L ≈ 2C + π(D+d)/2 + (D−d)²/(4C); small wrap = π−2 asin(|D−d|/(2C))
Open two-pulley drive, consistent pitch/datum diameters in metres. No crossed belt or idler. Existing approximate length/wrap kernels are reused.
VALICALC / MECHANICAL ENGINEERING SUITE / DS05
Flat Belt Drive Design Sheet
Size the geometry first, enter the actual belt length and recalculate. Review operating tensions and the ideal capstan traction estimate separately from material capacity.
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
mm
mm
rpm
kW
N
Actual operating span tension; not installation pretension.
kg/m
Percent; a user assumption, not a predicted slip value.
deg
0 = not specified; use applicable manufacturer requirements.
Example only. Verify the actual pulley/belt surface and operating condition.
02 / CALCULATE → SELECT → RECALCULATE
Calculation & checks
Actual center distance
500 mmActual pitch/datum length
1,476.24308 mmTheoretical length at preliminary center
1,476.24308 mmCenter adjustment
0 mmActual reduction ratio
2Driven RPM
750 rpmBelt speed
7.85398 m/sSmall-pulley wrap
168.52166 degEffective pull · total
190.98593 NTight tension · per belt/rib
290.98593 NSlack tension · per belt/rib
100 NEstimated span load on each shaft
389.49461 NCentrifugal tension · per belt/rib
6.1685 NIdeal capstan ratio limit
2.41664Required effective tension ratio
3.03541| State | Center (m) | Exact length (m) | Legacy approximate length (m) | Small wrap (rad) |
|---|---|---|---|---|
| Preliminary | 0.5 | 1.476243 | 1.476239 | 2.941258 |
| Actual / recalculated | 0.5 | 1.476243 | 1.476239 | 2.941258 |
Criterion-specific verification
- PASSED · Pitch/datum circle geometry
Positive, non-overlapping pitch/datum circles. Outside diameters, take-up and installation clearances remain unverified.
- PASSED · Selected-length recalculation
Exact pitch-line residual 0.00e+0 m.
- BLOCKED · Material stress and bending life
No current applicable product rating dataset. Operating load calculations do not establish allowable capacity.
- UNKNOWN · Entered minimum wrap criterion
No applicable minimum wrap supplied.
- FAILED · Ideal flat-belt traction estimate
Effective tension ratio 3.0354; capstan limit 2.4166 using entered μ. This is an ideal estimate.
Method and calculation trace
Actual dimensions control all downstream results. Ratio uses consistent datum/pitch diameters.
Exact tangent geometry solves length and center; the established approximate ValiCalc kernel is retained in the comparison table.
P/v gives total effective pull. 1 equal load-sharing belt/rib path(s); operating slack tension is entered rather than inferred from installation pretension.
Entered speed loss 0% affects driven RPM only; tension uses driver pitch-line speed.
Span-force vector estimate excludes weight and transient loads. No overall safety/capacity approval.
Assumptions & scope
Open two-pulley drive with no idler. Enter consistent actual datum/pitch diameters and lengths. Outside diameters, alignment and take-up travel still need checking.
Tensions are operating values; equal sharing across entered belts/ribs is an assumption. Shaft span-force estimate excludes pulley weight, bearing reactions and transient loading.
Capacity, fatigue, installation pretension and allowable speed require current product-specific evidence. No catalog dimensions or ratings are inferred.
The capstan check is an ideal engineering estimate using supplied friction and centrifugal tension. Passing it does not approve belt width, stress, bending life or adhesion.
Worked example
For 100/200 mm pulleys and 500 mm center, approximate length is 1476.239 mm. Selecting 1500 mm gives an exact ideal center of about 511.937 mm; the wrap and traction check are recalculated.
Calculation methods and sources
L = 2√(C²−δ²) + π(D+d)/2 + 2δ asin(δ/C); δ=|D−d|/2
Exact ideal tangent pitch-line geometry. A bounded bisection solves selected pitch length → physical center distance. No tooth deformation or installation tension correction.
ΔT = P/v; T tight = T slack + ΔT; R = √((Tt+Ts)²cos²α + (Tt−Ts)²sin²α)
α = asin(|D−d|/(2C)). Steady span-force estimate using entered slack tension or operating tension ratio. Equal belt/rib sharing is an explicit assumption; no rated belt count is inferred.
Gates Heavy Duty V-Belt Drive Design Manual, tension ratio D18; independent vector sum
(Tt−Tc)/(Ts−Tc) ≤ exp(μθ); Tc = m′v²
Ideal flexible flat-belt friction estimate with user-supplied μ and mass/length. Static-friction limit and centrifugal allowance, not manufacturer capacity.
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.