d = p/sin(π/z); L pitches ≈ (z1+z2)/2 + 2C/p + (z2−z1)²p/(4π²C)
Two-sprocket fixed-pitch roller/bush chain approximation. Larger quadratic root is checked after selecting actual integer links. Sprocket OD/tooth profile is separate.
VALICALC / MECHANICAL ENGINEERING SUITE / DS09
Chain Drive Design Sheet
Start with pitch, sprockets and preliminary centers. Select a physical link count, recalculate the centers and review the resulting motion and pull without mistaking breaking strength for allowable working load.
Verified mathematical models with explicit assumptions. Component capacity and applicability are shown as separate checks.
Labeled example inputs • SI calculations • Project revision 0 • No account or cloud upload
01 / ENGINEERING INPUTS
Define the operating point
mm
Use actual link pitch, not sprocket tooth spacing measured at the OD.
mm
rpm
kW
kg/m
N
User-supplied sag/tension estimate; no historical sag coefficient applied.
N
Not breaking load. Verify chain family, speed, lubrication, load spectrum and supplier conditions.
deg
0 = unspecified; pitch-circle estimate only.
02 / CALCULATE → SELECT → RECALCULATE
Calculation & checks
Reduction ratio
3Driven RPM
100 rpmMean link-advance speed
2.38125 m/sEffective working pull
1,259.84252 NCentrifugal tension estimate
5.67035 NEstimated tight-span tension
1,365.51287 NTheoretical links
131.58314Selected physical links
132Actual center distance
766.05029 mmCenter adjustment
4.05029 mmNominal chain pitch length
2,514.6 mmDriver pitch diameter
151.9948 mmDriven pitch diameter
454.91827 mmSmall sprocket wrap · pitch-circle estimate
157.19294 degFixed-pin articulation at driver
14.4 degIdeal fixed-pin chordal variation
0.78853 %| Links | Actual center (m) | Adjustment (m) | Selection |
|---|---|---|---|
| 130 | 0.74661 | -0.01539 | compare |
| 132 | 0.76605 | 0.00405 | selected |
Criterion-specific verification
- PASSED · Actual integer-link recalculation
132 links; residual 0.00e+0 pitches using the established two-sprocket approximation.
- PASSED · Link assembly
Even count permits alternating-link assembly in the modeled geometry; actual connecting hardware remains to be verified.
- BLOCKED · Rated capacity, lubrication and life
No applicable current supplier dataset; breaking strength is not treated as permissible working load.
- UNKNOWN · Supplied steady working-pull criterion
No allowable working-pull criterion supplied.
- UNKNOWN · Supplied minimum wrap criterion
Ideal pitch-circle wrap comparison only; actual engaged tooth count and product rating are separate.
Method and calculation trace
Mean speed = pitch × driver teeth × RPM / 60; pull = power / mean speed. No pitch-circle speed substitution.
Mass/length and slack-span tension are user inputs. Centrifugal estimate m′v² is added separately; no historical sag or impact coefficients.
Chain construction: roller. No overall capacity approval.
Theoretical 131.58314349441153 pitches → selected 132 → actual center 0.7660502867456284 m. Each size change reruns the inverse and forward residual.
No automatic 0.2–0.4% center shortening from historical guidance; required installation slack is a separate physical adjustment.
Chordal variation = 1−cos(π/z), relative to ideal maximum pitch-circle speed, for the fixed-pin polygon only.
Assumptions & scope
Two sprockets, no idler; link-count and center equations are geometric approximations. No automatic center shortening or sag allowance is applied. Actual OD, take-up travel and installation tension need separate verification.
Roller and bush chains use the fixed-pin pitch-polygon model. Silent fixed-pin geometry needs a matching supplier convention. Rocker-joint silent chain retains mean speed and pull only; center/articulation/chordal predictions are BLOCKED pending its product model.
Capacity, fatigue, wear life, shock load, lubrication and allowable speed are BLOCKED without current applicable product data. A steady working-pull comparison does not establish chain-strength approval.
Mean link-advance speed differs from instantaneous pitch-circle peripheral speed. Ideal chordal variation is not a vibration or noise prediction.
Worked example
25/75 teeth, 19.05 mm pitch and 762 mm preliminary center give 131.583143 theoretical links. Selecting 132 links gives 766.050287 mm actual center. The worksheet derives both directions and compares adjacent even counts.
Calculation methods and sources
v mean = pzn/60; F effective = P/v; F centrifugal = m′v²
Mean link-advance speed differs from pitch-circle peripheral speed. Working pull is not breaking strength or permissible load.
Articulation ≈ 2π/z; ideal chordal variation = (1−cos(π/z))×100%
Fixed-pin regular polygon model relative to its maximum pitch-circle speed. Not a vibration/noise prediction; rocker-joint silent chains need their own model.
Independent regular-polygon kinematics; Tập 1 Chapter 5 chain context.
Textbook references identify the method context. Historical numerical catalog, material and service-factor tables have not been copied or treated as current product ratings.
Related calculators and references
Existing component-selection Jobs → · All mechanical worksheets →
Common questions
Does this approve a real component?
No. The worksheet separates mathematical results from criterion-specific checks. Actual motor, belt, sprocket and chain capacity need applicable current manufacturer data and installation review.
What changes after choosing a physical size?
The worksheet recalculates the outputs and geometry from the entered actual dimensions or discrete tooth/link count. Dependent checks are reevaluated; previously saved results are not restored as approvals.