n out = n in/i; P out = ηP in; η total = Πη; T out = ηiT in
Serial passive motoring power flow; 0 < η ≤ 1. Rotation signs do not imply a reversible loss model.
Tập 1, 2.15–2.18 and 3.23–3.25; independent conservation-of-energy derivation.
VALICALC / MECHANICAL ENGINEERING SUITE / DS04
Gearbox Ratio Allocation Design Sheet
Allocate a required reduction across one to four serial stages. Compare your proposals or a bounded two-stage integer tooth search; the displayed objective is speed error, not a universal mechanical optimum.
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
rpm
rpm
kW
Allocation candidates
02 / CALCULATE → SELECT → RECALCULATE
Calculation & checks
Required total ratio
6 :1Selected total ratio
6 :1Selected output RPM
250 rpmSpeed error
2.22e-14 %Selected output torque
258.54721 N·mSelected stage 1 ratio
2.44949 :1Selected stage 2 ratio
2.44949 :1| Rank | Candidate | Stage ratios | Output RPM | Output torque (N·m) | RPM error (%) |
|---|---|---|---|---|---|
| 1 | Equal allocation · continuous | 2.4495 × 2.4495 | 250 | 258.547205 | 2.22e-14 |
| Shaft | RPM | Power (W) | Torque (N*m) | Cumulative efficiency | Stage loss (W) |
|---|---|---|---|---|---|
| 0 | 1,500 | 7,500 | 47.746483 | 1 | 0 |
| 1 | 612.372436 | 7,125 | 111.106794 | 0.95 | 375 |
| 2 | 250 | 6,768.75 | 258.547205 | 0.9025 | 356.25 |
Criterion-specific verification
- PASSED · Defined search objective
1 candidate(s). Minimize absolute speed error within entered bounds; ratio imbalance breaks ties. This does not optimize size, cost or strength.
- UNKNOWN · Physical gearbox layout and strength
Fixed-axis serial kinematics only. Check module, tooth interference, centers, bearings, housing and lubrication separately.
Method and calculation trace
i total = n input / n target = Πi stage. Equal allocation uses i total^(1/stages).
Discrete search keeps the entered driver teeth; recomputes every candidate's actual ratio, speed, torque and loss using the shared serial engine.
Assumptions & scope
Supports serial fixed-axis stages. Equal ratios are a numerical starting point. Coaxial layout, gear interference, module, housing, lubrication and capacity are not inferred.
Tooth candidates are geometric proposals within entered bounds, not manufactured gears or approved designs. No historical ratio-optimization coefficients are used.
Worked example
1500 → 250 RPM requires 6:1 overall. Two equal stages give √6 each; 20/60 and 20/40 teeth also give exactly 6:1.
Calculation methods and sources
Πij = n input/n target; equal starting ratio = i total^(1/k)
Continuous equal ratios or explicitly bounded integer tooth comparisons. Absolute RPM error is the stated objective; mechanical layout remains unverified.
Independent product-ratio derivation; Chapter 3 topology context, printed pp. 25–49. Historical optimization factors are not applied.
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.