Machine Design Databook Episode 3 part 8 docx

25-4 The equation relating the true rake angle to the corresponding chip flow angle The equation for locating the maximum rake angle The metal removal rate The approximate relationships b

25.1.2 Merchant’s circle for cutting forces

for a single-point metal cutting tool

The co-efficient of friction in orthogonal cutting

(Fig.25-3)

The shear force

The friction force

Mean shear stress

where

Ftor Fcð¼FzÞ ¼ tangential cutting force

perpendicu-lar to Fr(¼Fy) and Ff (¼Fx) in thevertical plane

Frð¼FyÞ ¼ radial force perpendicular to the

direction of feed and in the tal plane

horizon-Ff ð¼FxÞ ¼ feed force in the horizontal plane

against the direction of the feed

x, y and z are machine reference axes along feed force

Ff, radial force Fr, and cutting force Ftor Fc tions, respectively

φ ρ α

continuous chip Courtesy: ASTME, Tool Engineers’

Hand-book, 2nd Edition, McGraw-Hill Book Company, New

Work done in shearing the material

Work done in overcoming friction

The total work done in cutting

The shear angle (

The tangential cutting force

The values of K in Eq (25-12) are calculated from

m2¼ slope of Ftversus d graph (typical values 0.90 to1.4)

K ¼ overall correction coefficient, depends on actualconditions of tool angles and working condi-tions (varies from 0.9 to 1.0)

C ¼ coefficient characterized by material of job,condition of working tool, coolants, etc.(Table 25-1)

where

Km¼ material correction coefficient

K¼ correction coefficient, depends on back rackangle

Kc¼ correction coefficient for coolant used

K ¼ correction coefficient, depends on top rackangle

Values of Km, K, Kc, and K are taken from Tables25-2 and 25-3

TABLE 25-1

Values ofC and exponents

The chip flow angle

(Fig 25-4)

The equation relating the true rake angle to the

corresponding chip flow angle

The equation for locating the maximum rake angle

The metal removal rate

The approximate relationships between Ft ð¼FzÞ,

Ff ð¼FxÞ and Frð¼FyÞ

The turning moment on the work piece due to

tan-gential cutting force

rnþ ðd
rnÞ tan  ð25-13Þwhere rn¼ nose radius

 ¼ side cutting edge angle, deg

s ¼ feed rate, mm/rev

Q ¼ metal removal rate, cm3/min

The bending moment due to bending of the tool in the

vertical plane by tangential cutting force

25.1.3 Power

The total power at the cutting tool, Ptotal

After neglecting Pf and Pr, the power required at the

cutting tool, taking Vcfor Vtand Ptotal Pc

The gross or motor power

25.1.4 Specific power or unit power

Another relation connecting specific powers at

different cutting feeds and depths of cuts

Pr¼FrVr

1000¼ power required to feed in radial tion, kW The radial velocity is zero.Therefore Pris ignored

 ¼ mechanical efficiency of machine tool

Pt¼ tare power, the power required at no-load, kW

1000s1
m1d1
m2 ð25-25Þwhere Pc, Puin kW/m3/min, Ftin N, s and d in m,and Vcin m/s

Pu2¼ Pu1

s1s2

1
m1d1d2

1
m2

ð25-26Þ

25.1.5 Tool design

For comparison of Orthogonal Rake System (ORS),

Normal Rake System (NRS) and American (ASA)

tool nomenclature

25.1.6 Tool signatures

The tool signature of ASA, ORS and NRS

The tool signature for sintered carbide tipped single

TABLE 25-4

Typical values of specific power consumptionPsorPu

Comparison of tool nomenclature system

For general recommended various angles for HSS

m ¼ slope of the V curve

Side relief angle

Society of Tool and Manufacture Engineers, Fundamentals of Tool Design, Prentice Hall of India Private Ltd., New Delhi, 1969.

angle φ= side cutting edge angles

The velocity of the job or bar of diameter D1at speed

n1

m ’ 0:1 to 0.15 for high speed steels (HSS)

m ’ 0:2 to 0.25 for carbides

m ’ 0:6 to 1.0 got ceramicsand also taken from Table 25-7

V1¼ D1n1

TABLE 25-6

Recommended angle for high-speed-steel (HSS) single-point tools

High speed, alloy, and high-carbon tool

The velocity of the job or bar of diameter D2at speed

n2

For standard spindle speeds for machine tools

The relationship between the tool life, speed of cut,

feed and depth of cut

For standard speeds, feeds and etc

The approximate equation relating tool life to Brinell

’ 0:2 to 0.4 (average values)Refer to Tables 23-66 to 23-70

Recommended angles for carbide single-point tools

3 2 1

Tool life, t(min)

Courtesy: James Carvill, Mechanical Engineer’s Data

Ccf ¼ correction factor for the tool material (18-4-1HSS¼ 100) taken from Table 25-10

6

ffiffiffiffiffi60



r

¼ a factor which will correct the cutting speedfrom that obtained for a basic 60-minutetool life to the cutting speed for the desiredtool life

 ¼ tool life in minutesRefer to Fig 25-8

Refer to Fig 25-11

Refer to Fig 25-9

TABLE 25-9

Numerical value fork1

For machine tools with a straight line reciprocating

primary cutting motion

25.2.1 Lathe turning (Fig 25-9a)

The tangential cutting force

The maximum tangential force is also obtained from

equation

The maximum tangential cutting force in terms of

swing over the bed of the center lathe

(c) Planing machine

(b) Shaping machine

r

Editor, Machine Tool Design, volume 1, Mir Publishers, Moscow, p 21, 1968.

The maximum torque of the center lathe

The maximum swing over cross slide for universal

lathe

The maximum torque of the lathe by taking

hswðmaxÞ¼ 0:6hsw

The maximum feed force

The radial component of cutting force Fy ð¼FrÞ

(Fig 25-2)

The deflection of the tool taking into consideration

the effect of cantilever of tool

The maximum deflection of job or work piece in the

vertical plane due to cutting force Fc¼ Ft which

should not exceed 0.05 mm and Dw=Lw<1

The diameter of job or work piece

The length of job or workpiece which is equal to the

distance between centers of center lathe

The tangential component of cutting force is also

calculated from the equation

Another equation for the power due to tangential

component of cutting force

MtðmaxÞ¼ FtðmaxÞ

hswðmaxÞ2



ð25-37Þwhere hswðmaxÞ¼ maximum swing over cross-slidehswðmaxÞ¼ ð0:55 to 0:7Þhsw ð25-38Þ

MrðmaxÞ¼ 0:3FrðmaxÞhsw ð25-39Þ

Ff ¼ FxðmaxÞþ F
¼ 0:6FcðmaxÞ ð25-40Þwhere F
¼
Fr; FxðmaxÞ¼ 0:3FcðmaxÞ

Fr¼ reaction of the cutting force ¼ 2FcðmaxÞ

¼ coefficient of friction between bed of the latheand saddle¼ 0:15

l ¼ projected length of tool from the tool post, m

I ¼ moment of inertia of area of the cross-section ofthe tool (bh3=12)

b ¼ width of the tool shank, m

h ¼ depth of the tool shank, m

The torque

The minimum speed of work piece

The maximum speed of work piece

The bed width of lathe

The moment acting on tailstock body in the plane xz1

The moment acting on tailstock body in the plane xz2

The moment acting on tailstock body in the yz plane

For speeds and feeds for turning of metals and

plastics with HSS, carbide and Stellite tools

For cutting speeds and feeds for turning, facing and

boring of cast iron, non-ferrous and non-metallic

materials with HSS and carbide tools

25.2.2 Drilling machine

CALCULATION OF FORCES AND POWER IN

DRILLS (Fig 25-11)

For nomenclature of twist drills

The cutting speed for carbide tools may be taken as

where Mtin N m, Pcin kW, n0in rps and! in rad=s

where D ¼ diameter of job in mm

Mtxz1 ¼



Fz
Wj2

h ¼ lever arm of the vertical force, m (mm)

Fa¼ axial force with which tailstock center holds thejob, kN

Refer to Table 25-12

Refer to Table 25-13

Refer to Fig 25-11

Taper shank Tang

Tang

drive

Land Lip Web

Chisel edge

Chisel edge angle Margin

Drill diameter Body dia clearance

Clearance diameter Lip relief angle

Point angle

Shank

diameter

Shank length

Flutes Rakeor Helixangle

Flute length Overall

length

Body

Axis

Neck Straight shank

The equation developed experimentally and

analy-tically by Shaw and Oxford for torque of a twist

drill operating in an alloy steel with an hardness of

s0:8d1:8

1

cd

2



1þ

cd

0:2þ 3:2

cd

1:8

266

377

ð25-56Þwhere Mtin N m, c, s and d in m

TABLE 25-13

Cutting speeds and feeds rates for turning, facing and boring of cast iron, non-ferrous and non-metallic materials withHSS and carbide tools [Speed (at averageHB) for tool life of 112to 2 hours between grinds, m/min]

Key: 1 In case of shock and impact cuts, 70% of above speeds for carbide tools and 80% above speeds for HSS tools are used.

2 The above speeds are for cutting without cutting fluid.

3 A 10% reduction in the above speeds are recommended for soft, medium, hard, hard alloy and malleable irons.

The axial force or thrust acting on a drill

The equation for torque of a drill of regular

propor-tions whose c=d may be set equal to 0.18

The axial thrust for a drill of regular proportions

whose c=d is equal to 0.18

The equation for torque at the spindle of a drill based

on Brinell hardness number (HB)

The equation for axial thrust at the spindle of a

drill required for drilling which is based on Brinell

hardness number (HB)

Another equation for the turning moment on the drill

Another equation for the axial force acting on the





1þ

cd

0:2þ 2:2

cd

0:8

266

377

The constant C ¼ 2  106 for HSS drill drilling incarbon steel

Fa¼ 1:9  106

where Fain N, d and s in mThe constant C ¼ 1:9  106for HSS drill drilling incarbon steel

REAMERS (Fig 25-12)

The equation for torque of a reamer or core drill

The equation for axial thrust for a reamer or core drill

For tapping drill sizes for coarse threads

For cutting speeds and feeds for drills

For drill angles, cutting angles and cutting lubricant

for drilling with high speed steel drills

Mt¼ 37  106

Ks0:8d1:8

1

d1d

2



1þ

d1d

0:2

266

37

7 ð25-70Þwhere Mtin N m, s, d1and d in m

Fa¼ 2:7  109

Ks0:8d1:8

1

d1d

2



1þ

d1d

0:2

266

37

7 ð25-71Þ

where Fain N, s, d1and d in md1¼ diameter of hole to be enlarged, m

K ¼ a constant depending upon the number of flutes.Refer to Table 25-14

Courtesy: Wilson F W., Fundamentals of Tool Design, A.S.T.M.E.,

Prentice Hall of India Private Limited, New Dehli, 1969.

TABLE 25-15Tapping drill sizes for coarse threads

For elements of metal-cutting reamer

For reamer angles and cutting lubricants for reaming

with HSS reamers

25.2.3 Taps and tapping

Power, P, at the spindle of tap for tapping of V-thread

Refer to Fig 25-12

Refer to Table 25-18

P ¼ 6:3  10
3KmVpuc

0:15 þ1:75puc

ð25-72Þwhere

Km¼ material factor taken from Table 25-19

V ¼ cutting velocity, m/min

Cast iron

For material factor, Km, for use in drilling, reaming

tapping

For nomenclature of tap

For tip angles and lubricants for tapping with HSS

Body

Chamfer length

Margin

Chamfer relief Radial rakeangle

Chamfer-relief

width

Chamfer angle Straight flutes shown

(a)

Chamfer angle

Cutter sweep

Helical flutes right-hand helix shown

Actual size

Actual size

Helix angle Straight shank

Cast iron:

Length of square

Overall length 90…

Pitch

Internal center External center

Crest Flute

Thread angle Thread length

Positive rake angle

Chamfer length

Chamfer angle

Pitch diam

Axis

Root

Helix angle

Point diam

Thread half angle Front flank Rear flank

Major diam Minor diam

tapping calculations

Ultimate tensile

Tap angles and cutting lubricants for tapping with HSS taps

relief

Phenolic plastics, hard

rubber and fibers

a

25.2.4 Broaching machine

BROACHES (Figs 25-14 and 25-15) AND

BROACH-ING

For broach tooth form

For nomenclature of round pull broach

The allowable pull of internal or hole broach

The permissible load on push type of round broach

(Fig 25-15) using Euler’s column formula with both

ends free but guided

The allowable push in case of push type round

broaches when E ¼ 206:8 GPa in Eq (25-74)

Note: when (L=D) is greater than 25, a push broach is

considered as a long column and strength is based on

this If (L=D) is less than 25, the broach is considered

to act as a short column which resist compressive load

Faps¼ allowable push, N

A ¼ area of the minimum cross-section of broachwhich occurs at the root of the first roughingtooth or at the pull end, mm2

Back off angle Straight land

Land Pitch

Radius Depth

Rake angle

Pull end Front pilot

Shank Roughing teeth Semifinishteeth Finishingteeth Rearpilot supportRear

Broach "length"

Round hole broach Burnishing teeth

Follow rest grip Round hole broach with burnishers

Machine Tools Company.

The safe tensile stress for high speed steel

The number of teeth cutting at a time in case of

surface broaching

Sum of the length of all the teeth engaged at any

instant in broaching

The specific broaching/cutting force

n ¼ factor of safety to prevent broach damagebecause of sudden overloads due to hardspots in material, etc

n ¼ 3 or more dependent on slenderness ratio sut¼ tensile strength of the broach material, N/mm2

Dr¼ root diameter of the broach at 1=2L, mm

L ¼ length of broach from push end of first cuttingtooth, mm

sa¼ sut=n

as¼ 98 MPa for keyway broaches

as¼ 196 MPa for polygon broaches

as¼ 245 MPa for round/circular broaches

z ¼lmax

wherelmax¼ maximum length of workpiece, mm

p ¼ pitch of the broach teeth, mm

L ¼ Dz for circular/round broach ð25-77aÞ

ks¼ 4415 þ 3
108
24;515sz ð25-78Þwhere ksin N/mm2

Also refer to Table 25-21 for ks

TABLE 25-21

Specific broaching force,ks

The recommended speeds and feeds for broaching

The broaching force

Another equation for the broaching force in case of

key and splines broaching

¼ tensile strength of workpiece, N/mm2

 ¼ rack angle, deg

sz¼ rise per tooth, mmRefer to Table 25-22

F ¼ kksðDzÞsz for circular or round broaches

ð25-79aÞ

F ¼ kksðbzÞusszfor spline or key broaches ð25-79bÞ

F ¼ kksðlzÞszfor surface broaches ð25-79cÞwhere

b ¼ width of spline or key, mm

D ¼ diameter of broached hole, mm

l ¼ width to be broached in case of surface broach,mm

k ¼ coefficient (may be taken as 1.1 to 1.3)

z ¼ number of teeth engaged at a time

Recommended speeds and feeds for broaching

Another equation for the broaching force in case of

cylindrical broaching

The velocity of broaching

The power required for broaching by the broaching

machine

25.2.5 Milling machines

A knee horizontal-milling machine for plain or slab

milling

A knee-type vertical milling machine for face milling

For nomenclature and tool geometry of milling

cutters

For tool angles of millings cutters

The engagement parameter (Fig 25-19a)

where

C ¼ coefficient which takes into considerationcondition of cutting and characteristic of work-piece Taken from Table 25-25

sz¼ feed per tooth, mm (Table 25-25)m5¼ exponent taken from Table 25-25

 ¼ life of tool, min

su¼ stress of material, N/m2, from Table 25-24

Refer to Figs 25-18 and 25-19a

Refer to Table 25-26 and Figs 25-18 and 25-19a

k ¼ "¼

z



ffiffiffiffihD

r

ð25-84Þwhere

¼ engagement angle for milling depth, h

¼ 2

ffiffiffiffihD

For up-milling and down-milling processes

The minimum number of teeth for satisfactory cutting

action (Fig 20-19a)

The circumferential or circular pitch

Tool

Work surface

Workpiece

Machined surface

(b) Helical milling cutter

Column

Z

Y

X

The axial pitch

The number of teeth in engagement in case of plain

milling cutter whose helix angle is

The design equation for the number of teeth on

milling cutter

pa¼ pctan¼

ð25-90Þwhere b ¼ width of cutter, mm

z ¼ m ffiffiffiffiD

p

ð25-91aÞwhere m is a function of helix angle  Table 25-27gives values of m for various helix angles 

Base

Column

(a) Knee - type vertical milling machine

(b) Face milling cutter

Head

Table Saddle Knee

Z X Y

Work surface

Workpiece

Machined surface

milling Courtesy: G Boothroyd, Fundamentals of Metal

Machin-ing and Machine Tools, McGraw-Hill Book Company, New

Face of Tooth Back of Tooth Secondary clearance angle (α1) Primary clearance angle (α)

machine

25.2.5 Milling machines

A knee horizontal-milling machine for plain or slab

milling

A knee-type vertical milling machine for face...

Refer to Figs 25- 18 and 25-19a

Refer to Table 25-26 and Figs 25- 18 and 25-19a

k ẳ & #34 ;ẳ

z



hD

r

25 -84 ịwhere

ẳ engagement... class="text_page_counter">Trang 30

The axial pitch

The number of teeth in engagement in case of plain

milling cutter whose helix angle is

The design