Cam Follower Motion & Contact Force Calculator — Max Acceleration, Contact Force and Contact Severity Index
Calculate max acceleration, max contact force and contact severity index using cam lift, duration angle, speed, motion law and follower data.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Cam motion
Follower & spring
Cam geometry
Contact & limits
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Max acceleration formula:
h = cam lift / 1000
β = cam duration angle · π / 180
ω = 2 · π · cam speed / 60
a = Ca · h · ω² / β²
Max contact force formula:
k = spring stiffness · 1000
Fi = follower mass · a
Fs = k · h + preload force
F = Fi + Fs
Contact severity index formula:
R = base circle radius / 1000
b = contact width / 1000
I = √(F / (b · R))
Motion-law coefficients:
- Harmonic: Cv = π / 2, Ca = π² / 2, Cj = π³ / 2
- Cycloidal: Cv = 2, Ca = 2π, Cj = 4π²
- Constant acceleration: Cv = 2, Ca = 4, Cj = 8
Additional calculated values:
- v = Cv · h · ω / β
- j = Cj · h · ω³ / β³
- Fmin = preload force − Fi
- Contact loss occurs when Fmin ≤ 0
- Index ratio = I / allowable contact index
- Dynamic factor = F / Fs
- Dynamic severity = a / 9.81
where:
- a — max acceleration (m/s²)
- F — max contact force (N)
- I — contact severity index (-)
- h — cam lift converted from input length to metres (m)
- β — cam duration angle converted from degrees to radians (rad)
- ω — angular speed converted from rotational speed (rad/s)
- k — spring stiffness converted from input spring rate to N/m
- R — base circle radius converted from input length to metres (m)
- b — contact width converted from input length to metres (m)
- Cv, Ca, Cj — motion-law coefficients (-)
When to use this calculator
When to use this calculator:
- Estimate maximum follower acceleration from cam lift, cam duration angle, rotational speed and selected motion law.
- Calculate maximum contact force from follower inertia force, spring force and preload force.
- Check whether preload force is sufficient to keep the follower in contact when inertia force increases.
- Compare contact severity index against an allowable contact index defined by the user.
- Evaluate how cam speed, cam duration angle and motion law change dynamic severity and contact loading.
How to interpret the result
Max acceleration is defined as the peak follower acceleration generated by the selected cam motion law, cam lift, cam duration angle and cam speed.
Max contact force is defined as the sum of follower inertia force and maximum spring force. It increases when follower mass, max acceleration, spring stiffness, cam lift or preload force increases.
Contact severity index is defined as the square root of max contact force divided by contact width multiplied by base circle radius. It increases with max contact force and decreases with larger contact width or larger base circle radius.
- Safe — minimum normal force is greater than 0, index ratio is not greater than 0.8, index ratio is not greater than 1, and dynamic severity is not greater than 50.
- Warning — index ratio is greater than 0.8 while not greater than 1, or dynamic severity is greater than 50, with no contact loss.
- Invalid — minimum normal force is less than or equal to 0, or index ratio is greater than 1.
The result is used to evaluate follower acceleration, contact force level, contact-loss risk and contact severity against the allowable contact index.
Calculation example
Example:
A user checks a cam follower with a 12 mm lift, 90° cam duration angle and 600 rpm cam speed using a harmonic motion law.
- Cam lift: 12 mm
- Cam duration angle: 90°
- Cam speed: 600 rpm
- Motion law: harmonic
- Follower mass: 0.8 kg
- Spring stiffness: 20 N/mm
- Preload force: 80 N
- Base circle radius: 40 mm
- Contact width: 10 mm
- Allowable contact index: 1000
The calculated max acceleration is about 1184.35 m/s², the max contact force is about 1267.48 N and the contact severity index is about 1780.48.
Assumptions and limitations
- The selected motion law is limited to harmonic, cycloidal or constant acceleration.
- Cam lift is converted from millimetres to metres inside the calculation.
- Cam duration angle is converted from degrees to radians inside the calculation.
- Cam speed is converted to angular speed using ω = 2 · π · n / 60.
- Spring stiffness is converted from N/mm to N/m inside the calculation.
- Base circle radius and contact width are converted from millimetres to metres inside the calculation.
- Contact loss is evaluated from minimum normal force equal to preload force minus inertia force.
- Contact severity is evaluated using the user-defined allowable contact index.