Cam Pressure Angle, [μ]

Pressure-Angle represents the efficiency with which the cam transfers its motion and force to the follower, and vice versa.

Understanding Pressure Angle.

Imagine pushing a door to open it...

If you push the door handle at 90º to the door (perpendicular[⊥], or normal, to the door), you will open the door easily. You only need to overcome the inertia force of the door and any friction in the hinges.
If you push the door handle at 45º, then you will need to:
oHold on to the door's handle so that your hand does not slide across the door.
oThe reaction force with which the handle stops your hand sliding across the door is also the force pulling on the door's hinges, which also pull on the door frame. You hand also feel this force react against your hand.

The angle with which you push the door is similar to the pressure-angle between a cam-profile and the cam-follower lever.

Pressure Angle and Force Vectors 

Pressure Angle and Force Vectors

The three vectors of the 'force-triangle' [usually taken at the centre of the cam follower] that result from the contact between the cam-profile and the cam-follower are the:

Contact Force. [ 'Hypotenuse' of the force-triangle]. Its direction is normal to the cam at the cam-contact point.
Useful-Force. [ 'Adjacent' of the force-triangle]. Its instantaneous direction in which the cam-follower must move.
Useless-Force. [ 'Opposite' of the force-triangle]. Its direction will 'stretch a Swinging-Arm Follower, or 'bend' a Translating Follower.

From the three vectors, we can define Pressure-Angle

The Pressure Angle, μ, is, by definition, the angle between the direction in which the cam-follower must move and the direction normal to the cam at the point of contact between the cam and cam-follower.

 

Definition:

Pressure Angle, μ, is the 'angle between the direction in which cam-follower moves and the direction of the force transmission from the cam to the cam-follower'.

Pressure Angle = Cos-1

(

 

Useful Force

)

Contact Force


Pressure Angle Limits: Rules-of-Thumb

When a Cam has a Translating Cam-Follower, limit the Pressure Angle to less than ±30º
When a Cam has a Swinging Cam-Follower, limit the Pressure Angle to less than ±35º

To reduce the Pressure Angle

Improve the motion design. Can you increase the duration of a segment? Can you change the cam-law to one with a lower peak velocity?

Move the position of the cam-follower's pivot axis. Change the pivot-point of the cam-follower. Or, if the follower is a 'translating follower', 'offset translating follower'.

Increase the size of the cam. The pressure-angle will decrease as you increase the size of the cam.


Force Vectors with different Pressure Angles

We can compare Contact, Useful, and useless Forces

If we assume a 'Useful Force' of 100N, then with a:

Pressure Angle is 0º:   Contact Force = 100.0N;     Useless Force = 0N
Pressure Angle is 10º: Contact Force = 101.5N;   Useless Force = 16.7N
Pressure Angle is 60º: Contact Force = 200.0N;   Useless Force =  173.2N
Pressure Angle - 30 degrees

^^ Pressure Angle 30 degrees ^^

Pressure Angle = 30º

Useful Force      = 100N
Contact Force   = 115N
Useless Force    = 57.7N

The force that tries to 'stretch' the Cam Follower arm is 57.7% of the useless force.

The Contact Force is 15% more than the useful force.

Pressure Angle 45 degrees

^^ Pressure Angle 45 degrees ^^

Pressure Angle = 45º

Useful Force       = 100N
Contact Force    = 141.4N
Useless Force     = 100N

The force that tries to 'stretch' the Cam Follower arm is the same as the useless force.

The Contact Force is 41.4% more than the useful force.

Overturning Moment

The Overturning Moment applies to Flat-Faced Translating Follower. It is the product of the distance from the contact point to the sliding axis of the follower and the contact-force.

Pressure Angle does not apply to a translating, flat-faced follower, when the face is normal to the direction of travel.

Understanding Overturning Moment

Imagine you want to slide a plank of wood along a wall.

Imagine an 'axis' along the middle of the plank , that is coincident with the plank's centre-of-mass.
Ff = Friction-Coefficient [μ] × weight of the table [m×g]. [Note: do not confuse Friction-Coefficient, μ, and Pressure Angle, μ].
If you push the plank at a single point in a direction that is parallel to the the wall, and your hand is co-axial with the centre-of-mass 'axis', then the force needed will be the 'Frictional-Force'.

The plank will not tend to rotate. The wall does not need to react against the sides of the plank. It is as if the wall is not there.

Over-turning Moment

If you push the plank at a point nearer  to the wall [offset to the side of its centre-of-mass 'axis'], then you will tend to rotate [turn] the plank.

The 'Overturning Moment' = Frictional force[Ff] × perpendicular distance to your hand from plank's centre-of-mass 'axis'.

Clearly, the further away from the plank's centre-of-mass you push, the greater the over-turning moment.

Re-turning Moment

The overturning-moment will make the near corner of the plank press in to the wall and the other corner of the plank lift off the wall.

If the plank is being pushed between two walls, as if the two walls behave as a linear bearing then the reaction forces will be at the opposite ends of the plank.

Re-turning moment = contact force against walls at the corners of the tables × length of table = –ve overturning table.

If plank table is long, then the contact-force becomes less. If the plank is short, then the contact-force increases, but the overturning-moment remains the same.

Over-turning moment in Flat-faced Follower

These forces are the similar to those on a cam and flat-faced follower. During the motion of the follower, the contact point and the contact-force moves across the follower to one side then the other.

Over-turning moment = Contact-Force × distance to the 'sliding-axis' from the contact-point.

Re-turning moment = Reaction-Forces at Points at each end of the Lines in the Sliding-Joint × distance between Points in Sliding-Joint.

GA-OverturningMoment

In the image: we can see the top of a 'cam'.

The contact force is 20N, and it is 50mm from the vertical sliding axis of the cam-follower.

Thus:

Contact Force [20N] × Distance to Contact Point [50mm] = Overturning Moment [1000N.mm]

Overturning Moment = Re-turning moment of the slide.

Re-turning Moment [1000N.mm] = Length of Sliding-Part [30mm] × Reaction Forces [33.33N]

How to reduce the Over-turning Moment:

1.Improve the motion design.

Can you increase the duration of a segment? Can you change the cam-law to one with a lower peak velocity?

2.Move the position of the cam-follower's sliding axis relative to the cam's centre.

Change the the 'translating follower' to an 'offset translating follower' as alternative [Move the Sliding-Axis towards the Contact-Point.

This only applies when the contact force is is different for each direction of the followers motion.

3.Increase the size of the cam

This does not make any difference to the contact-force or overturning moment. However, the cam's radius of curvature increases, which will reduce its Hertzian Contact-stress.

4.Increase the length of the 'Sliding-Joint'

The contact force at each of the sliding-joint is inversely proportional to the length of the sliding-joint.

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