Design

Prof. Samy J. Ebeid ١

Bevel Gears

Part 17

١Bevel Gears

Bevel Gears

٢Bevel Gears

Design

Prof. Samy J. Ebeid ٢

Bevel Gears

The elements of both Bevel Gears should intersect at the

point of the shaft intersections. If this does not happen,

there shall be pure rolling at only one point of contact and

tangential sliding at all other points of contact. It is

impossible to have positive driving and sliding in the

same direction at the same time.٣Bevel Gears

Common tangent

plane to cones

Straight Bevel Gears

All sides of

tooth meet

at S.

٤Bevel Gears

Design

Prof. Samy J. Ebeid ٣

1. The involute teeth of a spur gear

are generated by the edge of a

plane as it rolls on a base

cylinder.

2. With the case of a bevel gear the

involute lies on a sphere.

3. It is hard to represent on a plane

surface the exact profile of a

bevel gear tooth lying on the

surface of a sphere.

4. An approximation known as

Tredgold’s approximation is used.

It uses a cone tangent to the

sphere at the pitch point. This

cone is known as the back cone

and can be developed as a spur

gear.

Formative or Equivalent Number of Teeth

٥Bevel Gears

Bevel Gears treated as Spur Gears on their back cones

٦Bevel Gears

Design

Prof. Samy J. Ebeid ٤

Bevel gears are

checked as Spur gears

with back cone

distances ρp and ρg

as radii and α = 15 ̊

ρp = dp / (2 cos δp)

ρg = dg / (2 cos δg)

zp = 12 to 18 for u = 4:1 to 1:1

= 10 to 15 for spiral teeth

Construction of Teeth on Back Cones

٧Bevel Gears

Fictive Number of Teeth

z’p = 2 ρp / m = 2dp / (m . 2 cos δp) = zp / cos δp

z’g = 2 ρg / m = 2dg / (m . 2 cos δg) = zg / cos δg

From z’ we can get the form factor ky

٨Bevel Gears

Design

Prof. Samy J. Ebeid ٥

Gear Terminology:

1. Pitch cone

2. Cone centre

3. Pitch angle

4. Cone distance

5. Addendum angle

6. Dedendum angle

7. Face angle

8. Root angle

9. Back cone

10. Back cone distance

11. Backing

12. Crown height

13. Mounting height

14. Pitch diameter

15. Outside or addendum cone diameter

16. Inside or dedendum cone diameter

٩Bevel Gears

v = 5 to 7 m/s for teeth cut with form cutters & Kv = 3 / (3+v)

v = 10 m/s for generated teeth with precision machines &

Kv = 6 / (6+v)

Ky estimated for z’ at α = 15 ̊

b/m = 6 to 10

Bevel Gear Proportions

Module = m

Addendum = 1 m

Dedendum = 1.2 m

Clearance = 0.2 m

Working depth = 2 m

Thickness of tooth = 1.5708 m

Bevel gears are not interchangeable

and are designed in pairs.

١٠Bevel Gears

Design

Prof. Samy J. Ebeid ٦

Speed Ratio for Bevel Gears

u = dg/dp = sin δg / sin δp

u = sin δg / sin (δ - δg)

δ = δp + δg

u = sin δg / (sin δ . cos δg - cos δ . sin δg)

tan δg = u . sin δ / (1 + u . cos δ)

For δ = 90 ̊ we get tan δg = u and tan δp = 1/u

١١Bevel Gears

Classification of Bevel Gears

Bevel Gears are classified depending upon the angle between

the shafts and the pitch surfaces.

Mitre Bevel Gears: Equal diameters

Equal teeth

Equal pitch angles

Shafts axes intersect at a right angle

Angular Bevel Gears: Shafts axes intersect at any

angle other than a right angle

١٢Bevel Gears

Design

Prof. Samy J. Ebeid ٧

Crown Bevel Gears:

-Shafts axes intersect at an angle greater than 90 ̊

-One of the bevel gears has a pitch angle = 90 ̊

-The crown gear corresponds to a rack in spur gearing

١٣Bevel Gears

External Bevel Gears: -When the teeth on the

bevel gear are cut on the

outside of the pitch

cone.

Internal Bevel Gears:

-When the teeth on the bevel

gear are cut on the inside of

the pitch cone.

Pitch angle: -˂90 ̊ = external bevel gear

-˃90 ̊ = internal bevel gear

-=90 ̊ = crown bevel gear

١٤Bevel Gears

Design

Prof. Samy J. Ebeid ٨

١٥Bevel Gears

١٦Bevel Gears

Design

Prof. Samy J. Ebeid ٩

١٧Bevel Gears

١٨Bevel Gears

Design

Prof. Samy J. Ebeid ١٠

١٩Bevel Gears

Static Strength

٢٠Bevel Gears

Design

Prof. Samy J. Ebeid ١١

Dynamic Strength

٢١Bevel Gears

Endurance Strength

٢٢Bevel Gears

Design

Prof. Samy J. Ebeid ١٢

٢٣Bevel Gears

Example B1

A 35 kW motor running at 1200 rpm drives a compressor at 780

rpm through a 90̊ bevel gear arrangement. The pinion has 30

teeth and the pressure angle is 14.5̊. The wheels are capable of

withstanding a dynamic stress:

σ= 140 x ((280/(280+v)) MPa , where v is the pitch line speed

in m/min. The form factor = 0.124 – (0.686/Te), where Te is the

number of teeth equivalent of a spur gear. The face width is

about 0.25 of the slant height of the pitch cone.

Determine:-module

-face width

-addendum and dedendum

-outside diameters

-slant height. ٢٤Bevel Gears

Design

Prof. Samy J. Ebeid ١٣

A pair of cast iron bevel gears connect two shafts at right

angles. The pitch diameters are 80 and 100 mm respectively.

The tooth profiles of the gears are of 14.5̊ form. The allowable

static stress for both gears is 55 MPa. If the pinion transmits

2.75 kW at 1100 rpm, find the module and number of teeth from

the stand point of strength and check the design from the

standpoint of wear. Take surface endurance limit as 630 MPa

and the modulus of elasticity for CI as 84 kN/mm2.

Example B2

٢٥Bevel Gears

Example B3

A pair of bevel gears (14.5̊ tooth form) connect two shafts at

right angles and transmits 9 kW. Determine the required module

and gear diameters for the following specifications.

Gear Pinion Particulars

6021z

Grey CISemi-steelMaterial

160200BHN

5585All. Static stress MPa

4201200Speed rpm

٢٦Bevel Gears

Design

Prof. Samy J. Ebeid ١٤

A pair of 20̊ full depth teeth bevel gears connect two shafts at right angles

with a velocity ratio 3:1. The cast steel gear has an allowable static stress of

70 MPa and that of the steel pinion is 100 MPa. The pinion transmits 37.5

kW at 750 rpm.

Determine:

1. Module and face width.

2. Pitch diameters.

3. Pinion shaft diameter.

Tooth form factor = 0.154 – (0.912/Te), where Te is the formative number of

teeth.

Width = 1/3 the length of pitch cone.

Pinion shaft overhangs by 150 mm.

Example B4

٢٧Bevel Gears