMISATION (details not available here)
5.1 MOUNTING OPTIONS
5.1.1 Nodal flange mounting
5.1.2 Roller bearing mounting
5.1.3 Resonant rod mounting
5.1.4 Tubular type mounting
5.2 TUNED ROD MOUNTING
5.3 TUBULAR MOUNTING
5.3.1 Initial tubular mounting design
5.3.2 Optimising tubular design
5.3.3 Maximum length
5.3.4 Tubular mounting tail design
5.3.5 Tubular mounting - finalised design
5.4 SUMMARY

6. MEASUREMENTS - DIES AND MOUNTINGS
6.1 EVALUATION OF MODE AND FREQUENCY
6.1.1 Physical methods for evaluating mode of vibration
6.1.2 Admittance / Impedance Plotter
6.2 RESULTS OF MEASUREMENTS ON ULTRASONIC DIES
6.2.1 Mode evaluation using talc
6.2.2 Admittance plotter measurements
6.2.2.1 Admittance plotter measurements - transducers
6.2.2.2 Admittance plotter measurements - die tuning
6.2.2.3 Admittance plotter measurements - dies and mountings
6.2.2.4 Admittance plotter measurements - mounting evaluation
6.2.3 Comparison with FE predictions
6.2.4 Accuracy of FE predictions
6.3 ESPI MEASUREMENTS
6.3.1 Principles of ESPI
6.3.2 Converting FE results to simulated ESPI plots
6.3.2.1 Pure modes
6.3.2.2 Distorted modes
6.3.3 Comparison of results
6.3.4 ESPI Summary
6.4 EVALUATION OF TUBULAR MOUNTING PERFORMANCE
6.4.1 Free vibrations of steel prototype
6.4.2 Admittance plotter measurements of mounting performance
6.4.3 Tubular mounting measurements - summary
6.5 MEASURED PROCESS FORCES
6.5.1 Evaluation of forming force in early work
6.5.2 Evaluation of forming force in later work
6.6 CONCLUSIONS

7. RECOMMENDATIONS FOR FURTHER WORK (details not available here)
7.1 FURTHER STUDIES
7.1.1 Effects of ultrasonics
7.1.2 Effects of process on die vibrations
7.1.3 Finite Element Analysis
7.2 NEW DESIGNS FOR ULTRASONIC TOOLING
7.2.1 New die designs
7.2.2 New ultrasonic mountings
7.2.3 Ultrasonic motor dies

8. CONCLUSIONS (details not available here)
Finite Element Analysis
Design of Ultrasonic Tooling
Verification of results
Project aims

APPENDICES (details not available here)
1. Theoretical analysis of neck forming process
2. Analysis of radial vibrations of a hollow cylinder
3. Example programs
4. Properties of materials used for ultrasonic dies
5. Die design graphs
6. Calculation of buckling loads
7. Ultrasonic equipment