{"id":744,"date":"2026-06-03T01:42:41","date_gmt":"2026-06-03T01:42:41","guid":{"rendered":"https:\/\/planetary-gearboxes.com\/?p=744"},"modified":"2026-06-03T01:42:41","modified_gmt":"2026-06-03T01:42:41","slug":"gear-ratio-inertia-matching-servo-planetary-gearbox","status":"publish","type":"post","link":"https:\/\/planetary-gearboxes.com\/bg\/gear-ratio-inertia-matching-servo-planetary-gearbox\/","title":{"rendered":"\u0421\u044a\u0432\u043f\u0430\u0434\u0435\u043d\u0438\u0435 \u043d\u0430 \u0438\u043d\u0435\u0440\u0446\u0438\u044f\u0442\u0430 \u0438 \u0438\u0437\u0431\u043e\u0440 \u043d\u0430 \u043f\u0440\u0435\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u043d\u043e \u0447\u0438\u0441\u043b\u043e \u0437\u0430 \u0441\u0435\u0440\u0432\u043e \u043f\u043b\u0430\u043d\u0435\u0442\u0430\u0440\u043d\u0438 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u043d\u0438 \u043a\u0443\u0442\u0438\u0438"},"content":{"rendered":"
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<\/div>\n
<\/div>\n
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\u041a\u043e\u0440\u0435\u044f \u0415\u0432\u044a\u0440-\u041f\u0430\u0443\u044a\u0440<\/span>
\nServo Drive Engineering<\/span><\/div>\n

Inertia Matching and Gear Ratio Selection for Servo Planetary Gearboxes \u2014 The Formula, the Trade-Off, and Worked Examples<\/h1>\n

Gear ratio selection is treated as a torque calculation by most engineers \u2014 divide the required output torque by the motor rated torque and select the nearest standard ratio. This approach misses the second, equally important function of the gear ratio: every factor of \u0430\u0437<\/em> in the ratio reduces the load inertia at the motor shaft by a factor of \u0430\u0437<\/em>\u00b2. Getting this calculation right is the difference between a servo axis that tunes cleanly and one that oscillates, settles slowly, or fails bearings prematurely through cyclic resonance loading.<\/p>\n

Get Inertia Matching Calculation Support \u2192<\/a><\/p>\n<\/div>\n<\/div>\n<\/section>\n

<\/p>\n

\n

The Two Functions of Gear Ratio \u2014 Torque Multiplication and Inertia Reduction<\/h2>\n

\u0410 \u043f\u0440\u0435\u0446\u0438\u0437\u043d\u0430 \u043f\u043b\u0430\u043d\u0435\u0442\u0430\u0440\u043d\u0430 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u043d\u0430 \u043a\u0443\u0442\u0438\u044f<\/a> placed between a servo motor and a load performs two simultaneous transformations. Both are governed by the gear ratio \u0430\u0437<\/em> \u2014 but they scale differently, and understanding this scaling difference is the core of correct ratio selection.<\/p>\n

\n
\n
Function 1 \u2014 Torque Multiplication<\/div>\n
\n
T_\u0438\u0437\u0445\u043e\u0434 = T_\u0434\u0432\u0438\u0433\u0430\u0442\u0435\u043b \u00d7 i \u00d7 \u03b7<\/div>\n
Scales linearly with i<\/div>\n
Double i \u2192 double T_output<\/div>\n<\/div>\n

Standard torque sizing: T_required = T_load \u00d7 SF, then i = T_required \/ (T_motor \u00d7 \u03b7). Most engineers stop here. This gives the minimum ratio needed for torque \u2014 but not necessarily the ratio that gives the best servo dynamics.<\/p>\n<\/div>\n

\n
Function 2 \u2014 Inertia Reduction \u2605 Often Missed<\/div>\n
\n
J_\u043e\u0442\u0440\u0430\u0437\u0435\u043d\u043e = J_\u043d\u0430\u0442\u043e\u0432\u0430\u0440\u0432\u0430\u043d\u0435 \/ i\u00b2<\/div>\n
Scales with i SQUARED<\/div>\n
Double i \u2192 quarter J_reflected<\/div>\n<\/div>\n

The load inertia as seen by the motor shaft is divided by i\u00b2. This means that a ratio change from 5:1 to 10:1 \u2014 a \u00d72 change \u2014 reduces the reflected inertia by a factor of 4. The inertia-matching effect of ratio is far more powerful than the torque-multiplication effect, yet it is the one most often absent from published selection guides.<\/p>\n<\/div>\n

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Both Constraints Together<\/div>\n
\n
i_min_torque = T_load \u00d7 SF \/ (T_motor \u00d7 \u03b7)<\/div>\n
i_optimal_inertia = \u221a(J_load \/ J_motor)<\/div>\n
Choose i that satisfies BOTH<\/div>\n<\/div>\n

In practice, i_optimal_inertia is often higher than i_min_torque \u2014 meaning inertia matching drives you toward a larger ratio than torque alone would require. The five-step decision framework later in this guide resolves conflicts between the two constraints.<\/p>\n<\/div>\n<\/div>\n<\/section>\n

<\/p>\n

\"High-precision<\/p>\n
EP series precision planetary gearboxes are available in single-stage ratios from 3:1 to 10:1, two-stage from 9:1 to 64:1, and three-stage from 60:1 to 516:1 \u2014 providing the full range needed to target the optimal inertia ratio for any servo application. View EP series specifications \u2192<\/a><\/div>\n<\/div>\n

<\/p>\n

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The Inertia Ratio Target \u2014 Why 1:1 to 3:1 Is the Universal Standard<\/h2>\n

The inertia ratio (J_reflected \/ J_motor) determines how well the servo motor can control the load. A motor driving a perfectly matched load (1:1 ratio) can apply full Kv gain, achieve minimum settling time, and respond instantaneously to position error commands. As the inertia ratio increases beyond 3:1, the control loop must reduce its gain to avoid exciting the mechanical resonance of the system \u2014 and every unit of Kv reduction translates directly to slower settling time and reduced positioning accuracy.<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n
\u041a\u043e\u0435\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043d\u0430 \u0438\u043d\u0435\u0440\u0446\u0438\u044f
\nJ_reflected \/ J_motor<\/th>\n		Max Kv Gain<\/th>\nSettling Time
\n(relative)<\/th>\n		Dynamic Positioning<\/th>\nGearbox Bearing Risk<\/th>\nAssessment<\/th>\n<\/tr>\n<\/thead>\n
1:1<\/td>\nFull<\/td>\n1.0\u00d7 (fastest)<\/td>\nBest<\/td>\nNegligible<\/td>\n\u2705 \u0418\u0434\u0435\u0430\u043b\u0435\u043d<\/td>\n<\/tr>\n
2:1<\/td>\nFull<\/td>\n1.0\u00d7<\/td>\nExcellent<\/td>\nNone<\/td>\n\u2705 Excellent<\/td>\n<\/tr>\n
3:1<\/td>\nFull<\/td>\n1.0\u00d7<\/td>\nVery good<\/td>\nNone<\/td>\n\u2705 Target maximum<\/td>\n<\/tr>\n
5:1<\/td>\n\u00d70.77<\/td>\n1,3\u00d7<\/td>\nReduced<\/td>\n\u041d\u0438\u0441\u043a\u043e<\/td>\n\u26a0\ufe0f Acceptable<\/td>\n<\/tr>\n
8:1<\/td>\n\u00d70.61<\/td>\n1.6\u00d7<\/td>\n\u041e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043e<\/td>\n\u0423\u043c\u0435\u0440\u0435\u043d\u043e<\/td>\n\u274c Avoid<\/td>\n<\/tr>\n
10:1<\/td>\n\u00d70.55<\/td>\n1.8\u00d7<\/td>\nPoor<\/td>\nHigh<\/td>\n\u274c Requires low Kv<\/td>\n<\/tr>\n
>10:1<\/td>\n\u00d70.45 or less<\/td>\n>2.2\u00d7<\/td>\nVery poor<\/td>\nVery high<\/td>\n\u274c Redesign needed<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Kv reduction factors and settling time multiples are approximate, based on velocity-loop bandwidth limitation analysis for inertia-dominated servo systems. Actual values depend on motor type, servo drive tuning algorithm, and mechanical compliance. Gearbox bearing risk column reflects planet carrier pin fretting risk from cyclic resonance loading \u2014 see the failure causes guide<\/a> for detail.<\/p>\n

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Why does high inertia ratio damage the gearbox?<\/strong> When the inertia ratio exceeds 5:1, servo engineers typically increase Kv to compensate for the sluggish response \u2014 pushing the gain toward mechanical resonance. The resulting drivetrain oscillation at 10\u201350 Hz imposes cyclic torque loading on the planet carrier bearings far beyond the smooth design load. Planet carrier pin bore fretting and bearing micro-pitting are the characteristic failure signatures of inertia-mismatch-driven oscillation in planetary gearboxes. Correct ratio selection eliminates this failure mode before commissioning.<\/p>\n<\/div>\n<\/section>\n

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The Formula \u2014 Calculating Optimal Gear Ratio from Inertia Data<\/h2>\n

The optimal gear ratio for inertia matching is the ratio that produces a reflected inertia equal to the motor rotor inertia (1:1 target). The formula derives directly from setting J_reflected = J_motor and solving for i:<\/p>\n

\n
Core Inertia Matching Formulae<\/div>\n
\n
\n
Reflected inertia at motor shaft:<\/div>\n
J_\u043e\u0442\u0440\u0430\u0437\u0435\u043d\u043e = J_\u043d\u0430\u0442\u043e\u0432\u0430\u0440\u0432\u0430\u043d\u0435 \/ i\u00b2<\/div>\n
J in kg\u00b7m\u00b2, i = gear ratio (output\/input)<\/div>\n<\/div>\n
\n
Optimal ratio (1:1 target):<\/div>\n
i_opt = \u221a(J_load \/ J_motor)<\/div>\n
Gives J_reflected = J_motor exactly<\/div>\n<\/div>\n
\n
Acceptable range (1:1 to 3:1):<\/div>\n
i_min = \u221a(J_load \/ (3\u00b7J_motor))
\ni_max = \u221a(J_load \/ J_motor)<\/div>\n
Any EP ratio within this range is acceptable<\/div>\n<\/div>\n
\n
Verify torque margin:<\/div>\n
T_available = T_motor \u00b7 i \u00b7 \u03b7
\n\u2265 T_load \u00b7 SF<\/div>\n
Must be satisfied independently of inertia<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
Step-by-step calculation procedure<\/div>\n
    \n
  1. Calculate J_load<\/strong> \u2014 total load inertia including all rotating and linear masses reflected to the output shaft (see next section for component formulae)<\/li>\n
  2. Read J_motor<\/strong> from the servo motor datasheet \u2014 this is the rotor inertia, specified in kg\u00b7m\u00b2 or kg\u00b7cm\u00b2<\/li>\n
  3. Calculate i_opt = \u221a(J_load \/ J_motor)<\/strong> \u2014 this is the ideal ratio for 1:1 matching<\/li>\n
  4. Identify EP series standard ratios within the acceptable band: i_min<\/strong> to i_opt<\/strong><\/li>\n
  5. For each candidate ratio, verify torque: T_available = T_motor \u00d7 i \u00d7 \u03b7 \u2265 T_load \u00d7 SF<\/strong><\/li>\n
  6. Select the highest ratio that satisfies both inertia and torque constraints \u2014 higher ratio generally provides better inertia matching within the acceptable band<\/li>\n<\/ol>\n<\/div>\n<\/section>\n

    <\/p>\n

    \n

    Calculating Load Inertia \u2014 Formulae for Common Machine Elements<\/h2>\n

    J_load is the total inertia of all elements driven by the gearbox output shaft, expressed at the output shaft. For rotary loads this is direct; for linear loads the mass must be reflected through the mechanical transmission (rack-pinion, ballscrew, or belt-pulley) to obtain an equivalent rotary inertia at the gearbox output.<\/p>\n

    \n\n\n\n\n\n\n\n\n\n\n
    Machine Element<\/th>\nInertia Formula<\/th>\nVariables<\/th>\nTypical Applications<\/th>\n<\/tr>\n<\/thead>\n
    Solid cylinder (disk)<\/td>\nJ = \u00bd m r\u00b2<\/td>\nm = mass (kg), r = radius (m)<\/td>\nRotary tables, flywheels, pulleys, drive rollers<\/td>\n<\/tr>\n
    Hollow cylinder<\/td>\nJ = \u00bd m (r_o\u00b2 + r_i\u00b2)<\/td>\nr_o = outer, r_i = inner radius<\/td>\nHollow shafts, pipe rollers, coil winders<\/td>\n<\/tr>\n
    Point mass at radius R<\/td>\nJ = m R\u00b2<\/td>\nm = mass (kg), R = distance from axis<\/td>\nWorkpiece on rotary table, cam follower, eccentric load<\/td>\n<\/tr>\n
    Linear mass via rack\/pinion<\/td>\nJ = m \u00d7 r_pinion\u00b2<\/td>\nm = linear mass, r = pinion radius<\/td>\nGantry axes, AGV drives, conveyor linear load<\/td>\n<\/tr>\n
    Linear mass via ballscrew<\/td>\nJ = m \u00d7 (pitch \/ 2\u03c0)\u00b2<\/td>\npitch in metres (e.g. 0.01m = 10mm)<\/td>\nCNC feed axes, servo press, linear stages<\/td>\n<\/tr>\n
    Belt\/pulley linear load<\/td>\nJ = m \u00d7 r_drive\u00b2<\/td>\nr_drive = drive pulley radius<\/td>\nConveyor belts, vertical lift axes, timing belt drives<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
    \n
    Important: Total J_load = sum of all elements at the output shaft<\/div>\n

    The gearbox output shaft drives multiple elements simultaneously \u2014 the output shaft coupling, any mechanical transmission components (pinion, pulley, ballscrew), and the end load. All of these must be included in J_load before calculating the reflected inertia. Omitting the pinion or pulley inertia is common and produces an underestimate of J_load by 10\u201330% for typical drive configurations. For a ballscrew-driven axis, the ballscrew body inertia alone (J_screw = \u00bd \u00d7 m_screw \u00d7 r_screw\u00b2) can represent 40\u201360% of total reflected inertia when the linear load is light.<\/p>\n<\/div>\n<\/section>\n

    <\/p>\n

    \n

    Three Fully Worked Examples \u2014 Indexer, AGV Drive, and CNC Rotary Axis<\/h2>\n

    <\/p>\n

    \n
    \n
    Example 1<\/div>\n
    4-Station Servo Rotary Indexer \u2014 Korean Electronics Assembly Line<\/div>\n<\/div>\n
    \n
    \u0414\u0430\u0434\u0435\u043d\u043e:<\/strong>
    \nIndex table: disc \u03a6500mm, 8kg steel
    \n4 fixture blocks: 3kg each at R=200mm
    \nServo motor: 750W, J_motor = 0.00200 kg\u00b7m\u00b2
    \nRequired: index 90\u00b0 in 0.5s, settle in 0.1s<\/div>\n
    Calculate J_load:<\/strong>
    \nJ_table = \u00bd \u00d7 8 \u00d7 0.25\u00b2 = 0.250 kg\u00b7m\u00b2
    \nJ_fixtures = 4 \u00d7 3 \u00d7 0.20\u00b2 = 0.480 kg\u00b7m\u00b2
    \nJ_total = 0.730 kg\u00b7m\u00b2<\/div>\n
    Optimal ratio:<\/strong>
    \ni_opt = \u221a(0.730 \/ 0.002) = 19.1
    \nNearest EP ratios: 16:1, 20:1
    \ni=16: ratio=1.4:1 \u2705 BEST CHOICE<\/span>
    \ni=20: ratio=0.9:1 \u2705 (over-reduced)<\/div>\n<\/div>\n
    Result:<\/strong> EP-ZDE-80 or EP-ZDF-80 at 16:1 (2-stage). J_reflected = 0.730\/256 = 0.00285 kg\u00b7m\u00b2 \u2192 ratio 1.4:1. Torque available: T_motor \u00d7 16 \u00d7 0.94 \u2265 T_load \u00d7 1.5. Settling time target of 0.1s is achievable with full Kv at 1.4:1 ratio. If EP-ZDE-80 at 2-stage is insufficient torque, step up to EP-ZDE-120 at 16:1.<\/div>\n<\/div>\n

    <\/p>\n

    \n
    \n
    Example 2<\/div>\n
    200kg AGV Drive Wheel \u2014 Korean AMR Logistics Platform<\/div>\n<\/div>\n
    \n
    \u0414\u0430\u0434\u0435\u043d\u043e:<\/strong>
    \nVehicle mass: 200kg, 2 drive wheels
    \nDrive wheel: \u03a6150mm, 1.5kg
    \nMotor: 400W, J_motor = 0.00080 kg\u00b7m\u00b2
    \nMax speed: 1.2 m\/s, max accel: 0.5 m\/s\u00b2<\/div>\n
    Calculate J_load:<\/strong>
    \nJ_wheel = \u00bd \u00d7 1.5 \u00d7 0.075\u00b2 = 0.0042 kg\u00b7m\u00b2
    \nJ_vehicle = (200\/2) \u00d7 0.075\u00b2 = 0.5625 kg\u00b7m\u00b2
    \nJ_total = 0.5667 kg\u00b7m\u00b2<\/div>\n
    Optimal + speed check:<\/strong>
    \ni_opt = \u221a(0.5667\/0.0008) = 26.6
    \ni=16: ratio=2.8:1 \u2705, n_motor=2,445rpm \u2705
    \ni=20: ratio=1.8:1 \u2705 BEST BALANCE<\/span>
    \ni=20: n_motor=3,056rpm \u26a0\ufe0f marginal<\/div>\n<\/div>\n
    Result:<\/strong> i=16 (EP-ZDWF-60 or EP-ZDE-60 at 16:1 2-stage) gives ratio 2.8:1 \u2014 acceptable and leaves speed headroom. i=20 gives better inertia matching (1.8:1) but n_motor at max speed approaches 3,056rpm \u2014 within spec (max 4,500rpm) but closer to continuous recommended limit of 3,000rpm. Specify i=16 for AGV speed headroom; i=20 if inertia mismatch causes observable oscillation at direction reversal. Use EP-ZDWF (square flange) for direct laser-cut chassis plate mounting without bore machining.<\/div>\n<\/div>\n

    <\/p>\n

    \n
    \n
    Example 3<\/div>\n
    CNC B-Axis Rotary Table \u2014 Horizontal Machining Centre<\/div>\n<\/div>\n
    \n
    \u0414\u0430\u0434\u0435\u043d\u043e:<\/strong>
    \nTable disc: \u03a6400mm, 25kg steel
    \nWorkpiece: 40kg, R=150mm (\u03a6300mm)
    \nMotor: 1500W, J_motor = 0.00600 kg\u00b7m\u00b2
    \nPeak cutting torque: 380 N\u00b7m, SF=1.5<\/div>\n
    Calculate J_load:<\/strong>
    \nJ_table = \u00bd \u00d7 25 \u00d7 0.20\u00b2 = 0.500 kg\u00b7m\u00b2
    \nJ_work = \u00bd \u00d7 40 \u00d7 0.15\u00b2 = 0.450 kg\u00b7m\u00b2
    \nJ_total = 0.950 kg\u00b7m\u00b2<\/div>\n
    Optimal ratio:<\/strong>
    \ni_opt = \u221a(0.950\/0.006) = 12.6
    \ni=12: ratio=1.1:1 \u2705 (but check torque)
    \nT_avail@12: T_m\u00d712\u00d70.94 \u2265 380\u00d71.5?
    \n\u2192 Use EP-ZDS-142, 16:1 for torque+stiffness<\/span><\/div>\n<\/div>\n
    Result + stiffness consideration:<\/strong> Inertia-optimal ratio is ~12:1 (ratio 1.1:1). However, peak cutting torque of 380 N\u00b7m with SF=1.5 requires T_available \u2265 570 N\u00b7m. This forces the EP-ZDS-142 at 16:1 (T_rated=910 N\u00b7m). The resulting inertia ratio at 16:1 is 0.950\/256\/0.006 = 0.6:1 \u2014 under-reflected (motor “feels” very little load inertia), but this is acceptable and beneficial for rapid indexing. More important: at 380 N\u00b7m peak torque, the crossover torque for ZDS-142 (Ct=44) is 8\u00d744=352 N\u00b7m \u2014 just below the peak cutting torque. Specifying EP-ZDS-142 rather than EP-ZDE-160 reduces elastic angular error by 15% at this torque level. See the torsional stiffness guide for the full crossover analysis.<\/div>\n<\/div>\n<\/section>\n

    <\/p>\n

    \"EP-ZDF<\/p>\n
    The EP-ZDF series<\/a> square-flange inline configuration covers single-stage ratios 3:1 to 10:1 and two-stage ratios 9:1 to 64:1 \u2014 providing the full range of standard ratios needed to target the inertia-optimal gear ratio for indexing, conveyor, and general servo automation applications without precision bore machining.<\/div>\n<\/div>\n

    <\/p>\n

    \n

    The Speed-Inertia Trade-Off \u2014 When Both Constraints Cannot Be Met Simultaneously<\/h2>\n

    In some applications, the ratio that gives optimal inertia matching produces a motor speed that exceeds the motor’s rated continuous speed at the required maximum output speed. This conflict \u2014 speed constraint versus inertia constraint \u2014 is the most common gear ratio dilemma in Korean servo automation design, particularly in AGV drives and high-speed conveyor systems.<\/p>\n

    \n
    Example: J_load = 0.50 kg\u00b7m\u00b2, J_motor = 0.00200 kg\u00b7m\u00b2, n_output_min = 60 rpm, n_motor_max = 3,000 rpm<\/div>\n
    \n\n\n\n\n\n\n\n\n\n\n
    \u0421\u044a\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 i<\/th>\nJ_reflected \/ J_motor<\/th>\nInertia OK?<\/th>\nn_motor at 60rpm output<\/th>\nSpeed OK?<\/th>\nOverall<\/th>\n<\/tr>\n<\/thead>\n
    3:1<\/td>\n27.8:1 \u274c<\/td>\n\u274c<\/td>\n180 rpm<\/td>\n\u2705<\/td>\nInertia fails<\/td>\n<\/tr>\n
    8:1<\/td>\n3.9:1 \u26a0\ufe0f<\/td>\n\u26a0\ufe0f marginal<\/td>\n480 rpm<\/td>\n\u2705<\/td>\nAcceptable with tuning care<\/td>\n<\/tr>\n
    10:1<\/td>\n2.5:1 \u2705<\/td>\n\u2705<\/td>\n600 rpm<\/td>\n\u2705<\/td>\n\u2705 Best choice<\/td>\n<\/tr>\n
    16:1<\/td>\n1.0:1 \u2705<\/td>\n\u2705 ideal<\/td>\n960 rpm<\/td>\n\u2705<\/td>\n\u2705 Optimal inertia<\/td>\n<\/tr>\n
    20:1<\/td>\n0.6:1 \u2705<\/td>\n\u2705 over-matched<\/td>\n1,200 rpm<\/td>\n\u2705<\/td>\nMotor under-utilised<\/td>\n<\/tr>\n
    64:1<\/td>\n0.06:1 \u2705<\/td>\n\u2705 but wasteful<\/td>\n3,840 rpm \u274c<\/td>\n\u274c over speed<\/td>\nSpeed fails<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
    \n

    Resolution rule:<\/strong> When the speed constraint limits how high the ratio can go, select the highest ratio that keeps motor speed within the recommended continuous range (3,000 rpm for EP series) at the required maximum output speed \u2014 then accept the inertia ratio that results. If this inertia ratio is above 5:1, compensate by specifying higher gearbox torsional stiffness (EP-ZDS series) to raise the resonant frequency and allow a higher servo Kv gain. Do not exceed motor speed limits for inertia matching \u2014 the motor thermal damage is irreversible.<\/p>\n<\/div>\n<\/section>\n

    <\/p>\n

    \n

    EP Series Complete Gear Ratio Reference \u2014 All Available Ratios by Stage Count<\/h2>\n

    The following table lists every standard gear ratio available across the EP series precision planetary gearboxes. Non-standard ratios can be manufactured to order \u2014 contact Korea Ever-Power application engineering with your i_optimal calculation for a custom ratio confirmation.<\/p>\n

    \n
    \n
    1-Stage (Ratios 3 to 10)<\/div>\n
    3:1<\/span>
    \n4:1<\/span>
    \n5:1<\/span>
    \n8:1<\/span>
    \n10:1<\/span><\/div>\n

    Highest efficiency (96%), lowest mass. Use for light loads with naturally good inertia matching (J_load\/J_motor already 3\u201330).<\/p>\n<\/div>\n

    \n
    2-Stage (Ratios 9 to 64)<\/div>\n
    9:1<\/span>
    \n12:1<\/span>
    \n15:1<\/span>
    \n16:1<\/span>
    \n20:1<\/span>
    \n25:1<\/span>
    \n32:1<\/span>
    \n40:1<\/span>
    \n64:1<\/span><\/div>\n

    94% efficiency. The primary range for inertia matching \u2014 covers the J_load\/J_motor ratios of 80\u20134,000 with excellent inertia-optimal selection. Most industrial servo automation falls here.<\/p>\n<\/div>\n

    \n
    3-Stage (Ratios 60 to 516)<\/div>\n
    60:1<\/span>
    \n80:1<\/span>
    \n100:1<\/span>
    \n120:1<\/span>
    \n160:1<\/span>
    \n200:1<\/span>
    \n256:1<\/span>
    \n320:1<\/span>
    \n516:1<\/span><\/div>\n

    90% efficiency. For very high J_load\/J_motor ratios (10,000\u2013270,000). Verify motor speed constraint carefully \u2014 at high ratios even modest output speeds require very low motor RPM, risking torque pulsation at low speed.<\/p>\n<\/div>\n<\/div>\n<\/section>\n

    <\/p>\n

    \"Planetary<\/p>\n
    Solar tracker drives, AGV wheels, and renewable energy servo systems represent applications where the inertia matching calculation differs from conventional machine tools \u2014 the load inertia is dominated by large rotating or moving masses, making gear ratio selection the primary lever for servo stability optimisation. EP series ratios from 3:1 to 64:1 cover all standard inertia-matching requirements for these applications. View EP series \u2192<\/strong><\/div>\n<\/div>\n

    <\/p>\n

    \n

    Five-Question Decision Framework for Gear Ratio Selection<\/h2>\n
    \n
    Gear Ratio Selection Decision Framework<\/div>\n
    Q1: What is i_optimal_inertia = \u221a(J_load \/ J_motor)?<\/div>\n
    \u2192 Calculate J_load from all elements. Look up J_motor on motor datasheet.<\/div>\n
    Q2: Is there an EP standard ratio within i_min to i_opt that also satisfies torque?<\/div>\n
    \u2514\u2500\u2500 YES \u2192 Select it. Calculation complete.<\/div>\n
    \u2514\u2500\u2500 NO \u2192 Continue \u2193<\/div>\n
    Q3: Does the torque-optimal ratio produce inertia ratio \u2264 5:1?<\/div>\n
    \u2514\u2500\u2500 YES \u2192 Accept the inertia mismatch. Use torque-optimal ratio. Monitor for oscillation.<\/div>\n
    \u2514\u2500\u2500 NO (ratio >5:1) \u2192 Continue \u2193<\/div>\n
    Q4: Does the speed constraint prevent using the inertia-optimal ratio?<\/div>\n
    \u2514\u2500\u2500 YES \u2192 Select highest ratio where n_motor \u2264 3,000 rpm. Accept inertia ratio result.<\/div>\n
    \u2514\u2500\u2500 NO \u2192 Inertia and torque constraints are the binding constraints. Reconsider motor size.<\/div>\n
    Q5: If inertia ratio >5:1 is unavoidable, is higher Ct (EP-ZDS) specified?<\/div>\n
    \u2514\u2500\u2500 YES \u2192 Proceed. Higher Ct raises resonant frequency, partially compensates.<\/div>\n
    \u2514\u2500\u2500 NO \u2192 Resonance risk. Either increase motor inertia (different motor) or add inertia flywheel to motor shaft.<\/div>\n<\/div>\n<\/section>\n


    \n<\/span><\/p>\n

    \n
    \n
    \n
    Need the Inertia Calculation Done for Your Specific Application?<\/div>\n

    Korea Ever-Power’s application engineering team performs complete inertia matching calculations \u2014 including J_load from your mechanical assembly data, i_optimal, standard EP ratio recommendation, and torque and speed verification. Provide your load mass, geometry, motor datasheet, and required speed\/torque for a complete gear ratio recommendation in Korean or English, at no charge for qualified OEM enquiries.<\/p>\n<\/div>\n

    Request Inertia Calculation \u2192<\/a><\/p>\n
    sales@planetary-gearboxes.com<\/div>\n<\/div>\n<\/div>\n

    <\/p>\n

    \n
    EP Series \u2014 Gear Ratio Reference for Inertia Matching<\/div>\n
    \n
    \n
    \u0421\u0435\u0440\u0438\u044f EP-ZDE<\/div>\n
    Round-flange inline \u00b7 1-stage: 3\u201310 | 2-stage: 9\u201364 | 3-stage: 60\u2013516<\/strong> \u00b7 <8 arcmin \u00b7 96%\/94%\/90% eff.<\/div>\n

    \u0412\u0438\u0436\u0442\u0435 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438\u0442\u0435 \u2192<\/a><\/p>\n<\/div>\n

    \n
    \u0421\u0435\u0440\u0438\u044f EP-ZDF<\/div>\n
    Square-flange inline \u00b7 same ratios as EP-ZDE \u00b7 4-bolt plate mount \u2014 no bore required<\/strong> \u00b7 ideal for fabricated indexer and conveyor frames<\/div>\n

    \u0412\u0438\u0436\u0442\u0435 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438\u0442\u0435 \u2192<\/a><\/p>\n<\/div>\n

    \n
    \u0421\u0435\u0440\u0438\u044f EP-ZDS<\/div>\n
    When inertia ratio >5:1 is unavoidable<\/strong> \u2014 Ct 130 N\u00b7m\/arcmin raises resonant frequency \u00b7 IP65 \u00b7 1,800 N\u00b7m \u00b7 partially compensates for high inertia mismatch<\/div>\n

    \u0412\u0438\u0436\u0442\u0435 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438\u0442\u0435 \u2192<\/a><\/p>\n<\/div>\n<\/div>\n

    \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u0439\u0442\u0435 \u0432\u0441\u0438\u0447\u043a\u0438 5 \u0441\u0435\u0440\u0438\u0438 EP \u2192<\/a><\/div>\n<\/div>\n<\/section>\n

    \u0420\u0435\u0434\u0430\u043a\u0442\u043e\u0440: Cxm<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

    Korea Ever-Power Servo Drive Engineering Inertia Matching and Gear Ratio Selection for Servo Planetary Gearboxes \u2014 The Formula, the Trade-Off, and Worked Examples Gear ratio selection is treated as a torque calculation by most engineers \u2014 divide the required output torque by the motor rated torque and select the nearest standard ratio. This approach misses […]<\/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-744","post","type-post","status-publish","format-standard","hentry","category-application-and-technical-guid"],"_links":{"self":[{"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/posts\/744","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/comments?post=744"}],"version-history":[{"count":2,"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/posts\/744\/revisions"}],"predecessor-version":[{"id":746,"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/posts\/744\/revisions\/746"}],"wp:attachment":[{"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/media?parent=744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/categories?post=744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/planetary-gearboxes.com\/bg\/wp-json\/wp\/v2\/tags?post=744"}],"curies":[{"name":"\u0440\u0430\u0431\u043e\u0442\u043d\u0430 \u0441\u0440\u0435\u0449\u0430","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}