Why involute gears have straight path of contact?

[rahulpark]

my lecturer keeps saying that path of contact of an involute gear is straight line but without the reason. i can't digest it as i can't find the reason for this behaviour. I'm trying my best to find the reason. Internet too can't find an answer. Books don't give a timeline of how it happens. Can anyone give a convincing answer?

 

[marellasunny]

you mean 'involute gear profile'.

 

[rahulpark]

Yes, it's involute gear profile

 

[OCR]

my lecturer keeps saying that path of contact of an involute gear is straight line

You're lecture's statement sounds right...

A property of the involute tooth form is that if the gears are meshed properly, the line of action is straight and passes through the Pitch Point of the gears.

http://en.wikipedia.org/wiki/Involute_gear

http://en.wikipedia.org/wiki/Gear#Line_of_Action



OCR

 

[marellasunny]

The usual way that lecturers today express advantages of involute profiles is by comparing them to the cycloidal gear tooth profile.Cost reasons apart,in an involute gear profile you can vary the distance between the pinion centre and driven gear centre without changing the angular velocity ratio(see law of gearing).This is very important for mechanical engineers as they don't have to worry about the tolerances so much.Big difference when compared to other profiles.

 

[Ranger Mike]

Spur or straight cut gears mess teeth along one line more quickly than spriral cut hypoid or involute gears. The pressure angle is max atthe start , goes to zero at mid rotation and returns to max pressure just prior to disengaement. This maximum pressure angle at the " tip " of the can cause high stress breakage with enough load. Spur gears are noisy and subject to higher shock due to more immediate contact upon engagement. The drive gear and driven gear must be located EXACTLY to permit proper meshing. Early Ford flatead engine automobiles used bevel (straight cut) ring and pinion differentials and would break teeth when horsepower was increased enough. Spiral cut gears engage at one POINT then gradually move this enagement point along the entire gear face yet maintain the same contact ANGLE PRESSURE from intial engagement to disengagement. These gears are smoother engaging and more quiet in operation and can handle more power load because of this gradually loading and holding the same pressure over the entire rotation. The drive and driven gear do not require as precise of a location as the spur gear and are less burdensome to assemble. Automobile manufacturers went to spiral bevel to handel the increased horsepower required for heavier vehciles and eventually settled on the hypoid design because they could lower the drive shaft and whole rear center of gravity.
Or something like that..

http://gearcutting.blogspot.com/2008/02/comparison-between-involute-and.html

 

[rahulpark]

You're lecture's statement sounds right...http://en.wikipedia.org/wiki/Involute_gear

http://en.wikipedia.org/wiki/Gear#Line_of_Action
OCR

i'm asking the mathematical and physical proof for this, not the statement

 

[marellasunny]

Spur or straight cut gears mess teeth along one line more quickly than spriral cut hypoid or involute gears. The pressure angle is max atthe start , goes to zero at mid rotation and returns to max pressure just prior to disengaement. This maximum pressure angle at the " tip " of the can cause high stress breakage with enough load. Spur gears are noisy and subject to higher shock due to more immediate contact upon engagement. The drive gear and driven gear must be located EXACTLY to permit proper meshing. Early Ford flatead engine automobiles used bevel (straight cut) ring and pinion differentials and would break teeth when horsepower was increased enough. Spiral cut gears engage at one POINT then gradually move this enagement point along the entire gear face yet maintain the same contact ANGLE PRESSURE from intial engagement to disengagement. These gears are smoother engaging and more quiet in operation and can handle more power load because of this gradually loading and holding the same pressure over the entire rotation. The drive and driven gear do not require as precise of a location as the spur gear and are less burdensome to assemble. Automobile manufacturers went to spiral bevel to handel the increased horsepower required for heavier vehciles and eventually settled on the hypoid design because they could lower the drive shaft and whole rear center of gravity.
Or something like that..

http://gearcutting.blogspot.com/2008/02/comparison-between-involute-and.html

But theory states distance between 2 involute gear profiles don't matter that much,take for example the 14.5 deg pressure angle set-ups.You could bring the gears close enough till the point of interference and bring them far apart enough keeping in mind the contact ratio never goes below 1.
I guess the velocity ratio stays constant in these distance limits no matter what.But,please clarify your point about distances between gears again.