Machine Design Databook 2010 Part 13 pps

c distance from the neutral axis of section to outer fiber, m incorrected for inertia effects of the piston and otherreciprocating parts, kN lbf Fc the component of force F acting along t

c distance from the neutral axis of section to outer fiber, m (in)

corrected for inertia effects of the piston and otherreciprocating parts, kN (lbf )

Fc the component of force F acting along the axis of connecting

rod, kN (lbf )

Fic magnitude of inertia force due to the weight of connecting rod

itself, kN (lbf )

Fr total radial force acting on the crankpin, kN (lbf )

F
total tangential force acting on the crankpin, kN (lbf )

i0¼ lo

do ratio of length to diameter of crank

K¼Di

Do ratio of inner to outer diameter of a hollow shaft

the computed bending moment

the computed twisting moment

r radius, throw of crankshaft, m (in)

Other factors in performance or special aspects which are included from time to

time in this chapter and are applicable only in their immediate context are not

given at this stage

FORCE ANALYSIS (Fig 24-1)

The radial component of force Fc acting along the

axis of connecting rod (Fig 24-1)

The tangential component of force Fcacting along the

axis of connecting rod (Fig 24-1)

The radial component of force Fic(Fig 24-1)

The tangential component of force Fic(Fig 24-1)

The total radial force acting on the crank

Fc1¼ Fccosð
þ Þ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiF

1

sin

The total tangential force acting on the crank

The resultant force on the crankpin

From Eqs (24-10) and (24-11) neglecting t=2 and

eliminating lothe equation for crankpin diameter

Empirical relation to determine the length of crankpin



ð24-9Þ

¼ Fcomb lwhere l¼lo

2þ c2¼ distance from centroidal axis

to the application of load (Fig 24-2), m (in)

do¼ 3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi32lFcomb

b

s

ð24-10Þwhereb¼ allowable bending stress, MPa (psi)

do¼Fcomb

do¼ 4

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi16F2 comb

Another relation for the crankpin length/diameter

ratio

Another relation for the crankpin diameter

HOLLOW CRANKPIN

The crankpin length/diameter ratio

The crankpin outside diameter

Crank arm

CRANK ON HEAD-END DEAD-CENTER

POSITION

When the crank is on the head-end dead-center

posi-tion, the section XX (Fig 24-2) of the arm is subjected

to bending moment

The direct compressive stress due to the load Fcomb

(i.e., more specifically by its component Fc)

The resultant stress in the crank arm at XX

CRANK ON CRANK-END DEAD-CENTER

POSITION

The direct tensile stress in the plane of the hub of

crankshaft section passing through the shaft center

due to load Fcomb(Fig 24-2)

The bending stress in the section due to bending

A¼ area of cross section of the arm at XX, m2(in2)

c¼ distance from the neutral axis of section to outerfiber of arm, m (in)

I¼ moment of inertia of the section, cm4

The resultant stress in the plane of the hub of

crank-shaft section passing through the crank-shaft center

CRANK PERPENDICULAR TO THE

CONNECTING ROD

The bending moment in the plane of rotation of the

crank

The bending stress

The torsional moment

The shear stress

The maximum normal stress for crank made of cast

iron

The maximum shear stress for the crank made of steel

DIMENSION OF CRANKSHAFT MAIN

BEARING (Fig 24-2 b)

The shaking force on the main bearing from F and Fr

(Fig 24-1b)

The diameter of main bearing taking into

considera-tion the bearing pressure on the projected area of

the crankshaft

The bending movement on the crankshaft

The torque on the crankshaft

The diameter of crankshaft taking into consideration

indirectly the fatigue and shock factors

lm¼ length of bearing, m (in)

p¼ allowable bearing pressure, MPa (psi)

l1¼lo

2þ h2þlm

2where

h2¼ hub length, m (in)

lo¼ length of crankpin, m (in)

lm¼ length of bearing on crankshaft, m (in)

where r¼ throw of the crank, m (in)

dm¼ 3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi16

The length of main bearing

Center of bearing

CENTER CRANK (Fig 24-6)

Crankpin

The maximum bending moment treating the crankpin

as a simple beam with concentrated load at the center Mbc¼Fcombðloþ h þ lmÞ

where

lo¼ length of crankpin, m (in)

lm¼ length of main bearing, m (in)

h¼ thickness of cheek, m (in)

0.825B + 9

to 0.6B 31B + 9.5

The diameter of the crankpin based on maximum

bending moment Mbc

The diameter of crankpin based on bearing pressure

between pin and the bearing

Dimensions of main bearing

The maximum bending moment treating the center

crank as a simple beam with load concentrated at

the center

The twisting moment

The diameter of crankshaft at main bearing taking

into consideration the fatigue and shock factors

The diameter of the crankshaft based on bearing

pressure

American Bureau of Shipping formulas for

center crank

The thickness h of the cheeks or webs (Fig 24-6)

The diameter of crankpins and journals (Fig 24-6)

The thickness h and the width b of crank cheeks must

satisfy the conditions

do¼ 3

ffiffiffiffiffiffiffiffiffiffiffiffiffi32Mbc

b

s

ð24-37Þwhereb¼ design stress, MPa (psi)

e

KbMbbþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðKbMbbÞ2þ ðKtMtÞ2q

b

s

ð24-44Þwhere

a¼ coefficient from Table 24-1A

D¼ diameter of cylinder bore, m (in)

p¼ maximum gas pressure, MPa (psi)

c¼ distance over the crank web plus 25 mm (1.0 in)(Fig 24-6)

b¼ allowable fiber stress, MPa (psi)

EQUIVALENT SHAFTS

A portion of a shaft length l and diameter d can be

replaced by a portion of length leand diameter de

The length heequivalent to crank web

The equivalent length crankshaft leof Fig 24-7 varies

between

The equivalent length of commercial crankshaft

for solid journal and crankpin according to Carter

(Fig 24-8)

The equivalent length of commercial crankshaft for

hollow journal and crankpin according to Carter

(Fig 24-8)

The equivalent length of crankshaft for solid journal

and crankpin according to Wilson (Fig 24-8)

The equivalent length of crankshaft for hollow

jour-nal and crankpin according to Wilson (Fig 24-8)

EMPIRICAL PROPORTIONS

For empirical proportions of side crank, built-up

crank, and hollow crankshafts

The film thickness in bearing should not be less than

the values given here for satisfactory operating

condi-tion:

Main bearings

Big-end bearings

The oil flow rate through conventional central

circumferential grooved bearings

le¼ l



ded



eþ 0:8a

D4 þ0:75b

D4 c



eþ 0:4DJ

D4 þbþ 0:4Dc

D4 c

þr
0:2ðDJþ DcÞ

ac3

ð24-51Þ

Le¼ d4 e

þr
0:2ðDJþ DcÞ

ac3

ð24-52Þ

For oil flow rate in medium and large diesel engines at

The delivery pressure in modern high-duty engines

For housing tolerances

where

Q¼ oil flow rate, m3/s (gal/min)

k¼ a constant ¼ 0:0327 SI units

¼ 4:86  104US Customary System Units

p¼ oil feed pressure, Pa (psi)

c¼ D
d ¼ diametral clearance, m (in)

 ¼ absolute viscosity (dynamic viscosity), Pa s (cP)

d¼ bearing bore, m (in)

L¼ land width, m (in)

" ¼ attitude or eccentricity ratioRefer to Table 24-1B

Coefficienta in the American Bureau of Shipping formula [Eq (24-44)]

TABLE 24-1CHousing tolerances

Oil flow rate

(gal/h/hp) Bed plate gallery to mains

with piston cooling

Lining or overlay thickness, mm

Relative fatigue strength

Guidance peak loading

MPa

Recommended journal hardness, V.P.N.

plated with lead-tin

Limit set by overlay fatigue in the case of medium/large diesel engines.

Suggested limits are for big-end applications in medium/large diesel engines and are not to be applied to compressors Maximum design loadings for main bearings will generally be 20% lower.

(Courtesy: Extracted from M J Neale, ed., Tribology Handbook, Section A11, Newnes-Butterworth, London, 1973)

semiminor axis of ellipse, m

c1 distance from the centroidal axis to the inner surface of curved

Hð¼ dÞ diameter of curved beam of circular cross section, m

e distance from centroidal axis to neutral axis of the section, m

cross section by performing the integration

Please note: The US Customary System units can be used in place of the above SI

Pure bending

The general equation for the bending stress in a fiber

at a distance y from the neutral axis (Figs 15-11 and

15-12)

The maximum compressive stress due to bending at

the outer fiber (Fig 24-12)

The maximum tensile stress due to bending at the

inner fiber (Fig 24-12)

Stress due to direct load

The direct stress due to load F

b¼ MbAe

y

d g b

θ dθ c f

Combined stress due to load F and bending

The general expression for combined stress

The combined stress in the outer fiber

The combined stress in the inner fiber

For values of radius to neutral axis for curved beams

r¼F

AMbAe

y

Values of radius to neutral axis for curved beams

the same for a box section in dotted lines with each

APPROXIMATE EMPIRICAL EQUATION

FOR CURVED BEAMS

An approximate empirical equation for the maximum

stress in the inner fiber

The stress at inner radius for a curved beam of

rectan-gular cross section

The stress at inner radius of circular cross section

The stress at inner radius of elliptical sections

accord-ing to Bacha

STRESSES IN RINGS (Fig 24-13 a)

Maximum moment for a circular ring at the point of

application of the load, A, Fig 24-13a

Another maximum momentb for a circular ring at a

point B 908 away from the point of application of load

Direct stress for the ring at point B 908 away from the

point of application of load

The general expression for bending moment at any

cross section DD at an angle
with the horizontal

(Fig 24-13b)

The stress due to direct load F at any cross section DD

at an angle
with the horizontal

riþ1

ro



ð24-64Þwhere

K¼ 1.05 for circular and elliptical sections

¼ 0:5 for all other sections

b¼ maximum width of the section, m (in)

where
ve sign refers to tensile load,

þ ve sign refers to comprehensive load

where
ve sign refers to comprehensive load,

þ ve sign refers to tensile load

The combined stress at any cross section

The moment, MbB, at the section 908 away from the

point of application of load (Fig 24-14)

CRANE HOOK OF CIRCULAR SECTION

F

Asin
Mb

Ae

y

y

A

r

The minimum combined stress

For crane hook of trapezoidal section

rðminÞ¼F

A

H2mro



where kiand koare stress factors which depend on

H=2rc; kiis the critical one which varies from13.5 to 15.4 as ratio H=2rcchanges from 0.6

to 0.4Refer to Fig 24-16 and Table 24-3

G

N U

P M

F F H E M

M

Z

B A D

L

R

E Z Z

K N

corrected for inertia effects of the piston and otherreciprocating parts, kN (lbf )

Fc the component of F acting along the axis of connecting rod, kN

(lbf )

Fir inertia force due to reciprocating masses, kN (lbf )

Fcr crippling or critical force, kN (lbf )

9806.6 mm/s2(32.2 ft/s2)

n0¼l

r ratio of connecting rod length to radius of crank

pf load due to gas or steam pressure on the piston, MPa (psi)

w specific weight of material of connecting road, kN/m3(lbf/in3)

deg

measured from the head-end dead-center position, deg

 angle between the center line of piston and the connecting rod,

deg

The velocity

DESIGN OF CONNECTING ROD (Fig 24-17)

Gas load

Load due to gas or steam pressure on the piston

Inertia load due to reciprocating motion

Inertia due to reciprocating parts and piston

The maximum value of Fir occurs when
¼ 08 or

when the crank is at the head-end dead center

At the crank-end dead center, when
¼ 1808, Fir

attains the maximum negative value, acting in

oppo-site direction

The combined force on the piston

The component of F acting along the axis of

connect-ing rod

The stress induced due to column action on account

of load Fcacting along the axis of connecting rod

(a) As per Rankine’s formula

v¼2rn

where r in m

Fg¼d2

Fir¼Wv2gr

cos
þcos 2

r

2 3

α

(b) As per Ritter’s formula

(c) As per Johnson’s parabolic formula

Inertia load due to connecting rod

The magnitude of inertia force (Fig 24-17) due to the

weight of the rod itself, not including the ends

The maximum bending moment produced by the

inertia force Ficis at a distance (2/3)l from wrist pin

The maximum bending stress developed in the rod

due to inertia force Fic

The crank angle (
) at which the maximum bending

moment occurs according to B B Low

The relation between the moment of inertia in the xx

and yy planes in order to have same resistance in

2

where

le¼ equivalent length, m (in)

k¼ radius of gyration, m (in)

n¼ end-condition coefficient (Table 2-4)

a¼ constant obtained from Table 2-3

9 ffiffiffi3p

MbðmaxÞ¼ Wv2l

9 ffiffiffi3

p

bðmaxÞ¼ Wv

2l

9 ffiffiffi3

DESIGN OF SMALL AND BIG ENDS

The diameter of crankpin at the big end

The diameter of the gudgeon pin at the small end

DESIGN OF BOLTS FOR BIG-END CAP

The diameter of bolts used for fixing the big-end cap

The expression for checking load for measuring

peripheral length of each thin-walled half-bearing

according to J M Conway Jonesa

The expression for total minimum nip, n

d

s

ð24-97Þwhere F1irðmaxÞis obtained from Eq (24-84)

d¼ design stress of bolt material, MPa (psi)

Wc¼ 6000Lhb

where

Wc¼ checking load, N

L¼ axial length of bearing, mm

hb¼ wall thickness of bearing, mm

Note: The ‘‘nip’’ or ‘‘crush’’ is the amount by which

the total peripheral length of both halves of bearing

under no load exceeds the peripheral length of the

housing of the bearing

The compressive load on each bearing joint face to

The bolt load required on each side of bearing to

compress nip for extremely rigid housing

The bolt load required on each side of bearing to

compress nip for normal housing with bolts very

close to back of bearing

The ratio of connecting rod length (l) to crank radius

D¼ housing diameter, mm (in)

hsl¼ steel thickness þ1lining thickness, mm (in)

m¼ sum of maximum circumferential nip on bothhalves of bearing, mm (in)

W¼ compressive load on each bearing joint face, N(lbf)

E¼ modulus of elasticity of material of backing, Pa(psi)

¼ 210 GPa (30.45 Mpsi) for steel

L¼ bearing axial length, mm (in)

y¼ yield stress of steel backing, Pa (psi)

¼ 350 MPa (50 kpsi) for white-metal-lined bearing

¼ 300 to 400 MPa (43.5 to 58 kpsi) for bearingwith copper-based lining

¼ 600 MPa (87 kpsi) for bearing with based lining

n0¼l

r¼ 3:4 to 4.4 single-acting engines ð24-98Þ

¼ 4.6 to 5.4 for double-acting engines

¼ 6.0 or more for steam locomotive engines

¼ 5 to 7 for stationary steam engines

¼ 3.2 to 4 for internal-combustion engines

¼ 1.5 to 2 for aero engines

DESIGN OF COUPLING ROD (Fig 24-18)

The centrifugal force due to the weight of the rod

The bending component of centrifugal force

The maximum bending moment due to the uniformly

distributed load of Fcb

The axial component of the centrifugal force

For some of the common cross sections of connecting

rods

For forces acting on a coupling rod

For proportions of ends of round and H-section

connecting rod

For proportions and empirical relations of steam

engine common strap end

Fc¼wv2

Fc¼Wv2

b

x Y Y

Y

Y

Y

Y b=4t

0.02B

0.27B

Rad

0.02 to 0.04B

0.06 to 0.13B 0.26 to 0.33B

Groove in bush

Groove in bush

connect-ing rods.

A area of cross section of piston head, m2(in2)

(Btu/in2/in/h/8F)

diameter of piston rod, m (in)

radial thickness of piston ring, m (in)

h1, h2, h3 thickness as shown in Fig 24-24, m (in)

i0¼ lg

R, Ri, Rh radius as shown in Fig 24-22b, m (in)

axial width of ring, m (in)

STEAM ENGINE PISTONS

Piston rods

The diameter of piston rod

The diameter of piston rod according to Molesworth

d¼ D

ffiffiffiffiffip

a

r

ð24-104Þwhere

p¼ unbalanced pressure or difference between thesteam inlet pressure and the exhaust, MPa (psi)

a¼u

n ¼ allowable stress, MPa (psi)Note:ais based on a safety factor of 10 for double-acting engines and 8 for single-acting engines (Thediameter of piston rod is usually taken as1

6to1

7thediameter of the piston.)

PROPORTIONS FOR PRELIMINARY

LAYOUT FOR PLATE PISTONS

Box type (Figs 24-22 a and 24-24)

Width of face

Thickness of walls and ribs for low pressure

The thickness of walls and ribs for high pressure

For dimensions of conical plate piston

For dimensions of cast-iron piston of 400 mm

diameter

Disk type (Fig 24-22b)

Width of face

Thickness of walls and ribs for low pressure

The hub thickness

The hub diameter

Width of piston rings

Thickness of piston rings

For dimensions of cast-iron piston

STRESSES

(a) Distributed load over the plate inside the outer

cylindrical wall (i.e., the areaR2

i)(1) Stress at the outer edge (Fig 24-22b)

(2) Stress at the inner edge (Fig 24-22b)

h¼ ð2R þ 50 cmÞ ð0:003pffiffiffipþ 0:0275 cmÞ ð24-108Þor

2¼ 3p4h2

(b) Load on the outer wall, pðR2
R2

iÞ distributedaround the edge of the plate

(1) Stress at the outer edge (Fig 24-22b)

(2) Stress at the inner edge (Fig 24-22b)

(3) The sum of the stresses at the outer edge

(4) The sum of the stresses at the inner edge

Dished or conical type (Fig 24-23)

An empirical formula for the thickness of conical

piston (Fig 24-23)

The height of boss

The diameter of boss

The thickness h1measured on the center line

For calculating hub diameter, width of piston rings,

and thickness of piston rings

h¼ 9:12pffiffiffiffiffiffiffiffiffiffiffiffipD=sin

Customary Metric ð24-123bÞwhere p and in kgf/mm2, D and h in mm

h¼ 1:825pffiffiffiffiffiffiffiffiffiffiffiffipD=sin
USCS ð24-123cÞwhere p and in psi, D and h in in

Dh¼ 1:5K for large pistons and light engines

PISTONS FOR INTERNAL-COMBUSTION

ENGINES

Trunk piston (Fig 24-25)

The head thickness of trunk pistons (Fig 24-25a)

COMMONLY USED EMPIRICAL

FORMULAS IN THE DESIGN OF TRUNK

PISTONS FOR AUTOMOTIVE-TYPE

ENGINES

Thickness of head (Fig 24-25a)

The head thickness for heat flow

th¼

ffiffiffiffiffiffiffiffiffiffiffiffi3PD2

16

s

ð24-127Þwhere

 ¼ 39 MPa (5.8 kpsi) for close-grained cast iron

¼ 56.4 MPa (8.2 kpsi) for semisteel or aluminumalloy

¼ 83.4 MPa (12.0 kpsi) for forged steel

2608C (5008F) for aluminum piston

c¼ 2.2 for cast iron

structural efficiency; (c and d) alternate pin designs.

Thickness of wall under the ring (Fig 24-25a and b)

The thickness of wall under the ring groove

The heat flow through the head

The root diameter of ring grooves, allowing for ring

clearance

Length L of piston

For chemical composition and properties of

alumi-num alloy piston

Gudgeon pin

The diameter of gudgeon pin

The length/diameter ratio of gudgeon pin

For gudgeon pin allowable oval deformation

For empirical relations and proportions of pistons

w¼ weight of fuel used, kJ/kW/h (lbf/bhp/h)

K¼ constant representing that part of heat supplied

to the engine which is absorbed by the piston

where Drand D in mm (in)

Refer to Table 24-10B

dr¼

ffiffiffiffiffiF

i0p

s

ð24-134Þwhere

F¼ maximum gas pressure corrected for inertia effect

of the piston and other reciprocating parts, kN(lbf )

p¼ working bearing pressure

¼ 9.81 MPa (1.42 kpsi) to 14.7 MPa (2.13 kpsi)

0.03 to 0.04B

0.26 to 0.3B

mm (in)

mm (in)

mm (in)

mm (in)

σ = 0.415P 2, P = GAS LOADAREA A

G DG EO N PIN /B

OSSBE ING PR

ESS URE

’P’

69 MN/m 2

(10000 lbf/in 2)

(9000 lbf/in 2) (8000 lbf/in 2) (7000 lbf/in 2) (6000 lbf/in 2) (5000 lbf/in 2)

62 MN/m 2 55.2 MN/m 2 48.3 MN/m 2 41.4 MN/m 2 34.5 MN/m 2

Butterworth-Heinemann, 1973.)

For fatigue stress in gudgeon pins

For empirical proportions and values of cylinder

cover, cylinder liner, and valves

Piston rings

Width of rings

For land width or axial width of piston ring (w)

required for various groove depths (g) and maximum

cylinder pressure, pmax

2.2 2.1 2.3 2.4 2.5 2.6

CYLINDER BORE DIAMETER (NOMINAL), mm

CYLINDER BORE DIAMETER (NOMINAL), in

L

b a MN/m 2 (lbf/in 2 )

0.150 0.200

0.250 g

w

0.300 0.350 0.400 0.450 0.500

0.600 0.650

ALUMINIUM PISTON LAND WIDTH W

TO DETERMINE LAND WIDTHS FOR PISTONS IN CAST IRON OR STEEL USE THE FOLLOWING CONSTANTS CAST IRON W FROM GRAPH × 0.700

STEEL W FROM GRAPH × 0.5

16.6 M N/m 2

15.2 M N/m 2

13.8 MN/m 2

12.4 MN/m

2

11.0 MN/m 2

9.65 MN/m 2

1200

1000

MAX CYLINDER PRESSURE, Ibf/in 2

2000 0.500

Handbook, Butterworth-Heinemann, 1973.)

h w

of piston ring

d r

pressure distribution around piston rings for four-stroke

engines (Courtesy: Piston Ring Manual, Goetze AG,

D-5093 Burscheid, Germany, August 1986.)

ring.

d

applied on piston ring.

Gap clearance

The modulus of elasticity of piston ring as per Indian

Standards

The bending moment produced at any cross section of

the ring by the pressure uniformly distributed over the

outer surface of the ring at an angle measured from

the center line of the gap of the ring (Figs 24-28e and

The radial distance from a point in piston ring to

obtain a uniform pressure distribution (Fig 24-28e)

according to R Munroa

5:37

d

h
1

3F

r¼ radius of neutral axis, mm (in)

p¼ pressure at the neutral axis of the piston ring, Pa(psi)

where

d¼ external piston ring diameter

h¼ radial depth or wall thickness of piston ring

En¼ nominal modulus of elasticity of material of thering

f¼ free ring gap

0.07to 0.08B



Fr3

EnI

2ð
1 cos 
1sinÞ

"

 ð3 sin  þ  cos Þ

#

where

F¼ (mean wall pressure  ring axial width)

r¼ radius of neutral axis, when the ring is in placeinside the cylinder (Fig 24-28e)

.25D

.38D J H

G

F

D

.18D to 21D 25 to 30D

18 to 22lbf/sq in of valve area

.65D

The relation between the ratio of fitting stressft to

nominal modulus of elasticity (En) in terms of h, d,

and f

The relation between the ratio of working stress (w)

to nominal modulus of elasticity (En) in terms of h, d,

and f

The relation between the ratio of the sum of (ftþ w)

to nominal modulus of elasticity (En) in terms of d and

h

For preferred number of piston rings

For properties of typical piston ring materials

 ¼ angle measured from bottom of the vertical linepassing through the center of the gap of thering as shown in Fig 24-28e

I¼ moment of inertia of the ring

0.16D

Two ribs thus (revolved section) Coreplug E

Cooling

water

connection N

D C

Copper joint

D 2.0

The circumferential clearance ( c) or gap between

For variable and constant radial contact pressure

distribution of piston ring

The diametral load which acts at 908 to the gap

required to close the ring to its nominal diameter, d

(Fig 24-28g)

The maximum bending stress at any cross section

which makes an angle  measured from the center

line of the gap of the ring

The maximum bending stress which occurs at ¼ ,

i.e., at the cross section opposite to the gap of the ring

The bending stress present in the ring of rectangular

cross section in terms of free gap ( f) of the ring,

when it is in place in the cylinder

The bending stress present in the ring of rectangular

cross section in terms of tangential force, F
(Fig

24-29)

The bending stress present in the case of slotted oil

control ring of rectangular cross section in terms of

free ring gap, f

wherebsoin N/mm2and

Ius¼ moment of inertia of the unslotted cross-sectionring, mm4

Im¼Iusþ Is2