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Monday, September 29, 2008

Bacterial Injection Machines

A. INTRODUCTION

The delivery of virulence factors directly into host cells is a fascinating aspect of pathogenesis. For Gram-negative bacteria to translocate virulence factors into host cells, at least three membranes must be passed (two bacterial and a host plasma membrane). Bacterial injection machines deliver virulence factors to a specific cellular location where they intersect and influence host mechanisms. This minireview focuses on the Gram-negative bacterial translocation systems that mediate type III and type IV secretion. Remarkably, although these systems are complex multiprotein structures, there is significant similarity and analogy in function, and thus a conserved mechanistic theme in pathogenicity emerges.

Currently there are seven identified types of macromolecular secretion systems in Gram-negative bacterial pathogens (1, 2). This minireview focuses on the two systems that deliver macromolecules directly into eukaryotic cells: type III secretion system (T3SS)1 and type IV secretion system (T4SS). The delivered macromolecules are referred to as effectors, as they affect and alter the host cellular process. Gram-negative bacterial effectors cross several biochemically distinct barriers, including the bacterial inner membrane, peptidoglycan layer, and outer membrane as well as the host plasma membrane, and even potentially intracellular host membranes. Plant pathogen effectors have the additional complexity of crossing the plant cell wall. The biochemistry of these delivery systems will be discussed, including what is known about how they are assembled and how they function.

B. TYPE III SECRETIONS SYSTEM

In the 1980s and 1990s researchers studying Yersinia, a genus that causes human diseases ranging from bubonic plague to gastrointestinal disease, found that the bacteria produced proteins that were thought to be associated with the outer membrane called Yops. Yops lacked classical signal sequences and were not secreted via a sec-dependent pathway and thus were assumed to be delivered by a new type of secretion system, which later became known as a T3SS, representing its order of discovery in secretion systems. In the last 10 years T3SS have been identified in more than 20 bacterial pathogens that infect plants and animals (Table I). Although there is a high degree of conservation among the components of the type III apparatus in different bacterial species, the pathogens often carry a distinct set of virulence factors with a variety of functions that can be translocated into either animal or plant cells. The overall theme of these T3SS is the direct delivery of proteins that alter and in effect "hijack" the infected host cell for the pathogen (reviewed in Refs. 3 and 4).

C. TYPE III APPARATUS COMPONENTS

Over 20 proteins are proposed to form a functional T3SS (Fig. 1A) (4, 5). YscN is thought to energize the secretion machinery, as it shares homology with the F0F1-ATPase and has an ATP-binding site. YscN from Yersinia and its homologue InvC from Salmonella typhimurium have been shown to have ATPase activity as mutations in the catalytic domain cause a loss of secretion (6, 7). YscN homologues are predicted to be located in the cytoplasm where they interact with membrane-bound components of the type III secretion apparatus, thereby energizing the system (4). It has been speculated that the ATPase polymerizes, by itself or with other components, to form the lower part of the T3SS, but this has not been shown. Lending support to this model, YscN has been shown to form a complex with three other cytoplasmic and/or inner membrane-associated Ysc proteins (8).

Many of the proteins involved in forming the T3SS have been localized or are predicted to be inner membrane proteins with varying numbers of transmembrane domains. For example the Yersinia YscV (LcrD) contains eight transmembrane domains and a large cytoplasmic C-terminal domain (9, 10). YscJ family members carry sec-dependent signal sequences and are lipoproteins (4, 11). The Pseudomonas syringae homologue HrcJ is associated with both inner and outer membranes (12), suggesting that it spans the periplasmic space.

Homologues of YscC (e.g. InvG, HrcC) are the only components of the type III apparatus that are clearly found in the outer membrane (1215). YscC belongs to a family of proteins (secretins) that are involved in transporting large molecules across the outer membrane probably by forming a channel (4). YscC and its homologues form a ring-shaped oligomeric complex in the outer membrane with approximately a 20-nm diameter. Experimentally it has been shown that InvG has a cleavable signal sequence at residue 25, indicating that secretins are exported by the sec-dependent pathway (16). It has been demonstrated that small outer membrane lipoproteins are required to increase the efficiency for the correct localization and functioning of the YscC homologues (13, 14, 1719). Recently we have shown that correct insertion and function of enteropathogenic Escherichia coli's (EPEC) EscC secretin in the outer membrane requires cytoplasmic and inner membrane components of the type III apparatus, namely EscN and EscV (20).

Sunday, August 31, 2008

METAL INJECTING MOLDING

Metal Injecting molding (MIM)
Metal injecting molding forms complex metal shapes without the need for machining. Any small shape which can be envisioned as a plastic molded part is now available to the designer in a variety of standard or custom metal formulations through his net shape forming process. Material properties can be specifically tailored to meet non-standard requirements.

Applications:

  • Surgical instruments
  • Electronic packaging
  • Automatic sensors
  • Implants
  • Tools

Materials:

Many popular materials are available, among them stainless steel, nickel iron, tungensten, copper, OHFC copper, molybdenum copper and tungsten alloys. Unique mixtures of compatible materials are possible.

Wednesday, August 6, 2008

Mass

Mass
Unit Name Symbol SI Equivalent
· a.u.of mass (electron rest mass)
mo,me
9.10938x10-31 kg
· assay ton

2.9167x10-2 kg
· atomic unit of mass (1H)
u,uma,AMU,Da(1H)
1.67353x10-27 kg
· atomic unit of mass (12C)
u,uma,AMU,Da(12C)
1.66054x10-27 kg
· atomic unit of mass (16O)
u,uma,AMU,Da(16O)
1.66001x10-27 kg
· attogram
ag
1x10-21 kg
· avogram

1.66036x10-24 kg
· bag(UK,cement)

42.6377 kg
· carat(metric)
ct.
2x10-4 kg
· carat(troy)
ct(troy)
2.05197x10-4 kg
· central
cH,cwt
45.3592 kg
· centigram
cg
1x10-5 kg
· dalton
u,uma,Da
1.66054x10-27 kg
· decagram
dag
1x10-2 kg
· decigram
dg
1x10-4 kg
· dram(troy)
dr (troy)
3.88793x10-3 kg
· dram or drachm
dr (ap), dr (apoth)
3.88793x10-3 kg
· dram or drachm (avoirdupois)
dr (av), dr (avdp)
1.77185x10-3 kg
· electront rest mass ( a.v.of mass )
mo,me
9.10939x10-31 kg
· exagram
Eg
1x1015 kg
· femtogram
fg
1x10-18 kg
· gamma (mass)
y
1x10-9 kg
· geepound (slug)
slug
14.5939 kg
· gigagram
Gg
1x106 kg
· grain (apothecary)
gr (apoth), gr (ap)
6.47989x10-5 kg
· grain (avoirdupois)
gr (avdp), gr (av)
6.47989x10-5 kg
· grain (troy)
gr (troy)
6.47989x10-5 kg
· gram
g
1x10-3 kg
· hectogram
hg
0.1 kg
· hundredweight(gross or long )
cH,cwt,lg cwt
50.8023 kg

Tuesday, August 5, 2008

Force

Force
Unit Name Symbol SI Equivalent
· a.u. of force
a.u.
8.23873x10-8 N
· crinal
crinal
0.1 N
· dyne
dyn
1x10-5 N
· gram force
gf
9.80665x10-3 N
· joule per centimeter
J/cm
100 N
· kilogram force
kgf,kgp
9.80665 N
· kilogram meter per square second
kg-m/s^2
1 N
· kilopound force
kipf
4448.22 N
· newton
N
1 N
· ounce force (av.)
ozf(av.)
0.278014 N
· pound force
lbf (av.),lbf
4.44822 N
· pound force foot per inch
lbf-ft/in
53.3786 N
· poundal
pdl
0.138255 N
· slug foot per square second
slug-ft/s^2
4.44822 N
· slug force

143.117 N
· square foot inch of mercury ( 0 C)
ft^2-inHg ( 0 C )
314.605 N
· square foot inch of mercury ( 15.56 C )
ft^2-inHg (15.56 C )
313.751 N
· ton force ( long )

9964.02 N
· ton force ( metric )

9806.65 N
· ton force ( short )

8896.44 N

Monday, August 4, 2008

Temperature

Temperature
Unit Name Symbol SI Equivalent
· celcius degree
C (273.15+1x) K
· fahrenheit degree
F (255.372+0.555556x) K
· kelvin
K 1 K
· rankine degree
R 0.555556 K

Temperature of color
Unit Name Symbol SI Equivalent
· mired

1x106 /K

Velocity change with temperature
Unit Name Symbol SI Equivalent
· foot per second per degree fahrenheit
ft/s-F 0.54864 m/s-K
· meter per second per degree celcius
m/s-C 1 m/s-K
· meter per second per kelvin
m/s-K 1 m/s-K

Sunday, August 3, 2008

Alloy Steels

A. General Information
Alloy steels comprise a wide variety of steels which have compositions that exceed the limitations of C, Mn, Ni, Mo, Cr, Va, Si, and B which have been set for carbon steels. However, steels containing more than 3.99% chromium are classified differently as stainless and tool steels.
Alloy steels are always killed, but can use unique deoxidization or melting processes for specific applications. Alloy steels are generally more responsive to heat and mechanical treatments than carbon steel.

B. AISI Designation
Typically, alloy steels are designated by distinct AISI (American Iron and Steel Institute) four-digit numbers. The first two digits indicate the leading alloying elements, while the last two digits give the nominal carbon content of the alloy in hundredths of a percent. Occasionally we see five-digit designations where the last three digits tell that the carbon is actually over 1%. Here is an example:

If a B shows up between the second and third digits of an AISI number, it means that this grade is a Boron steel; Sometimes a suffix H is attached to a AISI number to indicate that the steel has been produced to prescribed hardenability limits.

Up : XXX :x.xx% average carbon content

Down : 51100

13 xx:1.75Mn Manganese
23 xx:3.50Ni Nickle
31 xx:1.25Ni, 0.65-0.80Cr Nickle - Chromium
40 xx:0.20-0.25Mo Molybdenum
44 xx:0.40-0.52Mo
41 xx:0.50-0.95Cr, 0.12-0.30Mo Chromium - Molybdenum
46 xx:0.85-1.82Ni, 0.20-0.25Mo Nickle - Molybdenum
48 xx:3.5Ni, 0.25Mo
50 xx:0.27-0.65Cr Chromium
51 xx:0.80-1.05Cr
50 xxx:0.50Cr, 1.00C
51 xxx:1.02Cr, 1.00C
52 xxx:1.45Cr, 1.00C
61 xx:0.60-0.95Cr, 0.10-0.15V Chromium - Vanadium
92 xx:1.4-2Si, 0.65-0.85Mn, <0.65cr Silicon - Manganese
43 xx:1.82Ni, 0.50-0.80Cr, 0.25Mo Nickle - Chromium - Molybdenum
47 xx:1.05Ni, 0.45Cr, 0.20-0.35Mo
81 xx:0.30Ni, 0.40Cr, 0.12Mo
86 xx:0.55Ni, 0.50Cr, 0.25Mo
87 xx:0.55Ni, 0.50Cr, 0.25Mo
88 xx:0.55Ni, 0.50Cr, 0.20-0.35Mo
93 xx:3.25Ni, 1.20Cr, 0.12Mo
94 xx:0.45Ni, 0.40Cr, 0.12Mo

If a B shows up between the second and third digits of an AISI number, it means that this grade is a Boron steel; Sometimes a suffix H is attached to a AISI number to indicate that the steel has been produced to prescribed hardenability limits.

Saturday, August 2, 2008

Cooper

___ Cooper ___
29
Cu
63.546
Atomic Number 29
Atomic Weight 63.546
Electron Config. 2-2-6-2-6-10-1
Electron configuration order: 1s-2s-2p-3s-3p-3d-4s-4p-4d-4f-5s-5p-5d-5f-6s-6p-6d-7s

Mechanical Properties Conditions
Phase Temp. (K)
Density 8960 kg/m^3
Solid 298.15
Modulus of Elasticity 110.316 GPa
Solid 0
Thermal Expansion Coefficient 1.650x1o^-5/K
Solid 298.15

Electrical Properties Conditions
Temp. (K) Note
Electrical Resistivity 1.673x10^-8
293.15

Thermal Properties Conditions
Temp. (K) Pressure (Pa)
Melting Temperature 1357.77 K

101325
Boiling Temperature 2835.15 K

101325
Critical Temperature 8280 K


Fusion Enthalpy 208.7 J/g
0 101325
Heat Capacity 385 J/kg-K
298.15 100000
Thermal Conductivity 401 W/m-K
300 101325

Friday, August 1, 2008

Stainless Steel


A. General Information
Stainless steels are high-alloy steels that have superior corrosion resistance than other steels because they contain large amounts of chromium. Stainless steels can contain anywhere from 4-30 percent chromium, however most contain around 10 percent. Stainless steels can be divided into three basic groups based on their crystalline structure: austenitic, ferritic, and martensitic. Another group of stainless steels known as precipitation-hardened steels are a combination of austenitic and martensitic steels. Below are the general compositional contents of these groups.

B. Grades
Ferritic grades: Ferritic stainless steels are magnetic non heat-treatable steels that contain chromium but not nickel. They have good heat and corrosion resistance, in particular sea water, and good resistance to stress-corrosion cracking. Their mechanical properties are not as strong as the austenitic grades, however they have better decorative appeal.

Martensitic grades: Martensitic grades are magnetic and can be heat-treated by quenching or tempering. They contain chromium but usually contain no nickel, except for 2 grades. Martensitic steels are not as corrosive resistant as austenitic or ferritic grades, but their hardness levels are among the highest of the all the stainless steels.

Austenitic grades: Austenitic stainless steels are non-magnetic non heat-treatable steels that are usually annealed and cold worked. Some austenitic steels tend to become slightly magnetic after cold working. Austenitic steels have excellent corrosion and heat resistance with good mechanical properties over a wide range of temperatures. There are two subclasses of austenitic stainless steels: chromium-nickel and chromium-manganese-low nickel steels. Chromium-nickel steels are the most general widely used steels and are also known as 18-8(Cr-Ni) steels. The chromium nickel ratio can be modified to improve formability; carbon content can be reduced to improve intergranular corrosion resistance. Molybdenum can be added to improve corrosion resistance; additionally the Cr-Ni content can be increased.

Thursday, July 31, 2008

Aluminium

Aluminum

13
Al
26.981539
Atomic Number 13
Atomic Weight 26.981539
Electron Config. 2-2-6-2-1
Electron configuration order: 1s-2s-2p-3s-3p-3d-4s-4p-4d-4f-5s-5p-5d-5f-6s-6p-6d-7s

Mechanical Properties
Conditions
Phase temp. (K)
Density 2700kg/m^3
Solid
298.15
Modulus of Elasticity 62.053 GPa
Solid 0
Poisson Ratio 0.35 Solid
Thermal Expansion Coefficient 2.310x10^-5/K
Solid 298.15

Electrical Properties Conditions
Temp. (K)
Electrical Resistivity 2.655x10^-8 W-m
293.15

Thermal Properties Conditions
Temp. (K) Pressure (Pa)
Melting Temperature 933.47 K

101325
Boiling Temperature 2792.15K

101325
Critical Temperature 7850K


Fusion Enthalpy 397J/g

101325
Vaporization Enthalpy 10896.34J/g

101325
Heat Capacity 897J/Kg-K
298.15
100000
Thermal Conductivity 237 W/m-K
300
101325


Wednesday, July 30, 2008

Forging

A. Definition
Forging is the process by which metal is heated and is shaped by plastic deformation by suitably applying compressive force. Usually the compressive force is in the form of hammer blows using a power hammer or a press.

B. General Forging
Forging
refines the grain structure and improves physical properties of the metal. With proper design, the grain flow can be oriented in the direction of principal stresses encountered in actual use. Grain flow is the direction of the pattern that the crystals take during plastic deformation. Physical properties (such as strength, ductility and toughness) are much better in a forging than in the base metal, which has, crystals randomly oriented.

Forgings are consistent from piece to piece, without any of the porosity, voids, inclusions and other defects. Thus, finishing operations such as machining do not expose voids, because there aren't any. Also coating operations such as plating or painting are straightforward due to a good surface, which needs very little preparation.

Forgings yield parts that have high strength to weight ratio-thus are often used in the design of aircraft frame members.

A Forged metal can result in the following

Increase length, decrease cross-section, called drawing out the metal.
Decrease length, increase cross-section, called upsetting the metal.
Change length, change cross-section, by squeezing in closed impression dies. This results in favorable grain flow for strong parts



C. Forging Process

The metal can be forged hot (above recrystallization temperatures) or cold.

Open Die Forgings / Hand Forgings: Open die forgings or hand forgings are made with repeated blows in an open die, where the operator manipulates the workpiece in the die. The finished product is a rough approximation of the die. This is what a traditional blacksmith does, and is an old manufacturing process.

Impression Die Forgings / Precision Forgings: Impression die forgings and precision forgings are further refinements of the blocker forgings. The finished part more closely resembles the die impression.

Design Consideration:

Parting surface should be along a single plane if possible, else follow the contour of the part. The parting surface should be through the center of the part, not near the upper or lower edges. If the parting line cannot be on a single plane, then it is good practice to use symmetry of the design to minimize the side thrust forces. Any point on the parting surface should be less than 75º from the principal parting plane.
As in most forming processes, use of undercuts should be avoided, as these will make the removal of the part difficult, if not impossible.
Recommended draft angles are described in the following table.

Material Draft Angle (º)
Aluminum 0 - 2
Copper Alloys (Brass) 0 - 3
Steel 5 - 7
Stainless Steel 5 - 8

Generous fillets and radius should be provided to aid in material flow during the forging process. Sharp corners are stress-risers in the forgings, as well as make the dies weak in service. Recommended minimum radiuses are described in the following table.

Height of Protrusion
mm
(in)
Min. Corner Radius
mm
(in)
Min. Fillet Radius
mm
(in)
12.5
(0.5)
1.5
(0.06)
5
(0.2)
25
(1.0)
3
(0.12)
6.25
(0.25)
50
(2.0)
5
(0.2)
10
(0.4)
100
(4.0)
6.25
(0.25)
10
(0.4)
400
(16)
22
(0.875)
50
(2.0)

Ribs should be not be high or narrow, this makes it difficult for the material to flow.


Tolerances:

Dimension tolerances are usually positive and are approximately 0.3 % of the dimension, rounded off to the next higher 0.5 mm (0.020 in).
Die wear tolerances are lateral tolerances (parallel to the parting plane) and are roughly +0.2 % for Copper alloys to +0.5 % for Aluminum and Steel.
Die closure tolerances are in the direction of opening and closing, and range from 1 mm (0.040 inch) for small forgings, die projection area <>2 (23 in2), to 6.25 mm (0.25 inch) for large forgings, die projection area > 6500 cm2 (100 in2).
Die match tolerances are to allow for shift in the upper die with respect to the lower die. This is weight based and is shown in the the following table.

Material Finished Forging Weight
Trimmed kg (lb)
<> <> > 500
(> 1100)
Die Match Tolerance
mm (in)
Aluminum, Copper Alloys, Steel 0.75
(0.030)
1.75
(0.070)
5
(0.200)
Stainless Steel, Titanium 1.25
(0.050)
2.5
(0.100)
6.5
(0.260)

Flash tolerance is the amount of acceptable flash after the trimming operation. This is weight based and is shown in the following table.

Material Finished Forging Weight
Trimmed kg (lb)
<> <> > 500
(> 1100)
Flash Tolerance
mm (in)
Aluminum, Copper Alloys, Steel 0.8
(0.032)
3.25
(0.125)
10
(0.4)
Stainless Steel, Titanium 1.6
(0.064)
5
(0.2)
12.5
(0.5)

A proper lubricant is necessary for making good forgings. The lubricant is useful in preventing sticking of the workpiece to the die, and also acts as a thermal insulator to help reduce die wear.

Press Forgings: Press forging use a slow squeezing action of a press, to transfer a great amount of compressive force to the workpiece. Unlike an open-die forging where multiple blows transfer the compressive energy to the outside of the product, press forging transfers the force uniformly to the bulk of the material. This results in uniform material properties and is necessary for large weight forgings. Parts made with this process can be quite large as much as 125 kg (260 lb) and 3m (10 feet) long.

Upset Forgings: Upset forging increases cross-section by compressing the length, this is used in making heads on bolts and fasteners, valves and other similar parts.

Roll Forgings: In roll forging, a bar stock, round or flat is placed between die rollers which reduces the cross-section and increases the length to form parts such as axles, leaf springs etc. This is essentially a form of draw forging.

Swaging: Swaging - a tube or rod is forced inside a die and the diameter is reduced as the cylindrical object is fed. The die hammers the diameter and causes the metal to flow inward causing the outer diameter of the tube or the rod to take the shape of the die.

Net Shape / Near-Net Shape Forging: In net shape or near-net shape forging, forging results in wastage of material in the form of material flash and subsequent machining operations. This wastage can be as high as 70 % for gear blanks, and even 90+ % in the case of aircraft structural parts. Net-shape and near-net-shape processes minimize the waste by making precision dies, producing parts with very little draft angle (less than 1º). These types of processes often eliminate or reduce machining. The processes are quite expensive in terms of tooling and the capital expenditure required. Thus, these processes can be only justified for current processes that are very wasteful where the material savings will pay for the significant increase in tooling costs.


Tuesday, July 29, 2008

Reaming

A. Definition
Reaming is a process which slightly enlarges a pre-existing hole to
a tightly toleranced diameter.




B. General
Reamer is similar to a mill bit in that it has several cutting edges arranged around a central shaft, as shown below. Because of the delicate nature of the operation and since little material is removed, reaming can be done by hand. Reaming is most accurate for axially symmetric parts produced and reamed on a lathe.






C. Detailed Nomenclature for a Reamer
A more complete listing of reamer nomenclature is provided below.




D. Reamer Part Design
Reamed holes should not intersect with drilled holes, so the configuration below should NOT be implemented:





As with a drilled hole, clearance for chips is needed at the bottom of a reamed hole. This is illustrated below:





Reaming should not be relied upon to correct the location or alignment of a hole. Its primary purpose is to fine-tune the diameter of the hole.


Monday, July 28, 2008

Drilling

A. Definition
The process of using a multi - point tool to penetrate the surface of a workpiece and make a round hole.



B. General
Drilling is easily the most common machining process. One estimate is that 75% of all metal-cutting material removed comes from drilling operations.

Drilling involves the creation of holes that are right circular cylinders. This is accomplished most typically by using a twist drill, something most readers will have seen before. The figure below illustrates a cross section of a hole being cut by a common twist drill:





The chips must exit through the flutes to the outside of the tool. As can be seen in the figure, the cutting front is embedded within the workpiece, making cooling difficult. The cutting area can be flooded, coolant spray mist can be applied, or coolant can be delivered through the drill bit shaft. For an overview of the chip-formation process, see the chip formation section.

C. Characteristics
The characteristics of drilling that set it apart from other powered metal cutting operations are:
  • The chips must exit out of the hole created by the cutting.
  • Chip exit can cause problems when chips are large and/or continuous.
  • The drill can wander upon entrance and for deep holes.
  • For deep holes in large workpieces, coolant may need to be delivered through the drill shaft to the cutting front.
  • Of the powered metal cutting processes, drilling on a drill press is the most likely to be performed by someone who is not a machinist.
D. Drill Press Work Area
A view of the metal-cutting area of a drill press is shown below. The workpiece is held in place by a C-clamp since cutting forces can be quite large. It is dangerous to hold a workpiece by hand during drilling since cutting forces can unpredictably get quite large and wrench the part away. Wood is often used underneath the part so that the drill bit can overshoot without damaging the table. The table also has holes for drill overshoot as well as weight reduction. A three-jaw chuck is used since three points determine a circle in two dimensions. Four-jaw chucks are rarely seen since offset of the bit is not necessary. The next section contains illustrations of drill bit chuck. To get an idea of the differing configurations of three and four-jaw chucks, please see the equivalent lathe chuck .


Sunday, July 27, 2008

Drilling rpm




n = Vc x 1000 / phi x d





Explanation :
  • n = rpm
  • Vc = Cutting Speed in m/min
  • Phi = Constanta 3,14 or 22/7
  • d = Drill diameter

Saturday, July 26, 2008

Milling Rpm




n = Vc x 1000 / phi x d




Explanation :
  • n = rpm
  • Vc = Cutting Speed in m/min
  • Phi = Constanta 3,14 or 22/7
  • d = Cutter diameter

Friday, July 25, 2008

Material Removal Rate - Machining Power


Chip section

A
= a x s (mm^2)

Material removal rate

V
= a x s x u (cm^3/min)

Tangential cutting force

F
= a x s x Ks ( kgf/mm^2)

Machining power

P = a x s x Ks x V / 60 x 120 x efficiency

Explaination :

  • a = depth of cut
  • s = feed in mm/rev
  • V = cutting speed in m/min
  • Ks = spesific cutting force kgf/mm^2