It is important to know the payload-type when we design a cam-mechanism.

The Payload refers back to the Follower and back to the Cam-Profile and Cam-Shaft. Thus, the load that is on the Cam-Shaft is a function of the payload-type at the Follower.

Thus, the different payload-types result in different loads on the Cam-Shaft.

We derive the nominal output loading from the following Payload-Types.

A: Force or Torque: constant.

For example, friction, gravity, work loads.

B:  Force or Torque: proportional to displacement.

For example, a spring.

C : Force or Torque: proportional to velocity.

For example, viscosity.

D : Force or Torque: proportional to acceleration.

For example, inertia.

E : Force or Torque: conforms to a special function.

For example, an engine cycle.

EXAMPLE 1A: Gravity, Spring, and Inertia: Speed Dependence

The two images show the same payload-types on a cam mechanism, at two different speeds.

The payload-types in the example are:

• Constant Load 

• Spring Load 

• Inertia Load 

You can see that at high-speed the payload at is greater the payload at .  The inertia force is the only force to have increased. The phase at which the payload is a maximum is also different.

At the higher speed the load also becomes negative at , in the deceleration of the rise motion-segment.

EXAMPLE 1B : Gravity, Spring and Inertia: Different Pre-load of Spring

The image below shows the period of negative loading when the cam has a 'falling' motion.

In such a case, the Follower-Roller would lose contact with the Cam-Profile, and you would lose control of the payload.

To make sure the Follower-Roller remains in contact with the Cam-Profile:

•Improve the motion design to reduce the maximum negative acceleration.

•Use an enclosed track, a blade cam, or a conjugate cam

- or -

•Increase the Constant Load(A) or Spring Load(B)

Most indexing mechanisms, and many reciprocating and oscillating mechanisms, have a load that combines a Constant Load (A) and an Acceleration Load (D), with less significant amounts from the other load-types.

Constant Load - friction forces (bearing seals), gravitational force, and other work loads - can be resolved into a single force or torque resisting the output motion.

Acceleration Load - from the inertia of various masses - can be resolved into a single equivalent inertia connected to the Follower.

Total load = inertia load + constant load.

The peak of the total load usually is at the same point as the maximum inertia load.

Other common Payload Types

•Index mechanisms: Friction(A) + Inertia(D).

•Spring-loaded reciprocating mechanisms: Friction(A) + Spring Pre-Load(A) + Spring-Rate(B) + Inertia(D).

•Very high-speed mechanism: possibly significant Viscous Load (C) + Inertia Load(D).

The maximum value and proportion of each type of load component (A, B, C, D and E) depends on the application. Thus, there is an infinite number of load patterns. It is possible to tabulate normalized values for the most common combinations.

Payload for Conjugate Cams

The idealized design of Conjugate Cams eliminates the need for a Spring to maintain the contact of the Follower-Roller against the Cam-Profile. Frequently, the Follower-Roller rollers are adjusted, or designed, to give an 'optimal' pre-load against the Cam-Profile, so that the Follower-Rollers do not slip.

This is an idealized design. More frequently, manufacturing and machining tolerances, mean it is difficult to guarantee contact between throughout the cam's rotation.

The Follower-Roller will often lose contact during some part of the machine cycle.

Frequently, Conjugate Cams use a spring, air-cylinder or hydraulic device, to force one of the Follower-Rollers against the cam to eliminate backlash. The loading device only needs a short travel to compensate for manufacturing tolerances.

Inertia Load

The maximum inertia load ( from these simple equations, of course :

The Inertia Load or are nominal, and must be modified by the application of the Torsion-Factor,

and  

- Output Stroke (Angular Displacement)

- Output Stroke (Linear Displacement)

- Acceleration Coefficient

- Inertia Force at the Follower

- Inertia Torque at the Follower

- equivalent Inertia referred to the Follower

- equivalent payload mass at the Follower)

- Motion Period

Friction Load

A Constant Load, such as friction, is:

• for linear motion

• for rotary motion

Referred to the mechanism output in both cases. Add the Friction Load to the Inertia Load.

Spring Load

When there is an output load component that is proportional to displacement, such as a spring force, it is convenient to add the Maximum Spring Force to the Friction-Force, , or Friction-Moment, , as if it is a constant load.

In that case, the total output-load calculation is conservative. These are safe values for preliminary designs.

Load Mix: Inertia; Friction; Spring

As an alternative to the conservative loading, we can take all three load patterns into account. When appropriate, the maximum load can be adjusted downwards by a load-mix coefficient, .

Thus:

Pre-load Coefficient, K

Example Rotary Loads Mp: Minimum Non-Inertia Load Mf: Maximum Non-Inertia Load

The Spring Rate Effect is defined by a 'pre-load coefficient', . It applies to all cam systems. is the ratio of Minimum non-inertia loading : Maximum non-inertia loading. , = minimum non-inertia load (p = pre-load) , = maximum non-inertia load (f = full-load) Linear System Rotary System When there is no spring component to the load (see top image to the above), Thus,

Inertia Ratio, Q

The input-torque (drive torque) varies throughout the motion. The variation is a function of the output-load and the motion-law.

Since the output-load varies with the mix of inertia-load, spring-load, and constant-load, so too does the input-torque.

For all cases, the mix is defined with the factors and , as defined above.

For each motion-law, the instantaneous input-torque can be expressed as a function of the instantaneous output-load:

for linear motion

for rotary motion

Where: :

- cam output torque

- output force

- normalized velocity factor of cam-law

- linear output stroke

- angular input stroke

- output torque

- angular output stroke

- efficiency of the cam and follower mechanism

The instantaneous output load, or , is a function of the normalized motion-law factors, the load mix, and the payload.

Thus, the above equations can also be expressed as:

- or -

The maximum value of occurs during the acceleration phase.

It can be simply expressed by introducing a normalized Input-Torque Coefficient, .

Input Torque Coefficient (No Spring Loading, )

Thus:

- for linear motion

- for a rotary motion.

- Peak Input Torque

The value of , the Input-Torque Coefficient, can be evaluated for any motion-law and a range of load mix factors. The input torque patterns for some standard motion-laws are shown (below) for different values of and when (no spring loading). From these patterns it can be seen that there is a wide disparity between the input torques of different motion-laws, for all values of .