GEARS INTRODUCTION

CLASS NOTES FOR MECHANICAL

ENGINEERING

Gear is one of three modes of power

transmission from the driver to the

driven. In most of the cases, driver

is electric motor and the driven is

the machine. It may be a lathe,

drilling machine, shaper etc. There

are many types of gears. Different

types of gears are used in different

applications. Selection of a gear drive

mainly depends on the center distance,

velocity ratio and peripheral speed. It

also accounts for the power to be

transmitted. These have cycloid and

involute profiles. Involute profiles are

quite common. Cycloid profiles are used

with skew shafts.

 

 

1. GEAR NOMENCLATURE

Gear——–   Larger gear

Pinion——    smaller gear

2. COMMON TERMINOLOGY TO PINION AND GEAR

(i)    Addendum,

(ii)   Dedendum

(iii)  Tooth width

(iv)   Tooth depth

(v)    Tooth flask

(vi)   Tooth face

(vii)  Tooth clearance

(viii)  Back lash

(ix)   Pressure angle

(x)   Tooth profile

(xi)   Pitch circle diameter

(xii)  Number  of teeth

(xiii)  Circular pitch

(xiv)  Diametric pitch

 

 

 

Fig. Bevel gear Nomenclature

3. LAW OF GEARING

Law of gearing determines the profiles of the gears. It states that the tooth curves (profiles) should be such that common perpendicular to the profiles at the point of contact ‘P’ will at all times lie at the common tangent to the pitch circles. Common tangent is T T to the pitch circles. Common perpendicular passing through point of contact of involute profiles is AB

4. PITCH ANGLE OF PINION OR PITCH ANGLE OF THE GEAR

It is an acute angle at the center. It is the angle between the two lines joining the corresponding points on two consecutive teeth with the center.

5. CLEARANCE

When teeth are in contact at pitch circle point, then space, between the outer surface and inner surface of matching teeth is called clearance.

      6. DIFFERENT TYPES OF PITCHES

(a)    Circular pitch For  Pinion,  p_c  = πD_p /Z_p                       

For  Gear,     p_c = πD_g /Z_g 

Standard Circular pitches——-12 mm to 24 mm,  varying by 3mm                

Pinion pitch diameter D_p = Z_p. p_c /π

Gear pitch diameter    D_g =    Z_g. p_c /π

(b)   Diametric pitch, p_d  for pinion = Z_p / D_p

Diametric pitch, p_d for gear    = Z_g / D_g

Standard diametric pitches

(i)  24 mm to 48 mm  varying by 6 mm

(ii)  48 mm to 96 mm varying by 12 mm

(iii)  More preferable pitches 5,6,8,10,12,16,20,24,32 and 48 mm

(iv) Less preferable pitches 7,9,11,14,18,22,26,28,30,36,40 mm                         

2. RELATION BETWEEN CIRCULAR PITCH AND DIAMETRAL PITCH

         p_C.p_d = Π

Q. PRESSURE ANGLE

Pressure angle is the acute angle between common tangent to pitch circles and common tangent to base circles.

Q. BASE CIRCLE

Base circle – The smallest IMAGINARY circle on which the profile of the gear is laid out is called the base circle. r_b  = (D/2) cos φ.

Q. OTHER PARAMETERS

(i) Module ‘m’ =D/Z = length of diameter per teeth

(ii) Standard modules available are 1,1.25,1.5, 2, 2.5,3,4,5,6,8,10,12,16 and 20 (iii) Standard addendum = 1 m= 1 module

(iv) Standard dedendum = 1.157 m

(v) Addendum diameter = D + 2 a

(vi) diameter = D –2 d

(vii) Clearance = d – a = 0.157 m

(viii) b = width of the tooth measured parallel to shaft axis

MATERIALS OF GEARS

(i)   Metallic

(ii)  Non metallic

METALLIC GEARS

For metallic Spur gearing   velocity should be ≤ 330 m /min as beyond this noise & vibration becomes excessive.

(a)    Cast Iron where velocity is less and BHN = 200

(b)    Hardened  Steel for BHN = 200 to 300

(c)     Brass

(d)   Bronze

 NON METALLIC GEARS

Non-metallic pinion is used for spur gears if V is > 330 m/min to reduce the noise and vibration within permissible range

(a)    Treated cotton (pressed and molded at high temperatures)—Oil and water resistant

These Non-metallic gears are not self supporting and hence are provided with metallic shrouds at the two ends of the gears. When using non metallic (say pinion) with a metallic gear, the pinion should be selected with a face width large enough to permit the gears to contact only non-metallic portion of the pinion face, and must avoid the possibility of pinion (non-metal) contact with the metallic shrouds.

(b)   Synthetic resins Phenol type———- ——————-Oil and water resistant

Gear made from phenol resins require no supporting plates (or shrouds)

( C) Rawhide–It is affected by moisture and thus should not be used in the wet environment.

(a)    Plastic gears

(b)   Teflon gears

GEAR PROFILES

There are two profiles

(a) INVOLUTE PROFILE

Curve which satisfies the law of gearing is involute profile.

STANDARD INVOLUTE PROFILES

(i) 14 ½ involute,

addendum length =a = 1/p_d , Clearance = C = 0.157/p_d , N_{p min} =18

(ii) 20⁰ involute,

addendum length = a = 1/p_d , Clearance =C = 0.2/p_d ,     N_{p min} =18

(iii) 20⁰ stub involute,

addendum length = a= 0.8/p_d , Clearance =C = 0.2/p_d ,   N_{p min} =14

N_{p min}= Minimum No. of teeth on the pinion (smaller gear)

(b)   CYCLOID PROFILE USED ONLY WITH SKEW SHAFTS

STANDARD CYCLOID PROFILES ARE

(i) 14 ½ ⁰ Cycloid

(ii) 20⁰ full Cycloid

(iii) 20⁰ stub  Cycloid

(iv) 25⁰ Cycloid

 GEARS: Selection of a gear for a particular application depends on 

(a)  According to the layout of shaft axes 

(b) On the basis of power

(c)  On the basis of peripheral velocity 

(d) On the basis of velocity ratio  

ACCORDING TO THE LAYOUT OF SHAFT AXES 

 (i)  Parallel axes shafts

(a) Spur gearing

(i) speed ratio 8 to 20 in one stage

(ii) rotate in opposite directions

(iii) only one tooth in contact at one time.

(b) Internal gearing–Gears rotate in the same direction.

(c) Rack and pinion

(d) Helical gearing

(i) teeth inclined to shaft axis at an angle called the helix angle

(ii) smooth and noiseless operation

(iii) large power transmission

(iv) Two teeth in contact at one time.

(v) These are left and right handed.

(e) Herringbone gearing

(ii)  Interesting axes Shafts (if produced)

(a) Straight bevel gearing

( b) Spiral bevel gearing—inclined teeth

(iii) Shafts Axes neither parallel nor intersecting. Such axes are  Skew Axes.

There are three types of gearing for skew shafts.

(a) Worm gearing—for speed ratio up to 100 in one stage

(b) Hypoid gearing—non parallel, non-intersecting and cross shafts—used in rear axle of an automobile

(c) Spiral gearing

(c) ON THE BASIS POWER, VELOCITY AND VELOCITY RATIO

There is no hard and fast rule.  Few guidelines are:

(i)  Spur gear

(a) for medium H.P

(b) V 1000 ft/mint for metallic spur gear

c)    V.R. =3:7 to a maximum =10: 1

(ii)  Spur pinion (Non metallic)

(a)    For medium H.P

(b)    V 1000ft/mint

(iii) Helical spur gears

(a)  At high speeds and up to  60000 HP

(iv) Bevel Gears (a)Shaft at 90⁰ (b)  V.R. =2:3, max =6:1

(v) Worm gears

Uses of Worn gears

(i) high speed ratio

(ii) V R = 10 to 80 and max V R =500

(ii) Worm gears used where noise and vibrations problems exist at high speeds.

https://www.mesubjects.net/wp-admin/post.php?post=6178&action=edit         Question Answers Gears