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Chapter 4Surfaces, Tribology, Dimensional Characteristics, Inspection and
P d t Q lit AProduct Quality Assurance
Manufacturing Processes Prof. Tugrul Ozel
Surface Characteristics and Tribology
Surface conditions of a manufacturing part directly influence the processing and end use of that part:
• friction at tool/workpiece interface and wear of tools• effectiveness and control of lubrication during processing
(forging stamping rolling) and in end use (bearing shafts(forging, stamping, rolling) and in end use (bearing, shafts, all rotating and moving elements)
• appearance and the role of the surface in subsequent surface finishing operations (painting adhesive bondingsurface finishing operations (painting, adhesive bonding, coating)
• initiation of surface cracks and residual stresses that influence fatigue life and corrosion propertiesinfluence fatigue life and corrosion properties
• heat transfer and electrical conductivity between two bodies contacting each other
Manufacturing Processes Prof. Tugrul Ozel
Surface Structure and Properties
Unless the metal is process and kept in an inert (oxygen free) environment or it is a noble metal such as gold or platinum anenvironment, or it is a noble metal such as gold or platinum, an oxide layer usually develops on top of the work-hardened or amorphous layer.
FIGURE 4.1 Schematic illustration of the cross-section of the surface structure of metals. The thickness of the individual layers depends on processing conditions
d th i t S Aft E R bi i d B Bh h
Cross-Section of Metal Surface
Manufacturing Processes Prof. Tugrul Ozel
and the environment. Source: After E. Rabinowicz and B. Bhushan.
Examples of Oxide Layers•Iron oxide (FeO layer+Fe3O4 layer+Fe2O3layer)
•Aluminum oxide- Al2O3 (an amorphous layer)
•Copper oxide (Cu2O layer +CuO layer)
•Stainless steel – Chromium oxide CrO(passivation)
Manufacturing Processes Prof. Tugrul Ozel
Surface Structure and Properties
At microscale the surface of a manufactured part is not smooth and may show various different features:
•microcracks, craters, folds, laps, seams, inclusions, plastic deformation, residual stresses, oxide layerp , , y
•metallurgical transformations (heat affected zone, decarburization, recast layer, phase transformations,decarburization, recast layer, phase transformations, alloy depletion)
Manufacturing Processes Prof. Tugrul Ozel
Surface Finish and Surface Texture
•Surface finish should be considered in 3D. However, often the definition of surface parameters is based on a 2D profile sectionsection
•Flaws, or defects are random irregularities, such as cracks, scratches seams or tearsscratches, seams, or tears
•Lay, or directionality, is the direction of the predominant surface patternsurface pattern
•Roughness consists of closely spaced, irregular deviations
•Waviness is recurrent deviation from a flat surface
Manufacturing Processes Prof. Tugrul Ozel
Surface Finish
FIGURE 4 2 (a) standard terminology and symbols used to describe surface finish
Manufacturing Processes Prof. Tugrul Ozel
FIGURE 4.2 (a) standard terminology and symbols used to describe surface finish. The quantities are given in µ in. (b) Common surface-lay symbols.
Measuring gSurface
Roughness
FIGURE 4.4 (a) Measuring surface roughness with a stylus. The rider supports the stylus and guards against damage. (b) Path of the stylus in measurements of surface roughness (broken line) compared with the actual roughness profile. Note that the profile of the stylus’s path is smoother than the actual surface profile source; D. H. Buckley. Typical surface profiles produced by (c)than the actual surface profile source; D. H. Buckley. Typical surface profiles produced by (c) lapping, (d) finish grinding, (e) rough grinding, and (f) turning processes. Note the difference between the vertical and horizontal scales. Source: D. B. Dallas (ed.), Tool and Manufacturing Engineers Handbook, 3d. Ed. Copyright © 1976 , McGraw-Hill Publishing Company. Used with Permission.
Manufacturing Processes Prof. Tugrul Ozel
Measured Surface Roughness ProfileMeasured Surface Roughness Profile
FIGURE 4.3 Coordinates used for measurement of surface roughness, using Eqs. (4.2) and (4.2).
Manufacturing Processes Prof. Tugrul Ozel
Surface Roughness
Profile Height, Pt is the vertical distance between two parallel straight lines enveloping the acquired unfiltered profile within the evaluation length, lm.
Manufacturing Processes Prof. Tugrul Ozel
Surface Roughness
Surface roughness is generally described with 1 of 2 methods
R Arithmetic Mean Value the average of the absolute valuesRa- Arithmetic Mean Value- the average of the absolute values of the deviations from the center line of the surface
Ra b c d
=+ + + +⎛
⎜⎜
⎞⎟⎟
...Ra n
=⎝
⎜⎜⎜
⎠
⎟⎟⎟
Rq (formerly RMS)- Root Mean Squared-
Rq a b c dn
= + + + +2 2 2 2 ...
Both generally given in micrometers (microns) or microinches
1 μm = 10-6 m ≈ 40 μin human hair ≈ 40 μm
Manufacturing Processes Prof. Tugrul Ozel
1 μm 10 m ≈ 40 μin human hair ≈ 40 μm
Surface Roughness (continued)
Arithmetic mean value, (Ra)
a b c dL + + + +1Root-mean-square average, (Rq)R
Ly d x
a b c dna = =
+ + + +∫
1
0
. . .
Ra b c d
=+ + + +2 2 2 2 . . .
Rnq =
Manufacturing Processes Prof. Tugrul Ozel
Surface Roughness (continued)
Datum line AB is located such that the sum of the areas above the line is equal to the sum of areas below the qlineMaximum roughness height (Rt) is the height from theMaximum roughness height (Rt) is the height from the deepest valley to the highest peakValues R R Rt are given in μm or μin (1μm=40μin)Values Ra, Rq, Rt are given in μm or μin (1μm 40μin)Symbols for surface roughness
Manufacturing Processes Prof. Tugrul Ozel
Tribology: Friction, Wear and Lubricationgy ,Real Area of Contact
(a) Interface of two (b) the proportion of the apparent area contacting surfaces, showing the real areas of contact
to the real area of contact.
The ration of the areas can be as high as four to five orders of magnitude.
Manufacturing Processes Prof. Tugrul Ozel
Friction
Friction is defined as the resistance to relative sliding between two bodies in contact under a normal load. It is useful to consider that at microscale the interface between these two bodies is not entirely smooth and flat.
F/N A / A /Coefficient of friction
A B
μ= F/N= τAr/σAr=τ/σ
Ar ArB
Ar= real area of contact, junction, high stress, plastic deformation, adhesive bonding
Manufacturing Processes Prof. Tugrul Ozel
gB= area filled with oxides, lubricant or air
Coulomb Friction and Friction Factor
μτ τ
= = =F Af f f
N
F(1)μ
σ σN An nFf
Area, A
Co lomb LaCoulomb Lawμ= coefficient of friction
τ μσf n=
σConstant Shear Stress Law
m= friction shear factor
mkmff ===3
σστ (2)
Manufacturing Processes Prof. Tugrul Ozel
m friction shear factorf = friction factor 0 1≤ ≤m
Limits of Friction Force
Friction (continued)
Limits of Friction Force
3στ AkAAF =⋅=⋅=At values of larger N, it is better to use Constant Shear Stress Law of Friction,
3maxmax στ AkAAF
3σAF =
F3max σAF =
F/NFig 4.8
N
=F/Nμ
3σAF ≥mkmf == 3/στ
Manufacturing Processes Prof. Tugrul Ozel
Friction Force vs. Normal Force
FIGURE 4.6 Schematic illustration of the relation between friction force F and normal force N. Note that as the real area of contact approaches the apparent area, the friction force reaches a maximum and stabilizes. Most machine components operate in the first region. The second and third regions are encountered in metalworking operations, because of the high contact pressures involved between sliding surfaces, i.e., die and workpiece.
Manufacturing Processes Prof. Tugrul Ozel
Coefficient of Friction in Metalworking
COEFFICIENT OF FRICTION (μ)PROCESSCOLD HOT
RollingForging
0.05-0.10.05-0.1
0.2-0.70.1-0.2g g
DrawingSheet-metal formingMachining
0.03-0.10.05-0.1
0.5-2
-0.1-0.2
-
Table 4.1 Coefficient of friction in metalworking processes.
Manufacturing Processes Prof. Tugrul Ozel
Practical Values of Friction
Constant Shear Stress Law is more practical to use in forging while μ is more practical in sheet metal forming.
For various forming conditions, the value of m is:
0.05 to 0.15 in cold forging (conventional lubricant)0.2 to 0.4 in hot forging of steels (conventional lubricant)0.1 to 0.3 in hot forging of Ti & Ni alloys (with glass lubricant)0.7 to 1.0 in hot rolling (no lubricant)0.7 to 1.0 in hot rolling (no lubricant)
Manufacturing Processes Prof. Tugrul Ozel
Determination of Friction in Metal Forming
Lubricant and heat transfer interact. Therefore, friction test t id th ff t f t t (di hilli )must consider the effects of temperature (die chilling)
In hot forming, a good friction test must assure that:
a) specimen and die temperatures, and contact time between specimen & die must be the same as that in practice
b) surface / original surface must be approximately the same as that in practiceas that in practicec) relative velocity and surface pressure between deforming metal and dies must be the same as that in practice.
Manufacturing Processes Prof. Tugrul Ozel
The Ring Compression Test
The dimensions of the ring sample,The dimensions of the ring sample, temperatures and deformation speed must be selected to represent practical deformation conditions.
A flat ring is compressed bet een t o flatA flat ring is compressed between two flat platens. By measuring the I.D. of the deformed ring and comparing it with thedeformed ring and comparing it with the “calibration curves”, the value of μ or m can be determined.
Manufacturing Processes Prof. Tugrul Ozel
Friction and Barreling
FIGURE 4.7 (a) The effects of lubrication of barreling in the ring compression test: (a) With good lubrication, both the inner and outer diameters increase as the specimen is compressed; and with poor or no lubrication, friction is high, and the inner diameter decreases The direction of barreling depends on the relative motioninner diameter decreases. The direction of barreling depends on the relative motion of the cylindrical surfaces with respect to the flat dies. (b) Test results: (1) original specimen, and (2-4) the specimen under increasing friction. Source: A. T. Male and M. G. Cockcroft.
Manufacturing Processes Prof. Tugrul Ozel
The Ring Compression Test
Schematic of Metal Flow
Manufacturing Processes Prof. Tugrul Ozel
The Ring Compression Test
Manufacturing Processes Prof. Tugrul Ozel
Friction In Ring
Compression Tests
FIGURE 4.8 Charts to determine friction in ring compression tests: (a) coefficient of friction, µ; (b) friction factor m. Friction is determined from these charts from the percent reduction in height and by measuring the percent change in the internal diameter of the
specimen after compression
Manufacturing Processes Prof. Tugrul Ozel
specimen after compression.
WearWear is defined as the progressive loss or undesiredWear is defined as the progressive loss or undesired removal of materials from a surface. Wear has important technological and economic significance, especially if it alters the shape of the workpiece, tool and diealters the shape of the workpiece, tool and die interfaces, adversely affecting the manufacturing process include dull drill, worn cutting tools, and dies in metal working operations.
Adhesive wear takes place as shearing of the junction at the interface of two contacting bodies under a gtangential force. Adhesive wear is caused by sliding of the two bodies in contact. Based on the probability that a junction between two p y jsliding surfaces will lead to formation of a wear particle, the Archard wear law provides an expression for adhesive wear. LWkV
3=
Manufacturing Processes Prof. Tugrul Ozel
p3
Adhesive, Corrosive and Fatigue Wear
Abrasive wear is caused by a hard and rough surface, or a surface with hard protruding particles, sliding
i t th fagainst another surface.This type of wear removes particles by producing microchips, resulting in grooves or scratches on the
ft fsofter surface.
Corrosive wear, also called oxidation or chemical wear, i d b h i l l t h i l tiis caused by chemical or electrochemical reactions between the surfaces and the environment.
Fatigue wear is caused by surfaces being subjected to cyclic loading, such as in rolling contact in bearings.
Manufacturing Processes Prof. Tugrul Ozel
Adhesive Wear
FIGURE 4 10 Schematic illustration of (a) two asperities contacting (b) adhesionFIGURE 4.10 Schematic illustration of (a) two asperities contacting, (b) adhesion between two asperities, and (c) the formation of a wear particle.
Abrasive Wear
G S fFIGURE 4.11 Schematic illustration of abrasive wear in sliding. Longitudinal scratches on a surface usually indicate abrasive wear.
Manufacturing Processes Prof. Tugrul Ozel
Changes In Surface Profiles After Wear
FIGURE 4.9 Changes in originally (a) wire-brushed and (b) ground-surface profiles after wear. Source: E. Wild and K. J. Mack.
Manufacturing Processes Prof. Tugrul Ozel
Wear Coefficient LWkVp
kV3
=
UNLUBRICATED k LUBRICATED kMild steel on mild steel60-40 brass on hardened tool
steel
10-2 to 10-3
10-352100 steel on 52100
steelAluminum bronze on
10-7 to 10-10
10-8steelHardened tool steel on
hardened tool steelPolytetrafluoroethylene (PTFE)
ontool steel
10-4
10-5
Aluminum bronze onhardened steel
Hardened steel onhardened steel
10
10-9
f f ff
on tool steelTungsten carbide on mild steel 10-6
Table 4.2 Approximate order of magnitude for wear coefficient k in air
Manufacturing Processes Prof. Tugrul Ozel
Types Of Wear in Hot Forging
FIGURE 4 12 Types of wear observed in a single die used for hotFIGURE 4.12 Types of wear observed in a single die used for hot forging. Source: T. A. Dean.
Manufacturing Processes Prof. Tugrul Ozel
Lubrication
In plastic deformation, there are three basic friction conditions:
•Dry conditions (no lubricant, only oxide layers)
•Hydrodynamic lubrication (film thickness, larger than asperities, analysis possible)
•Boundary lubrication (asperity contact, empirical knowledge)
Manufacturing Processes Prof. Tugrul Ozel
Regimes of Lubricationa) Thick film b) Elasto-Hydrodynamicc) Dry contact d) Boundary film
FIGURE 4.13 Types of lubrication generally occurring in metalworking operations. Source: After W R D Wilson
Manufacturing Processes Prof. Tugrul Ozel
Source: After W. R. D. Wilson.
Characteristics of Lubricants Used in Metal Forming
•Reduce friction / good lubricity•Prevent sticking and gallingg g g•Provide good insulation especially in hot forming (glass as lubricant)•Reduce chemical reaction (inert)•Reduce erosion and wear (non-abrasive)Non polluting•Non polluting
•Easily applicable and removable (glass, graphite, dipping, spraying)p y g)•Available at reasonable cost
Manufacturing Processes Prof. Tugrul Ozel
Metal working fluidsMetal working fluids are used to:• Reduce friction• Reduce friction• Reduce wear, seizure, and galling• Improve material flow in dies and molds• Act as a thermal barrier between the workpiece and tool and die surfaces, thus
prevent workpiece cooling in hot working processes.prevent workpiece cooling in hot working processes.• Act as a release or parting agent to help in the removal or ejection of parts from
dies and molds.
Types:yp
1. Oils (mineral, animal, or vegetable based oils)2. Emulsion (a mixture of oil and water usually)3. Synthetic solutionsy4. Soaps5. Greases (semi-solid lubricants)6. Waxes (paraffin based)7. Solid lubricants
• Graphite• Molybdenum disulfide• Soft metals and polymer coatings• Glass
Manufacturing Processes Prof. Tugrul Ozel
• fullerenes
Surface Treatments, Coatings, and Cleaning
1. Improve resistance to wear, erosion, and indentationand indentation.
2. Control friction3. Reduce adhesion4. Improve lubrication5 I i t t i d5. Improve resistance to corrosion and
oxidation6. Improve fatigue resistance7. Rebuild surfaces on components
Manufacturing Processes Prof. Tugrul Ozel
8. Improve surface roughness9. Impart decorative features, color, or
special surface texture
Surface Treatments, Coatings, and Cleaning
1. Shot peening, water-jet peening, and laser shot peening2. Roller burnishing (surface rolling)3. Explosive hardening3. Explosive hardening4. Cladding5. Mechanical plating6. Case hardening7 H d f i7. Hard facing8. Thermal spraying9. Surface texturing10.Ceramic coatingg11.Vapor Deposition
1. Chemical vapor deposition2. Physical vapor deposition
12 Diffusion coating12.Diffusion coating13.Electroplating14.Anodazing15.Diamond-like Carbon coating
Manufacturing Processes Prof. Tugrul Ozel
Roller Burnishing Chemical Vapor Roller Burnishing Chemical Vapor Deposition (CVD)
The surface is cold A thermochemical process to worked by a hard polished roller.
pdeposit coatings on metal surfaces.
FIGURE 4.15 Examples of roller burnishing of (a) a conical surface and (b) a flat surface and the burnishing tools used Source: Cogsdill Tool Products
FIGURE 4.16 Schematic illustration of the chemical vapor deposition
Manufacturing Processes Prof. Tugrul Ozel
used. Source: Cogsdill Tool Products. of the chemical vapor deposition process.
Physical Vapor Deposition (PVD)
Main types of PVD• Ion Beam Sputtering
–the physical removal of material–Uses He or Ar ions to sputter material–Material deposits on substrate
• Electron Beam Evaporation–Employs high power E-Beam to
t t t t i levaporate target material
•Hard coatings for cutting tools
M lti l d ti f tti t l li ti•Multi-layered coatings for cutting tool applications
•Surgical tools
•Prosthetic devices
Manufacturing Processes Prof. Tugrul Ozel
•Self-lubricating coatings for bearing applications
Electroplating
A surface treatment i hi h thprocess, in which the
workpiece (cathode) is plated with a different pmetal (anode) in a bath containing water-base electrolyte solution
G SFIGURE 4.18 A coordinate measuring
hi i di i
electrolyte solution.
FIGURE 4.17 Schematic illustration of the electroplating process.
machine, measuring dimensions on an engine block. Source: Courtesy of Sheffield Measurement Division, Giddings & Lewis.
Manufacturing Processes Prof. Tugrul Ozel
Engineering Metrology
Engineering metrology is the science of measurement of dimensions such as length, angle, form, and position. It is critical f i t f t l f f t d t litof importance for control of manufactured part quality.
Accuracy is the agreement between the measured dimension and it t it dits true magnitude.
Precision (or repeatability) is the degree to which the instrument i t d tgives repeated measurements.
Resolution is the smallest dimension that can be read on an i t tinstrument.
Sensitivity is the smallest difference in dimensions that the i t t d t t di ti i h
Manufacturing Processes Prof. Tugrul Ozel
instrument can detect or distinguish.
Vernier Measuring Devices
•The fixed (main) scale gives the “coarse” measurement. Read the value before or even with the 0 on the sliding scale.
•The sliding (vernier) scale is used to discriminate between thereading of the main scale. Look for the line that matchesup with (one of) the coarse scale gradations for final value
Figure C-84, Kibbe ,et al.Machine Tool Practices
Aligned Next mark just inside vernier
5th Ed, Prentice Hall,1995.
Previous mark just inside vernierg ed
1.326”
Manufacturing Processes Prof. Tugrul Ozel
1.326
Figure C-90b, Kibbe ,et al. Machine Tool Practices 5th Ed, Prentice Hall,1995.
Micrometers
•Micrometers use a finely threaded screw to allow fine discrimination. The coarse scale (sleeve) divisions representth it h f th Th fi l (thi bl ) di id hthe pitch of the screw. The fine scale (thimble) divides each rotation into many (25) small increments.
•First get the coarse measurement from the fixed scale. Take thelargest value that can be seen below the rotating partlargest value that can be seen below the rotating part.
•The fine value is the largest value before the fixed 0.
0.072
0.237
Manufacturing Processes Prof. Tugrul Ozel
Figure C-134e, Kibbe ,et al. Machine ToolPractices 5th Ed, Prentice Hall,1995.
Figure C-134c, Kibbe ,et al. Machine ToolPractices 5th Ed, Prentice Hall,1995.
Gage Blocks
•Gage blocks provide an excellent way to establish a widevariety of heights.variety of heights.
•The key feature of gage blocks is the ability to stack themtogether in such a way as to drive out most of the air fromthe interface area this process is called “wringing”the interface area-- this process is called “wringing”
•Gage blocks are usually stacked-- this allows a small setto obtain virtually any height over a large range
•Gage blocks must be wrung when stacked-- otherwise the airlayer at the interface introduces error
•A properly wrung stack of gage blocks is held together byp p y g g g g yatmospheric pressure
Manufacturing Processes Prof. Tugrul Ozel
Sine Bar
The Sine Bar is a precision instrument used to measure orestablish anglesestablish angles
l
α
h
h
Manufacturing Processes Prof. Tugrul Ozel
h=l*sin(α), or α = sin-1(h/l)
Coordinate-M i M hiMeasuring Machine
Figure : (a) Schematic illustration of a coordinate-measuring machine. (b) A touch
(b) (c) (d)
Manufacturing Processes Prof. Tugrul Ozel
Figure : (a) Schematic illustration of a coordinate measuring machine. (b) A touch signal probe. (c) Examples of laser probes. (d) A coordinate-measuring machine with a complex part being measured. Source: (b) through (d) Courtesy of Mitutoyo Corp.
Coordinate-Measuring Machine for Car BodiesBodies
Figure 35.16 A large coordinate-measuring machine with two heads measuring various dimensions on a car body. Source: Courtesy of Mitutoyo Corp.
Manufacturing Processes Prof. Tugrul Ozel
Probes1. Contact
– touch trigger, analogscanning– scanning
– probe made of ruby– attaches to machines z-
axis– manually or motorized
2. Non-Contact– optical, laser– measuring small, narrow
complex shapesco p e s apes– objects that cannot be
measured by contact probe
Manufacturing Processes Prof. Tugrul Ozel
p– sharp workpiece images
CMM Errors
Systematic errorsreproducible between readingsreproducible between readingscaused by time, temp, probe deformation
Statistical errorsStatistical errorsmeasures quality of machineuncertainty of machines readingsuncertainty of machines readingssoftware cannot compensate
Manufacturing Processes Prof. Tugrul Ozel
Dimensional TolerancesDimensional Tolerance is defined as the permissible or acceptable variation in the dimensions (height, width, depth, diameter, angles) of a part. Tolerances are unavoidable because it is virtually impossible and unnecessary to manufacture two
t th t h i l th di i F th b lparts that have precisely the same dimensions. Further more, because close dimensional tolerances substantially increase the product cost, specifying a narrow tolerance range is undesirable economically.
•Basic size, deviation, and tolerance on a shaft, according to the ISO system.•Bilateral tolerances
Manufacturing Processes Prof. Tugrul Ozel
•Bilateral tolerances•Unilateral tolerances•Limit dimensions.
Tolerances and Surface Roughness
FIGURE 4.20 Tolerances and surface roughness obtained inroughness obtained in various manufacturing processes. These tolerances apply to a 25 mm (1 in )25-mm (1-in.) workpiece dimension. Source: J. A. Schey, Tribology in Metalworking: FrictionMetalworking: Friction, Lubrication, and Wear, ASM International, 1983.
Manufacturing Processes Prof. Tugrul Ozel
Engineering Drawing SymbolsSymbols
Figure: Geometric characteristic symbols to be indicated on engineering drawings of parts to be manufactured Source:parts to be manufactured. Source: Courtesy of The American Society of Mechanical Engineers.
Manufacturing Processes Prof. Tugrul Ozel
Quality assurance
• Quality assurance is the total effort by a manufacturer to ensure that its products conform to a detailed set of specifications and standards.• Quality must be built into a product• Total quality management
Statistical methods of quality control
• Sample size•Random sampling•Population•Lot size
Manufacturing Processes Prof. Tugrul Ozel
Frequency Distribution...Mean Arithmetic
21 +++ xxx n
( ) ( ) ( )...
deviation Standard
...
22
21
21
−++−+−=
+++=
xxxxxx
nxxxx
nn
n
σ1−n
σ
FIGURE 4.21 (a) A plot of the number of shafts measured and theirnumber of shafts measured and their respective diameters. This type of curve is called a frequency distribution. (b) A normal distribution curve indicating areas within each range of standard deviation. Note: The greater the range, the higher the percentage of parts that fall within it. (c) Frequency distribution curve, showing lower and upper specificationshowing lower and upper specification limits.
Manufacturing Processes Prof. Tugrul Ozel
Control Charts
RAxxUCLx 23 +=+= σ
RDUCLRAxxLCL
R
x
x
4
2
2
3=
−=−= σ
RDLCLR
R
3
4
=
FIGURE 4 22 C t l h t d iFIGURE 4.22 Control charts used in statistical quality control. The process shown is in statistical control, because all points fall within the lower and upper control limits. In this illustration, the sample size is five, and
Manufacturing Processes Prof. Tugrul Ozel
, p ,the number of samples is 15.
Control Chart Constants
SAMPLE SIZE A2 D4 D3 d223
1.8801.023
3.2672.575
00
1.1281.693
456789
0.7290.5770.4830.4190.3730 337
2.2822.1152.0041.9241.8641 816
000
0.0780.1360 184
2.0592.3262.5342.7042.8472 9709
10121520
0.3370.3080.2660.2230.180
1.8161.7771.7161.6521.586
0.1840.2230.2840.3480.414
2.9703.0783.2583.4723.735
Table 4 3 Constants for control charts
Manufacturing Processes Prof. Tugrul Ozel
Table 4.3 Constants for control charts.
Control Chart Examples
( ) P b i t b t f(a) Process begins to become out of control, because of factors such as tool wear. The tool is changed, and the process is then in statistical pcontrol.
(b) Process parameters are not set properly; thus, all parts are around the upper control limit.
( ) f(c) Process becomes out of control, because of factors such as a sudden change in the properties of the incoming material.
Manufacturing Processes Prof. Tugrul Ozel
the incoming material.