{"id":1619,"date":"2026-04-16T07:08:03","date_gmt":"2026-04-16T07:08:03","guid":{"rendered":"https:\/\/planetarygeardrive.top\/?p=1619"},"modified":"2026-04-16T07:08:03","modified_gmt":"2026-04-16T07:08:03","slug":"how-to-size-planetary-gearbox-guide","status":"publish","type":"post","link":"https:\/\/planetarygeardrive.top\/it\/application\/how-to-size-planetary-gearbox-guide\/","title":{"rendered":"How to size a planetary gearbox? Torque, speed, inertia, and service factor step by step"},"content":{"rendered":"<div style=\"font-family: 'Segoe UI',Arial,Helvetica,sans-serif; max-width: 100%; margin: 0 auto; color: #292524; line-height: 1.8; background: #fffbf5; padding: 28px 24px 40px; border-radius: 8px;\">\n<div style=\"background: #dbeafe; border-left: 5px solid #1d4ed8; padding: 18px 22px; border-radius: 0 8px 8px 0; margin-bottom: 30px;\">\n<p style=\"margin: 0; font-size: 14px; color: #c2410c; font-weight: bold; letter-spacing: 1px; text-transform: uppercase;\">Planetary Gearbox Basics<\/p>\n<p style=\"margin: 6px 0 0; font-size: 13px; color: #64748b;\">Core Keyword: planetary gearbox sizing \u00a0\u00b7\u00a0 Category: planetary-gearbox-basics<\/p>\n<\/div>\n<h2 style=\"font-size: clamp(22px,4vw,28px); font-weight: 900; color: #7c2d12; margin: 0 0 18px; line-height: 1.3;\">How to Size a Planetary Gearbox: Torque, Speed, Inertia, and Service Factor Step-by-Step<\/h2>\n<p style=\"font-size: 16px; margin-bottom: 20px; color: #292524; border-left: 3px solid #92400e; padding-left: 14px; background: #fff7ed; padding: 14px; border-radius: 0 6px 6px 0;\"><strong>Planetary gearbox sizing<\/strong> is a systematic process that begins with the load requirements and works backward through the drivetrain to identify the gearbox specifications \u2014 gear ratio, rated output torque, radial load capacity, and input speed limit \u2014 that ensure reliable long-term operation. Under-sizing a gearbox causes premature failure (bearing fatigue, tooth fracture, or housing cracks within the first 500\u20131,000 hours); over-sizing wastes money and adds unnecessary mass and inertia to the driven axis, reducing system bandwidth and acceleration capability. This guide walks through the complete sizing procedure with formulas and worked examples applicable to servo, stepper, and induction motor drives.<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Step 1: Define Load Torque at the Output Shaft<\/h2>\n<p>Start by calculating the torque required at the gearbox output shaft under the worst operating conditions. For a linear axis driven by a ball screw:<\/p>\n<div style=\"background: #fff7ed; border: 1px solid #fed7aa; border-radius: 6px; padding: 14px 18px; margin: 14px 0; font-family: monospace; font-size: 14px; color: #0f2d5a;\">\n<p>T_load = (F \u00d7 p) \/ (2\u03c0 \u00d7 \u03b7_screw)<\/p>\n<p>Where: F = axial force (N), p = ball screw lead (m), \u03b7_screw = ball screw efficiency (typically 0.85\u20130.95)<\/p>\n<\/div>\n<p>For a rotary load (conveyor drum, turntable, roller): T_load = J_load \u00d7 \u03b1 + T_friction, where \u03b1 is angular acceleration (rad\/s\u00b2) and T_friction includes all friction losses at the output (bearing drag, seal drag, gear mesh losses if any).<\/p>\n<p>For gravity-loaded vertical axes, include the static holding torque required to prevent the axis from back-driving when the motor is powered off: T_static = (m \u00d7 g \u00d7 p) \/ (2\u03c0 \u00d7 \u03b7_screw). This value must be less than the gearbox output shaft static torque rating, and the motor brake (if used) must be sized to hold this torque.<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Step 2: Apply the Service Factor<\/h2>\n<p>The required output torque calculated from load analysis should be multiplied by a <strong>service factor (SF)<\/strong> to account for shock loads, startup transients, vibration, ambient temperature, and safety margin. Service factors for planetary gearboxes typically range:<\/p>\n<ul style=\"margin: 8px 0 16px; padding-left: 22px;\">\n<li style=\"margin-bottom: 8px;\"><strong>Smooth load, uniform operation (conveyors, fans, pumps, winding reels):<\/strong> SF = 1.0\u20131.25<\/li>\n<li style=\"margin-bottom: 8px;\"><strong>Moderate shock (light presses, compressors, mixers, indexing tables):<\/strong> SF = 1.25\u20131.75<\/li>\n<li style=\"margin-bottom: 8px;\"><strong>Heavy shock (crushers, mills, heavy presses, punch presses, shredders):<\/strong> SF = 1.75\u20132.5<\/li>\n<\/ul>\n<p>For applications with frequent direction reversals (more than 10 reversals per minute) or significant vibration, add an additional 0.25\u20130.5 to the service factor. The gearbox rated output torque must equal or exceed: T_required = T_load \u00d7 Service Factor. Never select a gearbox with a rated torque lower than this calculated value \u2014 doing so will void the warranty and guarantee premature failure.<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Step 3: Select the Gear Ratio<\/h2>\n<p>The gear ratio determines both output speed and the torque multiplication from motor to load. Calculate the required ratio as:<\/p>\n<div style=\"background: #fff7ed; border: 1px solid #fed7aa; border-radius: 6px; padding: 14px 18px; margin: 14px 0; font-family: monospace; font-size: 14px; color: #0f2d5a;\">\n<p>i = n_motor \/ n_output_required<\/p>\n<p>Where: n_motor = motor rated speed (RPM), n_output = desired output shaft speed (RPM)<\/p>\n<\/div>\n<p>For servo systems, also calculate the inertia-matching ratio: i_optimal = \u221a(J_load \/ J_motor). Selecting a ratio close to the inertia-matching value minimizes settling time and improves servo bandwidth (typically achieving 3\u20135\u00d7 higher position loop gains). Round to the nearest standard ratio available in the gearbox catalog \u2014 common standard ratios are 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, 20, 25, 28, 30, 32, 35, 40, 48, 50, 64, 70, 80, 100.<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Step 4: Verify Input Speed Against Gearbox Maximum<\/h2>\n<p>Every planetary gearbox has a maximum rated input speed (n_max_input), typically 3,000\u20136,000 RPM for precision servo gearboxes. Verify that the motor’s rated speed at the operating point does not exceed this limit. For motor speeds above the gearbox input limit, a different gearbox must be selected, or the motor speed profile must be adjusted. Operating above the rated input speed causes:<\/p>\n<ul style=\"margin: 8px 0 16px; padding-left: 22px;\">\n<li style=\"margin-bottom: 6px;\">Excessive lubricant churning losses and overheating<\/li>\n<li style=\"margin-bottom: 6px;\">Cage instability in planet bearings<\/li>\n<li style=\"margin-bottom: 6px;\">Noise levels exceeding the gearbox design limits (typically +3\u20135 dB(A) per 10% over-speed)<\/li>\n<\/ul>\n<p>Our <a style=\"color: #c2410c; text-decoration: underline; font-weight: 600;\" href=\"https:\/\/planetarygeardrive.top\/it\/prodotto\/ep-306-inline-planetary-gearbox\/\">EP-306 Inline Planetary Gearbox<\/a> supports input speeds up to 6,000 RPM on precision grades, compatible with most standard servo motor speed ranges (3,000\u20136,000 RPM).<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Step 5: Check Radial and Axial Load on the Output Shaft<\/h2>\n<p>Gear, belt, or chain drives connected to the gearbox output shaft impose radial forces on the output shaft bearing. Similarly, helical gears and bevel gears impose axial loads. Compare the actual radial and axial loads against the gearbox output shaft load capacity published in the manufacturer’s catalog:<\/p>\n<ul style=\"margin: 8px 0 16px; padding-left: 22px;\">\n<li style=\"margin-bottom: 8px;\">For a belt or chain drive: F_radial \u2248 2 \u00d7 T_output \/ (pitch circle diameter of sprocket\/pulley)<\/li>\n<li style=\"margin-bottom: 8px;\">For a direct coupling: F_radial = 0 (assuming perfect alignment)<\/li>\n<li style=\"margin-bottom: 8px;\">Axial load from a helical output gear: F_axial = F_tangential \u00d7 tan(helix angle)<\/li>\n<\/ul>\n<p>If the calculated loads exceed the gearbox output shaft bearing capacity (typically specified as F_radial_max and F_axial_max at a given overhung load distance), select a larger gearbox housing size or add an external support bearing on the driven shaft. For belt drives, increasing the pulley diameter reduces radial force proportionally \u2014 doubling the pulley diameter halves the radial force.<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Step 6: Verify Thermal Capacity for Continuous Duty<\/h2>\n<p>For applications running at continuous duty (100% on-time, 24\/7 operation), verify that the gearbox thermal torque rating (T_thermal) is not exceeded. Thermal torque ratings are specified at standard ambient temperature (typically 20\u00b0C\u201325\u00b0C) with natural convection cooling. Derating applies for:<\/p>\n<ul style=\"margin: 8px 0 16px; padding-left: 22px;\">\n<li style=\"margin-bottom: 8px;\"><strong>Elevated ambient temperature (above 25\u00b0C):<\/strong> T_thermal_derated = T_thermal \u00d7 derating factor from manufacturer table \u2014 typically 1% per 1\u00b0C above 25\u00b0C up to a maximum ambient of 50\u00b0C.<\/li>\n<li style=\"margin-bottom: 8px;\"><strong>Enclosed mounting (no free air movement):<\/strong> additional derating of 10\u201320% typically applies because heat cannot dissipate by natural convection.<\/li>\n<li style=\"margin-bottom: 8px;\"><strong>High altitude (above 1,000 m):<\/strong> derating of 1% per 100 m above 1,000 m due to reduced air density and cooling capacity.<\/li>\n<\/ul>\n<p>For applications that exceed the thermal torque rating, consider forced ventilation (external fan blowing across the gearbox housing) or synthetic lubricant with higher thermal conductivity and viscosity stability.<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Step 7: Check Inertia Ratio for Servo Applications<\/h2>\n<p>For servo-driven systems, the reflected load inertia at the motor shaft must be within the motor manufacturer’s recommended inertia ratio. Calculate reflected inertia:<\/p>\n<div style=\"background: #fff7ed; border: 1px solid #fed7aa; border-radius: 6px; padding: 14px 18px; margin: 14px 0; font-family: monospace; font-size: 14px; color: #0f2d5a;\">J_reflected = J_load \/ i\u00b2 + J_gearbox<\/div>\n<p>The inertia ratio is then J_reflected \/ J_motor. Recommended maximum inertia ratios:<\/p>\n<ul style=\"margin: 8px 0 16px; padding-left: 22px;\">\n<li style=\"margin-bottom: 6px;\">High-performance positioning (CNC, robotics): ratio \u2264 3:1<\/li>\n<li style=\"margin-bottom: 6px;\">General automation (pick-and-place, indexing): ratio \u2264 5:1<\/li>\n<li style=\"margin-bottom: 6px;\">Velocity control (conveyors, fans): ratio \u2264 10:1<\/li>\n<\/ul>\n<p>If the inertia ratio exceeds the recommended value, increase the gear ratio (i) to reduce J_reflected proportionally to 1\/i\u00b2, or select a larger motor with higher rotor inertia.<\/p>\n<h2 style=\"font-size: 22px; font-weight: bold; margin: 30px 0 14px; color: #7c2d12; border-left: 4px solid #c2410c; padding-left: 14px; font-style: italic;\">Worked Example: Sizing a Planetary Gearbox for a CNC Feed Axis<\/h2>\n<div style=\"background: #fff7ed; border: 1px solid #fed7aa; border-radius: 6px; padding: 18px 20px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0f2d5a; margin: 0 0 10px;\">Application: CNC milling machine X-axis, ball screw driven<\/p>\n<ul style=\"margin: 0; padding-left: 18px; font-size: 14px;\">\n<li>Cutting force: 1,500 N; ball screw lead: 10 mm; ball screw efficiency: 90%<\/li>\n<li>Required table speed: 15 m\/min \u2192 n_screw = (15,000 mm\/min) \/ (10 mm\/rev) = 1,500 RPM<\/li>\n<li>Servo motor rated speed: 3,000 RPM<\/li>\n<li>Required ratio: 3,000 \/ 1,500 = 2:1 \u2192 not possible in planetary \u2192 round to 3:1 (standard)<\/li>\n<li>Load torque: (1,500 N \u00d7 0.01 m) \/ (2\u03c0 \u00d7 0.90) = 2.65 Nm at screw shaft<\/li>\n<li>Service factor: 1.5 (moderate shock for CNC) \u2192 required gearbox output = 2.65 \u00d7 1.5 = 3.98 Nm<\/li>\n<li>With 3:1 ratio: motor input torque = 3.98 \/ (3 \u00d7 0.97) = 1.37 Nm (motor must deliver \u2265 1.37 Nm continuous)<\/li>\n<li>Inertia check: load inertia = 0.0012 kg\u00b7m\u00b2; motor inertia = 0.0004 kg\u00b7m\u00b2; reflected inertia = 0.0012 \/ 9 = 0.000133 + gearbox inertia (0.00005) = 0.000183; ratio = 0.000183 \/ 0.0004 = 0.46:1 \u2014 well within limits.<\/li>\n<\/ul>\n<p style=\"margin: 10px 0 0; font-size: 14px;\"><strong>Selection:<\/strong> Single-stage 3:1 planetary gearbox, 60 mm frame size, rated output torque 7 Nm (provides margin above 3.98 Nm), input speed capacity 4,000 RPM, backlash \u22645 arcmin.<\/p>\n<\/div>\n<p>For this application, a single-stage 3:1 planetary gearbox rated for \u2265 5 Nm output torque would be selected, with input speed capacity \u2265 3,000 RPM. Review our <a style=\"color: #c2410c; text-decoration: underline; font-weight: 600;\" href=\"https:\/\/planetarygeardrive.top\/it\/inline-planetary-gearbox\/\">inline planetary gearboxes<\/a> for compatible sizing options in this torque class (30 mm to 180 mm frame sizes).<\/p>\n<p><!-- RELATED PRODUCTS \u2014 expanded with four product recommendations --><\/p>\n<div style=\"background: #fff7ed; border: 1px solid #fed7aa; border-radius: 8px; padding: 24px 28px; margin: 40px 0 28px;\">\n<p style=\"font-size: 13px; font-weight: bold; letter-spacing: 1.5px; text-transform: uppercase; color: #c2410c; margin: 0 0 12px;\">Related Products You May Need<\/p>\n<div style=\"display: flex; flex-wrap: wrap; gap: 12px;\">\n<div style=\"flex: 1 1 180px; background: #fff; border: 1px solid #fed7aa; border-radius: 6px; padding: 14px 16px; box-shadow: 0 1px 4px rgba(0,0,0,0.05);\">\n<p style=\"font-weight: bold; color: #7c2d12; margin: 0 0 4px; font-size: 14px;\">\u2699\ufe0f Servo &amp; Stepper Motors<\/p>\n<p style=\"font-size: 12px; color: #64748b; margin: 0;\">Motor torque, speed, and inertia data are required inputs for the full gearbox sizing calculation process. We supply matching motor flanges for all major brands.<\/p>\n<\/div>\n<div style=\"flex: 1 1 180px; background: #fff; border: 1px solid #fed7aa; border-radius: 6px; padding: 14px 16px; box-shadow: 0 1px 4px rgba(0,0,0,0.05);\">\n<p style=\"font-weight: bold; color: #7c2d12; margin: 0 0 4px; font-size: 14px;\">\ud83d\uded1 Electromagnetic Brakes<\/p>\n<p style=\"font-size: 12px; color: #64748b; margin: 0;\">Size the brake for static holding torque on vertical axes during power-off conditions. Our brake selection worksheet includes inertia and stopping time calculations.<\/p>\n<\/div>\n<div style=\"flex: 1 1 180px; background: #fff; border: 1px solid #fed7aa; border-radius: 6px; padding: 14px 16px; box-shadow: 0 1px 4px rgba(0,0,0,0.05);\">\n<p style=\"font-weight: bold; color: #7c2d12; margin: 0 0 4px; font-size: 14px;\">\u26d3\ufe0f Sprockets &amp; Drive Chains<\/p>\n<p style=\"font-size: 12px; color: #64748b; margin: 0;\">Chain drive output components \u2014 radial loads from chain tension must be included in gearbox sizing. We provide radial load calculators for all output configurations.<\/p>\n<\/div>\n<div style=\"flex: 1 1 180px; background: #fff; border: 1px solid #fed7aa; border-radius: 6px; padding: 14px 16px; box-shadow: 0 1px 4px rgba(0,0,0,0.05);\">\n<p style=\"font-weight: bold; color: #7c2d12; margin: 0 0 4px; font-size: 14px;\">\ud83d\udcca Torque Arm Kits<\/p>\n<p style=\"font-size: 12px; color: #64748b; margin: 0;\">Reaction torque arms for hollow shaft gearbox installations. Correct torque arm sizing requires the same torque and service factor calculations described above.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!-- CTA --><\/p>\n<div style=\"background: #7c2d12; border-radius: 8px; padding: 32px 28px; text-align: center; margin-top: 16px; border-top: 4px solid #92400e;\">\n<p style=\"font-size: 20px; font-weight: 800; color: #fff; margin: 0 0 10px;\">Get a Free Gearbox Sizing Consultation<\/p>\n<p style=\"font-size: 14px; color: #93c5fd; margin: 0 0 20px;\">Submit your application requirements \u2014 load torque, speed, duty cycle, environment \u2014 and our engineering team will recommend the optimal gearbox, ratio, and motor combination. We provide a full sizing report including torque verification, thermal check, and inertia matching within 48 hours.<\/p>\n<p><a style=\"display: inline-block; background: #fbbf24; color: #7c2d12; font-weight: 800; font-size: 15px; text-decoration: none; padding: 13px 34px; border-radius: 5px; letter-spacing: 0.5px;\" href=\"mailto:sales@planetarygeardrive.top\">Start Your Gearbox Selection \u2192<\/a><\/p>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Planetary Gearbox Basics Core Keyword: planetary gearbox sizing \u00a0\u00b7\u00a0 Category: planetary-gearbox-basics How to Size a Planetary Gearbox: Torque, Speed, Inertia, and Service Factor Step-by-Step Planetary gearbox sizing is a systematic process that begins with the load requirements and works backward through the drivetrain to identify the gearbox specifications \u2014 gear ratio, rated output torque, radial [&hellip;]<\/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":[2097],"tags":[1917,17,2300],"class_list":["post-1619","post","type-post","status-publish","format-standard","hentry","category-gearbox-selecton-guide","tag-inline-planetary-gearboxes","tag-planetary-gearbox","tag-planetary-gearbox-sizing"],"_links":{"self":[{"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/posts\/1619","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/comments?post=1619"}],"version-history":[{"count":1,"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/posts\/1619\/revisions"}],"predecessor-version":[{"id":1620,"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/posts\/1619\/revisions\/1620"}],"wp:attachment":[{"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/media?parent=1619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/categories?post=1619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/planetarygeardrive.top\/it\/wp-json\/wp\/v2\/tags?post=1619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}