عزم الدوران ونسبة تخفيض التروس الدودية: دليل الحساب
Supplier recommendation tables are built around the average application. Your application has its specific load, duty cycle, ambient temperature, and shock character. This guide walks through the four core formulas and three worked examples so you can verify any مخفض تروس دودي selection in under 20 minutes.
Why You Should Always Run the Numbers Yourself
Supplier recommendation tables are built for the median application — uniform load, 8 hours per day, 20°C ambient, minimal shock. Every time one of those conditions differs from your actual application, the recommendation may be wrong. Not dangerously wrong, but quietly wrong in a way that produces a failure at 6,000 hours instead of 20,000 hours, and nobody ever traces it back to the initial مخفض تروس دودي اختيار.
The calculation is not complex — it is four formulas that take 15 minutes on the first application and 5 minutes on every application after that. Running the numbers yourself also forces you to define your application precisely: actual output torque, not approximate; actual duty cycle, not “intermittent”; actual ambient temperature, not “room temperature.”
The most common worm gear reducer sizing errors — undersized service factor, ignored thermal power limit, underestimated ambient temperature — are all invisible in a recommendation table and all visible in a 15-minute calculation.
The Four Core Formulas
Every worm gear reducer selection calculation uses these four formulas. They build on each other in sequence — calculate them in order and you have a complete selection basis.
Reduction Ratio
أين: n_input = motor shaft speed (rpm); n_output = required output shaft speed (rpm)
Example: Motor 1,450 rpm, required output 29 rpm: i = 1,450 ÷ 29 = 50:1
Practical note: Standard ratios are 5, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 80, 100. If your calculated ratio falls between two standard values, always round up to the higher ratio (lower output speed) — never round down.
Output Torque (Theoretical)
أين: T₁ = motor shaft torque (N·m); i = ratio; η = efficiency at this ratio (decimal)
Important: Efficiency η is not constant — it depends on the ratio selected. See the Efficiency Reference Table in Section 4.
Example: T₁ = 4.0 N·m (motor), i = 50, η = 0.60: T₂ = 4.0 × 50 × 0.60 = 120 N·m
Required Input Power
Units: P_input in kW; T₂ in N·m; n₂ in rpm
The constant 9,550 converts between the rotational and power units. This is the power the motor must deliver — not the catalog motor power.
Example: T₂ = 120 N·m, n₂ = 29 rpm, η = 0.60: P_input = (120 × 29) ÷ (9,550 × 0.60) = 0.607 kW
Service Factor Correction
Apply SF to the actual required output torque before comparing to the catalog rating. The catalog T₂n must be ≥ T_required.
Example: T_actual = 120 N·m, SF = 1.5 (light shock, 8h/day): T_required = 120 × 1.5 = 180 N·m
Select a worm gear reducer with catalog T₂n ≥ 180 N·m at 50:1 ratio.
Service Factor (SF) Guide: The Parameter Most Often Underestimated
The service factor accounts for the actual load conditions relative to the catalog test conditions. A worm gear reducer catalog rating assumes uniform load at rated speed for the test duration. Every deviation from this baseline increases the effective load on the gears and bearings. SF translates your actual operating conditions into an equivalent catalog selection requirement.
| تحميل الشخصية | ≤2 h/day | 2–10 h/day | >10 h/day |
|---|---|---|---|
| حمل منتظم | 1.00 | 1.25 | 1.50 |
| Light shock | 1.25 | 1.50 | 1.75 |
| صدمة متوسطة | 1.50 | 1.75 | 2.00 |
| صدمة شديدة | 1.75 | 2.00 | 2.25 |
Typical Equipment Examples by Shock Category
Efficiency vs Ratio: The Reference Data You Need for Every Calculation
The efficiency of a worm gear reducer is not a single fixed value — it varies significantly with the reduction ratio. Using the wrong efficiency figure in your calculation produces incorrect input power and incorrect torque estimates. The following table provides realistic ranges for WP and NMRV series worm gear reducers using standard mineral ISO VG 220 oil at operating temperature.
| Ratio (i) | Efficiency η Range | Use in Calculation |
|---|---|---|
| 7.5:1 | 85–90% | η = 0.87 |
| 10:1 | 80–85% | η = 0.82 |
| 20:1 | 70–78% | η = 0.74 |
| 30:1 | 65–73% | η = 0.69 |
| 40:1 | 60–68% | η = 0.64 |
| 50:1 | 55–64% | η = 0.60 |
| 60:1 | 50–58% | η = 0.54 |
| 80–100:1 | 44–55% | η = 0.49 |
Upper end of range: high-tin bronze wheel (10%+ Sn), precision-ground worm shaft, synthetic PAO oil. Lower end: standard bronze, cut worm, mineral oil. Use the lower value of the range for conservative sizing.
Three Complete Worked Examples
Example 1: Conveyor Drive (Uniform Load, 8 h/day)
منح: Belt conveyor. Belt speed 1.2 m/s. Drive drum diameter 300 mm. Loaded belt mass 800 kg. Friction coefficient μ = 0.05. Running 8 h/day, uniform load.
Step 1 — Required drum rpm:
n_drum = (v × 60) / (π × D) = (1.2 × 60) / (π × 0.30) = 76 rpm
Step 2 — Belt drive force and torque:
F = m × g × μ = 800 × 9.81 × 0.05 = 392 N
T_drum = F × r = 392 × 0.15 = 58.8 N·m
Step 3 — Ratio:
i = 1,450 / 76 = 19.1 → select 20:1
Step 4 — Apply SF:
SF = 1.25 (uniform load, 8 h/day)
T_required = 58.8 × 1.25 = 73.5 N·m
Step 5 — Verify input power:
η at 20:1 = 0.74
P_input = (58.8 × 76) / (9,550 × 0.74) = 0.63 kW
Step 6 — Thermal check:
Continuous duty at 20°C: P_th for NMRV-050 at 20:1 = approx 3.2 kW ≫ 0.63 kW. Thermal margin adequate.
✓ Selected: NMRV-050 at 20:1
T₂n catalog ≥ 73.5 N·m at 20:1. Motor: 0.75 kW (next standard size above 0.63 kW).
Example 2: Agitator Drive (Moderate Shock, 16 h/day)
منح: Industrial slurry agitator. Required output torque 320 N·m at 28 rpm. Running 16 h/day, moderate shock (variable slurry density). Ambient 30°C. Open installation.
Step 1 — Ratio:
i = 1,450 / 28 = 51.8 → select 50:1
(Actual output rpm = 1,450 / 50 = 29 rpm — acceptable)
Step 2 — Apply SF:
SF = 2.00 (moderate shock, >10 h/day)
T_required = 320 × 2.00 = 640 N·m
Step 3 — Input power:
η at 50:1 = 0.60
P_input = (320 × 28) / (9,550 × 0.60) = 1.56 kW
Step 4 — Thermal check at 30°C:
Ambient factor at 30°C = 0.87
NMRV-090 at 50:1 P_th catalog = 4.8 kW
Corrected P_th = 4.8 × 0.87 = 4.18 kW ≫ 1.56 kW. ✓
✓ Selected: NMRV-090 at 50:1
T₂n at 50:1 must be ≥ 640 N·m. Confirm in catalog. Motor: 2.2 kW.
Example 3: Hoist Auxiliary Drive (Heavy Shock, Intermittent)
منح: Auxiliary hoist drum drive. Lift mass 1,200 kg. Lifting speed 0.4 m/s. Drum diameter 400 mm. Duty cycle: 15 seconds on, 45 seconds off. Self-locking required.
Step 1 — Drum torque:
F = 1,200 × 9.81 = 11,772 N
T_drum = F × r = 11,772 × 0.20 = 2,354 N·m
Step 2 — Drum rpm:
n_drum = (0.4 × 60) / (π × 0.40) = 19.1 rpm
Ratio: i = 1,450 / 19.1 = 75.9 → 80:1 (self-lock confirmed)
Step 3 — Duty cycle effective power:
DC = 15/(15+45) = 25%
P_eff = P_peak × √(DC) = P_peak × 0.50
Step 4 — Apply SF:
SF = 1.75 (heavy shock, ≤2 h/day equiv.)
T_required = 2,354 × 1.75 = 4,120 N·m
P_input peak: η at 80:1 = 0.50
P_peak = (2,354 × 19.1) / (9,550 × 0.50) = 9.43 kW
✓ Selected: WP135 at 80:1
T₂n ≥ 4,120 N·m. Motor: 11 kW. Thermal check: P_eff = 9.43 × 0.50 = 4.7 kW — verify P_th for WP135 at 80:1 at actual ambient.
Thermal Power Verification: The Check That Prevents Overheating Failures
For any continuous-duty application (S1 or duty cycle >50%), the thermal power verification is a mandatory additional step after the torque/ratio calculation. Many correctly sized worm gear reducers — torque and ratio confirmed — have failed because the thermal power limit was never checked.
Thermal verification procedure:
1. From the calculation, record the actual continuous input power P_input (kW).
2. From the selected worm gear reducer catalog, find P_th at the chosen ratio.
3. Apply ambient temperature correction factor (see K-05 article for full table).
4. Apply installation correction if enclosed (deduct 15–25%).
5. Confirm P_input < P_th (corrected). If not, upgrade to next frame size or add cooling.
Korean summer note: At 35°C ambient, the corrected P_th is approximately 80% of the catalog value. A worm gear reducer selected on catalog P_th without ambient correction will run over its thermal limit on warm summer days — even if it runs fine in winter. Always apply the ambient correction.
Four Calculation Mistakes That Show Up Most Often
Mistake 1: Using Motor Nameplate Power as Application Power
A 2.2 kW motor running a lightly loaded conveyor may deliver only 0.8 kW at the shaft under actual operating conditions. Using 2.2 kW in the calculation over-estimates the input power by 175%, producing an input power figure that makes the thermal check look worse than reality.
Correct approach: Calculate the actual required input power from the load parameters (Formulas 2 and 3). Use the motor nameplate only to confirm the motor is large enough — not as the input power for thermal assessment.
Mistake 2: Comparing Actual Torque Directly to Catalog T₂n Without SF
The catalog T₂n is the test-condition rating. Your application torque multiplied by SF is what must be below T₂n. Skipping the SF means selecting a worm gear reducer that meets the average torque demand but fails under the peak demand that occurs dozens of times per operating cycle.
Correct approach: Always calculate T_required = T_actual × SF before looking at the catalog. Never compare raw application torque to T₂n.
Mistake 3: Using Catalog Efficiency for Thermal Calculations
Catalog efficiency values represent the best case — full load, operating temperature, precision-ground worm, high-quality oil. At partial load, cold startup, or with standard-grade components, efficiency is lower — which means more heat is generated relative to the output power.
Correct approach: For thermal power calculations, use the lower end of the efficiency range (conservative value), not the catalog peak value. Err on the side of generating more heat in your calculation.
Mistake 4: Ignoring Ambient Temperature in the Thermal Check
Every worm gear reducer catalog thermal power P_th is specified at 20°C ambient. In Korean industrial environments, 30–35°C summer ambient is normal. At 35°C, P_th drops to 80% of the catalog value — a margin that turns a “passing” thermal check into a “failing” one.
Correct approach: Always apply the ambient temperature correction factor to P_th before comparing to actual input power. Use the hottest expected ambient for the installation location.
Frequently Asked Questions — Worm Gear Reducer Torque and Ratio Calculations
How much does it matter if the exact calculated ratio (e.g., 47.2:1) doesn’t match a standard ratio (50:1)?
How do I calculate the actual output torque from my motor nameplate data?
When a VFD (inverter) is used, how does that change the torque and ratio calculation?
How is total efficiency calculated for a two-stage worm gear reducer arrangement?
If the actual load turns out heavier than calculated, will the worm gear reducer fail immediately?
When the calculated T_required falls between two catalog sizes, should I always select the larger one?
Worm Gear Reducer Selection and Calculation Support
Korea Ever-Power’s engineering team provides application-specific worm gear reducer selection verification — including torque calculation check, service factor confirmation, and thermal power assessment for your actual ambient and duty conditions. Share your application parameters and we return a complete selection recommendation.
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