1
PRELIMINARY RESEARCH FOR THE DEVELOPMENT OF A HOT FORGING
DIE LIFE PREDICTION MODEL
A thesis presented to
the faculty of the
Fritz J. and Dolores H. Russ
College of Engineering and Technology of
Ohio University
in partial fulfillment of the
requirements for the degree
Master of Science
Thomas C. Grobaski
August 2004
2 This thesis entitled
PRELIMINARY RESEARCH FOR THE DEVELOPMENT OF A HOT FORGING
DIE LIFE PREDICTION MODEL
BY
THOMAS GROBASKI
has been approved for
the Department of Mechanical Engineering
and the Russ College of Engineering and Technology by
Bhavin Mehta
Professor of Mechanical Engineering
Dennis Irwin
Dean, Russ College of Engineering and Technology
3 Grobaski, Thomas C. M.S. August 2004. Mechanical Engineering PRELIMINARY RESEARCH FOR THE DEVELOPMENT OF A HOT FORGING DIE LIFE PREDICTION MODEL (119pp.)
Director of Thesis: Bhavin Mehta
ABSTRACT
The goal of this research was to provide a preliminary step into developing a complete forging die life model. The research involved analyzing the initial effects of (1) friction, (2) work-piece temperature, (3) die temperature, and (4) forging press stroke speed on effective die stresses, die surface temperatures, die/work-piece sliding velocities, die/work-piece contact pressures, and die surface temperatures were examined. To obtain the results the forging process was modeled (SolidEdge 3D Solid
Modeling Software), simulated (MSC.Superforge Software), and statistically setup and examined using two-level full factorial design of experiments (Analyzed with Minitab &
MS. Excel). The product reviewed was a 10inch diameter differential ring gear forged at the American Axle
Manufacturing, North Tonawanda, New York forging plant. The
4 ring gear is used in the rear differentials for Ford and GM trucks.
Approved:
Bhavin Mehta
Professor of Mechanical Engineering
5
ACKNOWLEDGEMENTS
First, I would like to thank my advisors for the help, guidance, and vision they provided when mine was blurriest.
I wish the best of luck to you on all your future endeavors, and thank you for all your time and resources you graciously provided.
Second, and foremost, I would like to thank my family and friends for keeping me sane, entertained, and grounded, while it was impossible to do so myself. Thank you for guiding and believing in me, I will never forget it (and
I’m sure you’ll never let me).
Finally, I would like to thank American Axle
Manufacturing and their North Tonawanda Forge Facility for opening there doors and allowing access to there forge facility. A special thanks to Dr. Bamidele Oyekanmi and
Matt Gersley for their time and cooperation.
6
TABLE OF CONTENTS
Abstract...... 3 Acknowledgements...... 5 List of Figures ...... 8 List of Tables...... 10
CHAPTER 1. Introduction...... 11 1.1 Problem Definition & Thesis Importance...... 12 1.2 Research Objective...... 13 1.3 Process Modeling & Prediction...... 14 1.4 Thesis Objective...... 16 1.5 Thesis Overview...... 18
CHAPTER 2. Fundamentals of Forging...... 19 2.1 Forging Today...... 20 2.2 Forging Processes...... 22 2.2.1 Metal Forging Methods...... 23 2.2.2 Open Die Process...... 24 2.2.3 Impression Die Process...... 24 2.2.4 Forging at Various Temperatures...... 25 2.3 Forging Future...... 26 2.4 Importance of Die Life Prediction...... 27
CHAPTER 3. Die Failure Modes...... 28 3.1 Forging Die Wear Mechanisms...... 31 3.1.1 Abrasive Wear Background...... 33 3.1.2 Adhesive Wear Background...... 36 3.1.3 Plastic Deformation...... 37 3.1.4 Modeling Mathematically Abrasive & Adhesive Wear ...... 38 3.1.4.1 Archard’s Wear Model...... 38 3.1.4.2 A Mathematical Approach to Wear...... 39 3.1.4.3 Stahlberg & Hallstrom Local Energy Approach..41 3.1.4.4 Plastic Deformation Model...... 41 3.2 Mechanical Fatigue...... 42 3.2.1 Stress-Life (S-N) Approach...... 44 3.2.2 Strain-Life Method...... 47 3.2.2.1 Coffin & Manson (Wöhler) Approach...... 47 3.2.2.2 Falk, Engel & Geiger’s Local Energy Approach.50 3.2.3 Fracture Mechanics Approach...... 51 3.3 Catastrophic Failure...... 54 3.4 Thermo-mechanical Fatigue...... 54
7 3.5 Overall Picture...... 57
CHAPTER 4. Forging Data & Outputs...... 58 4.1 Design of Experimentes...... 62 4.1.1 Factor Design Levels...... 62 4.1.1.1 Stroke Speed: High-Low Level...... 63 4.1.1.2 Work-piece Temperature: High-Low Level...... 63 4.1.1.3 Die Temperature: High-Low Level...... 64 4.1.1.4 Friction Factor: High-Low Level...... 64 4.2 Design of Experiments...... 64 4.2.1 Differential Ring Gear Specifications...... 66 4.2.2 3D-Model Construction using SolidEdge...... 68 4.2.3 MSC.Superforge Simulation Models Setup...... 69 4.2.3.1 Modeled Material Properties...... 72 4.2.3.2 Modeled Forging Press...... 73 4.2.3.3 Modeled Friction at Interface...... 73 4.2.3.4 Modeled Thermal Dynamic Setup...... 74 4.2.3.5 Modeled Forming Process Setup ...... 74
Chapter 5. Results...... 76 5.1 MSC.Superforge Buster Stage Outputs...... 76 5.2 Validation of Results...... 81 5.3 Statistical Analysis...... 82 5.3.1 Sliding Velocity: Normalized Plot & Analysis...86 5.3.2 Effective Stress: Normalized Plot & Analysis...87 5.3.3 Net Energy: Normalized Plot & Analysis...... 89 5.3.4 Final Temperature of Surface: Normalized Plot & Analysis...... 91 5.3.5 Z-Load Force: Normalized Plot & Analysis...... 93 5.3.6 Surface Contact Pressure: Normalized Plot & Analysis...... 95 5.4 Statistical Analysis Summation...... 96
Chapter 6. Conclusion...... 98 6.1 Future Research & Recommendations...... 99 6.2 Finale...... 100
References...... 101
Appendix A: American Axle Forging Specifications...... 105 Appendix B: MSC.Superforge Ring Gear Simulations...... 106 Appendix C: Material Properties...... 109 Appendix D: Forging Press Velocity Curves...... 112 Appendix E: Taylor’s Tool Life Equation...... 114 Appendix F: ANOVA Tables from Statistical Analysis...... 115
8
LIST OF FIGURES
Figure 1.1: Setup for Predicting Die Forging Life...... 17 Figure 2.1: Basic Forging Setup...... 22 Figure 3.1: Aspects of the Forging Process Design that Affect Wear and Fracture, Lange, K ...... 29 Figure 3.2: Failure Modes and Basic Criteria...... 30 Figure 3.3: Die Failure Mechanisms & Common Locations....31 Figure 3.4: Wear Mechanism’s and Mathematical Models.....32 Figure 3.5: Microscopic Wear Models...... 34 Figure 3.6: A) Metallurgical Weld B) Adhesion Joint Adhesive Wear [26]...... 37 Figure 3.7: Stages of Fatigue Process, [23]...... 43 Figure 3.8: Estimated S-N Curve (Whöler) for Steels...... 46 Figure 3.9: A) Universal Slopes B) Four Points - Coffin & Manson’s Graphical Fatigue [26]...... 47 Figure 3.10: Wohler Curve for Strain Life Approach [7]...49 Figure 3.11: Crack Propagation [13]...... 53 Figure 3.12: Basic Thermal Temperature Progress of Die...56 Figure 3.13: Thermo-mechanical Loading In-Phase [23].....56 Figure 4.1: SolidEdge Sketch for 3D Model Lower Die...... 58 Figure 4.2a to f: SolidEdge Dies .par Files ...... 69 Figure 4.3: Upper Die Blocker Stage, Isometric Position..70 Figure 4.4: Work-piece, Post Buster Stage ...... 70 Figure 4.5: Lower Die Blocker Stage, Isometric Position..70 Figure 4.6: Aligned Forging Process Setup...... 71 Figure 4.7: Positioned (Front View, Transparent Dies)....72 Figure 4.8: Axisymmetric 2D Model of Forging Process.....75 Figure 5.1a & b: Initial & Final 2D Setup of Forging Process...... 78 Figure 5.2: 2D Simulation Z-Force Load {lbs} on Upper Die...... 78 Figure 5.3: 2D Simulation Maximum Final Temperature of Upper Die Surface {°F}...... 79 Figure 5.4: 2D Simulation of Net Energy Supplied by Upper Die {J}...... 79 Figure 5.5: 2D Results: Max. Effective Stress {psi} in Upper Die...... 80 Figure 5.6: 2D Simulation of Maximum Sliding Velocity {in/s} at Upper Die and Work-piece Interface...... 80 Figure 5.7: 2D Simulation of Maximum Contact Pressure {psi} at Upper Die and Work-piece Interface...... 81 Figure 5.8: Normal Distribution Curve (α=.25)...... 83
9 Figure 5.9: Normal Probability Plot of the Effects for Sliding Velocity {in /s}...... 86 Figure 5.10: Normal Probability Plot of the Effects for Effective Stress {psi}...... 87 Figure 5.11: Normal Probability Plot of the Effects for Net Energy {J}...... 89 Figure 5.12: Normal Probability Plot of the Effects for Temperature of Upper Die Surface {psi}...... 91 Figure 5.13: Normal Probability Plot of the Effects for Z- Load Force on the Upper Die Surface {lbs}...... 93 Figure 5.14: Normal Probability Plot of the Effects for Maximum Contact Pressure on the Upper Die Surface {psi}...... 95 Figure 6.1: Complex Interactions of Forging Parameters and Wear, Artinger [27]...... 100
10
LIST OF TABLES
Table 4.1: Material/Process Data and Process Outputs.....60 Table 4.2: Empirically Determined Model Constants ...... 61 Table 4.3: DOE Uncoded and Coded Levels...... 66 Table 4.4: American Axle Ring Gear Process Parameters....67 Table 5.1: Blocker Stage Process Outputs...... 77 Table 5.2: Yatesing of Estimated Effect of Stroke Speed..84 Table 5.3: Results of All Analysis...... 97
11
CHAPTER 1
1.0 Introduction
Metal forming is a process that has been constantly revolutionizing and evolving along with man since the conception of fire. Throughout its history, metal forming has been an inadvertent sign of wealth, technology, and power. Around 0 A.D., the Roman Empire possessed the strongest swords, impenetrable armor, and as a result conquered country after country. Both armor and armory were forged from raw metallic alloys. During the dawn of
America, the Native Americans lost repeated battles because their arrows could not compete against the accurate and reliable pistols, muskets, and cannons of the American
Calvary, both fashioned from metal.
Finally, today’s outputs of automotive, aerospace, and industrial products are controlled by the countries that are producing the majority of accurate metal parts using the most cost efficient process control. Whether it is the
United States or China, metal forging is still one of the most tell tale signs of a countries growth and power.
As long as there is no material stronger, cheaper, and abundant then metallic materials, the world will forever
12 revolve around those who can control and form it the best.
Even though forging is not a new science it has been forever evolving with the help of super computers and finite element modeling. Recently it has become a more popular and inexpensive way of crafting net shaped and near net shaped metal products with less design time and cost.
As technology progresses, the spectrum of physical size products being generated is becoming larger with smaller design tolerances.
As a society, we are progressing toward nano-sized processors and at the same time 200-story skyscrapers.
This development results in tighter component tolerances, more complex geometrical products, increased quality, more accurate, and reliable manufacturing methods. There is not a more cost efficient way to manufacture today’s technological components, and tomorrow’s, then by metal forging.
1.1 Problem Definition & Thesis Importance
The ability to predict failure of forging dies is
important to any industry that which forges parts, or
incorporates forgings into part design. By reducing
manufacturing costs, it ensures a lower bottom line cost
13 for any producer, and therefore a more economical production method.
This will reduce costs by permitting die designers to more accurately determine a dies life cycle during the research and design phase of production. Visa vie creating a more accurate price quote for manufacturing costs. An accurate die life prediction will remove the cost incurred in manufacturing excess dies, and by reducing assembly line down time involved in repair and construction of new dies when the life cycle is underestimated.
By predicting die failure, redesign of work piece geometry and material, die material and surface treatment, lubrication, processing temperature, and forging velocity, can be optimized to obtain the most efficient and cost effective manufacturing process possible. It will also
“allow for the evaluation, with respect to quality, performance, and cost of alternate materials, processes, and process parameters for the affordable manufacturing of reliable components.” [36]
1.2 Research Objective
This project is part of an in-process venture in
cooperation with American Axle Manufacturing, located in
Detroit, Michigan and its Tonawanda, New York Forge
14 Facility. This is a researched based statistical analysis of the causes of die failure in the metal forging process.
By using the most appropriate governing relationships, a mathematical model similar to Taylor’s Tool Life Equation
[Appendix], ultimately will be developed and tested using experimental data and simulation results.
Once the research has been formulated and experimentally tested, it will be used to predict the approximate number of cycles till failure of forging dies, prior to actual manufacture of the dies. The research and model will aid in the education and training of future die designers and researchers, as well as, allow for more accurate and efficient product process modeling and manufacturer-customer interaction. Finally, the model once finished should reduce cost margins and product pricing
[30]. Prediction of die failure will be an enormous step for the forging industry, which has been slowly progressing away from its origins as a trial and error design process, and towards a more exact science.
1.3 Process Modeling & Prediction
Prediction of an event based on the statistical
extrapolation of data assuming that all affecting variables
remain the same. Predicting the number of cycles until the
15 failure of a die and the causes of the failure in design will be able to redesign influencing factors (i.e. part and die geometries) to optimize die life and production cost.
This prediction would not be feasible without the use of massive computing power to aid in the simulations.
The life of dies in the forging process has been consistently improving over the previous decades, due to an increase in the computing power of computers. Personal computing, as well as supercomputing, allow easier communication of forging resources, information, and experimentation, also faster and more accurate forging simulations. Internet resources, and FEA/ FEM technologies are aiding in the production of faster and more accurate results of forging simulations. These in turn lead to better overall part, tool press, and die design and optimization.
Prior to this ongoing project, no prediction process had ever been setup to provide accurate information of actual die life. The research for the initial part of the die life prediction model is strongly based on the results of multiple simulations run on MSC.Superforge software and the statistical calculations and prediction models were setup using Minitab and Microsoft Excel.
16 1.4 Thesis Objective
All research projects begin with an initial step. The
basis of this thesis is to start the die life prediction
model. The purpose of this project is to:
1) Identify the different modes in which a die can
fail, by using current metal failure models
2) Determine the parameters, and process outputs
which are needed by the models to determine die
life
3) Take a sample of the independent parameters and
test them using FEA forging software to determine
the process outputs
4) Use a multi-factor two level design of
experiments to determine the effects and
interactions of varying parameters on process
outputs
Future studies will allow the effects of the input
parameters to be linked to the total cycles until die
failure and an equation can be formulated to efficiently
and accurately determine die life.
INPUTS: OUTPUTS: RESULTS: 17 Forging Process SIMULATE: Forging Process CALCULATE: Cycles Data Outputs Till FEA Simulation, Mathematical Failure Forged Testing or Actual Failure Models Forging Run Results Empirical Material Constants Data
Redesign of inputs allowing Recalculation of for optimization of die life Significance Level (α) REDESIGN PHASE: Figure 1.1: Setup for Predicting Die Forging Life
For this project, a single forged part was analyzed.
That part is a differential ring gear produced by American
Axle Manufacturing. The examined controllable inputs were the stroke speed, die temperature, work-piece temperature, and the frictional coefficient of the lubricant at the die- billet interface.
After the effects of the inputs on the outputs were quantified and verified for the ring gear the interactions and effects of parameter inputs were reviewed to determine which caused the greatest effect.
In the future the model will be generalized to incorporate in more materials (given the thermal and mechanical properties are known), various forging temperatures, forging geometries, and finally various forging processes.
18 1.5 Thesis Overview
The entire thesis contains 6 chapters in addition to
the appendices & references. The first chapter outlines
the background of forging and the objectives of the main
project, as well as the objectives of this research and the
overall perspective of the document. The second chapter
gives the fundamentals of forging and its industry. The
following chapter gives a literature review of forging and
the failure mechanisms of forging dies. The fourth chapter
describes the experimental setup and experimentation
preformed. Chapter 5 discusses the results of the
experimentation and the validation of the data. Followed by
the Chapter 6 conclusions, future recommendations and
processes required in completing the prediction model.
19
CHAPTER 2
2.0 Fundamentals of Forging
Forging is the oldest known metal working process, dating back almost 4000 years to the Bronze Age. Modern forging is now a scientific process based on empirical formulas and testing. High-powered hammers and infrared radiation heating are replacing the days of the trial and error “smithing” process.
Improving technology leads to an increase in the skill required to produce quality-forged parts. Accuracy and reliability no longer lies in the hands of the operator, but rests on the shoulders of the machine and die designers
[30]. These improvements, along with many others, give the forging process a decided edge over the rest of the metal manufacturing industries.
Advances in the forging process produce improved metallurgical properties for high strength components with superior internal integrity. Improvements in control systems have led to a more repeatable process, with greater uniformity and extremely tight tolerances.
Despite producing a cost efficient, highly accurate, repetitious product, the forging industry is still affected
20 by poor markets and recessions. Being an intermediate process, the forging industry can be influenced from both ends of the market, i.e. decreased demand or decreased raw materials. Even with this vulnerability, the forging industry is a major metal processing force.
2.1 Forging Today
The industry itself is a niche industry that is a key
link between metal suppliers and end users. Overall forging
is a $7 – billion/year industry and the industrial backbone
of durable goods that comprise 20% of the United States
Gross National Product (GNP) [30]. They range in size from
less than an ounce to more than 150 tons and found in
machines, vehicles and equipment used to generate our
industrial economy. Any material can be forged, but the
most prevalent are steel(s), aluminum, brass, tungsten,
copper, nickel, magnesium, and titanium. Forgings are
prevalent in various industries including, but not limited
to:
• Automotive
• Agricultural machinery
• Petrochemical valves and fittings
• Hand tools and hardware
21 • Railroad and off-highway equipment
• General industrial equipment
• Marine equipment
• Aerospace industries
With more than two-thirds of forged products in the
United States concentrated in the four major: Aerospace industry (30%), automotive and truck manufacture (20%), off-highway vehicles (10%), and military equipment (10%).
As forging proceeds away from a trial and error process towards a more exact science with definitive formulas, the popularity of this economic and mass producing process will grow [30].
Competition for metal forging comes from, casting, welding, and machining. It provides a stronger product with fewer defects, more reliability, better heat treated properties, and more adaptability then casting. More consistent metallurgical properties, more simplified production and cost savings than welding. Finally, it yields less scrap, requires fewer secondary operations, and allows for a broader size range than machining.
22 2.2 Forging Processes
Forging is performed by applying compressive forces,
through two dies, to a metal (work-piece) above the yield
strength resulting in plastic deformation of the billet.
This process refines the grain structure of the metal,
removes any gas pockets or voids, improves chemical
segregation, mechanical and physical properties, and
therefore increases reliability and consistency.
By manipulating the process and output properties,
parts are held to exceptionally tight tolerances. These
parts require only a few processes to produce a finished
product. With these exceptional controllable properties and
versatility, it is easy to see the importance of forged
parts to almost every facet of industry.
Figure 2.1: Basic Forging Setup [30]
23
2.2.1 Metal Forging Methods
Forging is a term used to describe a process in which raw stock metal is formed to the shape of a die by plastic deformation. The part of the machine that applies the energy required for the deformation is known as the up- setter die. The stock material comes in the form of blooms, billets, bars, or ingots, and is formed into rough, close tolerance or net shape depending on the forging process. To generate forging outputs a range of machinery types are used. Among the most common machines are:
• Hammers – Heavy rams are dropped on to the work-
piece, using the weight of the up-setter to
supply the energy required to form the metal.
This process requires multiple hits and has less
accuracy.
• Presses – Main types are mechanical (flywheel &
yoke type), hydraulic, and screw type. Each gives
a range of forging performance conditions and can
be single or multi-blow machines.
24 2.2.2 Open Die Process
The open die process is a hot forming process which uses a flat, convex, or concave up-setter die to shape the work-piece. The range of the size of the part and the number of blows supplied are limitless. The open die workspace allows the work-piece the freedom to move in multiple directions. The part is compressed axially, with no lateral constraint. This process is commonly used for upsetting, cogging, drawing, punching, hollow forging, and closing in.
Also part of the open die family is the ring rolling and orbital rolling where a mandrel is used to increase the center diameter of a billet after a hole has previously been punched through it. Sometimes ring and orbital rolling are classified as separate processes all together.
2.2.3 Impression Die Process
Commonly known as “closed die forging”, the impression die process has a slightly smaller range of forging sizes and blows required. A good process for parts weighing in up to 60000lbs, the closed die provides both axial force and lateral constraint while allowing excess metal (if any required) to flow into a flange location. This process is by far the most popular form of forging since it can
25 provide tighter tolerances for both axial and lateral directions.
Flange or scrap material from impression die forging can be completely removed and impression die forging can be a net shape forging process. This process often does not allow for complex geometries or multi-blow operations.
2.2.4 Forging at Various Temperatures
Forgings can be produced at multiple temperature levels. Room temperature (or no heat added process) forging is commonly called cold forging. This process is less costly, less heat energy consuming, provides greater dimensional accuracy, and can be very efficient for mass production of small parts (less than 50lbs.). The downfall is that it requires much larger pressures to form the metal requiring large machinery and more frequent tool wear.
At the other end of the temperature spectrum is hot forging, where the work-piece is heated up to about 75% of its melting temperature. As the temperature of the work- piece, prior to forging approaches the melting temperature, the flow stress and energy required to form the material is decreased. Therefore, the strain rate or rate of production can be increased. This is a more expensive approach to
26 metal forging and can be detrimental, leading to die failure by thermal stresses.
In between hot and cold forging is warm forging. At about 50% of the material melting temperature, warm forging reduces the high flow stresses found in cold forging, and increases dimensional accuracy, reduces thermal stresses and energy for preheating found in hot forging.
2.3 Forging Future
As the technological trend of producing smaller, less
expensive and more reliable products continues, the forging
industry, which produces the components, will continue to
grow. Since forging is a highly reliable, repetitious and
environmentally friendly process there is no doubt it is a
staple for future manufacturing.
The future of forging is an energy efficient,
automated process with little scrap, and a much higher
turnover rate. It will be safe, clean, and environmentally
friendly. To achieve this, research in improving the
empirically driven processes used today must be preformed
[30].
27 2.4 Importance of Die Life Prediction
To keep decreasing the cost and increasing product
output, the forging industry must constantly be reducing
the bottom line cost by optimizing the design and
manufacturing cycles. One way to do this is by accurately
being able to predict the tooling life cycles of the
forging process. By being able to predict die failure,
dies are optimized to utilize material and time. This
research document is the primary step in producing a fully
interactive die life prediction model.
28
CHAPTER 3
3.0 Die Failure Modes
Failure of dies is a very complex and time dependent phenomenon. The work-piece, dies, press, environment, surface coatings, and lubricants all interact in a cause and effect relationship that result in a poor product and a failed die. The actual causes of the hot forging die failure can be limited to three main failure modes and sub- categories:
1. Wear – Slow removal of die material leading to poor
part tolerances. Prominent wear in areas subjected
to large sliding velocity and high pressure. Major
categories of wear are [3, 10]:
a. Abrasive Wear
b. Adhesive Wear
c. Corrosive Wear
d. Erosive Wear
e. Plastic Deformation
2. Fatigue – Slow buildup of microscopic cracks leading
to rapid nucleation and fracture.
a. Mechanical Fatigue - Occurs in small areas
exposed to large pressures [23].
29 b. Thermal Fatigue – Temperature gradients
causing strains most notably on flat
surfaces exposed to long work-piece contact
times [32].
3. Catastrophic Fracture – Caused by designer,
operator, material defect resulting in low cycle
failure [26]
a. Extreme thermal shock - Rare
b. Extreme mechanical strains
c. Poor material properties
d. Poor die design
e. Poor process setup and operation
Figure 3.1: Aspects of the Forging Process Design that
Affect Wear and Fracture, Lange, [26]
30
Failure Mode Die Failure Criteria
Adhesive Wear
Abrasive Wear
Corrosive Wear Forged Product Out of Tolerance Specifications Erosive Wear
Plastic Deformation
Elastic Fatigue
Micro Cracking Initiated Plastic Fatigue in Dies Leading to Gross Failure of Die
Thermal Fatigue
Immediate Massive Die Catastrophic Failure Cracking
Figure 3.2: Failure Modes and Basic Criteria
The following parts of the chapter will outline the various failure mechanisms and current mathematical models used to predict the mechanism.
31
Figure 3.3: Die Failure Mechanisms & Common Locations [26]
3.1 Forging Die Wear Mechanisms
For metal-on-metal, sliding interfaces there are
numerous wear mechanisms. Among them are [3]:
• Adhesive Wear Mechanisms – Bonding or welding
• Single-Cycle Wear Mechanisms – Plastic
deformation or abrasive wear
• Repeated-Cycle Wear Mechanisms- fatigue or
delamination
• Chemical Mechanisms – Oxidation or corrosive
• Thermal Mechanisms – Loss due to melting
• Tribofilm Mechanism – Surface film erosion
• Electrical Discharge Mechanisms
• Atomic Mechanisms – Migration of atoms
32 The wearing mechanisms for hot forging are limited to three types. The non-sliding (1), sliding/tribological(2), and single-cycle wear mechanisms(3) are the most common forms, with the three different mathematical models being adhesive, abrasive, and plastic deformation.
Corrosive and erosive wear mechanisms take time to develop, and rarely result in die failure alone. Dies that suffer erosive or corrosive wear, fail mainly by aiding in the mechanical fatigue, thermal fatigue, or tribological wear.
Forging Die Wear Mechanisms
Adhesive Single-Cycle Deformation Tribological Mechanism Mechanisms Mechanism
Adhesive Mechanism Plastic Abrasive Wear Deformation
Storen Plastic Archard’s Deformation Model. Archard’s Model Model
Holm’s Stahlberg & Feldman & Adhesive Model Hallstrom Energy Monagut Model Approach
Indirect Effect Direct Effect
Figure 3.4: Wear Mechanism’s and Mathematical Models
33 3.1.1 Abrasive Wear Background
The wear mechanism is the most common form of die failure, and of the three major forms of wear, abrasive wear is the most widespread. The amount of die material removed by abrasive wear is directly proportional to interface pressure and the amount of material sliding over the surface. Abrasive wear is also inversely proportional to the hardness of the surface work-piece and die surface.
Such factors as die material, die surface hardness, die core & surface temperature, work-piece temperature, and lubrication all affect the amount of die wear [3].
In hot forging, an oxide scale forms on the surface of the die due to the chemical reaction between oxygen and steel at the surface, as the forging process progresses abrasive oxide scales break free and act as abrading particles [26].
The broken oxide scale along with the lubricant at the die/work-piece interface creates a tribological system, which when exposed to the high pressures and sliding velocity of the work-piece creates an excellent system for abrasively wearing steel dies. Although, dies often have a harder mechanical surface property then the work-piece they are exposed to, still tend to wear as a result of localized
34 strain hardening of the work-piece during the forging process.
Processes such as plasma, ion or gas nitriding, surface plating or coating, and new ceramic or alloy technologies that increase the surface hardness severely decrease wear, but can often lead to increased cracking and spalling. The decrease in wear volume is a result of the harder, smoother die surface sliding against the softer work-piece surface, which reduces the microscopic particle wear.
At a micro-level, wear occurs in four ways: Micro- cutting, micro-fracture, micro-fatigue, and grain pullout.
These micro-level wear models will be used later to develop a more accurate wear model [3].
Figure 3.5: Microscopic Wear Models [26]
35 Another major cause of abrasive wear is the scale size and its build up. The rate at which the oxide scale builds up is directly proportional to the exposed environment, higher temperatures and a humid atmosphere leads to faster oxide scale buildup. By increasing forging temperature, initially wear will decrease, due to a lower flow stress of the material, which results in less forging load, and ultimately, less pressure at the interface. Increasing temperature, increases scale formation, causing an insulation effect resulting in less heat transfer from the work-piece to the die (reducing thermal fatigue).
Unfortunately, this larger scale is more apt to separate from the die surface and cause wear. The separation of the scale is a secondary wear asperity.
Scale buildup is not always a negative sign.
Increased scales help to insulate and keep the billet hotter and working at a lesser flow stress. Scale also acts as a lubricant when it remains attached to the surface.
Finally, scale buildup is neither a completely good, nor bad, sign for forging, but it is an outside factor that will need to be accurately modeled to produce a precise die life predictor [3]. For this experiment, scale is
36 negligible, but will need to be included in the final model.
3.1.2 Adhesive Wear Background
Mostly prevalent in cold forging, adhesive wear or galling can still be found in the elevated temperature environment of hot forging.
Metallic adhesion occurs in the absence of lubricant and oxide scale, and raw work-piece and die are in direct contact under extremely high load pressures, and extremely low sliding velocities. The two surfaces adhere to each other through a chemical affinity at the interface. This type of adhesion is commonly known as cold welding. Wear occurs from ejecting the work-piece from the die, resulting in removal of part of the surface along with it. The opposite can also occur where the work-piece leaves remnants welded to the die surface [3].
When the reverse occurs, the material will most likely break off, and act as tribological agent, causing abrasive wear. This is a more common result of metallic adhesion and is very tough to simulate. To reduce adhesive wear, the hardness of the die surface, the lubricant coverage, and the sliding velocity could be increased, or by decreasing the forging load. To model both adhesive and
37 abrasive wear, the basic method is Archard’s Wear Model.
Figure 3.7 shows the difference in a weld versus a cold adhesion joint, the adhesion shows that the metal boundary stays in tact, but a bond between metals is developed.
Figure 3.6: A) Metallurgical Weld B) Adhesion Joint
Adhesive Wear [26]
3.1.3 Plastic Deformation
The third of the major types of die wear, for the hot forging process, is plastic deformation. It is the direct result of an excessive pressure being applied, which is greater than the yield strength of the die material. This is often given its own category, but can be considered a single-cycle wear process. Also it is often given that excessive pressure is a result of poor die design or
38 operator error (i.e. machine calibration or incorrect shimming of the dies), but the yield strength of the die is effected by a hot billet heating the surface of the die, therefore, lowering the yield strength. Cooler dies, or different die materials, help reduce the amount of plastic deformation, therefore extending die life [3].
On a microscopic scale, plastic deformation occurs by a process known as slip. Slip is where adjacent planes of atoms move within the crystal structure of the metal.
Eventually these slip bands will join, and result in failure of the die [12]. For a final model, material slip behavior will need to be accounted for.
3.1.4 Modeling Mathematically Abrasive & Adhesive Wear:
Wear is the most predominant form of die failure, unfortunately, it is the most difficult to mathematically model. This is because of the abundant number of factors that affect the different methods of wear. Many different approaches have been formulated to try to accurately predict the amount of wear.
3.1.4.1 Archard’s Wear Model
The oldest method is Archard’s wear model. Archard found that wear, for adhesive and abrasive mechanisms, is a
39 function of local normal pressure, sliding distance, and time.
δW = k * p *δL (Archard’s Wear) [3.1] δW = Volume of Material Moved in Time δt δt = Time Interval of Cycle k = Archard’s Die Wear Coefficient p = Normal Contact Load δL = Sliding Distance in δt
Archard’s wear equation gives an output of volume of
the material removed during a specific time interval. The
accuracy relies heavily on the empirically found Archards
wear coefficient, K. This is a good model to use when only
two materials with known coefficients will be used.
Modeling wear involves various material and process data,
which do to the abundant amount time and cost are almost
impossible to obtain, also the formula tends to be
inaccurate for modeling surface variations such as hardness
differences and geometries. Therefore, a more accurate
wear model needs to be developed. Felder & Montagut took
the Archard model one-step further and solved it for wear
depth, and incorporated material hardnesses. This model is
very useful for two dimensional plane analyses [31].
3.1.4.2 A Mathematical Approach to Wear
Based on the Archard approach, Felder and Montagut
expanded the model and included several different
40 substitutions to reach a simpler form for the abrasive wear model:
δV = A*∆Z ABR [3.2]
K ABR k = m [3.3] H d
p = σ n * A [3.4] δL = V∆T [3.5]
K ABR *σ n *V∆T ∆Z ABR = m (Felder & Montagut’s) [3.6] H d A = Apparent Contact Area
∆ZABR = Abrasive Wear Depth KABR = Experimental Coefficient M Hd = Die Hardness Coefficient M = Hardness Coefficient (m=2 Common Steels)
σN = Local Normal Pressure ∆T = Time Interval of Process
Using essentially the same setup, Holm produced a model for adhesive wear [31]. Holm’s model is a function of interface velocity, temperature distribution, and normal stresses.
K ADH *σ n *V * ∆T ∆Z ADH = (Holm’s Wear) [3.7] H WP
∆ZADH = Adhesive Wear Depth KADH = Experimental Adhesive Coefficient HWP= Work-piece Hardness Coefficient
According to J.H. Kang [18] “Holm defined the wear phenomenon of two contacting bodies as the disappearance of atoms on the material surfaces” and also suggested “ that wear theories are of a macro proportion.
41 3.1.4.3 Stahlberg & Hallstrom Energy Approach to Wear
Another approach is an energy balance approach to wear modeling. This model accounts for the energy supplied by the machine, using the first law of thermodynamics, the amount of material removed is proportional to the dissipation of that energy per unit area.
W = C*τ*L (Wear Energy Model) [3.8] −1.25*q m*σ ⎛ ⎞ τ = E *⎜1− e σM ⎟ ⎜ ⎟ [3.9] 3 ⎝ ⎠ W = Wear (Volume of Material Removed) C = Ratio of Tool Hardness & Work-piece
σM = Average Stress τ = Shear Stress l = Sliding Distance m = Friction Factor
σE = Flow Stress of Material q = Contact Pressure
This model uses the ratio of the material hardness, work performed, and gives the output of volume of material removed [16]. Performed by Stahlberg, and Hallstrom, this method was proved to be more accurate than a model based on contact pressure and surface hardness (comparable to
Archard’s).
3.1.4.4 Plastic Deformation Model
Plastic deformation is the result of excessive surface pressures, which become greater than the yield strength of
42 the material. By analyzing the contact pressure exerted on
the dies by the work-piece, a simple model for deformation
is formulated.
Sy = 2.8* HB (Storen’s Plastic Deformation) [3.10]
σZ ≥ SY ≥ 0.75*[2.8* HB ] [3.11]
Since the yield strength is directly proportional to the Brinell hardness, a correlation between hardness and contact pressure can be formed to determine if failure will occur [6].
3.2 Mechanical Fatigue
Metal fatigue is a process that causes premature
failure or damage of a component subjected to repeated
loadings far below the static yield strength of the
material. The extreme complexity of the process makes it
difficult to accurately describe and model at a microscopic
level. However, the necessity to predict metal fatigue
failure has led to three different approaches [23]:
1. Stress Life (S-N) Approach
2. Strain Life Approach
3. Fracture Mechanics Approach
The fatigue process can also be broken down into three
major phases - initiation life, propagation life and
catastrophic failure [1].
43
Fatigue Process
Evolution of Crack Short Macro- Final the dislocation Nucleation Crack Crack Fracture structure Growth Growth
Macro-crack Initiation Stage Macro-crack Propagation Stage
Figure 3.7: Stages of Fatigue Process, [23]
Initiation is the development and early growth of a small micro-scale crack. These minute cracks propagate by slip plane, extending in from the surface at roughly 45 degrees, and no more than two to five grains from the origin. Propagation life is the portion of total life spent growing a crack to failure.
The transition from initiation to propagation is possible to define, but depends upon many variables being accurately measured. Variables such as size, materials, and methods used to detect cracks make the transition tough to detect. This second stage occurs over many plateaus and is in the direction of the normal tensile stress. Finally, after the crack rapidly nucleates it leads to metal failure.
44 The final stage, or failure, can be brittle or ductile, or both and is normally a single cycle overload
[8].
For forging dies, the alternating stresses are a result of the massive pressures, which are forced on the dies during the forging process. These stresses cause strains at the micro-crack tip regions, therefore exceeding the plastic limit, resulting in the advancement of cracks and finally catastrophic die failure.
3.2.1 Stress-Life (S-N) Approach
The stress-life method was founded well over 100 years ago, and was the standard method used to quantify metal fatigue. Most accurately used for high cycle fatigue failure, the stress life approach (or Wöhler approach) uses a log-log stress versus cycles till failure diagram to display data [1].
Unfortunately, this approach ignores true stress- strain behavior and treats all strains as elastic, and does not separate the crack initiation phase from propagation
[13]. This is extremely significant in die forging where mechanical failure could be the result of plastic deformation [1].
45 In 1910, Basquin solved used a log-log scale and plotted a linear relationship using true stess amplitude.
The S-N curve can be written as Basquin, or Falk Engel and
Geiger have as [12]:
(1 / b) ⎛ σ ⎞ ⎜ a ⎟ NF = ND *⎜ ⎟ (Basquin S-N curve) [3.12] ⎝σ D ⎠
⎛ σ MIN ⎞ R = ⎜ ⎟ (Stress Ratio) [3.13] ⎝σ MAX ⎠
⎛ σ a ⎞ A = ⎜ ⎟ (Amplitude Ratio) [3.14] ⎝σ M ⎠ NF = Number of cycles till failure ND = Number of cycles till fatigue limit σa = Stress Amplitude σD = Stress at Fatigue Limit(Endurance Limit) b = Slope of the graphical line
Since forging dies are loaded and then completely unloaded, they ideally have ratios of R=0 and A=1, this means that using Gerber or Goodman’s equations to deduce the cycles till failure is useless. Therefore, the graphical approach was used and a endurance limit was estimated as Se ≈.5*SU (for hardness comparison, Se(ksi)
≈.25*BHN for BHN≤400, or if BHN≥400, Se≈100ksi). The fatigue limit stress (σD) was estimated using the results of the R.R. Moore test which stated that endurance limit situations must take into account factors including: Size, loading type, surface finish, surface treatments, temperature and environment [33].
46 σD = Se*CLOAD*CSIZE*CSURF*CTEMP*CENV (Norton) [3.15] σD = Adjusted Fatigue Limit Se = Fatigue Limit (ksi) CLOAD = Load Factor CSIZE = Size Factor CSURF = Surface Factor CTEMP = Temperature Factor CENV = Environment Factor
SN
Su
Sm=0.90 Su
Stress σa
σD ≈.5*SU
3 6 N1≈10 NF N2≈10 Cycles Till Failure, (N) Figure 3.8: Estimated S-N Curve (Whöler) for Steels [33]
As stated earlier, there are major weaknesses to this theory. For this application it will be used as a rough estimate of life to compare the strain life and fracture mechanics approaches with.
47 3.2.2 Strain-Life Methods
3.2.2.1 Coffin & Manson (Wöhler) Approach
In the 1950’s, Coffin and Manson independently
proposed that the log of the plastic strain range (∆εP) is
linearly related to number of cycles till failure (NF) [34].
This graphical method has proved to be a much more accurate approach for high load, low cycle fatigue failure. This is because the strain-life approach is based on plastic strain or deformation and is directly measured and quantified.
High stress regions, such as sharp corners or notches, are the most susceptible to plastic strain. In these locations, where mechanical fatigue failure would be most prevalent the strain-life method will predict failure.
Figure 3.9: A) Universal Slopes B) Four Points -Coffin
– Manson Graphical Fatigue [27]
48 The primary hardening and softening of the die is modeled as a steady-state cyclical deformation, in which the stress-strain response remains constant is known as a hysteresis loop [23]. Using this theory the plastic strain amplitude can be found by using equation 3.16. Combining the Coffin-Manson relationship (Equation 3.17) for plastic strain amplitude with the Manson-Halford Law (Equation
3.18) for elastic strain, fatigue leads to equation 3.19, known as the modified Wöhler curve.
Forging dies are subjected loading then unloading, instead of loading then reverse loading, therefore the mean stress (σM) is not equal to zero, and the Manson-Halford law is used instead of the more recognized Basquin Law.
Finally, when metal structure fails it displays progressive creep, neck formation, and finally quasi-static fracture
[23].
49
εF’
c
Wöhler Curve
Log Strain εF’/E Elastic Strain b
Plastic Strain 0 10 2Nt
Log Cycles till Failure (2NF)
Figure 3.10: Wohler Curve for Strain Life Approach [7]
εA,MECH = εA,EL + εA,PL (Hysteresis Loop) [3.16] c εA,PL = εF '(2NF ) (Coffin - Manson Law) [3.17] σ '−σ ε = F M (2N )b (Manson - Halford Law) [3.18] A,EL E F σ '−σ ε = F M (2N )b + ε '(2N )c (Wöhler Law) [3.19] A,TOT E F F F 1 ⎛ ε '∗E ⎞ (b−c) ⎜ F ⎟ 2Nt = ⎜ ⎟ (Transition Point) [3.20] ⎝ σF ' ⎠
εA,MECH = Total Strain Amplitude εA,EL = Elastic Strain Amplitude εA,EL = Plastic Strain Amplitude σM = Mean Stress Amplitude σF’ = Cyclic Fatigue Stress Coefficient b = Cyclic Stress Exponent εF’ = Cyclic Fatigue Strain Coefficient c = Cyclic Strain Exponent E = Modulus of Elasticity NF = Number of Cycles Till Failure
50 The cycles till failure (NF), is therefore a function of parameters εF, c, σF, b, E, and εA.
The local strain-life approach is recognized by the
American Society of Testing and Materials (ASTM) and the
Society of Automotive Engineers (SAE) as a useful and accurate way of measuring fatigue life.
This approach does not take into account crack growth, and failure is considered when “equally stressed volume of material fails”. Because of this, strain-life is considered an “initiation” life estimate [1]. Also, not all materials maybe modeled using this estimate, but for general steels it is most accurate.
3.2.2.2 Falk, Engel & Geiger’s Local Energy Approach
Based off cold forging tests performed in Germany, by
Falk, Engel and Geiger, an alternative method for modeling mechanical fatigue was compared and contrasted to the
Wöhler approach.
The energy criterion for fatigue fracture approach takes into account multi-axial stress conditions by adding directional-dependent damage portions. Assuming plastic strain is neglected, only the modified elastic strain energy density (∆We++) is considered.
51
e++ 1 ⎛ ∆σ ⎞⎛ ∆ε ⎞ ∆W = ⎜ + ∆σM ⎟⎜ + εM ⎟ [3.21] 2 ⎝ 2 ⎠⎝ 2 ⎠ ∆Weff = ∆We++ - ∆Wh [3.22] 1 ⎛ 2E ∗∆Weff ⎞ 2b 2N = ⎜ ⎟ F ⎜ 2 ⎟ [3.23] ⎝ σ F ⎠ ∆We++ = Elastic Strain Energy ∆Wh = Hydrostatic Strain Energy Density σF = Coefficient of Fatigue ∆σ = Stress Range ∆σM = Mean Stress ∆ε = Strain Range εM = Mean Strain Falk, Engel, and Geiger’s research found that in bulk metal forming the local energy approach was much more accurate then the Wöhler approach [11].
3.2.3 Fracture Mechanics Approach
As previously stated, fatigue crack growth takes place in three modes, which are denoted by stage I, II, and III.
The first stage is micro-crack initiation, followed by rapid nucleation, and then macro-crack component failure.
Jaroslav Polack [23] stated, “The essential feature of fracture mechanics characterization of fatigue crack growth begins with determination of the stress and strain fields around a crack subjected to cyclic loading.” If forging dies are assumed to be isotropic, simplified fracture mechanics can be modeled.
52 Unfortunately, this model relies on a stress intensity factor, which is virtually impossible to quantify with the complex forging die geometry. Therefore, a kinetics approach based on linear elastic fracture mechanics into fatigue.
Crack growth rate v=da/dn (i.e. crack advance per cycle) depends on the extent of the crack and the intensity of the external load. Cyclic fatigue occurs in region II, therefore this relationship of straight-line crack growth can predict metal failure. This is known as Paris’s Law,
Equation 3.14, and is used for a pulsating tension condition (R=0 Loading) [13]. In this model microstructure and mean stress have less influence on fatigue crack growth in region II.
da v = = A(∆K)P (Paris Law) [3.24] dN Nf af da 1 af da dN = = ∫ ∫ P P p/2 ∫ p/2 [3.25] Ni ai A()∆K A *Y *∆σ * π ai a ⎛ a (-p/2)+1 − a (-p/2)+1 ⎞ N = ⎜ f i ⎟ F ⎜ P p/2 ⎟ [3.26] ⎝ ()- p/2+1 *A*Y*∆σ *π ⎠ 1 ⎛ Kc ⎞ af = ⎜ ⎟ ⎜ ⎟ [3.27] π ⎝ σ max * Y ⎠ a = Crack Length {in} v = Crack Growth Rate {in/Cycles} A = Reference Crack Growth Rate
53 (Find (A) By Extending Line to ∆K = 1Mpa) ∆K = Stress Intensity Amplitude P = Slope of the Line (P = 3.0-3.25 for steels) Y = Geometry Coefficient (Function of Crack Length & Width) KC = Fracture Toughness (from monotonic test properties) aF = Failure Length {in} NF = Cycles Till aF is Reached
Figure 3.11: Crack Propagation [13]
Typical values for the material constants p and A, were found from Barsom’s study results for steels, and are conservative. By selecting an initial failure crack length the number of cycles until failure can be calculated from equation 3.26.
54 3.3 Catastrophic Failure
Mechanical, or catastrophic failure, is the result of massive pressures applied that are greater than the ultimate strength of the die material. This is caused by machine, design or operator error that results in one cycle until failure. This mode of failure is virtually unpredictable and unstoppable, and can be modeled if the effective stress of the forging process is greater than the ultimate stress of the die material (σeff>Sult).
This mechanical stress can also be caused by thermal shock when an extreme temperature change causes mechanical stresses that are greater then ultimate strength of the material. Often found in metal casting or hot extrusion, this can happen hot forging, if a hot work-piece causes extreme die heating and a low temperature lubricant is applied.
3.4 Thermo-mechanical Fatigue (TMF)
Thermal fatigue failure or thermo-mechanical fatigue is the result of cyclical heating and cooling of die surface at a temperature of 30-40% of the absolute die melting temperature. The thermo-mechanical fatigue is the hardest to model at high temperatures due to several factors including [13].
55 • Oxidation – Oxides form insulation barrier
• Creep/Relaxation
• Transient temperature gradients at startup and
shutdown
• Unequal heating of dies
• Time dependent
• Accelerated crack growth rates
• Multiple Damage Mechanisms
Thermal fatigue is the result of cyclical stresses between the surface and interior of the die. The hot work- piece heats the surface of the die, the die material to expands, resulting in a compression force with the cooler interior of the die. After which the situation is reversed when the die surface is rapidly cooled by application of a room temperature lubricant[26]. This causes a tension between the surface, and the now heated, interior of the die. The cyclic compressive and tension result in heat checks or craze cracks. The strain amplitude caused by the temperature gradient along with material compositional purity influences the fatigue life greatly [32].
To model thermo-fatigue failure method the local strain life method described for mechanical fatigue was
56 used, with the strain found from thermal expansion of metal, equation 3.23 [37].
General Basic Thermal Temperature Progress of Die TWP,H
TWP,L IR Preheat Die Heating End of Cycle From WP Die Heating Cooling From WP
TDIE_INT
TRAD
TDIE_SURF
TAMB
Time (Shift) Figure 3.12: Basic Thermal Temperature Progress of Die
Thermo-mechanical Loading In-Phase T
t
σ
ε
σM
t ε
σ
t
Figure 3.13. Thermo-mechanical Loading In-Phase [23]
57 εTMF = (εA,Pl + εA,El )+ εTH [3.28]
εTH = α(T2 - T1) [3.29] 2()1− ν1 σ1 2(1− ν2 )σ2 α(T2 −φT1) + [3.30] E1 E2 n n ⎛ Cεf ⎞ NFεP = Cεf ∴ NF = ⎜ ⎟ [3.31] ⎝ εP ⎠ da = a (ε )q [3.32] dN ρ P
⎡ (1− ν1)σ1 (1− ν2 )σ2 ⎤ εP = ⎢α(T2 − T1) − − ⎥ [3.33] ⎣ E1 E2 ⎦ α = Mean Coefficient of Thermal Expansion ν = Poisson’s Ratio σ = Stress (1,2 denote max. & min.) N = Number of Cycles till Crack Initiation n = Material Constant
εP = Plastic Strain Range C = Material Constant (between 0-1) εf = True Deformation to Fracture Material Property a = Crack Length r & q = Material Dependent Constants
3.5 Overall Picture
These failure methods will be used as a continuation
method in obtaining the final goal of an applicable die
failure model. By taking the input variables, and testing
or simulating the forging process, the intermediate
variables (i.e. stress, strain, etc.) can be determined.
Using the failure models just shown, with these
intermediate variables will specify which failure method
will occur in the least number of cycles. This method of
failure is then the dominate die failure method.
58
CHAPTER 4
4.0 Forging Data & Outputs
Chapter 3 discussed the multiple metal failure prediction models that were analyzed to identify the variables required to estimate metal failure. The parameters required to estimate die failure must be qualified and quantified to produce a valuable working prediction model. The variables can be organized into three main categories by breaking each failure model down and regrouping.
1. Material/Process Data
2. Process Outputs
3. Empirical Constants
Material data is comprised of independent variables based on the different tooling parts including the dies, work-piece, lubricant, press and environment. For each of the separate tooling features there are the mechanical, chemical, electrical, and thermal properties. Material data are the input parameters into a forging operation.
The various material properties were obtained from the abundant sources of previously tested materials included in the ASTM Metals and Materials Handbooks, matweb.com,
59 independent research laboratory testing (ORNL), Metal
Processing Journal, etc. These sources, and many others, provide accurate data for various materials that are forged, also the effects of temperature, humidity, and other environmental factors that lead to altered physical properties. Ohio University can measure and test the unpublished material properties accurate variables. For the failure models previously described in chapter 3, the material data is displayed in Table 4.1.
60
Table 4.1: Material/Process Data and Process Outputs MATERIAL & PROCESS DATA FORGING PROCESS OUTPUTS 1. Die & Work-piece: 1. Material Sliding: •Hardness •Distances •Initial Temperature •Velocities •Ductility 2. Heat Transferred: •Ultimate Tensile Strength •Conduction (WP to Die) •Modulus of Elasticity •Convection (WP & Die to Env.) •Tempering Curves •Radiation (WP to Die & Env.) •Yield Strength 3. Final Temperature of: •Poisson’s Ratio •Die •Tempering Curves •Work-piece •Surface Roughness •Environment •Toughness 4. Forging Load Force •Geometry 5. Contact Pressures at: •Thermo-physical Properties •Die/Work-piece Interfaces 2. Surface Coatings: 6. Effective Stress: •Physical Properties •Ranges 3. Environment: •Amplitude •Ambient Temperature 7. Total Strain Range From: •Environmental Humidity •Elastic Strain •Environmental Oxygen Content •Plastic Strain •Preheat of Dies & Work-piece •Thermal Strain 4. Lubricant: 8. Strain Rate •Thermo-physical Properties 9. Strain Hardening of: •Friction Factor •Die Surfaces •Coverage and Thickness •Work-piece 5. Forging Press •Press Type •Stroke Velocity Curve •Stroke Acceleration Curve •Press Rigidity •Press Stroke Length •Press Repeatability & Accuracy 6. Miscellaneous •Operator Quality •Cooling Time of Work-piece & Die •Contact Time of Die, Work-piece & Lubricant
61 Process outputs are the results of the forging process
(stress, strain, etc.). They are dependent upon the material/process data (pressure, temperature, etc.), also known as independent variables [Table 4.1].
Once the effects of the independent variables upon the process outputs are known, the number of cycles till failure of the dies, can be estimated using the various die failure models outlined in Chapter 3.
The die failure models rely heavily upon the accuracy of empirically determined constants. The constants and coefficients in Table 4.2, are from the failure models previously described.
Table 4.2: Empirically Determined Model Constants
Empirical Constants 1. Archard Model's: •Adhesive Wear Constant •Abrasive Wear Constant 2. Felder & Montagut’s: •Hardness Coefficient 3. Stahlberg & Hallstrom’s: •Friction Factor 4. Coffin-Manson’s: •Cyclic Fatigue Stress Factor •Cyclic Fatigue Strain Factor •Cyclic Stress Coefficients •Cyclic Strain Coefficients 5. Local Energy Approach’s: •Coefficient of Fatigue 6. Fracture Mechanic Model's: •Geometry Coefficient 7. Thermal Mechanical Fatigue Model’s •Material Constants
62 After obtaining the material/process data and the
process outputs, and empirically modeled constants are
determined, the cycles till die failure can be estimated.
Using a multi-factor, two level full factorial design,
the effects of the independent variables on the die cycles
till failure are estimated. From this setup, a formula
equivalent to the Taylor’s Tool Life [Appendix] will be
constructed. This equation will be employed to quickly,
efficiently, and accurately determine the forging die life
longevity.
4.1 Design of Experiments Breakdown
The purpose of this research is to determine the
effects caused by varying the forging process input
parameters on the process outputs that are required to
determine die life. This preliminary step will show how the
model will be setup, determined and run.
4.1.1 Factor Design Levels
The design of the experiment is a four factor, high-
low two level tests. The analysis was limited to four
factors initially, because of time and monetary
constraints, therefore only requiring 24 =16 simulations.
Once research funds are secured, the number of factors
63 tested can be expanded in the future. The four factors were selected by deeming that which was believed to affect the forging outputs the greatest. The factors chosen were:
1. Forging Press Stroke Speed
2. Work-piece Temperature
3. Die Temperature
4. Friction Factor at Die-Work-piece Interface
The four factors were then given high/low values based upon their average values provided by AAM.
4.1.1.1 Stroke Speed: High-Low Level
For stroke speed, the upper bound velocity the press was capable of was 47 strokes per minute. To find the lower bound for stroke velocity (36spm), the difference between the upper bound (47spm) and average stroke speed (41spm) and subtracting it from the average.
4.1.1.2 Work-piece Temperature: High-Low Level
The Work-piece upper bound, or high-level, temperature was set at the maximum possible forging temperature for
AISI 4320 Steel (2300˚F). The lower bound was set at approximately 65% of the melting temperature (2600˚F
*0.65≈1700˚F, the simplistic definition of hot forging) of the AISI 4320 Steel [8].
64 4.1.1.3 Die Temperature: High-Low Level
The high/low factor levels for the die temperature were obtained from AAM as die temperature after preheating prior to the first forging cycle (300˚F Flow level), and the maximum temperature obtained during forging shift
(800˚F high level).
4.1.1.4 Friction Factor: High-Low Level
The friction factor levels were determined from the
ASM Handbook V.11: Failure Prevention, Protection, and
Analysis [8]. The low level for friction (0.2) was empirically determined from the test of lubricated mild steel sliding on hardened steel. The high level for friction (0.7) was from un-lubricated mild steel sliding on hardened steel.
4.2 Design of Experiments Setup
Many steps were taken to determine the forging press outputs to be studied.
First, the multiple forging die failure models were reviewed to find the necessary process outputs required to predict die life.
Second, the necessary process outputs were cross- referenced with the outputs that are obtainable from
65 testing and those obtainable by simulation. Since there is no forging press located at Ohio University, alternative methods needed to be installed to begin the research and perform the experimentation.
To calculate the process outputs, the MSC.Superforge finite element modeling software used specifically for simulating the forging process was employed. The results of the multiple MSC.Superforge simulations were verified by visiting the American Axle plant in North Tonawanda, where the actual RG-3607 differential ring gear being modeled and simulated are originally formed. AAM supplied the material/process data and various known process outputs have been compiled from years of testing and actual ring gear forging. The AAM specs for RG-2607 are provided in
Table 4.4.
The forging simulation were performed at the CAD/CAE laboratory at Ohio University, and the validity of the results were verified, by comparing the results to the AAM supplied information. The design of experiments setup did not need to be randomized, since the outside factors are negligible with computer simulation. The coded and uncoded setup are located in Table 4.3.
66
Table 4.3: D.O.E. Uncoded and Coded Levels
Uncoded DOE Coded DOE
(d) Run # Run # (defg)
Yates Code Avg. Stroke Speed (in/s) Temp WP {°F} Stroke Speed Friction (g) Temp Die {°F} Friction (NA) WP Temp. (e) Die Temp. (f) 0 8.4 1700 300 0.2 0 -1 -1 -1 -1 1 1 8.4 1700 300 0.7 1 -1 -1 -1 1 g 2 8.4 1700 800 0.2 2 -1 -1 1 -1 f 3 8.4 1700 800 0.7 3 -1 -1 1 1 fg 4 8.4 2300 300 0.2 4 -1 1 -1 -1 e 5 8.4 2300 300 0.7 5 -1 1 -1 1 eg 6 8.4 2300 800 0.2 6 -1 1 1 -1 ef 7 8.4 2300 800 0.7 7 -1 1 1 1 efg 8 11 1700 300 0.2 8 1 -1 -1 -1 d 9 11 1700 300 0.7 9 1 -1 -1 1 dg 10 11 1700 800 0.2 10 1 -1 1 -1 df 11 11 1700 800 0.7 11 1 -1 1 1 dfg 12 11 2300 300 0.2 12 1 1 -1 -1 de 13 11 2300 300 0.7 13 1 1 -1 1 deg 14 11 2300 800 0.2 14 1 1 1 -1 def 15 11 2300 800 0.7 15 1 1 1 1 defg
4.2.1 Differential Ring Gear Specifications
After multiple meetings with American Axle
Manufacturing Engineers, the process parameters were discussed and determined [Table 4.4].
67 Table 4.4: American Axle Ring Gear Process Parameters
Material Data: Work-piece = AISI 4320 Steel Die Material = H-13 Tool Steel Lubricant = AML-145 (Synthetic Graphite) Lubricant Temperature = Room Temperature Ambient Temperature = 70-75F Surface Coating = None Surface Treatment = Nitriding (.008-.012dp) Die Surface Hardness = 45-47 Rockwell Forging Load = 1st Stage = <450 tons 2nd Stage = 450-600 tons 3rd Stage = 1950-2200 tons Press Type = Diesel Mechanical Yoke Press Stroke Speed = 45 Strokes Per Minute Press Stroke Length = 14" Workpiece Temperature Initially = 2300F Workpiece Temperature Finally = 2200F Die Surface Temperature Initially = 300F Die Surface Temperature Mid-Shift = 600F Height Reduction = 1st = 6.5" to 3.22" 2nd = 3.22" to 2.215" 3rd = 2.215" to 1.906"
*Also all die geometries were supplied via AutoCAD Drawings
Using the supplied parameters the mechanical, thermal, electrical, and chemical properties of the die, work-piece, and lubricant were researched in the ASTM Metals and
Materials Handbook, along with Matweb.com, and material supplier information [Appendix]. To construct an accurate model of the forging process in MSC.Superforge these factors needed to be as accurate as possible.
68 4.2.2 3D-Model Construction using SolidEdge
The dies for all three stages were drawn to scale using SolidEdge 3D-Solid Modeling Software prior to actual simulation in MSC.Superforge. The AAM supplied AutoCAD drawings were used to model the dies. A revolved protrusion command of a 2D sketch from the supplied drawings provided the die models (Figure 4.1). The solid models are displayed in Figure 4.2.
Figure 4.1: SolidEdge Sketch for 3D Model Lower Die
69
UPPER DIES
a) Buster Stage c) Blocker Stage e) Finisher Stage
LOWER DIES
b) Buster Stage d) Blocker Stage f) Finisher Stage
Figure 4.2a-e: SolidEdge Dies .par Files
Post construction of the dies, the SolidEdge part files (.par) were saved as Stereo Lithography files (.stl) to be imported into MSC.Superforge models which insure accurate integration.
4.2.3 MSC.Superforge Simulation Models Setup
The dies and work-piece were imported as .stl files into the forging software MSC.Superforge 2004, and were then meshed using the default size. Later the parts are remeshed for optimization [Figure 4.3-4.5].
70
Figure 4.3: Upper Die Blocker Stage, Isometric Position
Figure 4.4: Work-piece, Post Buster Stage
Figure 4.5: Lower Die Blocker Stage, Isometric Position
The upper die and lower die were aligned with the work-piece [Figure 4.6].
71
Figure 4.6: Aligned Forging Process Setup
By shortening the upper dies stroke length from the actual 14 inches to 3.58 inches simulation time is reduced.
To do this the Positioner function in Superforge moved the upper die down until it was touching the top of the work- piece which was resting a top the bottom die as shown in
Figure 4.7:
72
Figure 4.7: Positioned Superforge Setup (Front View,
Transparent Dies)
The properties and bounds of the forging process are added to insure the models accuracy.
4.2.3.1 Modeled Material Properties
The materials are from the MSC.Superforge Materials
Library and the mechanical and thermal properties were compared with properties found in the ASTM Handbook and matweb.com. Any discrepancies were changed to match the
ASTM Handbook values. The material for the upper and lower dies was H-13 tool steel (900-1200˚C) ion nitrided and for the work-piece was AISI 4337 steel which had been altered to meet the properties of the AISI 4320 steel used at AAM.
73 The mechanical, chemical, and thermal properties for both
dies and work-piece are in the Appendix.
4.2.3.2 Modeled Forging Press
The next step was to create the customized forging
press with the appropriate properties. Using the
MSC.Superforge function to manually create a modeled press.
A mechanical scotch yoke press was selected and given the
14inch stroke length and the high/low stroke speeds chosen
for the design of experiments. The high/low velocity
graphs of the press are included in the Appendix.
4.2.3.3 Modeled Friction at Interface
The friction factor added is a combination of the
Coulumb Friction Model and Plastic Shear Friction.
τ=µ*P (Plastic Friction) [4.1] τ=M*τYIELD (Coulomb Friction Model) [4.2] τ= Friction Force µ = Friction Coefficient P = Forging Load M = Friction Factor τYIELD= Flow Stress in Shear
The numerical values for the friction factors were chosen from ASTM Handbook values for steel on steel sliding with no lubricant (µ=0.7), this was the assumed high, and the low was also attained from the ASTM values for,
74 lubricated steel on steel sliding (µ=0.2) and were incorporated in the high/low experimental design.
4.2.3.4 Modeled Thermal Dynamic Setup
The next steps for the material setup pertained to the initial bounds for the temperature and thermal properties of the work-piece and dies. The work-piece and die initial temperatures were set using two separate values from the
DOE. The thermal properties matched the thermal properties obtained from the ASTM Handbook. The final additions of the ambient temperature of the environment, and the time allotted between processes. The process is modeled by incorporating the work-piece and die heat transfer to the surrounding environment, which is dependent upon the time of exposure.
4.2.3.5 Modeled Forming Process Setup
With the material, press, thermal, and frictions properties specified, the actual forging simulation specifics were set. Actual stroke length of the simulation after positioning is entered for each process. The mesh size of the dies and the work-piece were set at 0.10 inch.
Chosen using a trial and error approach, the initial mesh at .25inch (1/2 the smallest geometry size) was reduced
75 till less than a .01% change in maximum effective stress
was observed. The total forging stroke is divided into 10
analysis steps, and was designed as a closed die forging
operation with a flange. The forging process was modeled
as a finite element solution set [Appendix] rather than a
finite volume, to increase accuracy.
The forging dies and work-piece are cylindrical in
shape and geometry. Therefore, a 2D axisymmetric slice was
used to model the forging process [Figure 4.8].
Figure 4.8: Axisymmetric 2D Model of Forging Process
Reducing the amount material modeled, lessons the number of nodes analyzed, therefore accelerating computational time without weakening the integrity of the analysis [Appendix].
76 CHAPTER 5
5.0 Results The simulation, of each stage of the three stages required to forge the AAM ring gear, were simulated in
MSC.Superforge.
The process outputs were then analyzed using Microsoft
Excel and Minitab Release 14. The results of the main effects and secondary, tertiary, and fourth order interaction effects on the process outputs were calculated.
To save space and time, the effects on the upper die of
Blocker Stage (Stage B) of the ring gear forging process is explained in detail, and the remaining two stages’ results are summarized in the Appendix.
5.1 MSC.Superforge Buster Stage Outputs
The results of the Superforge simulations for the
Buster Stage are in Table 5.1. These values were the maximum values taken from each output. A real world working model would have to take into account the values of each at every node in order to develop an accurate calculation of the number of cycles till failure.
77 Table 5.1: Blocker Stage Process Outputs
STAGE B) PROCESS OUTPUT RESULTS Z-Load Temp. Net Eff. Sliding Cont. Force Final Energy Stress Vel. Press.
Run # Yates {lbf} {°F} {J} {Psi} {in/s} (Psi) Upper Upper Upper Upper Up Int WP-Die Int. 0 1 12300.0 504.8 1.392E+05 6333.0 11.060 2.203E+04 1 a 12190.0 488.6 1.764E+05 3041.0 10.910 2.513E+04 2 b 9939.0 937.2 1.385E+05 3714.0 11.170 2.312E+04 3 ab 13160.0 931.9 1.345E+05 6768.0 10.920 2.261E+04 4 c 6406.0 570.4 7.477E+04 2358.0 11.410 1.263E+04 5 ac 7801.0 561.5 1.074E+05 2929.0 11.040 1.187E+04 6 bc 6376.0 1004.6 7.473E+04 4256.0 11.290 1.246E+04 7 abc 5481.0 1003.7 6.860E+04 3287.0 11.050 1.070E+04 8 d 15790.0 417.5 1.244E+05 6055.0 14.420 2.264E+04 9 ad 10710.0 457.1 1.379E+05 7496.0 14.290 2.255E+04 10 bd 7307.0 905.1 1.232E+05 2499.0 14.380 1.786E+04 11 abd 16450.0 904.7 1.372E+05 7806.0 14.690 2.119E+04 12 cd 6441.0 515.3 7.713E+04 4454.0 14.750 1.435E+04 13 acd 5101.0 506.9 1.101E+05 1840.0 14.610 1.171E+04 14 bcd 6407.0 963.2 7.711E+04 2635.0 14.470 1.369E+04 15 abcd 9318.0 956.8 1.100E+05 4337.0 14.560 1.276E+04
These results were ripped from the results of simulations run in MSC.Superforge. The numerical values are the maximum values that occurred at the specified location.
The simulations were run using 2D analysis for all runs, but were compared to previously run 3D simulations to maintain the integrity of the results. These results are compared in Appendix. The percent differences between the
2D and 3D results were negligible. The following shows the achieved results for the first run (run #: 0):
78
Figure 5.1a & b: Initial & Final 2D Setup of Forging
Process
Figure 5.2: 2D Simulation Z-Force Load {lbs} on Upper Die
79
Figure 5.3: 2D Simulation Maximum Final Temperature of
Upper Die Surface {°F}
Figure 5.4: 2D Simulation of Net Energy Supplied by Upper
Die {J}
80
Figure 5.5: 2D Results: Max. Effective Stress
{psi}
Figure 5.6: 2D Simulation of Maximum Sliding Velocity
{in/s} at Upper Die and Work-piece Interface
81
Figure 5.7: 2D Simulation of Maximum Contact Pressure
{psi} at Upper Die & Work-piece Interface
Figures 5.2 through 5.7 show the output results obtained from MSC.Superforge. Each image shows a colored contour image of the 2D blocker stage of the work-piece, upper and lower dies.
5.2 Validating Results
To validate the simulated results some basic areas
were examined. The results for the second stage forging
load was averaged out to roughly 435tons. This value is
82 within the supplied AAM range of 400-500tons for this forging cycle. Also high work-piece sliding velocity (seen in Figure 5.6) and high contact pressures (seen in Figure
5.7) indicate areas of high wear (according to Archard’s).
These areas are the very common areas in which wear was occurring on the real life dies. Also heat checks, from thermal fatigue, were observed on the surface which experienced the largest thermal gradient (shown in Figure
5.3).
5.3 Statistical Analysis of Results
The values for each output process were entered into
Minitab Statistical Analysis Software. Since the simulations were run using computer software, there are a few assumptions that are made:
1. The run order of the simulations had no bearing on the
out come of the tests
2. The simulations are repeatable, with accurate
repeatable results
3. No outside or environmental factors could affect the
simulations
To display the results of the design of experiment and the simulations, the data was formulated into “Normalized
Plot of the Effects Charts”. These charts display the data
83 with the non-significant effects following a normal distribution. Each chart is fitted with a linear trend- line and significant effects will vary from the normal distribution and have a high residual from the trend line.
The further the point from the line the larger the effects on the response variable.
These charts are graphed with a Significance Level
(α=.25), which states any values that has a t-value greater than the 0.25 significance level will be marked as a significant effect [Figure 5.8]. Once the die life prediction model is calculated the significance level will need to be readjusted to accurately calibrate the models, and remove any unnecessary effects calculations. This will help expedite the design process in the long run.
α<0.25 α<0.25
Figure 5.8: Normal Distribution Curve (α=.25)
84 “Yatesing” was employed for analyzing the data, and normalizing the plots [4] the Yates code for each run is shown in Table 5.1.
Table 5.2: Yatesing of Estimated Effect of Stroke Speed
EST. EFFECT OF STROKE SPEED {in/s} Z-Load Temp. Force Final Net Energy {lbf} {°F} {J} Upper Est. D Upper Upper (only) d - 1 = 3.490E+03 8.730E+01 -1.480E+04 ad - a = 1.480E+03 3.148E+01 -3.850E+04 bd- b = 2.632E+03 3.208E+01 -1.530E+04 abd – ab = 3.290E+03 2.716E+01 2.700E+03 cd – c = 3.500E+01 5.515E+01 2.360E+03 acd – ac = 2.700E+03 5.463E+01 2.700E+03 bcd - bc = 3.100E+01 4.140E+01 2.380E+03 abcd - abc = 3.837E+03 4.694E+01 4.140E+04 AVG = 4.839E+02 4.702E+01 -2.133E+03 Effective Sliding Contact Stress Velocity Pressure {Psi} {in/s} (Psi) WP-Die Est. D Upper Up Int Int. d - 1 = 2.780E+02 3.360E+00 6.060E+02 ad - a = 4.455E+03 3.380E+00 -2.580E+03 bd- b = 1.215E+03 3.210E+00 -5.260E+03 abd – ab = 1.038E+03 3.770E+00 -1.420E+03 cd – c = 2.096E+03 3.340E+00 1.720E+03 acd – ac = 1.089E+03 3.570E+00 -1.600E+02 bcd - bc = 1.621E+03 3.180E+00 1.230E+03 abcd - abc = 1.050E+03 3.510E+00 2.060E+03 AVG = 5.545E+02 3.415E+00 -4.755E+02
The Yates difference between specified runs (d-1=d, df-f=d, etc.) was performed to find the specific effect and
85 then average value of that effect. In Table 5.2 the yatesing for the estimated main effect of stroke speed is shown.
The averaged estimated effects of stroke speed on each of the various process outputs were graphed with the results of the other main effects, secondary, tertiary, and fourth order effects. The graph was setup with the effects as the independent variable, and the percent value as the dependent variable. Performed to determine which would produce the largest effect on the individual process outputs.
The normal probability plots are shown in Figure 5.9 through Figure 5.16 and span the range of effects of the process outputs found in Table 5.3. These charts were obtained from Minitab, but the calculations were checked using Microsoft Excel hand calculations.
86
5.3.1 Sliding Velocity: Normalized Plot & Analysis
Normal Probability Plot of the Effects (response is Sliding Velocity Up {in/s}, Alpha = .25)
99 Effect Type Not Significant 95 D Significant
90 C Factor Name AD AFriction 80 BDie Temp 70 CWP Temp t D Stroke Speed n 60 e
c 50 r 40 Pe 30 20
10 A
5 BC
1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Effect Lenth's PSE = 0.084375
Figure 5.9: Normal Probability Plot of the Effects for
Sliding Velocity {in /s}
The Figure 5.9 shows that the stroke speed (D) has the greatest effect on the sliding velocity. This is obvious, as the press speed increases the work-piece will be caused to flow at a faster pace. This increased sliding velocity would show an increase in die wear according to all the wear models discussed in Chapter 3, but maybe offset by an increase in work-piece temperature. Also shown in this
87 plot is that WP Temp (C) and the secondary interaction of
Friction and Stroke Speed each have a positive effect on sliding velocity greater than the significance level
(α=0.25). The main effect of friction causes a negative effect of -0.011, and the interaction of Die Temperature and WP Temperature cause the greatest negative effect of -
0.115.
5.3.2 Effective Stress: Normalized Plot & Analysis
Normal Probability Plot of the Effects (response is Effective Stress Up {psi}, Alpha = .25)
99 Effect Type Not Significant 95 AB Significant
90 Factor Name AFriction 80 BDie Temp 70 CWP Temp t D Stroke Speed n 60 e
c 50 r 40 Pe 30 20
10
5 C
1 -3000 -2000 -1000 0 1000 2000 3000 Effect Lenth's PSE = 1112.25
Figure 5.10: Normal Probability Plot of the Effects for
Effective Stress {psi}
88 The normal probability plot of the effects on the response of effective stress (Figure 5.10), show that the combination of Friction and Die Temperature (AB=1623.5psi) caused the most significant increasing effect on effective stress in the upper die of stage B. This increase in effective stress, increases the stress range, hence decrease cycles till mechanical fatigue failure (according to Wöhler S-N cycle) and would cause a more rapid propagation of cracks according to the fracture mechanics.
The WP Temperature (C=-2202.0psi) had the greatest decrease effect on effective stress. This would increase cycles until mechanical fatigue failure, but decrease the cycles until Thermo-mechanical Fatigue Failure (See Section
3.4).
89
5.3.3 Net Energy: Normalized Plot & Analysis
Normal Probability Plot of the Effects (response is Net Energy {J}, Alpha = .25)
99 Effect Type Not Significant 95 A Significant
90 CD Factor Name ABD AFriction 80 BD BDie Temp 70 CWP Temp t D Stroke Speed n 60 e
c 50 r 40 Pe 30 20 AB 10 B
5 C
1 -60000 -50000 -40000 -30000 -20000 -10000 0 10000 20000 Effect Lenth's PSE = 7380
Figure 5.11: Normal Probability Plot of the Effects for
Net Energy {J}
The normalized probability of the effects on Net
Energy, shown in Figure 5.11, displays the affect of the effects on the net energy possessed by the upper die in the forging process. The plots reveal that the main effect of
Friction (A=19131.5J) has the greatest effect on the net energy delivered by the upper die. The secondary interaction effect of WP Temperature and Stroke Speed was the second greatest (CD=14342.5J), followed by the interaction of Friction, Die Temperature, and Stroke Speed
90 (ABD=10047.5J) and Die Temperature and Stroke Speed
(BD=9927.5J).
These results are valuable for determining the volume of wear using the Stahlberg & Hallstrom approach. The WP
Temperature (C= -51432.5J) alone had the greatest negative effect on the net energy, this is do to the increased flow stress of the material requiring less force to forge the billet. The Die Temperature (B= -10432.5J) was the next largest negative effect, do to the reduction in heat transfer away from the work-piece, allowing it to maintain a higher temperature and lower flow stress continually throughout the cycle. The last significant interaction was the secondary interaction of Friction and Die Temperature
(AB= -9942.5).
91
5.3.4 Final Temperature of Surface: Normalized Plot & Analysis
Normal Probability Plot of the Effects (response is Temperature Up Surface {F}, Alpha = .25)
99 Effect Type Not Significant 95 B Significant
90 C Factor Name BD AFriction 80 BDie Temp 70 CWP Temp t D Stroke Speed n 60 e
c 50 r 40 Pe 30 20
10
5 D
1 0 100 200 300 400 500 Effect Lenth's PSE = 7.63125
Figure 5.12: Normal Probability Plot of the Effects for
Temperature of Upper Die Surface {psi}
The obvious effect of the design factor, die temperature level, had the greatest effect on the upper die surface temperature. The next closest effect and highest outside factor was the temperature of the work-piece
(C=66.9ºF). This is a result of the extended contact time between the work-piece and die surface. After the WP Temp, the interaction of Die Temperature and Stroke Speed had an
92 effect of 10.113ºF, which fell slightly above the significance level and is attributed to the increased friction energy dissipated through heat energy into the die.
The only significant negative effect measured was the
Stroke Speed (D=-47.013ºF), because heat transfer is a function of time, by decreasing the billet contact time with the upper die the amount of energy transferred is reduced.
Reducing the temperature increase of the die surface in effect reduces the thermal strain range of the die, therefore increasing the number of cycles until failure by thermal mechanical fatigue.
93
5.3.5 Z-Load Force: Normalized Plot & Analysis
Normal Probability Plot of the Effects (response is Z-Load Force Up Die {lbs}, Alpha = .25)
99 Effect Type Not Significant 95 AB Significant
90 ABD Factor Name AFriction 80 BDie Temp 70 CWP Temp t D Stroke Speed n 60 e
c 50 r 40 Pe 30 20
10 ABC
5 C
1 -6000 -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 Effect Lenth's PSE = 956.812
Figure 5.13: Normal Probability Plot of the Effects for Z-
Load Force on the Upper Die Surface {lbs}
The largest effect on the Z-Load Force was from the interaction of Friction and Die Temperature
(AB=2439.37lbs). This increase was expected, the increase in friction reduces the flow of material of the die therefore requiring more force to forge the ring gear.
The interaction of Friction, Die Temperature, and
Stroke Speed (ABD=2179.3lbs) caused a positive increase in
Z-load force as a result of adding a faster strain rate to
94 the interaction only slightly (260lbs) reduced the effect of the Friction and Die Temperature by themselves. The effect of WP Temperature had a decrease in the maximum forging load required by -5564.0lbs. This is a result of the decreased flow stress required to forge a part closer to its melting temperature. Reducing the maximum Z-Force load felt by the die reduces abrasive and adhesive wear according to Archard’s wear model. In addition, it reduces the chance of plastic deformation or plowing occurring in the die.
95
5.3.6 Surface Contact Pressure: Normalized Plot & Analysis
Normal Probability Plot of the Effects (response is Contact Pressure {Psi}, Alpha = .25)
99 Effect Type Not Significant 95 CD Significant
90 ABD Factor Name AFriction 80 BDie Temp 70 CWP Temp t D Stroke Speed n 60 e
c 50 r 40 Pe 30 20 B 10 AC
5 C
1 -10000 -7500 -5000 -2500 0 Effect Lenth's PSE = 761.25
Figure 5.14: Normal Probability Plot of the Effects for
Maximum Contact Pressure on the Upper Die Surface {psi}
The effect of WP temperature and Stroke Speed
(CD=1687.0psi) had the largest positive effect on material contact pressure on the die surface. The resultant increase in contact pressure has increasing effect on wear.
This is observed by all three mathematical models for wear, but most directly for the local energy wear approach in
Section 3.1.4.3. As indicated the WP Temperature (C = -
9620psi) had the greatest decreasing effect on contact
96 pressure. The absolute value of the effect of WP
Temperature dwarfs the positive effects of Stroke Speed and
WP Temperature. The decreasing effects of the secondary interaction of Friction and WP Temperature, is the result of the large decrease by WP Temperature on contact pressure.
5.4 Statistical Analysis Summation
The statistical analysis shown above gives a brief view of a way to eliminate significant time in analyzing the effects of various factors on intermediate outputs.
These intermediate outputs can then be used to calculate the number of cycles till die failure. Once this is attained the values for the significant level will need to be readjusted, allowing for more or less interactions to be accounted for. This will in the long run reduce significant computational time and will lead to a more accurate overall model. Also the need to employ fractional factorial analysis or Taguchi Method will also aid in the decrease in time consumption.
Currently, this statistical analysis may seem vague, but by determining which variables and interactions cause the greatest effect on the intermediate variables, future
97 expansions to different geometries, materials will be more efficiently calculated and identifiable.
Table 5.3: Summation of All Effects Studied
SIGNIFICANT EFFECTS Positive Negative RESPONSE STUDIED: Main 2nd 3rd Main 2nd EFFECTIVE STRESS C=- {psi} AB=1623.5 2202.0 A = CD = ABD = B = - AB = - NET 19.132 14.34 10.04 10.43 9.942 ENERGY {kJ} C = - BD = 9.93 51.43 B = FINAL DIE 448.13 BD =10.13 D SURFACE TEMP{F} C = 66.94 ABD = C = - Z-LOAD AB = 1713 1452.8 1448.3 FORCE {lbs} BCD = 1711.8 D = AD = A = - BC = - SLIDING 3.415 0.143 0.11 .115 VELOCITY {in/s} C = 0.168 MAX. CD = ABD = B = - AC = - CONTACT 1687.5 1217.5 1065 1490 PRESSURE C = - {psi} 9620
Code Actual Letter Friction A WP Temperature B Die Temperature C Stroke Speed D
98 CHAPTER 6
6.0 Conclusion
This research is a preliminary step in developing a universal metal forging die life equation. The point of researching (1)friction, (2)initial die temperature,
(3)work-piece temperature, and (4)forging press stroke speed effects on (1)die stress, (2)net energy, (3)sliding velocity, (4)contact pressure, (5)final surface temperature, and (6)load force is to ultimately predict the most likely mode of die failure. Once the most probable mode of die failure is calculated, a forecast of the forging press cycles until die failure can be determined.
The results of this research show that the forging process die outputs responses are affected significantly by only a small number of main effects, or interaction of those effects. The significance level for this research was set high (α=.25) showing that any effect that had an effect greater than 25%, above or below the zero effect was deemed significant. For instance, analysis of the load force [Figure 5.13] revealed that the only significant main effect was the change of work-piece temperature. As research on this subject is furthered, and actual effect of input processes on the cycles till failure is calculated,
99 the significance level of these primary studies can be altered to optimize the final equation.
6.1 Future Research & Recommendations To develop a full-scale die life model capable of predicting die failure mode, location and cycles, all the effects of forging inputs on die life must be researched and quantified [Figure 6.1]. This research will have to span the spectrum of forging temperatures, die formations, and estimate the effects of future die geometries. An equation can then be formulated that calculates the number of cycles till failure based off the significant process inputs raised to an empirically determined exponents
[Appendix].
As mentioned this is an extremely time consuming and tedious process that depends upon the accuracy of the measured empirical constants in the metal failure equations and upon the accuracy of the effects of the forging process inputs on the quantified outputs.
To decrease the massive time that is required for this research, finite element modeling and forging simulations must be incorporated, and its results must be validated via actual forging process results. Therefore, a faster method of determining actual significant forging effects on die
100 life can be estimated and non-significant effects will be
weeded out. This process will allow the time required to
develop the model decrease as the number of factors
incorporated is increased.
Figure 6.1: Complex Interactions of Forging Parameters
and Wear, Artinger [27]
6.2 Finale Just as the forging die life prediction equation itself will be a valuable tool in the cost reduction, design and optimization of forging dies for the forging industry, the research preformed for this thesis will be a valuable primary step in developing the die life equation.
101
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[29.] Schijve, Jaap. Fatigue of Structures and Materials. Kluwer Academic Publishers. Dordrecht, Netherlands. 2001.
[30.] Shivpuri, Rajiv. “Friction and Wear of Dies & Die Materials .” Adapted from “Wear of Dies and Molds in Net Shape Manufacturing.” Report ERC/NSM-88-05 N.S.F. Engineering Research Center, Ohio State University. 1998.
104 [31.] Shivpuri, R. Babu, Sailesh, & Ribeiro, Dilmarj. “Materials and Surface Engineering for Precision Forging Dies.” Precision Forging Consortium Ohio Aerospace Institute and National Center for Materials Sciences. June 10, 1999:
[32.] Simons, Eric N. Metal Wear: A Brief Outline. Fredrick Muller Limited. London Great Britain. 1972.
[33.] Sobczyk, K. Stochastic Approach to Fatigue: Experiments, Modeling, and Reliability Estimation. CISM, Udine. Italy. 1993.
[34.] Subramanian, C., Sumerville, E., & Venkatesan, J.,”Wear Process in Hot Forging Press Tools.” Materials & Design. Elsevier Science Ltd. Apr. 1996: 289-294. Vol. 16 Number 5.
[35.] Unknown. Product Design Guide for Hot Forging. Forging Industry Association (F.I.A.). www.forging.org. 2002.
[36.] Unknown. “Help Files.” MSC.Superforge 2004.
[37.] Weronski, Andrzej & Tadeusz Hejwowski. Thermal Fatigue of Metals. Marcel Dekker, Inc. New York, New York. 1991.
105
APPENDICES
Appendix A: American Axle Forging Specifications and AutoCAD Die Drawings Table A: American Axle Manufacturing Forging Specs: Ring Gear RG3709 As of Oct. 2003 Material Data: Work-piece = AISI 4320 Steel Die Material = H-13 Tool Steel AML-145 (Synthetic Lubricant = Graphite) Lubricant Temperature = Room Temperature Ambient Temperature = 70-75F
Surface Coating = No Surface Treatment = Nitriding (.008-.012dp) Die Surface Hardness = 45-48 Rockwell Forging Load = 1st Stage = <450 tons 2nd Stage = 450 to 600 tons 3rd Stage = 1950-2200 tons
Press Type = Diesel Mechanical Yoke Press Stroke Speed = 45 Strokes Per Minute Press Stroke Length = 14"
Workpiece Temperature Initially = 2300F Workpiece Temperature Finally = 2200F Die Surface Temperature Initially = 300F Die Surface Temperature Mid-Shift = 600F
Height Reduction = 1st = 6.5" to 3.22" 2nd = 3.22" to 2.215" 3rd = 2.215" to 1.906"
106
Appendix B: :Table B: MSC.Superforge Ring Gear Simulation Setup MODELS: Drawn in SolidEdge imported to Superforge via .stl files. AutoCAD Drawings in Appendix D. II. STAGE B - BLOCKER STAGE A. Upper Die = Dynamic with Heat Transfer 1) Model = RG (2) Blocker - Top Ins TF6706.stl 2) Material = H-13 Tool Steel Modified to meet ASTM Handbook Specs. 3) Press = Mechanical Scotch Yoke a) Stroke Length = 14" Total b) High Level Velocity (Chart B.1) 47 Strokes Per Min. c) Low Level Velocity (Chart B.2) 36 Strokes Per Min. 4) Friction = Combination Coulomb & Plastic Shear Theory a) High Level Friction µp = 0.7 µc = 0.7 b) Low Level Friction µp = 0.2 µc = 0.2 5) Die Temperature (initially) a) Heat Transfer Coefficient to Ambient = 50 {W/m^2*K} b) Heat Transfer Coefficient to Work-piece = 6000 {W/m^2*K} c) Emissivity for Radiation to Ambient = .25 Unitless d) High Level Temperature Tdie = 800F e) Low Level Temperature Tdie = 300F B. Lower Die = Rigid Stationary with Heat Transfer 1) Model = RG (2) Blocker - Bottom Ins TF6706.stl 2) Material = H-13 Tool Steel Modified to meet ASTM Handbook Specs. 3) Friction = Combination Coulomb & Plastic Shear Theory a) High Level Friction µp = .7 µc = .7 b) Low Level Friction µp = .2 µc = .2 4) Die Temperature (initially) a) Heat Transfer Coefficient to Ambient = 50 {W/m^2*K} b) Heat Transfer Coefficient to Work-piece = 6000 {W/m^2*K} c) Emissivity for Radiation to Ambient = .25 Unitless d) High Level Temperature Tdie = 800F
107 e) Low Level Temperature Tdie = 300F C. Work-piece 1) Model = Auto Shape – Cylinder a) Radius = 1.75" b) Height = 6.50" 2) Material = AISI_4337 Steel From MSC.Superforge Library, Customized to meet ASTM Handbook Specs. 3) Work-piece Temperature (initially) a) Heat Transfer Coefficient to Ambient = 50 {W/m^2*K} b) Heat Transfer Coefficient to Work-piece = 6000 {W/m^2*K} c) Emissivity for Radiation to Ambient = .25 Unitless d) High Level Temperature Twp = 2300F e) Low Level Temperature Twp = 1700F D. 2D Simulation = Axisymmetric Forging Process * Initially performed in 3D, but simulation took ~3hrs, results then compared to 2D which took less time E. Simulation Control = Forming Process 1) Stroke = 3.9136" (Once dies and WP are positioned) 2) Element Size a) Work-piece Element Size* = 0.10" b) Die Element Size* = 0.10" * Element size was chosen based on preliminary trial and error: result v. simulation time tradeoff. 3) Simulation Steps* = 10 Equal Divisions * Number of Steps were chosen based on preliminary trial and error: result v. simulation time tradeoff. 4) Forging Process = Closed Die with Flash F. Cooling Time 1)Cooling Time = 2 seconds G. Simulation 1) Check Data 2) Run Restart H. Die Stress Simulation Upper Die I. Die Stress Simulation Lower Die J. Results 1) Effective Stress - Upper Die 2) Effective Stress - Lower Die 3) Net Energy - Upper Die Chart 4) Z-Force Load Chart - Upper and Lower Loads 5) Temperature - Upper Die Surface 6) Temperature - Upper Die Interior 7) Temperature - Lower Die Surface 8) Temperature - Lower Die Interior 9) Maximum Sliding Velocity - Upper Die
108 10) Maximum Sliding Velocity - Lower Die 11) Contact Pressure - Work-piece/Die Interface
109
Appendix C: Material Properties
Table C.1: H-13 Steel, 0.008-0.012dp Nitride AISI H-13 Steel UNS T20813
Composition %C %Fe %Mn %Cr %Ni %Mo 0.20- 0.80- 0.32-0.45 96 0.50 1.20 .30 Max 1.1-1.75
Mechanical Properties Elastic Properties Param. SI Units English Units Density ρ1 7761 {kg/m^3} 0.2818 {lb/in^3}
45-48 45-48 Hardness Rockwell C HR (46) {NA} (46) {NA} Knoop HK 570 {NA} 570 {NA} Brinell 3000 HB 422-455 {NA} 455 {NA} Vickers Hv 549 {NA} 549 {NA} Tensile Strength, Ultimate σu 1.50E+09 {Pa} 2.18E+05 {psi} Yield σy 1.41E+09 {Pa} 2.04E+05 {psi} Elongation at Yield 0.13 % 0.13 % Reduction of Area 47 % 47 % Modulus of Elasticity E1 2.07E+11 {Pa} 3.00E+07 {psi} Bulk Modulus 1.40E+11 {Pa} 2.03E+07 {psi} Shear Modulus 8.10E+10 {Pa} 1.16E+07 {psi} Poissons Ratio V1 0.3 {NA} 0.3 {NA}
Plastic Properties SI Units English Units Minimum Yield Stress V1 4.00E+06 {Pa} 580 {psi} Yield Constant C1 0 {NA} 0 {NA} Strain Rate Hard Exp. M1 0 {NA} 0 {NA} Wear Coefficient K1 1.30E-04 {NA} 1.30E-04 {NA}
Thermal Properties {J/Kg- {BTU/lb- Heat Capacity C1 460 K} 0.11 degF} {BTU- Thermal Conduct. @ in/hr- 27C K1 17.6 {W/m-K} 122 ft²-°F} {BTU- at 204C K1 23.4 {W/m-K} 162 in/hr-
110 ft²-°F} {BTU- in/hr- at 649C K1 26.8 {W/m-K} 186 ft²-°F} Coeff. of Therm. {µm/m- {µin/in- Exp. @ 0C α1 10.40 K} 5.80 F} {µm/m- {µin/in- CTE @ 100C α1 11.30 K} 6.30 F} {µm/m- {µin/in- CTE @ 250C α1 12.40 K} 6.90 F}
111
Table C.2: 4320 Steel, Normalized above 1168K (1640ºf) AISI 4320 UNS G43200
Composition %C %Fe %Mn %Cr %Ni %Mo 0.17-0.22 96 0.55 0.5 1.83 0.25
Mechanical Properties Elastic Properties Param. SI Units English Units Density ρ2 7850 {kg/m^3} 0.284 {lb/in^3} Hardness, Rockwell C HR 21 {NA} 21 {NA} Knoop HK 255 {NA} 255 {NA} Brinell 3000 HB 232 {NA} 232 {NA} Vickers Hv 247 {NA} 247 {NA} Tensile Strength, Ultimate σu 7.93E+08 {Pa} 1.15E+05 {psi} Yield σy 4.60E+08 {Pa} 6.67E+04 {psi} Elongation at Break 20.8 % 20.8 % Modulus of Elasticity E2 2.05E+11 {Pa} 2.97E+07 {psi} Bulk Modulus 1.40E+11 {Pa} 2.03E+07 {psi} Shear Modulus 8.00E+10 {Pa} 1.16E+07 {psi} Poissons Ratio V2 0.3 {NA} 0.3 {NA} Izod Impact 73 {J} 53.8 {ft-lb}
Plastic Properties SI Units English Units Minimum Yield Stress V2 2.60E+07 {Pa} 3770.98 {psi} Yield Constant C2 0 {NA} 0 {NA} Strain Rate Hard Exp. M2 0 {NA} 0 {NA} Wear Coefficient K2 1.30E-04 {NA} 1.30E-04 {NA}
Thermal Properties {J/Kg- {BTU/lb- Heat Capacity C2 472 K} 0.114 degF} {BTU- Thermal in/hr- Conductivity K2 49.8 {W/m-K} 309 ft²-°F} Coeff. of Thermal Expansion α2 1.50E-05 {1/K} 8.37E-06 {1/degF}
112
Appendix D: Forging Press Velocity Curves
Figure F.1: Velocity v. Time Plot of Mech. Yoke Press
40
30 Upper Die 47 strokes per min Upper Die 36 strokes per min
20 } s / n
i 10 Stage A Figure F.2 e {
i BDC BDC
per D 0 0.0178 0.0245 0 0.005 0.01 0.015 0.02 0.025 0.03 ty of Up i c -10 lo Ve Figure F.3
-20
-30
-40 Time (s)
Velocity Curve of Low Level Stroke Speed(36ppmin) from Top of Work-piece to BDC (in/s)
0.00E+00 0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01 3.00E-01
-5.00E+00 )
-1.00E+01 Die (in/s
per Velocity (in/s) Up
city
o -1.50E+01 Vel
-2.00E+01
-2.50E+01 Time (s)
113
Velocity Curve of High Level Stroke Speed (47ppmin) from Top of Work-piece to
Time (s) for Stroke at 0.00E+00 0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01
-5.00E+00
-1.00E+01
) -1.50E+01
Mech Yoke at 47 parts per min city (in/s lo e -2.00E+01 V
-2.50E+01
-3.00E+01
-3.50E+01
114
Appendix E: Taylor’s Tool Life Equation
History: 1906, Frederick W. Taylor determined a relationship between cutting speed (V) and tool life (T). This formula of:
V * Tn = C Equation A.1: Taylor’s Tool Life Formula
This formula determines the tool life and is dependent upon the constants n and C. Graphed on a log-to-log graph this relationship provides the user with a linear relationship and an approximate time length till tool failure. This basic form of Taylor’s original study can be expanded to include more effecting variables and take on the form:
V * Tn * fn1 * dn2 = C Equation A.2: Expanded Taylor’s Tool Life Formula
In this expanded version, (f) represents the feed rate, and (d) represents the depth of cut. Both are raised to individual constants. Using this basic strategy a forging die life formula can be created. As an example:
n1 n2 n3 n4 n5 Nf = P * Td * Twp * V * H * t …… Equation A.3: Example of Die Life Prediction Formula (P) = Forging Load (Td) = Temperature of Die (Twp) = Temperature of Work-iece (V) = Velocity of Dies (H) = Hardness Ratio of Dies (t) = Forging Process Length (Nf) = Cycles till Failure Above is an example of how a die life prediction model could appear once research is finished.
115
Appendix F: ANOVA Tables from Statistical Analysis Statistical analysis of design of experiments is validated by the analysis of variance (ANOVA) of the effects. Pioneered by Ronald Fisher in the 1920’s, the research run in this experiment is a random effects analysis. 16 simulations were run resulting in 15 degrees of freedom.
General Linear Model: Z-Load Force, Temperature , ... versus Friction, Die Temp Factor Type Levels Values Friction fixed 2 0.2, 0.8 Die Temp fixed 2 300, 800 WP Temp fixed 2 1700, 2300 Stroke Speed fixed 2 8.4, 11.0
Analysis of Variance for Z-Load Force Up Die {lbs}, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Friction 1 737452 737452 737452 0.16 0.698 Die Temp 1 4111770 4111770 4111770 0.89 0.367 WP Temp 1 93629814 93629814 93629814 20.19 0.001 Stroke Speed 1 234983 234983 234983 0.05 0.826 Error 11 51017288 51017288 4637935 Total 15 149731306 S = 2153.59 R-Sq = 65.93% R-Sq(adj) = 53.54%
Analysis of Variance for Temperature Up Surface {F}, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Friction 1 3 3 3 0.02 0.890 Die Temp 1 803309 803309 803309 5418.02 0.000 WP Temp 1 17923 17923 17923 120.88 0.000 Stroke Speed 1 8841 8841 8841 59.63 0.000 Error 11 1631 1631 148 Total 15 831706 S = 12.1765 R-Sq = 99.80% R-Sq(adj) = 99.73%
Analysis of Variance for Net Energy {J}, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Friction 1 1464210225 1464210225 1464210225 7.07 0.022 Die Temp 1 435348225 435348225 435348225 2.10 0.175 WP Temp 1 10581208225 10581208225 10581208225 51.06 0.000 Stroke Speed 1 18190225 18190225 18190225 0.09 0.773 Error 11 2279581675 2279581675 207234698 Total 15 14778538575 S = 14395.6 R-Sq = 84.58% R-Sq(adj) = 78.97%
116 Analysis of Variance for Z-Force Up (Cht) {lbs}, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Friction 1 1.35387E+11 1.35387E+11 1.35387E+11 1.91 0.194 Die Temp 1 1.61765E+11 1.61765E+11 1.61765E+11 2.29 0.159 WP Temp 1 22710490000 22710490000 22710490000 0.32 0.582 Stroke Speed 1 38239802500 38239802500 38239802500 0.54 0.478 Error 11 7.77996E+11 7.77996E+11 70726936591 Total 15 1.13610E+12 S = 265945 R-Sq = 31.52% R-Sq(adj) = 6.62%
Analysis of Variance for Effective Stress Up {psi}, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Friction 1 1690000 1690000 1690000 0.55 0.476 Die Temp 1 39601 39601 39601 0.01 0.912 WP Temp 1 19395216 19395216 19395216 6.26 0.029 Stroke Speed 1 1229881 1229881 1229881 0.40 0.542 Error 11 34092486 34092486 3099317 Total 15 56447184 S = 1760.49 R-Sq = 39.60% R-Sq(adj) = 17.64%
Analysis of Variance for Sliding Velocity Up {in/s}, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Friction 1 0.048 0.048 0.048 2.33 0.155 Die Temp 1 0.000 0.000 0.000 0.00 0.946 WP Temp 1 0.112 0.112 0.112 5.40 0.040 Stroke Speed 1 46.649 46.649 46.649 2243.23 0.000 Error 11 0.229 0.229 0.021 Total 15 47.038 S = 0.144206 R-Sq = 99.51% R-Sq(adj) = 99.34%
Analysis of Variance for Contact Pressure {Psi}, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Friction 1 4225 4225 4225 0.00 0.971 Die Temp 1 4536900 4536900 4536900 1.49 0.248 WP Temp 1 370177600 370177600 370177600 121.51 0.000 Stroke Speed 1 902500 902500 902500 0.30 0.597 Error 11 33510950 33510950 3046450 Total 15 409132175 S = 1745.41 R-Sq = 91.81% R-Sq(adj) = 88.83%
117 Residual Plots for Net Energy {J} Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values 99 20000 90 10000 l t a n e
du 0 c 50 i r s Pe Re -10000 10 -20000 1 -30000 -15000 0 15000 30000 80000 100000 120000 140000 160000 Residual Fitted Value
Histogram of the Residuals Residuals Versus the Order of the Data
3 20000
10000 y l
2 a nc
du 0 i ue s q e r 1 Re -10000 F
-20000 0 -20000 -10000 0 10000 20000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Residual Observation Order
Residual Plots for Temperature Up Surface {F} Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values 99 10 90
l 0 t a n e du c 50 i r
s -10 Pe Re 10 -20
1 -30 -30 -15 0 15 30 400 600 800 1000 Residual Fitted Value
Histogram of the Residuals Residuals Versus the Order of the Data
6.0 10
y 4.5 l 0 a nc du i ue 3.0 s -10 q e r Re F 1.5 -20
0.0 -30 -30 -20 -10 0 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Residual Observation Order
118 Residual Plots for Z-Load Force Up Die {lbs} Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values 99 4000 90
l 2000 t a n e du c 50 i
r 0 s Pe Re 10 -2000
1 -4000 -5000 -2500 0 2500 5000 5000 7500 10000 12500 Residual Fitted Value
Histogram of the Residuals Residuals Versus the Order of the Data 6.0 4000
y 4.5 2000 l a nc u d ue 3.0 0 si q e r Re F 1.5 -2000
0.0 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Residual Observation Order
Residual Plots for Contact Pressure {Psi} Normal Probability Plot of the Residuals Residuals Versus the Fitted Values 99 2000 90 l t a n 0 e du c 50 i r s Pe Re -2000 10
1 -4000 -4000 -2000 0 2000 4000 12000 15000 18000 21000 24000 Residual Fitted Value
Histogram of the Residuals Residuals Versus the Order of the Data
4 2000
y 3 l a
nc 0 du i ue 2 s q e r Re -2000 F 1
0 -4000 -4000 -3000 -2000 -1000 0 1000 2000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Residual Observation Order
119 Residual Plots for Effective Stress Up {psi} Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values 99
90 1000 l t a
n 0 e du c 50 i r s -1000 Pe Re 10 -2000 -3000 1 -4000 -2000 0 2000 4000 3000 4000 5000 6000 Residual Fitted Value
Histogram of the Residuals Residuals Versus the Order of the Data
4.8 1000 y 3.6 l
a 0 nc du i ue s q 2.4 -1000 e r Re F 1.2 -2000
-3000 0.0 -3000 -2000 -1000 0 1000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Residual Observation Order
Residual Plots for Sliding Velocity Up {in/s} Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values 99
90 0.2 l t a n e du c 50 i r s 0.0 Pe Re 10
1 -0.2 -0.30 -0.15 0.00 0.15 0.30 11 12 13 14 15 Residual Fitted Value
Histogram of the Residuals Residuals Versus the Order of the Data 4
0.2
y 3 l a nc du i ue 2 s q
e 0.0 r Re F 1
0 -0.2 -0.2 -0.1 0.0 0.1 0.2 0.3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Residual Observation Order