Premium Cycloidal Simulator · Tutorial
Cycloidal Drive Contact & Stress Analysis: A First‑Pass Tutorial
A cycloidal drive’s load capacity is limited as much by the Hertzian contact between the housing pins and the disc lobes as by the gear teeth themselves. Run the analysis in the Premium Cycloidal Simulator: set up a nominal drive, run the full housing-pin contact sweep, and make controlled material and thickness comparisons — without treating the panel as a design approval.
1Before you run
What the panel needs
This tutorial walks through a full cycloidal drive contact stress analysis: a steel baseline run, then two controlled comparisons — material stiffness and disc thickness — so you can see exactly what drives the reported peak stress up or down, and why neither comparison alone proves a material or thickness choice.
Scope: this is a first-pass, linear-elastic Hertzian contact analysis. It does not calculate a safety factor, validate a material selection, or predict fatigue life. Material strength, heat treatment, surface finish, lubrication, contamination, fatigue duty cycle, tolerances, and a suitable safety factor remain engineering decisions outside this panel.
The Contact & Stress Analysis panel evaluates the housing-pin contact over a crank-angle sweep. Start from a valid drive geometry. The lobe count is derived by the app: with 30 external pins, the drive has 29 lobes.
Drive inputs
Ring diameter, external-pin count, and external-pin diameter define the stationary ring interface. The output mechanism is set by its pin count, pin diameter, and output-disk diameter. Eccentricity controls the orbit; shaft-hole diameter and disc thickness complete the physical disc definition.
Analysis inputs
Enter the applied input torque and choose its unit. Young’s modulus and Poisson ratio define the elastic-contact response for each material.
2Baseline setup
Enter the controlled baseline
Use the following baseline exactly. It makes later differences attributable to one stated change at a time.
For this tutorial, use a representative steel baseline: Same Material enabled, with Young’s modulus of 206 GPa and Poisson ratio of 0.30 for the disc, housing pins, and housing. These are generic elastic properties, not a specific steel grade or a material-approval result.
| Group | Setting | Value |
|---|---|---|
| Ring | Fixed ring diameter / external pins / pin diameter | 100 mm / 30 / 6 mm |
| Output | Output pins / pin diameter / output disk | 6 / 8 mm / 62 mm |
| Disc | Eccentricity / shaft hole / thickness / phase | 1.2 mm / 40 mm / 5 mm / 1 |
| Load | Input torque | 10 Nm |
| Material | Same Material / elastic modulus / Poisson ratio | On (Shared) / 206 GPa / 0.30 |
3Run and read
Run the full analysis and read the baseline
- In Contact & Stress Analysis, set Input Torque to 10 Nm. Leave Same Material enabled and enter the steel baseline properties shown above.
- Select Run Full Analysis. The Premium full run sweeps 181 samples from 0° through 180°.
- Read the three summary cards and then inspect the stress-envelope and force-distribution charts. Select 30°, 60°, 90°, and 120° to change the force snapshot.
Dashboard reading: the three summary cards are calculated from the displayed selected-angle set (30°, 60°, 90°, and 120°), while the line chart shows the complete 0°–180° sweep. For this baseline, the summary-card peak is 410.49 MPa; the highest point anywhere on the full sweep is 434.66 MPa at 150°.
Baseline checkpoint
- Record: the 434.66 MPa full-sweep peak at 150° together with the three summary-card values. The later runs will re-read both the peak magnitude and its crank-angle location.
- Use: the next two comparisons change one input group at a time and then re-read these same outputs, giving each observed difference a clear cause.
4Material swap
Compare to a different material
For this comparison, use aluminum (AL) as the different material. Keep Same Material enabled and replace the shared steel properties with 69 GPa and 0.33. Because the disc, pin, and housing are being treated as one uniform material, one shared property pair is the clearest setup:
| Field | Value |
|---|---|
| Same Material | On (Shared) |
| Shared elastic modulus | 69 GPa |
| Shared Poisson ratio | 0.33 |
Do not change geometry, torque, phase, or any other analysis input. Run Full Analysis again. This is a stiffness-model comparison, not a statement that aluminum is suitable for the product.
Engineering observation — material stiffness
- Why stress drops: for this Hertzian line-contact model, with geometry and axial contact length fixed,
σmax ∝ √(F E*). For identical materials,E* = E / [2(1 − ν2)], giving approximately 113.2 GPa for steel and 38.7 GPa for aluminum. A softer contact deforms more, creating a wider pressure patch in the rolling direction and reducing peak pressure. - Theory check: the predicted stress ratio is
√(38.7 / 113.2) = 0.585; the full-sweep results give254.39 / 434.66 = 0.585. The match confirms that the solver responds consistently with the Hertz relation it implements. - Why force barely moves: Cycle-Max force changes from 42.96 N to 44.05 N, about 2.5%, because torque equilibrium and geometry primarily determine the required load. Elastic compliance only redistributes it slightly among pins, while full-sweep peak stress falls about 41.5%.
- What this means: lower calculated stress does not make aluminum the better material. Aluminum alloys generally have far lower allowable contact stress than hardened gear or bearing steels. Alloy, heat treatment, hardness, surface condition, lubrication, and fatigue duty must be evaluated separately. This run demonstrates stiffness sensitivity, not improved design margin.
5Thickness case
Restore steel, then change only thickness
Restore the steel baseline first: Same Material on, 206 GPa, and 0.30. Keep every baseline geometry and load value, then change disc thickness from 5 mm to 10 mm and run Full Analysis.
Engineering observation — disc thickness and axial contact length
- Why stress drops: for line contact with material and geometry fixed,
σmax ∝ √(F / B), whereBis the contact length along the pin axis, modeled here as equal to disc thickness. - Theory check: doubling thickness from 5 mm to 10 mm predicts
1 / √2 = 0.707. The full-sweep results give307.23 / 434.66 = 0.707, matching the model relation to the displayed precision. - What this means: doubling thickness reduces peak stress by about 29.3%, not 50%. Each further doubling applies the same 0.707 multiplier but produces a smaller absolute reduction in MPa, while disc material volume and axial envelope increase roughly in proportion to thickness. The benefit comes with diminishing absolute returns and packaging and mass tradeoffs.
6Cross-run comparison
Compare the recorded full runs
| Scenario | Only intended change | Selected-angle peak stress | Cycle-Max force | Cycle-Mean peak force | Full-sweep peak stress |
|---|---|---|---|---|---|
| Steel baseline | — | 410.49 MPa | 42.96 N | 37.19 N | 434.66 MPa @ 150° |
| Uniform aluminum stiffness | 69 GPa, ν = 0.33 for disc, pin, housing | 239.43 MPa | 44.05 N | 37.45 N | 254.39 MPa @ 150° |
| Steel, 10 mm disc | Thickness 5 → 10 mm | 290.67 MPa | 42.39 N | 37.06 N | 307.23 MPa @ 150° |
Cross-run conclusion
- Load versus stress: torque establishes the load; stiffness and axial contact length govern how that load becomes contact stress. Cycle-Max force stays between 42.39 N and 44.05 N, a span of about 4% relative to the baseline, while full-sweep peak stress ranges from 254.39 MPa to 434.66 MPa.
- Peak location: all three full-sweep peaks occur at 150°. Changing uniform material stiffness or disc thickness changes the peak magnitude in these runs, but not its crank-angle location.
- Central consistency check: the 0.585 material ratio matches the effective-modulus prediction, and the 0.707 thickness ratio matches the axial-contact-length prediction. This shows that the implemented model follows its Hertzian square-root scaling; it is not independent validation against physical testing.
- Design use: use these comparisons to understand sensitivity, then compare the calculated stress with a separately justified allowable contact stress and safety factor. The panel alone does not establish material suitability, fatigue life, or design approval.
7Reference
Assumptions, limitations, and glossary
Model assumptions
- Ideal theoretical geometry with no profile modification.
- No manufacturing or assembly errors: eccentricity, pin radius, and pin-position errors are zero.
- Rigid housing support; pin-to-housing deformation is not modeled.
- Idealized load sharing with perfect geometry and zero clearance assumptions.
- Linear-elastic Hertzian contact behavior.
Terms used in the panel
- Peak Housing Contact Stress: highest selected-angle Hertzian stress.
- Cycle-Max Housing Force: largest pin force among the selected-angle snapshots.
- Cycle-Mean Peak Force: mean of each snapshot’s highest housing-pin force.
- Active Loaded Contacts: housing pins carrying non-zero modeled load at the selected angle.
- Stress envelope: stress value traced over the full crank-angle sweep.
Symbols used in the observations
- F: normal force carried by the contacting pin pair.
- E*: effective contact modulus combining the elastic response of both contacting materials.
- ν: Poisson ratio.
- B: contact length along the pin axis, modeled here as equal to disc thickness.
- σmax: maximum Hertzian contact pressure, reported by the panel as contact stress.
Model reference: Li et al., “Design and Load Distribution Analysis of the Mismatched Cycloid-Pin Gear Pair in RV Speed Reducers,” Machines, 2022, 10, 672. This tutorial reflects the Premium UI workflow and solver behavior in this repository at the time of writing.
8FAQ
Frequently asked questions
Does cycloidal drive contact stress depend on the housing and pin material?
Yes. In this linear-elastic Hertzian model, peak contact stress scales with the square root of the effective contact modulus. Swapping a shared 206 GPa steel baseline for 69 GPa aluminum — with every other input unchanged — dropped the full-sweep peak stress from 434.66 MPa to 254.39 MPa, about a 41% reduction. See section 4 for the run and the theory check.
How does disc thickness affect cycloidal drive contact stress?
Increasing disc thickness widens the modeled axial contact length, and peak stress scales with the inverse square root of that length. Doubling thickness from 5 mm to 10 mm reduced the full-sweep peak stress by about 29%, not 50%, so each further doubling gives a smaller absolute benefit for a proportional increase in material and axial envelope. See section 5.
What does a Hertzian contact stress analysis assume?
This panel assumes ideal theoretical tooth geometry with no profile modification, zero manufacturing or assembly error, a rigid housing, idealized load sharing, and linear-elastic material behavior. It reports a first-pass stress result, not a safety factor or fatigue life prediction. See the full list in section 7.
Is a lower calculated contact stress enough to choose a material?
No. A lower Hertzian stress result only reflects lower stiffness in the model — it says nothing about allowable contact stress, which for a softer material like aluminum is typically far lower than for hardened steel. Material selection also requires alloy, heat treatment, hardness, surface finish, lubrication, and fatigue duty to be evaluated separately, then compared against a justified allowable stress and safety factor.
