This document provides an overview of metal drawing operations. It discusses the introduction to drawing, general operations like conditioning materials, process descriptions for shapes like rods/wires and tubes. It covers process requirements including tools, equipment, dies and load calculations. The key points are that metal drawing is a process that uses tensile forces to reduce cross-sectional area and elongate metal by pulling it through a die, important factors include the amount of reduction, speed, material properties and temperature. It can produce various shapes like rods, wires and tubes for different applications.
Effect of Process Parameters on Micro Hardness of Mild Steel Processed by Sur...IOSR Journals
Surface grinding process can be utilized to create flat shapes at a high production rate and low
cost.. In this investigation, indigenously designed set up were used for evaluating the surface grinding process
was established. An experimental investigation was carried out to study the effect of surface grinding process
parameters i.e. Inlet pressure of coolant, grinding wheel speed, work-piece speed, and nozzle angle on the micro
hardness of the mild steel specimen. In the present study Horizontal spindle and reciprocating table type
surface grinding machine fitted with test rig is used and cutting fluid is applied through the convergent nozzle to
throw the cutting fluids at the cutting zone. In order to evaluate the effect of selected process parameters, one
variable approach has been used in the present study. Plots of various Micro Hardness responses have been
used to determine the relationship between the output response and the input parameters. The value of
microhardness of grinded mild steel work-piece varies from 292.63 to 370.73 HV
Forming operations are those in which the shape of a metal piece is changed by plastic deformation; for example, forging, rolling, extrusion, and drawing are common forming techniques.
Wear Analysis of Tool in Milling YTL7D SteelIJRES Journal
In the process of milling die steel YTL7D, the properties of high hardness and high wear resistance of
the workpiece material led to that the tool Subjected to severe wear, and the life of the tool is lower. In this
research, the wear law of rake face and flank face of the ball end mill was discussed. And the tool wear
mechanism in the process of milling YTL7D steel is revealed in this paper, to provide a theoretical guidance for
the development of rational process and follow-up studies.
Slide helps in generating an understand about the intuition and mathematics / stats behind association rule mining. This presentation starts by highlighting the difference between causal and correlation. This is followed Apriori algorithm and the metrics which are used with it. Each metric is discussed in detail. Then a formulation has been generated in classification setting which can be used to generate rules i.e. rule mining.
Other Reference: https://www.slideshare.net/JustinCletus/mining-frequent-patterns-association-and-correlations
This presentation gives a high level idea on the working of reinforcement learning and the general settings associated with it. Mainly this presentation presents the algorithms which are present in the reinforcement learning.
Slide explaining the distinction between bagging and boosting while understanding the bias variance trade-off. Followed by some lesser known scope of supervised learning. understanding the effect of tree split metric in deciding feature importance. Then understanding the effect of threshold on classification accuracy. Additionally, how to adjust model threshold for classification in supervised learning.
Note: Limitation of Accuracy metric (baseline accuracy), alternative metrics, their use case and their advantage and limitations were briefly discussed.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
1. 1
A Report on Metal
Drawing Operations
Submitted to: Prof. B.S.S. Daniel
Submitted by: Mohit Rajput
12216014
2. 2
Table of content
1) Introduction to drawing……………………………………………….. 3
2) General operations in metal drawing operation i.e. conditioning of
material................................................................................................... 6
3) Process description based on shapes obtained by drawing……………. 9
a) Rod and Wire Drawing……………………................................. 9
b) Tube drawing process………………………………………....... 10
4) Process Requirements- Tools and Equipment………………………… 13
a) Rod, bar and tube drawing……………………………………… 13
b) Wire Drawing…………………………………………………... 14
c) Tool- Die……………………………………………………….. 16
d) Other tools……………………………………………………… 17
4) Load Calculation………………………………………………………. 18
a) Analysis of wire drawing……………………………………….. 18
a) Analysis of wire drawing with friction…………………………. 19
5) Associated defects and how to avoid them……………………………. 21
6) References……………………….…………………………………….. 23
3. 3
1. Introduction:
Metal drawing is a manufacturing process to do bulk deformation in metal work is worked
upon to reduce its cross section area. The bulk deformation signifies the massive change in
shape and significant amount of deformation has been done. By forcing the work through a
die (mold) having smaller cross section area than work piece reduction in crossection is
achieved. In the drawing process metal work is drawn through a die by means of tensile force
which is applied at the outlet side. For the work flow through die a reduction in cross
sectional area takes place which results in corresponding increase in length.
The distinction between metal drawing and to metal extrusion process should be clearly
understood that being the force applied. In drawing operation work is being pulled through
the die opening while in extrusion the work is being pushed through the die.
The images below shows the concept and distinction between the two processes.
Image source [10] Metal Drawing
Image source [] A Typical metal drawing operation.
The avg. strain rate is proportional to the reduction in diameter d1/d0, the contact length l and the velocity υ.
4. 4
Image source [26] Metal Extrusion
Factor/ Parameter influencing the nature of product acquired by metal drawing operation
incorporates:
1. Amount of reduction
2. Geometry of cross section
3. Speed at which product is drawn
4. Material nature
a. Yield strength/flow stress.
b. Ductility.
c. Strain hardening.
d. Strain rate sensitivity.
e. Effect of temperature on yield strength and ductility.
f. Effect of hydrostatic pressure on yield strength and ductility.
g. Instability and fracture strength.
5. Temperature of working,
6. Die (mold)
a. Die material
b. Die angle
7. Friction and lubrication
In the process work will start yielding when the force required to pull the work piece through
a die exceeds its yield strength. In metal drawing yielding of work in this way is not desired.
In the process when the force needed to pull the work piece through a die exceeds yield
strength of work, it will start yielding which is undesired. Presence of friction causes
hampering to metal flow, heating and wearing of die, and because of its presence, excess
force needs to be applied. Theoretically the maximum possible amount of area reduction can
be obtained by preventing yielding of the work piece and is usually about 60%. In practice
5. 5
reduction in area range generally from 15% to about 45%. In order to achieve more reduction
in cross section area 2 or more dies are used in corresponding manner. When drawing every
step causes a reduction in cross area region consequently creating an increment long and
therefore a corresponding increase in speed is required in between each step. In wire drawing
methodology to conquer this issue “capstans” are used for both to accommodate the increase
in speed and also to apply tensile stress. To signify the reduction of a round crossection i.e.
difference between initial and final diameter the term ‘draft’ is usually used.
Image source [3] Metal Drawing processes causes
elongation of grain in work
Image source [3] Multi-pass is used get desired
crossection
Image source [3] Some of the products formed by drawing operation
6. 6
2. General operations in metal drawing operation i.e.
conditioning of material
The metal drawing process conditioning of the work piece is the initial step toward
manufacturing. Conditioning of work is usually performed to accomplish the desired
characteristics which may include higher reduction in cross section area, better surface finish,
enhanced mechanical properties or geometry. By tempering with work various properties can
be attained henceforth preparation of work is an essential operation and is done before as well
in between the drawing operation cycles. For the preparation of work heat treatment is done
as well as surface treatment like cleaning and covering are done furthermore pointing is
performed.
Heat treatment plays a very significant role in metal forming processes. Typically for metal
drawing procedure work preparation is started with annealing of work which is done to
fundamentally to remove the residual stress from it. In modern practices drawing procedure
are generally done cold this is done to accomplished higher dimensional exactness, smooth
surface completion, and to attain enhanced mechanical property. In practical cases these both
hot and cold working processes needs to be tailored in a way to get the desired property. In
hot working deformation will be done at a temperature greater than 0.6Tm where both
recovery and recrystallization process happens at the same time with deformation. In Cold
working temperature is kept well below 0.5Tm but sufficient to keep material malleable and
not induce crack while deforming, recovery process in this are ineffective. Recrystallization
in hot working causes the elimination of deformed work hardened grain takes place by the
formation of new strain free grains hence higher strain is achieved when utilizing hot
working. It is known that with increase in temperature flow stress of material decrease hence
a hot worked material could easily be deformed to the desired state. But absence of
recrystallization in cold working process work hardening is retained and hence high force is
required to further deform a material along with this large deformation won’t be possible
without causing fracture, unless work hardening is released by heat treatment. A general
practice in metal drawing operation is to annealing the work after each cycle till a close about
strain is achieved and then cold worked is done in order to get better surface completion and
more dimensional exactness.
Some of the procedure which also need to be done for the actual metal drawing process
include the conditioning of work surface for the generation of the surfaces which can easily
7. 7
hold lubrication for the easy draw ability of the metal through die, surface treatment is a
necessity. The procedure begins with cleaning of the surface which in modern practice is
done using shot blasting or dipping the work in a medium which is usually acidic. This is
followed up by the neutralisation process in which work piece is immersed in lime to remove
any traces of acid, work may then be dried. After the cleaning and neutralisation phase the
work is conditioned which involves the application of various type of chemical based on the
work material and process need. The main aim of these chemical is to help work surface to
sustain lubrication for easy draw ability and also the prevent work from atmospheric
consumption, even to material which are corrosion safe.
Lubrication plays a crucial role in metal drawing process and is applied on the work surface
along with this tool-work interface is also needed to be well lubricated. It is needed to be
applied for the reducing the friction coefficient which helps in easy flow of work from the die
along with reduced force, stickiness, power, tool wear, better surface finish and removal of
heat from the tooling. The consideration which needs to taken into account while choosing a
lubrication include:
Hot working or Cold working
Work material
Ease of application
Chemical reactivity with work material and tool
Cost
Type of lubrication
Dry Drawing: In this work and dies is completely immersed in lubricant
Wet Drawing: In this surface of the work to be drawn is coated with lubricant.
Coating: Work is coated with soft metal which acts as solid layer of lubricant.
Ultrasonic vibration of die and mandrel
8. 8
Once work is prepared it is worked upon its one end to make it pointed this is done in order
to allow the work to be inserted through the die as die opening is smaller than the original
cross section of bar. The end is then gripped at this end and the work is pulled through.
The last product is generally termed as Cold Finished or Cold Drawn on account of the fact
that the last drawing operation out of the many is always performed cold, this is done to
achieve better surface finish along with lesser resilience and enhanced mechanical properties.
Image source [3] A cross sectional view of die and a rod
Image source [27]
Pointed
9. 9
3. Process description based on the shapes that can be obtained
The metal drawing operation utilises the use of tensile forces for drawing the work. This
process usually involves plastic deformation caused because of drawing through the die
which reduces its cross section area, elongate it in length and extends the work piece grain in
longitudinal course. In the process distinctive cross area states of the metal work piece can be
attained to by changing the pass on likewise tubes can be drawn with the assistance of
mandrel. The shapes of the general drawn products include round and polygonal shapes
which may either be hollow or solid. The metal drawing process for rod, bar, wire and tube
drawing operation has been elucidated below.
Some Tube
Drawing
Products
Some Rod/
Bar Draw
products
Image
source [3]
a. Rod Drawing
Rod drawing (a.k.a. bar drawing) is a metal drawing process in which typically metal of lager
cross section is subjected to compressional forces by a converging die and hence thereby
causing plastic deformation reduction of cross section area. This standard is comparative for
both wire too for bar drawing operation just distinction being in the last cross section area of
the last product. The essential distinction in the middle of wire and bar drawing is last size
cross area of product i.e. if the product is under 5mm it will be prepared through wire
drawing procedure otherwise by bar drawing system are utilized. Other distinction between
these two is the use of greater feed stock if there should arise an occurrence of bar drawing
10. 10
this is done reason a same volume of stock will be extended significantly more when
decrease in cross area is done to lower quality. In wire drawing large amount of reduction in
cross area is required which is achieved by drawing wire subsequently through many die and
this process is a continuous process. Rod drawing is generally done in a single step.
Some of the uses of Rod and wire drawing:
Electrical wiring
Wires for mechanical application like wire framework
Structures construction
Wire rope
Wire fencing
Bolts
Rivets
Screw
Springs
Hand tools
Needles
Nails etc.
b. Tube Drawing
This metal drawing process is used to draw hollow shapes, particularly round hollow tubes
are the major products but hollow tubes with different shapes can be obtained too. In the
process by differing the size of mandrel and die variation in thickness can be achieved as well
as carious length and width/diameter can be achieved. Though need of mandrel in
unnecessary but in superfluous used to take into account the resilience which would have
been present if mandrel would not have been present also some time array of operation may
be needed for the generation of certain crossections. For the generation of longer tubes
floating mandrel type drawing is used in this the mandrel is not secured and are arranged in a
manner that the set up stay fit. For the era of tube with lower dimensional lapses gliding too
altered mandrel is utilized.
Tube drawing processes are delegated:
11. 11
Sinking
Plug Drawing
o Fixed plug
o Floating Plug
Mandrel drawing
Image source [10] In this tube is not provided
with any backing from inside and hence among
the wall thickness, internal and external
diameter only the ED is proper. The use of this
procedure (a.k.a. Tube sinking) is restricted
tubes with small ID.
Image source [10] In this tube is fitted with an
plug and tube is drawn through the hole present in
between the die and the madrel. In this product
take the dimension of of the spacing available in
the middle of plug and die hole.
Image source [10] In this procedure plug is not
attached to mandrel but rather is fitted in by
pushing into tube. The shape of this plug forces
it to stay in that position.
Image source [27] Here plug is not utilized instead
mandrel is constrained into tube. This mandrel and
tube is then pulled from one side.
Various tube drawing process.
12. 12
Some of use of tubes drawing
Container preparation
Boilers and heat exchangers
Pipes for transporting fluids
Automobile industry: for rear axle of vehicles
Fine capillary tubes
Tubes for special applications
Electronics
Aircraft
Medical etc.
13. 13
4. Process Requirements- Tools and Equipment
a) Rod, bar and tube drawing
As for rod, bars and tube which cannot be curled, drawing bench is utilized for the drawing
operation. For starting the procedure the pointed edge is fed into the drawing die and the tip
of the work is braced by jaws of the draw head. It is forced to move by the mean of forces
created by hydraulics causing the drawing of work through die and thereby causing plastic
deformation of work. The last shape obtained is in accordance to the die.
The tube drawing operation is very much similiare to rod and bar drawing but with the
additional use of mandrel for the internal diameter.
14. 14
Image source [10] General apparatus of the machines used drawing tubes, rods and bar
b) Wire drawing
In wire drawing operation drawing is done in numerous steps i.e. work is drawn from an
array of dies for the reduction in crossection area. As this process is cold run and higher
amount of strain is required, accordingly in between annealing is done for the removal of
strain hardening. When drawing each step causes a decrease in crossection area thereby
causing an increment in length and therefore a corresponding increment in speed is required
in between each stage. In procedure to overcome this issue “capstans” are used for both to
accommodate the increment in speed and also to apply tensile stress.
Wire drawing equipment working layout
15. 15
Image source [10] Picture above lays out the points of interest for the drawing operation for wire
For wire drawing operation Bull block (a.k.a. rotating draw) is a standard mechanical
assembly. Rotating draw creates a continuous tensile force on drawn wires. This mechanical
assembly is used for drawing very long wires.
Bull Block Apparatus for wire drawing
16. 16
c) Tool- Drawing die
For the industrial purposes dies used based on the requirement for the drawing operation and
cost. Usually mandrel and dies are made up of similar material. Material for die are usually
selected based on the facts given below:
• Tungsten Carbide: cheapest, larger die are accessible, shock resistance, minor life
expectancy, utilized for steel wire drawing.
• Natural Diamond: high thermal conductivity, wear safe, gives magnificent wire
surface, high life expectancy, limited accessibility in desired high quality and amount.
• Synthetic singlecrystal: Larger size extent, dependably a uniform material, high
thermal conductivity and gives incredible wire surface but is pricey right now.
• Polycrystalline Diamond: Shock safe, high life expectancy, Wear safe, cost
adequacy yet may get harmed at a temperature over 700 degree Celsius.
• Additional to this cast iron steel dies are utilized in hot working process. Usually for
the protection of Carbide and steel die are coated with titanium nitride and chromium.
Die design
As the work flow through the mold it passes
through distinctive sections the first section is a
bell opening. It doesn't touch the work however
helps in proper lubrication of the work and allow
for it easy entry in mold without damaging the
die.
After opening bell approach section is there, then
there is bearing surface. Bearing surface hold the
precise geometry for crossection for drawing. In
the end there is exit zone, these are planned in a
manner to protect drawn work.
Image source [10]
17. 17
Image source [27]
d) Some other tools
Pointer- it is utilized to put taper.
Pullin dogs – this is an instrument utilized for grasping the wire end at the way out of
die.
Butt welders – utilized for welding/ joining wire ends
18. 18
5. Load Calculation
a) Analysis of wire drawing
Consider the drawing of a wire through a frustum shaped draw die, as shown below,
Image source [4]. Schematic of wire drawing process
Some of the term associated with wire drawing are:
Area reduction (r) 𝑟 =
(𝐴 𝑜−𝐴 𝑓)
𝐴 𝑜
----------------------1
Drawing ratio (R) 𝑅 = 𝐴 𝑜/ 𝐴𝑓 = 1 ÷ (1 − 𝑟) ---------------------- 2
where, Ao initial cross section area
Af final cross section area
Some of the important parameter of drawing process are:
Strength of work material
Temperature
Speed of drawing
Co-efficient of friction
Die-angle
Reduction of area
Drawing ratio
Approximate expression based on strain energy or plastic deformation energy for drawing
force after ignoring friction and redundant work can be written as:
Draw pressure (p) 𝑝 = 𝑌 ln (
𝐴 𝑜
𝐴 𝑓
) = 𝑌 ln(𝑅) = 𝑌 ln(
1
1−𝑟
) --------------------3
Where, Y average flow stress of the material.
The Draw pressure is independent on draw ratio R.
As draw ratio is increased the draw pressure increases.
19. 19
b) Analysis of wire drawing with friction
Image source [4] Stresses acting on a small elemental section in the drawn body
Let’s consider an element in shape of frustum of the work inside the die.
Where,
As is the circular surface area of the element taken.
a is the half angle of the die.
Ao is the cross area of work at the die entry.
Af is the cross area at the die exit.
Surface area of element can be written as:
𝐴 𝑠 =
𝐴 𝑜−𝐴 𝑓
𝑆𝑖𝑛 𝛼
------------------------------4
Forces acting on the elemental work are:
𝐹𝑜𝑟𝑐𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑛𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝑝 𝐴 𝑠 sin 𝛼
𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑐𝑒𝑠 = 𝜇 𝑝 𝐴 𝑠 𝐶𝑜𝑠 𝛼
𝐷𝑟𝑎𝑤 𝐹𝑜𝑟𝑐𝑒 = 𝐹
Balancing the force:
𝑝 𝐴 𝑠 sin 𝛼 + 𝜇 𝑝 𝐴 𝑠 𝐶𝑜𝑠 𝛼 = 𝐹 ----------5
Substituting for As from 4, we get:
𝑝 (𝐴 𝑜 − 𝐴𝑓) + 𝜇𝑝(𝐴 𝑜 − 𝐴 𝑓)𝑐𝑜𝑡𝛼 = 𝐹
20. 20
𝐹 = (𝐴 𝑜 − 𝐴𝑓)𝑝[1 + 𝜇𝑐𝑜𝑡𝛼] -------------6
By considering a frictionless drawing operation p can be eliminated.
In absence of friction:
𝐷𝑟𝑎𝑤 𝑓𝑜𝑟𝑐𝑒 = 𝐹 = (𝐴 𝑜 − 𝐴𝑓)𝑝 = 𝑌′
ln (
𝐴 𝑜
𝐴 𝑓
) 𝐴 𝑜
From this, we can write:
𝑝 =
𝐴 𝑜
𝐴 𝑜− 𝐴 𝑓
𝑌′
ln(
𝐴 𝑜
𝐴 𝑓
) ------------7
Substituting 7 in 6, we get:
𝐹 = 𝐴 𝑜 𝑌′
ln(
𝐴 𝑜
𝐴 𝑓
)(1 + 𝜇𝑐𝑜𝑡𝛼) -------------8
Or, the draw stress with friction can be written as:
𝑝 = 𝑌′
ln(
𝐴 𝑜
𝐴 𝑓
)(1 + 𝜇𝑐𝑜𝑡𝛼) -----------------9
It can be seen from the above equation, that draw stress is dependent on the die angle.
It can be inferred from the above equation that higher the die angle, higher the draw stress
required
Schey equation can also be used for measuring the draw stress. It is given as:
𝜎 𝑑 = 𝑌′(1 +
𝜇
tan 𝛼
)𝜃ln(
𝐴 𝑜
𝐴 𝑓
) ------------9A
Where, 𝜃 = 0.88 + 1.2
𝐷
𝐿 𝑐
which accounts for redundant deformation and it is called
inhomogeneity factor.
D is average diameter of the billet,
Lc is contact length of the wire in the die.
𝐿 𝑐 =
𝐷 𝑜−𝐷 𝑓
2 sin 𝛼
and 𝐷 =
𝐷 𝑜+𝐷 𝑓
2
We can determine the draw force from 2.9A as:
𝐹 = 𝐴𝑓 𝜎 𝑑
21. 21
6. Associated Defects and how to dodge them
Defects associated with metal drawing includes:
Internal Cracking: This type of cracks are created due to generation of internal stresses to
which internal breakage of product around centerline may happen. The probable explanation
behind this are the improper flow of metal high die angle as well as low friction
Surface Defect: In these excessive force on surface because of friction wreckage is caused
this happens because of the presence of various micro defects on surface also if operated at
high speed.
Cupping defect: This is observed when in drawn work has uneven crossection. The
conceivable explanation behind this are:
Work is strain hardened to its limit.
Inclusions presence form weak spots.
Draft is too high.
If oil/lubrication wasn't appropriate for the process
Image source [20]
Countermeasures for defects in metal drawing process are:
For the prevention of defect metal flow should be properly controlled.
By the mean of lubrication friction between die and work needs to be tailored
properly
Mold selection should be properly.
Force required to pull the work piece should not exceed the metal yield strength.
22. 22
During Cold working performing low crossection reduction because of this surface of
the drawn part will have compressive residual stress at the surface which will
improves the product life.
Sometime straightening needed to be done which is done using mechanical equipment
Image source [11] Schematic showcasing the straightening1of drawn rod