Machine Design Databook Episode 3 part 6 ppsx

The bending stress present in the case of slotted oilcontrol ring of rectangular cross section in terms of tangential load, F The tangential load or force required for opening of a recta

The bending stress present in the case of slotted oil

control ring of rectangular cross section in terms of

tangential load, F

The tangential load or force required for opening of a

rectangular cross-section piston ringa

The piston ring parameter (k) in terms of tangential

load F
for rectangular cross-section rings

The tangential load or force required for opening of

rectangular cross-section slotted oil control rings

The piston ring parameter (k) in terms of free ring gap

( f) for rectangular cross-section slotted oil rings for

use in Eq (24-142g)

The piston ring parameter (k) in terms of the constant

pressure ( p) for rectangular cross-section rings also

for use in Eqs (24-142f ) and (24-142g)

The radial thickness of the ring at a section which

makes an angle measured from the center line of

the gap of the ring

Is¼ moment of inertia of the slotted cross-sectionring, mm4

lco¼ twice the diameter between center of gravity andoutside diameter, mm

pE

dðd
hÞ2

h¼ 3

ffiffiffiffiffiffiffiffiffiffiffi24pr4E

ssin2

a Goetze AG, Piston Ring Manual, 3rd ed., Burscheid, Germany, 1987.

The maximum thickness of the ring which occur

opposite the gap of the ring (i.e., at ¼ )

For piston ring dimensional deviation, hardness, and

minimum wall pressure

For cylinder bore diameter

hmax¼

ffiffiffiffiffiffiffiffiffiffiffi24pr4E

TABLE 24-7

Recommended hardness for piston rings of IC engines

Nominal diameter, d, mm Hardness HRD

TABLE 24-8Minimum wall pressure for piston rings of IC engines

Compression rings Oil rings

a Gasoline.

TABLE 24-10C

Preferred number of piston rings

Differential pressure Std atm 0–9 10–14 15–24 25–29 30–49 50–99 100–200

MPa 0–0.88 0.98–1.37 1.47–2.35 2.45–2.85 2.94–4.80 4.90–9.71 9.81–19.61 psi 0–128 142–199 213–341 355–412 426–696 710–1406 1422–2844

Tensile strength, t elasticity, En Brinell Bulk expansion, 

Metallic:

Carbide malleable irons 400–580 58.0–84.1 140–160 20.3–23.2 250/320 Excellent Malleable and/or nodular 540–820 78.3–119.0 155–165 22.5–24.0 200/440 Poor irons

Mechanical properties Tensile strength, Modulus of Designation Grade Hardness st , MPa elasticity, E, MPa Main application Steel

GOE 61 Cr steel, 17% Cr min 380–450 HV 30 1200approx 230 000 approx Compression rings GOE 62 Cr-Si steel 500–600 HV 30 1900approx 210 000 approx Coil spring loaded

rings GOE 64 Cr-Si steel 450–550 HV 30 1700approx 210 000 approx Compression rings GOE 65A Cr steel, 11% Cr min,

high C

300–400 HV 30 1300approx 210 000 approx Compression rings,

nitrided GOE 65B Cr steel, 11% Cr min,

low C

270–420 HV 30 1300approx 220 000 approx Coil spring loaded

rings and segments, nitrided Cast Iron

GOE 12 Unalloyed non

heat-treated gray cast iron

94–106 HRB 350 min 85 000 typical Compression and oil

control rings GOE 13 Unalloyed non heat-

treated gray cast iron

97–108 HRB 420 min 95 000–125 000 Compression and oil

control rings GOE 32 Alloyed heat-treated

gray cast iron with

carbides

109–116 HRB 650 min 130 000–160 000 Compression rings

GOE 44 Malleable cast iron 102–111 HRB 800 min 150 000 min Compression rings GOE 52 Spheroidal graphite cast

iron

104–112 HRB 1300 min 150 000 min Compression rings GOE 56 Spheroidal graphite cast

iron

40–46 HRC 1300 min 150 000 min Compression rings

Source: Goetze Federal Mogul Burscheid GmbH, Piston Ring Manual, 4th ed., January 1995, Burscheid, Germany, reproduced with permission

24.5 DESIGN OF SPEED

REDUCTION GEARS AND

VARIABLE-SPEED DRIVES

a center distance, m (in)

number of pinions or planetary pinion (Fig 24-36)

A center distance (also with subscripts) (Fig 24-36)

area of reduction gear housing, m2(in2)

An noncooled, i.e., ribbed, surface of housing of reduction gear

drive, m2(in2)

Ac cooled surface of reduction gear drive, m2(in2)

Aw surface area of contact of teeth when one-fourth of all teeth of

wheel in wave-type reduction gears are engaged, m2(in2)

d1 diameter of pinion, m (in)

diameter of rigid immovable rim with internal teeth of

wave-type reduction gears, m (in)

d2 diameter of gear, m (in)

diameter of flexible movable wheel rim with external teeth of

wave-type reduction gear, m (in)

dmax maximum diameter of the circumference of the belt

arrangement on the V-belt of a variable-speed drive, m (in)

dmin minimum diameter of the circumference of the belt

arrangement on the V-belt of a variable-speed drive, m (in)

D¼dmax

dmin velocity control range for a V-belt drive

D1 velocity control range for a V-belt drive with only one

adjustable pulley

D2 velocity control range for a V-belt drive with two adjustable

pulleys

e working height of a V-groove of the pulley, m (in)

Fmax maximum load acting on the pinion, kN (lbf )

Fm mean load acting on the pinion, kN (lbf )

h height of tooth, m (in)

coefficient of heat transfer, W/m2K (Btu/ft2h8F)

hn coefficient of heat transfer of noncooled surface, W/m2K (Btu/

ft2h8R)

hc coefficient of heat transfer of cooled surface, W/m2K (Btu/ft2h

8R)

ha addendum of tooth, m (in)

hf dedendum of tooth, m (in)

i transmission or speed ratio

knl¼Fmax

Fm nonuniform load distribution factor

L distance between the axes of the pinions (Fig 24-36d)

rmin minimum radius of the circumference of the belt arrangement

on the V-belt of a variable-speed drive, m (in)

t1 temperature of lubricant,8C (8F)

ta ambient temperature,8C (8F)

z1, z2 number of teeth on sun pinion and planetary pinion of epicyclic

gear transmission, respectively, Fig 24-36number of teeth on pinion and gear, respectively

z3 number of teeth on ring gear 3 (Fig 24-36a)

zs number of teeth on smaller wheel

!1,!2 angular speed of pinion and gear, respectively, rad/s

deformation, m (in)

clearance between the pinions which should be at least 1 mm

(in) half-cone angle of V-belt, deg

ca allowable compressive stress, MPa (psi)

Transmission or speed ratio for single reduction gear

For different types of gear reduction drives

2 4

3

L

L H

H

9 Single-reduction worm gear with worm arranged sideways

PLANETARY REDUCTION GEARS

First condition—mating

The sum of the radii of the addendum circles of the

mating pinions in planetary reduction gears should

be smaller than the distance between their axes

(Fig 24-36d) so that the top of the pinions should

not touch each other

L

∆

A 1,2

2π a

π a

(d) (a)

A2,3

A1,21

FIGURE 24-36 Planetary reduction gears.

Second condition—coaxiality

The center distance of each pair of wheels should be

equal (Fig 24-36)

The relationship between teeth in corrected or

uncor-rected gears (Fig 24-36a)

The relationship between teeth in corrected or

uncorrected gears (Fig 24-36c) to ratify two

con-ditions

(i) First condition

(ii) Second condition

L¼ 2A1;2sin

a¼ z2mþ 2mð1 þ Þ þ
ð24-144Þwhere

Third condition—coincidence

The condition for the teeth and spaces of the meshed

gears should coincide when the pinions are arranged

uniformly over the circumference

The moment acting on smaller wheel

CONDITIONS OF PROPER ASSEMBLY OF

PLANETARY GEAR TRANSMISSION

Two planetaries

Both the driving pinion (sun pinion) and the

plane-taries may have either an even or an odd number of

teeth

Three planetaries

If z1(number of teeth on sun pinion) is divisible by 3,

then z2(number of teeth on planetary pinion) must

If z1is even, then z2must be even

If z1is odd, then z2must be odd

¼ 1.4 to 1.6 for gears of 7th degree of accuracy

¼ 1.1 to 1.2 when floating central wheels are used

to equalize the load

WAVE-TYPE REDUCTION GEARS

Transmission or gear ratio

The necessary deformation

The condition for obtaining the module for the drive

The module of the drive from Eq (24-152)

The tooth height

The tooth addendum

The tooth dedendum

The rim width

The total surface area of contact of teeth when

one-fourth of all teeth of wheel are engaged

The torque transmitted

VARIABLE-SPEED DRIVES (Figs 24-34 and

24-37, and Table 24-12)

For schematic arrangements of various

variable-speed drives

The velocity control range for V-belt drive with only

one adjustable pulley

The relation between dmaxand dminof V-belt drive

The velocity control range for V-belt drive from Eqs

Refer to Figs 24-34 and 24-37

D1¼dmax

dmax¼ dminþ 2ðe
hÞ ð24-161aÞ

dmax¼ dminþ b cot
2h ð24-161bÞ

The velocity control range for V-belt drive when two

pulleys are adjustable

The total range of velocity control of variable-speed

drive of two adjustable pulleys of V-belt drive

The working height of the V-groove of the pulley

The width of standard V-belt

x

x x

x

L H

The larger ratio of width to height of specially profiled

The area of housing required for dissipating heat

generated in a closed-type reduction gear drive

operating in an oil bath at stable thermal equilibrium

condition

The thermal equilibrium condition of reduction gear

drive which has a housing of noncooled surface

(ribbed surface) and cooled surface (cooled by

blow-ing of air by fan)

The expression for coefficient of heat transfer of the

housing or reduction gear drive blown over by air

The velocity of air which depends on impeller velocity

For minimum weight equations for gear systems

For total weight equations for gear systems

For K factors for preliminary estimate of spur and

helical gear size

For comparison of five gear systems

v’ 0:005nim/s (ft/min)

ni¼ impeller speed, rpmRefer to Table 24-13

Refer to Table 24-14

Refer to Table 24-15

Refer to Table 24-16

TABLE 24-12

Velocity control range (D), efficiency (), and allowable power transmitted (Pal) for variable-speed drives

Serial no in

TABLE 24-11

Transmission ratio (i), efficiency (), and allowable transmitted power (Pal) for reduction gears

Single- and triple-spur and helical reduction gear 24-35, 10–60

serial nos 3a, 4a

The following symbols are used in Tables 24-13 to 24-16: a¼ number of branches in an epicyclic gear:

C¼ ð2Mt=KÞ, m3; d¼ pitch diameter, m (in); i ¼ gear speed ratio; io¼ overall ratio; is¼ dp=ds¼ zp=zs¼ speedratio of planet gear to sun gear; j¼ number of idlers; K ¼ a factor from Table 24-15; Mt¼ input torque, N m (lbfin);ðioþ 1Þ=io¼ i0

o

TABLE 24-13

Minimum weight equations for gear systems

Simple train (offset) 2i3þ i 2 ¼ 1

Offset with idler 2i3þ i 2 ¼ i 2 þ 1

Offset with two idlers 2i 3 þ i 2 ¼i2þ 12

Offset with j idlers 2i3þ i 2 ¼i2þ 1j

Double-reduction 2i 3 þ2ii02

o ¼i2iþ 10o Double-reduction, double

3 þ2i2

i0o ¼i22iþ 10o Double-reduction, four

3 þ2ii02

o ¼i24iþ 10o Double-reduction, j

3 þ2ii02

o ¼i2jiþ 10o Planetary (theoretical) 2i3sþ i 2

s ¼0:4ðio
1Þa 2þ 1Star (theoretical) 2i3sþ i 2

s ¼0:4i2aþ 1

TABLE 24-14Total weight equations for gear systemsParticular Equation

Offset ðbd 2 =CÞ ¼ 1 þ1iþ i þ i 2 Offset with

idler ðbd 2 =CÞ ¼ 1 þ1iþ i þ i 2 þii2þ i 2 Offset with

two idlers ðbd 2 =CÞ ¼1

2 þ12i þ i þ i 2 þi2

2i þi22 Double-

reduction ðbd 2 =CÞ ¼ 1 þ1iþ 2i þ i 2 þii2

o þi2i2þ i 2 Double-

reduction, double branch

ðbd 2 =CÞ ¼12þ2i1þ 2i þ i 2 þi

2

ioþi

2 2i þi2 2

reduction, four- branch

s þ is þ i 2

s þ0ai:4i2

s þ0:4ia2

TABLE 24-15

K factors for preliminary estimate of spur and helical gear size

K factor Hardness HB ; Pitch line

Engine driving compressor 225–180 >20.5 0.032–0.050 0.314–0.49 0.314–0.49

Aircraft, planetary 60RC–60RC 15.3–51 0.492 (at take off) 4.82 4.82

die casting

TABLE 24-16

A comparison of five gear systems (all systems producing 0.746 kW at 18 rpm)

a center distance, m (in)

dimensions as shown in Fig 24-42

b gear face width, m (in)

d1 diameter of smaller wheel, m (in)

d2 diameter of larger wheel, m (in)

i number of grooves, m (in)

P power transmitted, kW (hp)

p0 permissible pressure, kN/m (lbf/in)

vm mean circumferential velocity, m/s (ft/min)

R cone distance, m (in) (Fig 24-40)

half the included angle of the groove, deg ranges from 128 to 188

(should not exceed 208) angle of friction, deg

 coefficient of friction between wheels

0 coefficient of friction between shaft of wheel and bearings

!l,!2 angular speeds of smaller and larger wheels, respectively, rad/s

1, 2 cone center angles of smaller and larger wheels, respectively,

deg

SPUR FRICTION GEARS

Plain spur friction wheels (Fig 24-38)

The radial pressure on the wheels

The tangential force due to radial pressure F

The power transmitted

The gear face width

Grooved spur friction wheel (Fig 24-39)

The radial force on the wheel for each groove

The total tangential force

The power transmitted

p0dn0 Customary Metric ð24-175bÞwhere P in kW, p0in kgf/mm, n0in rps, and b and d

The empirical relation for the depth of the groove

The recommended value for the mean circumferential

Fr

δ

FIGURE 24-39 Grooved spur friction gears.

The tangential force transmitted

The least axial thrust on the small wheel

The least axial thrust on the big wheel

Running

The reaction in this case is designated by FR bp0

(where p0is the permissible unit pressure)

F0t¼ F0Rcos ¼1000P

F0t¼ F0Rcos ¼75P

vmCustomary Metric ð24-182bÞ

The tangential force transmitted

The least axial thrust on the small wheel

The least axial thrust on the big wheel

DISK FRICTION GEARS (Fig 24-41)

The torque on the driving shaft

d1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

d2þ d2q

24

d1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

d2þ d2q

24

d2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

d2þ d2q

24

d2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

d2þ d2q

24

The tangential force acting on the driven wheel for the

minimum speed at minimum diameter of driving disk

The tangential force acting on the driven wheel for the

maximum speed at maximum diameter of driving disk

Mt¼716,000P

n Customary Metric ð24-189dÞwhere Mtin kgf mm, P in hpm, and n in rpm

FIGURE 24-41 Variable-speed disk friction gearing.

The minimum thrust to be applied to the disk for the

The minimum force available on the chain sprocket at

minimum speed of driven wheel

The maximum force available on the chain sprocket

at maximum speed of driven wheel

where varies from 0.6 at low speeds when d ¼ d1

to 0.8 at high speeds, when d¼ d2

F1cs¼Ft1d

where

d¼ diameter of driven wheel, m (in)

d3¼ diameter of chain sprocket, m (in)

F2cs¼Ft2d

BEARING LOADS OF FRICTION GEARING

(Fig 24-42, Table 24-17)

Driven shaft

The horizontal force on bearing A due to the

tangen-tial force Ft

The vertical force on bearing A due to thrust Faand

the force on the chain sprocket Fcs

The resultant load on bearing A

The horizontal force on bearing B due to the

tangen-tial force Ft

The vertical force on bearing B due to the thrust Fa

and the force on the chain sprocket Fcs

The resultant force on bearing B

e Chain

FIGURE 24-42 Bearing loads of disk friction gearing.

Driving shaft

The horizontal force due to thrust Faon bearing D

The horizontal force due to the tangential force Fton

the bearing D

The resultant force on the bearing D

The horizontal force due to thrust Faon the bearing C

The horizontal force due to the tangential force Fton

q

ð24-209Þ

TABLE 24-17

Design data for friction gearing

pressure, p 0 Coefficient of pressure,p 0 Coefficient of of friction

Material of driver kN/m lbf/in cast iron Material of driver kN/m lbf/in cast iron aluminum

24.7 MECHANICS OF VEHICLES

a center distance, m (in)

a constant in Eq (24-216b)

A frontal projected area of vehicle, m2(ft2)

b face width of gear, m (in)

a constant in Eq (24-216b)

B width of bearing, m (in)

c distance between adjacent rotating parts, m (in)

C constant (also with suffixes)

Dt maximum diameter of torus, m (in)

Dw diameter of wheel, m (in)

Ef flow loss in each member of hydraulic torque converter, N m

(lbf in)

Esh shock loss in each member of hydraulic torque converter, N m

(lbf in)

F driving force at the tire, kN (lbf )

Fmax maximum permissible load on the pitch circle of any particular

pair of gears, kN (lbf )

h thickness of housing, m (in)

l distance between support bearings on a shaft in gearbox, m (in)

l0 distance between bearings of overhanging shaft, m (in)

l1 distance of rotating part from the bearing, m (in)

l2 distance of bearing from the wall, m (in)

l3 cap height from bolt to end, m (in)

l4 distance of rotating parts from the bearing cap, m (in)

l5 width of boss of rotating parts, m (in)

l6 distance of coupling to cap, m (in)

l7 distance between gear and shaft, m (in)

l8 distance of rotating parts from inner wall of housing, m (in)

Mt output torque of the engine, N m (lbf in)

Mtt torque at the tire surface, N m (lbf in)

Mti the input torque, N m (lbf in)

Mto the reaction to the output torque, which is opposite in direction

to output torque, N m (lbf in)

Mtf the torque that must be applied to transmission housing to

balance the moments of internal friction, oil churning, etc.,

N m (lbf in)

Mtr the torque reaction of the transmission housing due to the gear

reduction in transmission, N m (lbf in)

ni speed of driving shaft, rpm

no speed of driven shaft, rpm

r radius of the driving wheel, m (in)

rmi mean radius of inflow to the runner, m (in)

rmo mean radius of outflow from the runner, m (in)

BEARING LOADS OF FRICTION GEARING

(Fig 24-42, Table 24-17)

Driven shaft

The horizontal force on bearing... smaller and larger wheels, respectively,

deg

SPUR FRICTION GEARS

Plain spur friction wheels (Fig 24 -38 )

The radial pressure on the wheels

The tangential... gearing.