BIZOMAT MAKEOS · Mechanics
Cam Follower Return Spring Check (Inertia Force, Jump Speed)
Is my follower return spring strong enough to keep the follower on the cam at this speed, and at what speed will the follower start to jump?
Check of the spring that holds a cam follower against the cam: the peak deceleration of the follower for the motion law, rise, cam angle and speed (as the cam follower motion tool), the inertia force at that point, where in the rise it occurs, the spring force there from its preload and rate, the margin against jump, the speed at which the follower would leave the cam, and the largest spring force against the spring’s rating.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Motion law | choice | Motion law of the rise. |
| Rise (lift) | mm | Total rise of the follower. |
| Cam angle for the rise | ° | Cam angle over which the rise happens. |
| Cam speed | rpm | Cam speed. |
| Follower moving mass (with a third of the spring) | kg | Mass of the follower and everything moving with it, plus about a third of the spring. |
| Spring | ||
| Spring force with the follower at rest (bottom) | N | Force the spring exerts with the follower at the bottom of its travel. |
| Spring rate | N/mm | Rate of the spring. |
| Required margin over the inertia force | How much the spring force must exceed the inertia force where deceleration peaks. | |
| Largest force the spring is rated for | N | Largest load the spring can take without overstress (at full lift). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Motion law
- What it is
- The motion curve the cam profile follows during the rise; it sets the size of the peak acceleration and where in the rise it occurs.
- Units and format
- Choose one of 4 options from the list: Simple harmonic; Cycloidal; Constant acceleration (parabolic); 3-4-5 polynomial.
- Example
- The form opens with “Cycloidal” selected as a worked example. Choose the option that matches your case.
What this means: Rise (lift)
- What it is
- The total lift of the follower from its lowest to its highest position over the rise.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Peak deceleration and inertia force rise in proportion to the lift.
What this means: Cam angle for the rise
- What it is
- The angle the cam turns through while the follower completes its rise.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Peak deceleration falls with the square of the cam angle, so a longer rise angle reduces the inertia force sharply.
What this means: Cam speed
- What it is
- The rotational speed of the camshaft in service; check at the highest speed the machine runs.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Inertia force rises with the square of the speed.
What this means: Follower moving mass (with a third of the sprin…
- What it is
- The mass of the follower and everything moving with it, such as push rod, slide or valve, plus about one third of the spring’s own mass.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.001 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Inertia force is proportional to the moving mass.
- Get it right
- Enter kilograms; grams typed as kilograms overstate the inertia force a thousand times.
Spring
What this means: Spring force with the follower at rest (bottom)
- What it is
- The force the spring already pushes with when the follower is at the bottom of its travel: the installed preload.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More preload adds directly to the spring force where deceleration peaks and raises the jump speed.
What this means: Spring rate
- What it is
- The spring’s stiffness: the extra force per millimetre of compression, from the spring maker or a load test.
- Units and format
- Enter a number in N/mm: newtons per millimetre. The form accepts 0 N/mm to 10000000 N/mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 N/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter N/mm; a rate in N/m must be divided by 1000.
What this means: Required margin over the inertia force
- What it is
- The ratio by which the spring force must exceed the follower’s inertia force at the point of peak deceleration for the follower to stay on the cam.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest force the spring is rated for
- What it is
- The largest force the spring can take without overstress, from the spring maker; it is compared with the spring force at full lift.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Peak acceleration = c h ω² ÷ β² with c for the law (as the cam follower motion tool); the peak deceleration has the same size.
- It occurs at the end of the rise (harmonic), ¾ of the cam angle (cycloidal), from half the rise (parabolic) or at 0.789 of the angle (3-4-5); the spring force there = F₀ + k × lift at that point.
- Jump speed = speed × √(spring force ÷ inertia force); spring force at full lift = F₀ + k h.
- Example: the follower decelerates at 28.274 m/s², needing 42.412 N; the spring gives 114.55 N there, so the follower jumps at about 493.03 rpm.
Limitations
- Rigid follower and linkage; elasticity adds vibration that can cause jump earlier.
- Gravity and friction ignored; a vertical follower moving down gains help from gravity on the return.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a cam follower return spring
- Find the highest safe cam speed
- Check a cam after a speed increase
Who it is for
- Machine designers
- Automation engineers
- Design engineers
What you get
- Peak deceleration and inertia force
- Spring force where it peaks and the margin
- Jump speed and full-lift spring force
Interpreting the result
- Inertia force rises with the square of speed: a 40% speed increase roughly doubles the spring force needed.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2284–2309, 304–320. Topic reference; no source tables or recommended settings are reproduced.
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Open the Cam Follower Return Spring Check (Inertia Force, Jump Speed) calculator