The Four Functions a High Gear Ratio Simultaneously Performs
Most engineers select gear ratio by calculating: T_output = T_motor × i × η, then choosing the smallest i that delivers the required output torque. This is correct for the torque function — but a gear ratio performs three additional functions simultaneously, and for high-ratio applications (i ≥ 64:1) these additional functions often drive the specification more strongly than torque alone.
Scales linearly with ratio. Standard selection calculation. Limited by the gearbox output torque ceiling — increasing i beyond the point where motor torque × i × η equals the output ceiling gives no additional torque benefit.
Scales with i squared. At i=100, the load inertia is reduced 10,000× at the motor shaft. This is why high-ratio applications can use small motors without inertia matching problems — a 50 kg·m² rotary table reflected through i=200 becomes just 0.00125 kg·m² at the motor shaft.
At i=320, a motor running at 3,000 rpm produces only 9.4 rpm at the output. For very slow tracking applications (solar azimuth ≈ 0.25 rpm, antenna ≈ 0.05 rpm), high ratio is the only way to achieve these output speeds while keeping the motor in its stable servo operating range.
A 10,000-line encoder produces 40,000 counts/rev of the motor shaft. Through i=100, this becomes 4,000,000 counts/output-rev — giving 0.000090° (0.32 arcsecond) theoretical positioning resolution. This is why heavy rotary tables achieve sub-arcsecond positioning without expensive absolute encoders on the output shaft.
Suunnittelun merkitys: For slow-speed, high-inertia applications — rotary tables, solar trackers, antenna drives — the ratio specification is often driven by Functions 3 and 2 (output speed and inertia) rather than Function 1 (torque). The motor needed for a 500 N·m output through i=200 is only 2.78 N·m rated torque (545W at 3,000 rpm) — far smaller than the torque magnitude suggests. Start the ratio selection from output speed and inertia, not from torque.
EP Series Complete Ratio Table — All Standard Ratios from 3:1 to 516:1
The EP series precision planetary gearboxes cover 27 standard gear ratios across three stage counts. Non-standard ratios are available for volume orders — contact Korea Ever-Power application engineering with your exact ratio requirement and the nearest standard ratio will be identified or a custom stage combination confirmed.
| Stage Count | Available Ratios | Hyötysuhde η | Heat at 1 kW input | Takaisku | Primary Use Case |
|---|---|---|---|---|---|
| 1-vaiheinen | 3 · 4 · 5 · 8 · 10 | 96% | 40 W | <8 kaariminuuttia | High speed, light load, maximum efficiency |
| 2-vaiheinen | 9 · 12 · 15 · 16 · 20 25 · 32 · 40 · 64 |
94% | 60 W | <8–12 kaariminuuttia | Most servo automation: robot joints, CNC, AGV, packaging |
| 3-Stage ★ | 60 · 80 · 100 · 120 160 · 200 · 256 · 320 · 516 |
90% | 100 W | <8–15 arcmin | High-torque/slow-speed: rotary tables, solar, antenna, conveyors |
Three independent stages at 96% each would give 0.96³ = 88.5%. The published 90% for EP 3-stage units reflects that intermediate stages in a compound planetary unit share some mechanical elements and operate at lower relative speeds — the per-stage friction is not fully independent. The 90% figure is the certified efficiency at rated load; at light load, efficiency can be somewhat lower due to fixed friction losses (seals, bearing drag) dominating at low transmitted power.
The Output Torque Ceiling — The Constraint Most High-Ratio Guides Omit
The most common misconception in high-ratio planetary gearbox selection is that increasing the gear ratio indefinitely increases the available output torque. In reality, the gearbox output shaft, output bearing, and final-stage planet carrier have a maximum torque capacity set by the size of the mechanical components — the output torque ceiling. Above this ceiling, increasing ratio brings no additional torque: the gearbox will fail before the motor can transmit more torque through it.
| EP Series Frame | Lähtömomentti Ceiling (N·m) |
Max Motor T at i=100, η=0.90 |
Max Motor T at i=200, η=0.90 |
Max Motor T at i=320, η=0.90 |
Typical Motor Class |
|---|---|---|---|---|---|
| EP-ZDE-60 | 16 Nm | 0.18 N·m | 0.09 N·m | 0.06 N·m | 50–100W servo motor |
| EP-ZDE-80 | 50 Nm | 0.56 N·m | 0.28 N·m | 0.17 N·m | 100–200W servo motor |
| EP-ZDE-120 | 110 N·m | 1.22 N·m | 0.61 N·m | 0.38 N·m | 400–750W servo motor |
| EP-ZDE-160 | 450 N·m | 5.00 N·m | 2.50 N·m | 1.56 N·m | 750W–2.2kW servo |
| EP-ZDS-115 | 210 N·m | 2.33 N·m | 1.17 N·m | 0.73 N·m | 400–1,500W servo + IP65 |
| EP-ZDS-142 | 910 Nm | 10.1 N·m | 5.06 N·m | 3.16 N·m | 2.2–7.5kW servo + IP65 |
| EP-ZDS-190 | 1 800 Nm | 20.0 N·m | 10.0 N·m | 6.25 N·m | 7.5–22kW servo + IP65 |
Max motor T = output ceiling / (i × η). These are the motor torque ratings that will exactly load the gearbox output to its rated ceiling at the given ratio. Exceeding these values overloads the gearbox regardless of whether the motor can supply more. ZDE 3-stage available up to i=516:1; ZDS 3-stage availability — consult Korea Ever-Power application engineering.
Backlash Across Multiple Stages — The Answer Most Engineers Get Wrong
A common concern about multi-stage planetary gearboxes is backlash accumulation: if each stage has <8 arcmin of backlash, does a 3-stage unit have <24 arcmin of total backlash at the output? The answer is definitively no — and the correct understanding of this principle is essential for high-ratio precision applications.
Earlier stages contribute progressively less to output backlash because their dead-band is divided by all subsequent stage ratios. In practice, the EP series published backlash for multi-stage units (<8 arcmin for ZDE/ZDS at the output) already accounts for all stages’ contributions. A 3-stage EP-ZDE-160 at 320:1 has the same <8 arcmin output backlash specification as a 1-stage EP-ZDE-160 at 3:1 — because the first two stages’ backlash contribution is reduced by ratios of 8× and 40× respectively before reaching the output.
When specifying a 3-stage EP-ZDE or EP-ZDS unit for a precision rotary table or positioning application, the backlash specification is not degraded relative to the single-stage version. Specify backlash as you would for any EP series unit: <8 arcmin (ZDE/ZDS standard) is the correct figure regardless of stage count. The certified value applies to the output shaft.
At very high ratios (i ≥ 200:1), the angular equivalent of backlash as seen at the motor shaft becomes extremely small — barely detectable. However, the physical backlash at the output shaft is unchanged. For slow-speed precision positioning, the output-side backlash remains the relevant specification, and EP series <8 arcmin remains applicable.
Motor Speed Constraint — The Lower Bound on Practical Gear Ratio
In most servo applications, the constraint on ratio selection comes from the upper side — maximum motor speed limits how high the ratio can be. For slow-speed tracking and positioning applications, the constraint comes from the lower side: the motor must run fast enough for stable servo control. Below approximately 50 rpm motor speed, servo current ripple, encoder resolution per unit time, and velocity loop stability all degrade. This sets a minimum practical motor speed that, combined with the required output speed, sets a minimum practical gear ratio.
| Hakemus | Required n_output |
i=64 n_motor |
i=100 n_motor |
i=200 n_motor |
i=320 n_motor |
Min viable i |
|---|---|---|---|---|---|---|
| Rotary table (fast index) | 30 rpm | 1,920 ✅ | 3,000 ✅ | 6,000 ⚠ | 9,600 ❌ | i≤100 |
| Robot J1 (moderate speed) | 8 rpm | 512 ✅ | 800 ✅ | 1,600 ✅ | 2,560 ✅ | i=64 typical |
| Heavy conveyor drive | 15 rpm | 960 ✅ | 1,500 ✅ | 3,000 ✅ | 4,800 ⚠ | i=80–200 |
| Solar tracker azimuth | 0.25 rpm | 16 ❌ | 25 ⚠ | 50 ✅ | 80 ✅ | i≥200 |
| Antenna tracking | 0.05 rpm | 3.2 ❌ | 5 ❌ | 10 ❌ | 16 ⚠ | i≥320, or stepper |
✅ n_motor ≥ 100 rpm: stable servo operation. ⚠ n_motor 25–100 rpm: marginal, requires low-speed-optimised servo drive. ❌ n_motor < 25 rpm: servo velocity loop unstable; use stepper motor or direct-drive with servo on position only. Motor max speed 4,500 rpm; recommended continuous ≤ 3,000 rpm.
Solar tracker design insight: A solar azimuth drive requires 0.25 rpm output (one full rotation in 24 hours × some tracking margin). At i=100, the motor runs at 25 rpm — below the stable servo range. At i=200, the motor runs at 50 rpm — marginal but achievable with a modern servo drive that supports low-speed operation. At i=320, the motor runs at 80 rpm — well within standard servo control range. This is why 200:1 to 320:1 ratios are standard in precision solar tracker drive designs, not because the torque requires it (a modest motor handles the wind load at high ratio) but because the output speed requires it for servo stability.
Position Resolution at the Output — From i=32 to i=320 with a 10,000-Line Encoder
One of the least-discussed benefits of high gear ratio in precision positioning applications is the multiplication of encoder resolution at the output shaft. A 10,000-line motor encoder (40,000 counts/rev after ×4 quadrature decoding) produces a theoretical minimum step size at the output that decreases linearly with ratio. This is why heavy rotary tables can achieve sub-arcsecond positioning without a dedicated output encoder — the motor encoder resolution, multiplied through the gear ratio, provides sufficient resolution for most positioning requirements.
| Vaihdesuhde i | Total encoder counts per output revolution |
Degrees per count | Arcseconds per count | Margin vs ±0.01° tolerance |
Suitable for |
|---|---|---|---|---|---|
| 32:1 | 1,280,000 | 0.000281° | 1.01″ | 35× | Indexer, robot joints J3–J6 |
| 64:1 | 2,560,000 | 0.000141° | 0.51″ | 71× | Robot J1/J2, precision indexer |
| 100:1 | 4,000,000 | 0.000090° | 0.32″ | 111× | Rotary table, heavy conveyor |
| 200:1 | 8,000,000 | 0.000045° | 0.16″ | 222× | Solar tracker, antenna, slow index |
| 320:1 | 12,800,000 | 0.000028° | 0.10″ | 356× | Telescope, precision antenna |
| 516:1 | 20,640,000 | 0.000017° | 0.063″ | 573× | Max EP ratio; very slow rotation |
Encoder: 10,000-line incremental, ×4 quadrature = 40,000 counts/motor-rev. Margin column: ratio of ±0.01° tolerance to resolution per count. Actual achievable positioning accuracy is limited by backlash (<8 arcmin = 0.133°) — encoder resolution is not the binding constraint. With CNC backlash compensation active, achievable accuracy approaches 3–5× of encoder resolution in practice.
High-Ratio Application Matrix — Recommended EP Series by Use Case
| Hakemus | T_req (Nm) |
n_out (rpm) |
Suhde i | Moottori koko |
EP Recommendation | Selection Driver |
|---|---|---|---|---|---|---|
| Heavy rotary table (500mm Φ, 50kg) | 250 | 2 | 80:1 | 400W | EP-ZDE-160, 80:1 | Torque + slow speed |
| Robot J1 base (heavy, 200kg arm) | 400 | 8 | 64:1 | 1.5kW | EP-ZDS-142, 64:1 | Torque + stiffness |
| Heavy conveyor (1,000kg load) | 800 | 15 | 100:1 | 1.5kW | EP-ZDS-142, 100:1 | High torque + IP65 |
| Solar tracker azimuth | 500 | 0.25 | 200:1 | 750W | EP-ZDE-160, 200:1 | Speed constraint |
| Antenna positioning drive | 300 | 0.05 | 320:1 | 400W | EP-ZDE-120, 320:1 | Speed + resolution |
| Screw tightening (M30+) | 350 | 5 | 100:1 | 400W | EP-ZDE-120, 100:1 | Torque, SF=2.5 |
| Wind turbine yaw drive | 50,000 | 0.01 | 516:1 | 22kW | EP-ZDS-190, 516:1 | Highest ratio + torque |
High-Ratio Selection Checklist — Five Questions Before Specifying Above 64:1
If torque: calculate T_motor × i × η and verify against output ceiling. If speed: calculate n_motor = n_out × i and check ≥ 50 rpm. If inertia: J_reflected = J_load / i² — for large loads, high ratio solves inertia matching that no other method achieves. Identify which constraint drives i before calculating torque.
Check: T_motor_rated × i × η ≤ T_output_ceiling for the selected EP frame. If it exceeds the ceiling, either select a larger frame (ZDE-120 vs ZDE-80) or reduce motor size. Do not exceed the output torque ceiling — it causes premature gear and bearing failure regardless of service factor.
n_motor = n_out_max × i. Verify n_motor ≤ 3,000 rpm recommended (4,500 rpm absolute). For very slow output speeds, verify n_motor ≥ 50–100 rpm minimum for stable servo operation. If n_motor falls below minimum, increase ratio or consider stepper motor.
Calculate annual energy cost difference: 3-stage loses 100W per kW vs 40W for 1-stage. For continuous 1kW duty, this is 525 kWh/year = $52.5/year at Korean industrial rate. For intermittent duty, this is negligible. Confirm motor sizing accounts for 90% efficiency (not 96%).
At i=100, a 10,000-line motor encoder gives 0.32″ resolution at the output — adequate for most industrial positioning. If backlash (<8 arcmin = 480″) must be compensated to better than 10% (48″), a direct output encoder is needed.
Korea Ever-Power application engineering provides high-ratio selection support including output torque ceiling verification, motor speed constraint analysis, encoder resolution calculation, and 3-stage efficiency cost estimation. Provide your required output torque, output speed, and positioning tolerance for a complete EP series 3-stage recommendation in Korean and English.
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