{"id":715,"date":"2026-06-01T08:53:20","date_gmt":"2026-06-01T08:53:20","guid":{"rendered":"https:\/\/planetary-gearboxes.com\/?p=715"},"modified":"2026-06-01T08:53:20","modified_gmt":"2026-06-01T08:53:20","slug":"planetary-gearbox-inertia-matching-ratio-calculation","status":"publish","type":"post","link":"https:\/\/planetary-gearboxes.com\/nl\/planetary-gearbox-inertia-matching-ratio-calculation\/","title":{"rendered":"Traagheidsafstemming van planetaire tandwielkasten \u2014 Overbrengingsverhouding en servoprestaties"},"content":{"rendered":"
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<\/p>\n

\"planetary<\/p>\n
\n
Engineering Reference \u00b7 J_ratio \u00b7 Optimal Ratio \u00b7 Servo Bandwidth \u00b7 Calculation Guide<\/div>\n

Planetary Gearbox Inertia Matching \u2014
\nGear Ratio Selection for Servo Performance<\/h1>\n

Every Korean servo engineer knows that inertia ratio matters<\/strong> \u2014 but few have a systematic method for calculating it across all three drive topologies (direct coupling, belt drive, rack and pinion) and using it to select the optimal gear ratio. A mismatched inertia ratio does not usually cause immediate failure: it causes servo instability, limits achievable bandwidth, and forces the control engineer to detune the gains \u2014 permanently capping machine throughput below the hardware’s potential.<\/p>\n

Bekijk de EP-AB precisieserie \u2192
\n<\/a><\/p>\n<\/div>\n<\/section>\n

<\/p>\n

\n

Why Inertia Ratio Controls Servo Performance \u2014 The Physics Behind the Rule<\/h2>\n

Every planetary gearbox inertia matching guide and servo motion control textbook states a rule: keep the load-to-motor inertia ratio below a target value \u2014 commonly cited as 5:1, 10:1, or 30:1 depending on the source. Korean engineers who follow this rule without understanding its physical origin often apply it incorrectly \u2014 choosing targets that are either too conservative (forcing an unnecessarily large gearbox) or too permissive (accepting instability they cannot tune away).<\/p>\n

The physical origin of the inertia ratio limit is the servo control loop’s ability to reject torque disturbances. Consider a servo motor driving a load through a gearbox. The motor encoder measures motor shaft position; the servo controller computes a torque command to correct position error. When an external disturbance torque acts on the load \u2014 a cutting force, an impact, a sudden friction change \u2014 the motor must produce a corrective torque to restore the commanded position. The speed at which the motor can detect and correct the disturbance is the servo loop bandwidth.<\/p>\n

\n

THE INERTIA RATIO AND BANDWIDTH RELATIONSHIP<\/p>\n

Motor equation of motion (at motor shaft, load reflected through i):<\/p>\n

T_motor = (J_motor + J_load\/i\u00b2) \u00d7 \u03b1_motor + T_friction<\/p>\n

Define: J_total = J_motor + J_load\/i\u00b2
\nJ_ratio = J_load_reflected \/ J_motor = (J_load\/i\u00b2) \/ J_motor<\/p>\n

Servo bandwidth \u03c9_c (rad\/s) \u2014 simplified open-loop:
\n\u03c9_c \u221d K_p \/ J_total = K_p \/ [J_motor \u00d7 (1 + J_ratio)]<\/p>\n

\u2192 Achievable bandwidth decreases as J_ratio increases
\n\u2192 At J_ratio = 1: bandwidth = K_p \/ (2 \u00d7 J_motor) \u2014 50% of ideal
\n\u2192 At J_ratio = 5: bandwidth = K_p \/ (6 \u00d7 J_motor) \u2014 17% of ideal
\n\u2192 At J_ratio = 10: bandwidth = K_p \/ (11 \u00d7 J_motor) \u2014 9% of ideal<\/p>\n

This bandwidth reduction limits how fast the servo can:
\n\u2022 Respond to position commands (limits acceleration profile steepness)
\n\u2022 Reject disturbances (limits stiffness against cutting\/impact forces)
\n\u2022 Settle to target position (limits positioning time)<\/p><\/div>\n<\/div>\n

The inertia ratio rule is not a binary pass\/fail threshold \u2014 it is a continuous performance trade-off. J_ratio = 3 does not mean “acceptable” and J_ratio = 4 mean “unacceptable.” It means that at J_ratio = 4, the achievable bandwidth is 20% of the single-inertia ideal, and at J_ratio = 3 it is 25%. Whether that 5 percentage point difference matters depends on the application’s required acceleration profile and disturbance rejection.<\/p>\n

For planetary gearbox inertia matching in Korean industrial practice, the target J_ratio thresholds differ by application type. High-dynamic packaging and robot joint axes target J_ratio \u2264 3. General servo positioning axes accept \u2264 10. Speed-controlled drives (conveyors, screw rotation) are often comfortable at \u2264 30. The gear ratio selection problem is to find the ratio that places the reflected inertia within the appropriate J_ratio target for the application.<\/p>\n<\/section>\n

<\/p>\n

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Reflected Inertia Calculations \u2014 Three Drive Topologies in One Reference<\/h2>\n

The reflected inertia formula differs for each drive topology \u2014 direct rotary coupling, linear motion via ball screw or rack-and-pinion, and belt or chain drive. Korean engineers working across different machine types frequently apply the rotary formula to a linear drive or forget to include the gearbox’s own inertia contribution. The following derivations cover all three topologies correctly.<\/p>\n

<\/p>\n

\n

\u2460 Direct rotary coupling \u2014 rotating load (turntable, joint)<\/h3>\n
\n
\n
J_load_reflected = J_load \/ i\u00b2<\/p>\n

Total reflected inertia at motor:
\nJ_total = J_motor + J_gearbox_input + J_load\/i\u00b2<\/p>\n

J_ratio = J_load_reflected \/ J_motor
\n= J_load \/ (i\u00b2 \u00d7 J_motor)<\/p>\n

Note: J_gearbox_input is provided in
\nKorea Ever-Power EP datasheet (typically
\n5\u201315% of J_motor for standard servo motor)<\/p><\/div>\n<\/div>\n

Toepassingen:<\/strong> Robot joints (Art5), rotary tables, CNC B\/C axis, IMM rotary table (Art19)<\/p>\n

Key insight:<\/strong> J_ratio improves as i\u00b2. Doubling the ratio reduces reflected inertia by 4\u00d7. This is why a 3:1 ratio reduces a 36:1 J_ratio to just 4:1 (= 36\/3\u00b2).<\/div>\n<\/div>\n<\/div>\n

<\/p>\n

\n

\u2461 Linear motion \u2014 ball screw or rack-and-pinion (linear axis)<\/h3>\n
\n
\n
Ball screw: lead = L (m\/rev of screw)
\nJ_mass_at_screw = m \u00d7 (L\/2\u03c0)\u00b2<\/p>\n

With gearbox ratio i (motor\u2192screw):
\nJ_mass_reflected = m \u00d7 (L\/2\u03c0)\u00b2 \/ i\u00b2<\/p>\n

Also include: J_screw = \u00bd \u00d7 m_screw \u00d7 r_screw\u00b2
\nJ_screw_reflected = J_screw \/ i\u00b2<\/p>\n

Rack-and-pinion (pinion on gearbox output):
\nJ_mass_reflected = m \u00d7 r_pinion\u00b2 \/ i\u00b2
\n(m = total moving mass, r_pinion = pitch radius)<\/p><\/div>\n<\/div>\n

Toepassingen:<\/strong> CNC linear axes, gantry drives, IMM injection axis (Art19), packaging film pull (Art10)<\/p>\n

Key insight:<\/strong> For linear motion, the load inertia depends on both machine mass AND the mechanism geometry (lead or pitch radius). A heavy machine table is not necessarily high inertia \u2014 a short lead ball screw dramatically reduces reflected inertia.<\/div>\n<\/div>\n<\/div>\n

<\/p>\n

\n

\u2462 Belt or chain drive \u2014 reel or pulley load (film reel, conveyor)<\/h3>\n
\n
\n
Belt\/chain moves load mass m at belt speed v_belt:
\nJ_load_at_drive_pulley = m \u00d7 r_pulley\u00b2<\/p>\n

With gearbox ratio i (motor\u2192drive pulley):
\nJ_load_reflected = m \u00d7 r_pulley\u00b2 \/ i\u00b2<\/p>\n

Also include rotating reel\/drum:
\nJ_reel = \u00bd \u00d7 m_reel \u00d7 r_reel\u00b2
\nJ_reel_reflected = J_reel \/ i\u00b2<\/p>\n

Variable reel radius (film depleting):
\nCalculate at r_full and r_empty;
\nworst case is r_full (maximum J)<\/p><\/div>\n<\/div>\n

Toepassingen:<\/strong> HFFS film reel (Art10), conveyor head drums (Art11), solar tracker film actuator (Art7)<\/p>\n

Key insight:<\/strong> Film reels present the most extreme J_ratio variation \u2014 from near-zero (empty reel) to maximum (full reel). The system must be stable at both extremes. Gear ratio is chosen to keep the full-reel J_ratio at the target; the empty-reel condition is then motor-dominated and inherently stable.<\/div>\n<\/div>\n<\/div>\n

\n\n\n\n\n\n\n\n\n
Drive Topology<\/th>\nJ_load_reflected formula<\/th>\nScales as<\/th>\nWorst-case condition<\/th>\n<\/tr>\n<\/thead>\n
Rotary (direct)<\/td>\nJ_load \/ i\u00b2<\/td>\n1\/i\u00b2<\/td>\nFull load, maximum J_load<\/td>\n<\/tr>\n
Ball screw linear<\/td>\nm\u00d7(L\/2\u03c0)\u00b2 \/ i\u00b2<\/td>\n1\/i\u00b2<\/td>\nMaximum table\/load mass<\/td>\n<\/tr>\n
Rack and pinion<\/td>\nm\u00d7r_pinion\u00b2 \/ i\u00b2<\/td>\n1\/i\u00b2<\/td>\nMaximum carriage mass<\/td>\n<\/tr>\n
Belt \/ film reel<\/td>\nm\u00d7r_pul\u00b2 \/ i\u00b2 + J_reel\/i\u00b2<\/td>\n1\/i\u00b2<\/td>\nFull reel radius, maximum load<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/section>\n

<\/p>\n

\n

The Optimal Gear Ratio for Inertia Matching \u2014 Derivation and Practical Application<\/h2>\n

There is a mathematically optimal gear ratio for a given motor and load \u2014 the ratio that minimises the total effective inertia seen by the servo control loop, producing the highest possible servo acceleration for a given motor torque. Korean servo engineers who know this formula can select their first-pass gear ratio analytically rather than iteratively.<\/p>\n

\n
\n
\n

OPTIMAL RATIO DERIVATION<\/p>\n

Motor acceleration: \u03b1 = T_motor \/ J_total
\nJ_total = J_motor + J_gearbox + J_load\/i\u00b2<\/p>\n

Maximise \u03b1 by minimising J_total with respect to i:
\nd(J_total)\/di = -2\u00d7J_load\/i\u00b3 + 0 = 0… wait,
\nthis isn’t the right objective. The true objective:<\/p>\n

Maximise load acceleration \u03b1_load = \u03b1_motor \/ i
\n= T_motor \/ [i \u00d7 (J_motor + J_gearbox + J_load\/i\u00b2)]<\/p>\n

d(\u03b1_load)\/di = 0 \u2192 solving:
\ni_optimal = \u221a(J_load \/ (J_motor + J_gearbox))<\/span><\/p>\n

At i_optimal: J_ratio = J_load\/i\u00b2 \/ J_motor \u2248 1.0
\n(reflected load inertia = motor inertia)<\/p>\n

This gives J_ratio \u2248 1 at the optimal ratio \u2014
\nthe load appears to the motor as an equal mass.<\/p><\/div>\n<\/div>\n

The optimal ratio formula has a beautifully simple physical interpretation: the gear ratio that maximises load acceleration is the one that makes the reflected load inertia equal to the motor inertia. At this ratio, exactly half the motor torque accelerates the motor itself and half accelerates the load \u2014 a 50\/50 split that is thermodynamically efficient and mechanically balanced.<\/p>\n

In practice, i_optimal often falls between standard catalogue ratio steps. A Korean servo engineer who calculates i_optimal = 17.3 must choose between i = 15 and i = 20 from the catalogue. Both are acceptable \u2014 the inertia ratio varies only modestly across this range. The engineer should also verify that the chosen ratio delivers the required output speed at the motor’s rated RPM.<\/p>\n

Korea Ever-Power application note: <\/strong>
\nFor applications where the optimal ratio falls between standard EP-AB catalogue steps (e.g. i=20 and i=25), the EP-ADS series<\/a> offers non-standard ratios (i=16, 21, 31, 61, 91) that more closely match the calculated optimum. For applications where exact inertia optimisation justifies the non-standard ratio, ADS avoids the need for VFD frequency adjustment to compensate for a ratio mismatch.<\/span><\/div>\n<\/div>\n
\"Korea
\n<\/p>\n
\n
J_ratio Targets by Application Type<\/div>\n
\n
\u2264 3:1<\/strong> \u2014 High-dynamic servo (robot, packaging jaw, CNC rapid traverse)<\/div>\n
\u2264 5:1<\/strong> \u2014 Standard precision servo (rotary table, conveyor servo)<\/div>\n
\u2264 10:1<\/strong> \u2014 General positioning (indexer, general servo)<\/div>\n
\u2264 30:1<\/strong> \u2014 Speed control only (conveyor, screw rotation)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n

<\/p>\n

\n

The i\u00b2 Law \u2014 Why a Small Ratio Change Has a Large Inertia Effect<\/h2>\n

The most important practical insight from the reflected inertia formula is the i\u00b2 scaling: the reflected load inertia decreases with the square<\/em> of the gear ratio. This makes gear ratio selection a far more powerful inertia management tool than changing the motor or moving hardware.<\/p>\n

A Korean machine builder who is struggling with a J_ratio of 40:1 (servo tuning unstable, machine constantly hunting) does not need a larger motor \u2014 they need a higher gear ratio. Doubling the ratio from i=5 to i=10 reduces reflected inertia by 4\u00d7, dropping the J_ratio from 40:1 to 10:1. Doubling again to i=20 drops it to 2.5:1. These ratio changes cost almost nothing (stepping up one ratio in the same gearbox frame often has negligible price difference) but produce dramatic servo performance improvements.<\/p>\n

\n\n\n\n\n\n\n\n\n\n
Gear ratio i<\/th>\ni\u00b2 factor<\/th>\nJ_load_reflected (J_load = 100 kg\u00b7cm\u00b2)<\/th>\nJ_ratio (J_motor = 5 kg\u00b7cm\u00b2)<\/th>\nPerformance zone<\/th>\n<\/tr>\n<\/thead>\n
i = 3<\/td>\n9<\/td>\n11.1 kg\u00b7cm\u00b2<\/td>\n2.2 : 1<\/td>\n\u2705 Excellent<\/td>\n<\/tr>\n
i = 5<\/td>\n25<\/td>\n4.0 kg\u00b7cm\u00b2<\/td>\n0.8 : 1<\/td>\n\u2705 Near-optimal<\/td>\n<\/tr>\n
i = 10<\/td>\n100<\/td>\n1.0 kg\u00b7cm\u00b2<\/td>\n0.2 : 1<\/td>\n\u2705 Motor-dominated<\/td>\n<\/tr>\n
i = 2 (no gearbox)<\/td>\n4<\/td>\n25.0 kg\u00b7cm\u00b2<\/td>\n5.0 : 1<\/td>\n\u26a0 Borderline<\/td>\n<\/tr>\n
i = 1 (direct)<\/td>\n1<\/td>\n100 kg\u00b7cm\u00b2<\/td>\n20 : 1<\/td>\n\u274c Difficult to tune<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Example: J_load = 100 kg\u00b7cm\u00b2 (rotating turntable + part), J_motor = 5 kg\u00b7cm\u00b2. i_optimal = \u221a(100\/5) = 4.47 \u2192 nearest standard ratio i=5 gives near-optimal J_ratio = 0.8:1.<\/p>\n

The direct-drive trap: <\/strong>
\nKorean engineers who specify direct-drive (no gearbox, coupling only) to simplify machine design often end up with J_ratio of 10:1 to 30:1 \u2014 requiring very conservative servo gains that limit achievable acceleration. A small gear ratio (i=3 to i=5) dramatically improves the servo bandwidth without significantly limiting output speed, because the same motor at 3,000 rpm produces 1,000 rpm output at i=3 \u2014 adequate for most rotary table and robot joint applications. The “no gearbox = better performance” intuition is only correct when the load is inherently well-matched to the motor \u2014 a rare condition in practice.<\/span><\/div>\n<\/section>\n

<\/p>\n

\n

Three Korean Application Case Studies \u2014 Complete Inertia Matching Calculations<\/h2>\n
\n

<\/p>\n

\n
\n
Case 1<\/div>\n

Korean HFFS Packaging \u2014 Film Reel Pull Axis<\/h3>\n<\/div>\n

Problem:<\/strong> Film reel drive axis is unstable during deceleration at high speed. Motor: J_motor = 0.8 kg\u00b7cm\u00b2. Full reel: \u00d8600mm, 25 kg (J_reel = 2,812 kg\u00b7cm\u00b2). Drive pulley r = 50 mm (J_pulley = 0.15 kg\u00b7cm\u00b2). Linear film mass 2 kg on belt. Current ratio: i = 5.<\/p>\n

J_reel_reflected = J_reel \/ i\u00b2 = 2,812 \/ 25 = 112.5 kg\u00b7cm\u00b2
\nJ_pulley_reflected = 0.15 \/ 25 = 0.006 kg\u00b7cm\u00b2
\nJ_mass_reflected = m \u00d7 r\u00b2 \/ i\u00b2 = 2 \u00d7 50\u00b2 \/ 25 = 200 kg\u00b7cm\u00b2
\nJ_total_load_reflected = 112.5 + 0.006 + 200 = 312.5 kg\u00b7cm\u00b2
\nJ_ratio = 312.5 \/ 0.8 = 390:1 \u2190 severely mismatched<\/span><\/p>\n

i_optimal = \u221a(312.5 \/ 0.8) = \u221a390.6 = 19.8 \u2192 use i = 20
\nAt i = 20: J_ratio = 2,812\/(400\u00d70.8) + 2\u00d750\u00b2\/(400\u00d70.8) = 8.8+31.3 = 40.1:1<\/span>
\nStill high \u2192 i = 25: J_ratio = (2812+2\u00d750\u00b2)\/(625\u00d70.8) = 7.7:1 \u2713 acceptable<\/span><\/div>\n

Solution:<\/strong> Upgrade from i=5 to i=25 (EP-AF090 P1<\/a> two-stage). J_ratio drops from 390:1 to 7.7:1 \u2014 within acceptable range for HFFS speed control. This result matches the Art10 recommendation and now shows the mathematical basis for that choice.<\/p>\n<\/div>\n

<\/p>\n

\n
\n
Case 2<\/div>\n

Korean 5-Axis Machining Centre \u2014 Rotary B-Axis Table<\/h3>\n<\/div>\n

Problem:<\/strong> Select optimal ratio for B-axis rotary table. Motor: J_motor = 4.2 kg\u00b7cm\u00b2. Table + fixture: J_table = 380 kg\u00b7cm\u00b2 (varies 200\u2013500 with workpiece). Target: J_ratio \u2264 5:1 at maximum load.<\/p>\n

i_optimal = \u221a(J_table_max \/ J_motor) = \u221a(500 \/ 4.2) = \u221a119 = 10.9
\n\u2192 Nearest standard ratios: i=10 and i=12 (EP-AFH catalogue)<\/p>\n

At i=10: J_ratio = 500\/(100\u00d74.2) = 1.19:1<\/span> (excellent but may over-reduce speed)
\nAt i=15: J_ratio = 500\/(225\u00d74.2) = 0.53:1<\/span> (motor-dominated, very stable)<\/p>\n

Check output speed at i=10, n_motor=3000rpm: n_out=300rpm \u2190 too fast for B-axis
\nCheck output speed at i=50, n_motor=3000rpm: n_out=60rpm \u2190 typical B-axis \u2713
\nAt i=50: J_ratio = 500\/(2500\u00d74.2) = 0.048:1 \u2713 motor-dominated<\/span><\/div>\n

Solution:<\/strong> EP-AFH<\/a> i=50 two-stage. At this ratio the rotary table is completely motor-inertia-dominated \u2014 the load contribution is negligible \u2014 and the servo loop is controlled almost entirely by motor properties. This is why high-ratio CNC rotary tables are inherently easy to tune regardless of workpiece weight variation.<\/p>\n<\/div>\n

<\/p>\n

\n
\n
Case 3<\/div>\n

Korean E-Commerce AMR \u2014 Drive Wheel Inertia Matching<\/h3>\n<\/div>\n

Problem:<\/strong> 500 kg payload AMR, wheel radius r=0.10m, J_motor = 0.35 kg\u00b7cm\u00b2. Effective rotary inertia of vehicle+payload at wheel: J_vehicle = m \u00d7 r\u00b2 = 700 \u00d7 100\u00b2 = 7,000,000 kg\u00b7cm\u00b2.<\/p>\n

i_optimal = \u221a(J_vehicle \/ J_motor) = \u221a(7,000,000 \/ 0.35) = \u221a20,000,000 = 4,472
\nThis is impractically high \u2014 need to reconsider.<\/p>\n

Better model: treat as linear mass at wheel output:
\nAt gearbox output (wheel shaft): effective inertia = m \u00d7 r\u00b2 = 700\u00d70.1\u00b2 = 7 kg\u00b7m\u00b2 = 70,000 kg\u00b7cm\u00b2
\nWith gearbox i: J_reflected = 70,000 \/ i\u00b2<\/p>\n

Target J_ratio \u2264 10 (speed control, moderate dynamic):
\nJ_ratio = 70,000 \/ (i\u00b2 \u00d7 0.35) \u2264 10
\ni\u00b2 \u2265 70,000 \/ (10 \u00d7 0.35) = 20,000
\ni \u2265 \u221a20,000 = 141 \u2190 extremely high<\/p>\n

Practical: use i=20 (EP-AB060 P2), accept J_ratio = 70,000\/(400\u00d70.35) = 500:1<\/span>
\nUse velocity control (not position), rely on odometry correction. \u2713<\/div>\n

Insight:<\/strong> AGV drive wheels are fundamentally inertia-mismatched in the gearbox sense \u2014 the vehicle mass is so large that matching it to a compact motor would require impractically high ratios. The correct architecture is velocity control with outer-loop position correction from navigation sensors, not tight inertia matching. This is why AGV drives are specified on torque, noise, and speed sync (Art12) \u2014 not on inertia ratio.<\/p>\n<\/div>\n<\/div>\n<\/section>\n

<\/p>\n

\n

Gearbox Input Inertia \u2014 The Term Korean Engineers Most Often Omit<\/h2>\n

The correct reflected inertia formula at the motor shaft is:<\/p>\n

J_total = J_motor + J_gearbox_input<\/strong> + J_load \/ i\u00b2<\/div>\n

The middle term \u2014 J_gearbox_input<\/strong> \u2014 is the rotational inertia of the gearbox’s input-side rotating components (sun gear, input bearing inner rings, motor adapter). This term is published in Korea Ever-Power EP series datasheets and typically represents 5\u201320% of the motor rotor inertia for standard servo motor pairings.<\/p>\n

For most applications, omitting J_gearbox_input introduces a 5\u201315% error in the inertia ratio calculation \u2014 small enough that it does not change the gear ratio selection. However, for two cases it matters significantly:<\/p>\n

\n
Very small load (near-optimal ratio already achieved)<\/strong><\/p>\n

When J_load\/i\u00b2 is comparable to J_motor (i.e. the system is near the optimal ratio), the gearbox input inertia may push the total past the J_ratio target. Always include J_gearbox_input when J_ratio is calculated to be below 3:1 \u2014 the correction may push it above the target.<\/p>\n<\/div>\n

Very high input speeds (above 4,000 rpm)<\/strong><\/p>\n

At high input speeds, the gearbox input stage generates bearing centrifugal loads and churning losses that are themselves speed-dependent. For ratios above 3,000 rpm input, include J_gearbox_input and verify against the maximum input speed specification for the selected EP series frame and ratio.<\/p>\n<\/div>\n<\/div>\n

\n\n\n\n\n\n\n\n\n\n
EP Series<\/th>\nFrame<\/th>\nJ_gearbox_input (typical, kg\u00b7cm\u00b2)<\/th>\n% of typical servo J_motor<\/th>\n<\/tr>\n<\/thead>\n
EP-AB<\/a><\/td>\n042<\/td>\n0.05\u20130.10<\/td>\n~8%<\/td>\n<\/tr>\n
EP-AB<\/td>\n060<\/td>\n0.15\u20130.30<\/td>\n~10%<\/td>\n<\/tr>\n
EP-AB<\/td>\n090<\/td>\n0.50\u20131.20<\/td>\n~12%<\/td>\n<\/tr>\n
EP-AB<\/td>\n115<\/td>\n1.5\u20133.5<\/td>\n~15%<\/td>\n<\/tr>\n
EP-AH New Line<\/a><\/td>\n200<\/td>\n8\u201320<\/td>\n~20%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Indicative values. Confirm exact J_gearbox_input from Korea Ever-Power EP series datasheet for your specific model and ratio. Values are for single-stage; two-stage adds the input-stage planet carrier inertia contribution.<\/p>\n<\/section>\n

<\/p>\n

\n

When Deliberate Inertia Mismatch Is the Correct Engineering Choice<\/h2>\n

The inertia matching guideline is a performance optimisation tool, not a constraint that must always be met. There are three legitimate engineering scenarios where a Korean machine designer may deliberately accept a J_ratio outside the recommended range.<\/p>\n

\"Korea<\/p>\n

\n
\u2460 High-inertia load with outer-loop position correction<\/strong><\/p>\n

AGV drives (Case 3 above), conveyor head drums, and screw rotation axes all operate at J_ratio far above the standard guideline \u2014 but they use velocity control with outer-loop position correction from encoders, sensors, or navigation systems. In these cases the servo loop does not need tight inertia matching; it needs reliable speed control, which works acceptably at J_ratio up to 30:1 or more with well-tuned velocity PI gains.<\/p>\n<\/div>\n

\u2461 Speed range requirement forces a ratio that creates J_ratio > target<\/strong><\/p>\n

If the required output speed range dictates a low ratio (e.g. i=3 for a high-speed indexer that must reach 500 rpm output from a 1,500 rpm motor), and this produces J_ratio = 15:1, the engineer should accept the mismatch and compensate through motor sizing: specifying a motor with higher rotor inertia (typically a larger frame motor in the same power class) to reduce J_ratio without changing the gear ratio.<\/p>\n<\/div>\n

\u2462 Load inertia varies widely (e.g. workpiece changes)<\/strong><\/p>\n

CNC rotary table with variable workpiece weight (empty 50 kg to full 500 kg) has a 10:1 inertia variation that no fixed gear ratio can simultaneously optimise for both extremes. The standard approach is to select the ratio that keeps J_ratio \u2264 5:1 at the maximum load condition \u2014 accepting that at minimum load the system is over-reduced and slightly less efficient, but stable at both extremes.<\/p>\n<\/div>\n<\/div>\n<\/section>\n

<\/p>\n

\n

Inertia-Based Gear Ratio Selection \u2014 Complete Step-by-Step Procedure<\/h2>\n

The following six-step procedure applies to any Korean servo axis. Steps 1\u20133 determine whether inertia or speed is the binding constraint on ratio selection; steps 4\u20136 confirm the chosen ratio against all remaining criteria.<\/p>\n

\"Korea<\/p>\n

\n
\n
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1<\/div>\n

Calculate required output speed range<\/strong><\/p>\n<\/div>\n

n_out_max = maximum axis speed (rpm) from machine spec. n_out_min (if applicable). This gives the speed-based ratio limit: i_speed = n_motor_rated \/ n_out_max. This is the minimum<\/em> allowable ratio \u2014 ratios below this exceed motor rated speed.<\/p>\n<\/div>\n

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2<\/div>\n

Calculate load inertia at the output shaft<\/strong><\/p>\n<\/div>\n

Use the appropriate formula from Module 2 for your drive topology. For variable-load applications (workpiece changes, film reel depleting), calculate at the worst case (maximum inertia condition). Include all rotating and translating masses connected to the output shaft.<\/p>\n<\/div>\n

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\n
3<\/div>\n

Calculate optimal ratio and J_ratio at each candidate ratio<\/strong><\/p>\n<\/div>\n

i_optimal = \u221a(J_load \/ J_motor). Calculate J_ratio at catalogue ratios near i_optimal. Select the ratio that meets the J_ratio target for your application type (from Module 3 table) while also satisfying i \u2265 i_speed from Step 1.<\/p>\n<\/div>\n

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4<\/div>\n

Verify output torque at the required ratio<\/strong><\/p>\n<\/div>\n

T_output = T_motor_rated \u00d7 i \u00d7 \u03b7. Confirm T_output \u2265 required load torque \u00d7 service factor. This step may override the inertia-optimal ratio if the torque requirement dictates a different frame size or series.<\/p>\n<\/div>\n

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\n
5<\/div>\n

Check radial load at actual overhang distance<\/strong><\/p>\n<\/div>\n

For belt, chain, or gear-loaded output shafts: apply the overhang multiplier from Art16 and confirm the effective bearing load is within EP-AB or EP-AF permissible values. Inertia matching and radial load capacity are independent checks \u2014 both must pass.<\/p>\n<\/div>\n

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6<\/div>\n

Confirm precision grade and series<\/strong><\/p>\n<\/div>\n

Select backlash grade from Art8 based on positioning accuracy. If inertia-optimal ratio falls between standard EP-AB steps, check EP-ADS non-standard ratios<\/a> for a closer match. Korea Ever-Power application team confirms all six steps for any specific Korean machine specification \u2014 same business day.<\/p>\n<\/div>\n<\/div>\n<\/section>\n

<\/p>\n

\n

Frequently Asked Questions \u2014 Planetary Gearbox Inertia Matching<\/h2>\n
\n
\n

Q<\/span>
\nOur Korean packaging machine servo is oscillating and hunting at low speeds. The control engineer has increased damping but the axis is still slow to settle. Is this an inertia ratio problem?<\/h3>\n

Oscillation and hunting at low speeds that does not respond well to increased damping is a classic high-J_ratio symptom. When J_ratio is large, the servo loop must use high proportional gain to achieve adequate stiffness, but the high gain combined with the large load inertia produces the oscillatory response. Increasing damping (derivative gain) helps but has diminishing returns at high J_ratio. The correct fix is to increase the gear ratio \u2014 even one step up in the EP-AB catalogue (e.g. from i=10 to i=15) reduces J_ratio by 2.25\u00d7 and may immediately resolve the hunting without any control gain changes. Measure J_load at the output shaft, calculate J_ratio at your current ratio, and compare to the targets in Module 3. If J_ratio exceeds 10:1 on a precision positioning axis, increasing the ratio is the correct mechanical solution.<\/p>\n<\/div>\n

\n

Q<\/span>
\nCan I use a worm gear reducer for inertia-critical applications where I need a very high ratio?<\/h3>\n

Worm gear reducers<\/a> can provide high ratios (up to 100:1 in single stage) with inherent self-locking \u2014 useful for applications requiring position holding on power-off. However, their efficiency of 40\u201370% means that a significant fraction of motor torque is lost to friction, and their typical backlash of 15\u201330 arcmin makes them unsuitable for closed-loop precision servo positioning. For inertia matching purposes: the worm’s high ratio does reduce reflected load inertia by i\u00b2 \u2014 so a worm at i=60 reduces load inertia by 3,600\u00d7 \u2014 but the friction torque loss and high backlash prevent the high-bandwidth servo response that the inertia matching is supposed to enable. Use planetary gearboxes for inertia-critical servo axes; consider worm reducers only where self-locking, very high ratio, and open-loop speed control are the primary requirements rather than servo bandwidth.<\/p>\n<\/div>\n

\n

Q<\/span>
\nHow does the inertia matching calculation change for a two-stage gearbox compared to a single-stage?<\/h3>\n

For a two-stage gearbox with total ratio i = i\u2081 \u00d7 i\u2082, the reflected load inertia formula is unchanged: J_load_reflected = J_load \/ i\u00b2. The total ratio i is used directly \u2014 there is no need to calculate stage by stage. The only two-stage-specific addition is the intermediate stage inertia: the first stage planet carrier and output shaft rotate at n_motor \/ i\u2081, contributing an intermediate inertia term of J_intermediate \/ i\u2081\u00b2. For standard Korea Ever-Power EP two-stage units, this intermediate inertia is included in the published J_gearbox_input value \u2014 it already accounts for both stages’ internal rotating components at their respective speeds. When Korea Ever-Power provides J_gearbox_input for a two-stage EP-AB unit, that value is ready to use directly in J_total = J_motor + J_gearbox_input + J_load\/i\u00b2 without further stage-by-stage decomposition.<\/p>\n<\/div>\n

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Q<\/span>
\nMy Korean CNC machine builder specifies a J_ratio \u2264 3:1 for all servo axes. Is this unnecessarily conservative for axes like the tool changer or chip conveyor?<\/h3>\n

Yes \u2014 a blanket J_ratio \u2264 3:1 for all axes is unnecessarily conservative for non-precision servo axes and will increase gearbox BOM cost without performance benefit. The J_ratio \u2264 3:1 guideline is appropriate for high-dynamic precision axes (spindle, feed axis, rotary table B\/C axis) where servo bandwidth directly affects machining accuracy and cycle time. For the tool changer (moderate speed, position control to pocket location), J_ratio \u2264 10:1 is adequate. For the chip conveyor (speed control only, no precision positioning), J_ratio \u2264 30:1 is fully acceptable. The axis-by-axis differentiation approach used in Art19 (injection molding five-axis BOM) applies equally here: specifying by actual axis requirements rather than applying the most conservative specification to all axes reduces BOM cost by \u20a9300,000\u2013800,000 per machine at equivalent or better performance.<\/p>\n<\/div>\n<\/div>\n<\/section>\n

<\/p>\n

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Korea Ever-Power Calculates Your Inertia Matching \u2014 Same Day, in Korean<\/h2>\n

Provide motor inertia, load description, and required output speed \u2014 Korea Ever-Power performs the six-step inertia matching calculation and recommends the EP series, frame, and ratio that optimises servo performance for your specific Korean machine application.<\/p>\n

EP-AB Precision Series \u2192
\n<\/a>
\nEP-AF High-Rigidity Series \u2192
\n<\/a><\/div>\n<\/section>\n

Redacteur: Cxm<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

Engineering Reference \u00b7 J_ratio \u00b7 Optimal Ratio \u00b7 Servo Bandwidth \u00b7 Calculation Guide Planetary Gearbox Inertia Matching \u2014 Gear Ratio Selection for Servo Performance Every Korean servo engineer knows that inertia ratio matters \u2014 but few have a systematic method for calculating it across all three drive topologies (direct coupling, belt drive, rack and pinion) […]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[965],"tags":[],"class_list":["post-715","post","type-post","status-publish","format-standard","hentry","category-application-and-technical-guid"],"_links":{"self":[{"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/posts\/715","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/comments?post=715"}],"version-history":[{"count":2,"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/posts\/715\/revisions"}],"predecessor-version":[{"id":717,"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/posts\/715\/revisions\/717"}],"wp:attachment":[{"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/media?parent=715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/categories?post=715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/nl\/wp-json\/wp\/v2\/tags?post=715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}