PPT: Gear Trains | Theory of Machines (TOM) - Mechanical Engineering PDF Download

 Page 1


Contact Ratio
• To transmit rotational motion continuous there must be at least one pair of 
contacting teeth at all times
• Typically, there are more than one pair in contact, hence overlapping of teeth
• Contact Ratio is used to provide quantitative measure of the amount of overlap
?????????????? ?????????? ?? ?? =
??????????h ???? ???????????? ???????? ????????h
???????? ????????h (?? ?? )=
2?? ?? ?? 2
?? 2
Page 2


Contact Ratio
• To transmit rotational motion continuous there must be at least one pair of 
contacting teeth at all times
• Typically, there are more than one pair in contact, hence overlapping of teeth
• Contact Ratio is used to provide quantitative measure of the amount of overlap
?????????????? ?????????? ?? ?? =
??????????h ???? ???????????? ???????? ????????h
???????? ????????h (?? ?? )=
2?? ?? ?? 2
?? 2
?? ?? =
???? ???????? ????????h
=
????
???????? ????????h
=
???? ?? ?? ???? = ???? +???? + ???? +????
- ???? +???? +???? ???? = ?? ?? +???? -????
???? = ???????? ?? ?? =?? ?? 1
+?? ?? 2
?? ?? =
( ?? 2
?? 1
-?? 2
?? 1
)
1
2
+( ?? 2
?? 2
-?? 2
?? 2
)
1
2
-???????? ?? 2?? ?? ?? 2
?? 2
Contact Ratio
Page 3


Contact Ratio
• To transmit rotational motion continuous there must be at least one pair of 
contacting teeth at all times
• Typically, there are more than one pair in contact, hence overlapping of teeth
• Contact Ratio is used to provide quantitative measure of the amount of overlap
?????????????? ?????????? ?? ?? =
??????????h ???? ???????????? ???????? ????????h
???????? ????????h (?? ?? )=
2?? ?? ?? 2
?? 2
?? ?? =
???? ???????? ????????h
=
????
???????? ????????h
=
???? ?? ?? ???? = ???? +???? + ???? +????
- ???? +???? +???? ???? = ?? ?? +???? -????
???? = ???????? ?? ?? =?? ?? 1
+?? ?? 2
?? ?? =
( ?? 2
?? 1
-?? 2
?? 1
)
1
2
+( ?? 2
?? 2
-?? 2
?? 2
)
1
2
-???????? ?? 2?? ?? ?? 2
?? 2
Contact Ratio
Question
The pitch circle radii of two involute spur gears in mesh are 51.5mm 
and 64.2mm. The outer circle radii are 57.5mm and 71.2mm, 
respectively, the operating pressure angle being 20 degrees. 
Determine 
1) Length of the path of contact
2) Contact ratio if the number of teeth on the larger gear is 20
?? ?? = ?? ?? ?????? ??
Page 4


Contact Ratio
• To transmit rotational motion continuous there must be at least one pair of 
contacting teeth at all times
• Typically, there are more than one pair in contact, hence overlapping of teeth
• Contact Ratio is used to provide quantitative measure of the amount of overlap
?????????????? ?????????? ?? ?? =
??????????h ???? ???????????? ???????? ????????h
???????? ????????h (?? ?? )=
2?? ?? ?? 2
?? 2
?? ?? =
???? ???????? ????????h
=
????
???????? ????????h
=
???? ?? ?? ???? = ???? +???? + ???? +????
- ???? +???? +???? ???? = ?? ?? +???? -????
???? = ???????? ?? ?? =?? ?? 1
+?? ?? 2
?? ?? =
( ?? 2
?? 1
-?? 2
?? 1
)
1
2
+( ?? 2
?? 2
-?? 2
?? 2
)
1
2
-???????? ?? 2?? ?? ?? 2
?? 2
Contact Ratio
Question
The pitch circle radii of two involute spur gears in mesh are 51.5mm 
and 64.2mm. The outer circle radii are 57.5mm and 71.2mm, 
respectively, the operating pressure angle being 20 degrees. 
Determine 
1) Length of the path of contact
2) Contact ratio if the number of teeth on the larger gear is 20
?? ?? = ?? ?? ?????? ?? Primary Gear Characteristics
• Pressure angle/ tooth profile
• Face Width
• Gear ratio or number of teeth on both gears
• Centre to centre distance
• Module
Page 5


Contact Ratio
• To transmit rotational motion continuous there must be at least one pair of 
contacting teeth at all times
• Typically, there are more than one pair in contact, hence overlapping of teeth
• Contact Ratio is used to provide quantitative measure of the amount of overlap
?????????????? ?????????? ?? ?? =
??????????h ???? ???????????? ???????? ????????h
???????? ????????h (?? ?? )=
2?? ?? ?? 2
?? 2
?? ?? =
???? ???????? ????????h
=
????
???????? ????????h
=
???? ?? ?? ???? = ???? +???? + ???? +????
- ???? +???? +???? ???? = ?? ?? +???? -????
???? = ???????? ?? ?? =?? ?? 1
+?? ?? 2
?? ?? =
( ?? 2
?? 1
-?? 2
?? 1
)
1
2
+( ?? 2
?? 2
-?? 2
?? 2
)
1
2
-???????? ?? 2?? ?? ?? 2
?? 2
Contact Ratio
Question
The pitch circle radii of two involute spur gears in mesh are 51.5mm 
and 64.2mm. The outer circle radii are 57.5mm and 71.2mm, 
respectively, the operating pressure angle being 20 degrees. 
Determine 
1) Length of the path of contact
2) Contact ratio if the number of teeth on the larger gear is 20
?? ?? = ?? ?? ?????? ?? Primary Gear Characteristics
• Pressure angle/ tooth profile
• Face Width
• Gear ratio or number of teeth on both gears
• Centre to centre distance
• Module
Gear Trains
• Combination of gears that is used for transmitting motion from one shaft 
to another is known as a Gear Train
• Two or more gears working in a sequence (train) are called a gear train
• Idler gear
• A single idler gear is used to reverse the direction
• Gear Trains
1. Simple gear train
2. Compound gear train
3. Epicyclic gear train