{"id":760,"date":"2026-06-03T02:22:05","date_gmt":"2026-06-03T02:22:05","guid":{"rendered":"https:\/\/planetary-gearboxes.com\/?p=760"},"modified":"2026-06-03T02:22:05","modified_gmt":"2026-06-03T02:22:05","slug":"planetary-gearbox-backlash-explained-arcmin-linear-error","status":"publish","type":"post","link":"https:\/\/planetary-gearboxes.com\/da\/planetary-gearbox-backlash-explained-arcmin-linear-error\/","title":{"rendered":"Forklaring af planetgearsl\u00f8r: Guide til line\u00e6r fejl fra Arcmin til mm"},"content":{"rendered":"
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Korea Ever-Power<\/span>
\nTechnical Deep-Dive<\/span><\/div>\n

Planetary Gearbox Backlash Explained: What Arcminutes Actually Mean at Your Load Radius<\/h1>\n

Backlash specifications for precision planetary gearboxes and servo gear reducers are listed in arcminutes. But machine engineers don’t build in arcminutes \u2014 they build in millimetres. An 8 arcmin backlash figure means nothing until you know your load radius. At 500 mm it produces a 1.16 mm positioning error. At 100 mm it is only 0.23 mm. This guide converts the numbers, explains what actually causes them, and shows how to specify the right precision grade without paying for precision you cannot use.<\/p>\n

Request a Free Backlash Specification Review \u2192<\/a><\/p>\n<\/div>\n<\/div>\n<\/section>\n

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What Backlash Actually Is \u2014 and How It Is Measured<\/h2>\n

In a precision planetary gearbox, backlash is the angular free play measurable at the output shaft when the input shaft is held stationary and the output is loaded alternately in positive and negative directions with a small test torque. It is the total angular dead-band that the output shaft sweeps through when load direction reverses \u2014 the gap between gear teeth in mesh, expressed as the angular equivalent at the output shaft.<\/p>\n

The standard test method (per ISO 9283 and consistent with DIN EN 61800 servo equipment standards) applies a load equal to \u00b13% of the gearbox’s allowable output torque. This specific load level is chosen deliberately: it is large enough to fully take up any geometric clearance in the gear meshes, but small enough that torsional elastic deflection of the gearbox components is negligible \u2014 so what is measured is pure geometric backlash, not a mix of backlash and stiffness.<\/p>\n

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Why arcminutes \u2014 not degrees or millimetres?<\/div>\n

Gearboxes are rotational devices. Their inherent accuracy specification must be angular. Degrees are too coarse \u2014 a precision gearbox at 0.133\u00b0 backlash sounds large, but that is only 8 arcmin, a very standard specification. Arcminutes provide the right resolution: 1 arcmin = 1\/60th of a degree = approximately 0.0167\u00b0. The metric system equivalent for angular error is milliradians (mrad), but arcminutes dominate the planetary gearbox industry and all EP series datasheets are specified in arcmin.<\/p>\n<\/div>\n

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The measurement procedure in practice<\/div>\n

Fix the gearbox input shaft rigidly. Attach a precision torque arm to the output shaft at a known radius. Apply a positive test torque equal to 3% of rated torque and read the angular position (encoder or dial gauge). Apply negative test torque of equal magnitude and read again. The total angular displacement between the two readings is the backlash value. Korea Ever-Power measures and certificates backlash for every EP series unit before shipment, with the measurement performed at the \u00b13% test load standard.<\/p>\n<\/div>\n<\/div>\n

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Unit conversion: arcmin \u2194 degrees \u2194 radians<\/div>\n
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1 arcmin = 1\/60 degree = 0.01667\u00b0 = 0.000291 radians<\/div>\n
8 arcmin = 0.1333\u00b0 = 0.002327 radians<\/div>\n
Linear error at radius R: E_linear = R \u00d7 tan(\u03b8_rad)<\/div>\n
For small angles: E_linear \u2248 R \u00d7 \u03b8_rad \u00a0(error <0.01% for backlash <60 arcmin)<\/div>\n<\/div>\n<\/div>\n<\/section>\n

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\"Precision<\/p>\n
Cross-section of the EP series precision planetary gearbox showing the three-point gear mesh where backlash is measured. View EP series specifications \u2192<\/a><\/div>\n<\/div>\n

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The Table Every Servo Gearbox Engineer Needs \u2014 Arcmin to Millimetre Linear Error at Five Load Radii<\/h2>\n

The following table converts every standard servogearkasse<\/strong> backlash specification \u2014 from ultra-precision at 1 arcmin through standard-grade at 30 arcmin \u2014 into the actual linear positioning error at five practical load radii. All values are calculated using the exact formula E = R \u00d7 tan(\u03b8) where \u03b8 is the backlash angle in radians. For typical precision planetary gearbox backlash values below 30 arcmin, the small-angle approximation introduces less than 0.01% error.<\/p>\n

The load radius is the distance from the gearbox output shaft centreline to the point where positioning accuracy is being measured or required \u2014 for example, the tip of a robot arm, the cutting tool of a CNC spindle, or the contact point of a conveyor drive roller.<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n
Modreaktion<\/th>\nAngle (\u00b0)<\/th>\nR = 50 mm<\/th>\nR = 100 mm<\/th>\nR = 200 mm<\/th>\nR = 500 mm<\/th>\nR = 1,000 mm<\/th>\nEP Series<\/th>\n<\/tr>\n<\/thead>\n
<1 arcmin<\/td>\n0.017\u00b0<\/td>\n0.015 mm<\/td>\n0.029 mm<\/td>\n0.058 mm<\/td>\n0.145 mm<\/td>\n0.291 mm<\/td>\nUltra-precision custom<\/td>\n<\/tr>\n
<3 arcmin<\/td>\n0.050\u00b0<\/td>\n0.044 mm<\/td>\n0.087 mm<\/td>\n0.175 mm<\/td>\n0.436 mm<\/td>\n0.873 mm<\/td>\nHigh-precision CNC \/ laser<\/td>\n<\/tr>\n
<5 arcmin<\/td>\n0.083\u00b0<\/td>\n0.073 mm<\/td>\n0.145 mm<\/td>\n0.291 mm<\/td>\n0.727 mm<\/td>\n1.454 mm<\/td>\nGeneral servo positioning<\/td>\n<\/tr>\n
<8 arcmin \u2605<\/td>\n0.133\u00b0<\/td>\n0.116 mm<\/td>\n0.233 mm<\/td>\n0.465 mm<\/td>\n1.164 mm<\/td>\n2.327 mm<\/td>\nEP-ZDE \/ EP-ZDF (frames 60\u2013160); EP-ZDS (all)<\/td>\n<\/tr>\n
<12 arcmin<\/td>\n0.200\u00b0<\/td>\n0.175 mm<\/td>\n0.349 mm<\/td>\n0.698 mm<\/td>\n1.745 mm<\/td>\n3.491 mm<\/td>\nEP-ZDE-40; EP-ZDE 2-stage<\/td>\n<\/tr>\n
<15 arcmin<\/td>\n0.250\u00b0<\/td>\n0.218 mm<\/td>\n0.436 mm<\/td>\n0.873 mm<\/td>\n2.182 mm<\/td>\n4.363 mm<\/td>\nEP-ZDE 3-stage; conveyors<\/td>\n<\/tr>\n
<25 arcmin \u25b2<\/td>\n0.417\u00b0<\/td>\n0.364 mm<\/td>\n0.727 mm<\/td>\n1.454 mm<\/td>\n3.636 mm<\/td>\n7.272 mm<\/td>\nEP-ZDWE \/ EP-ZDWF (80\u2013160, 1-stage)<\/td>\n<\/tr>\n
<30 arcmin \u25b2<\/td>\n0.500\u00b0<\/td>\n0.436 mm<\/td>\n0.873 mm<\/td>\n1.745 mm<\/td>\n4.363 mm<\/td>\n8.727 mm<\/td>\nEP-ZDWE-60 (1-stage)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\u2605 = Standard precision class for EP-ZDE\/ZDF\/ZDS inline series. \u25b2 = Right-angle input series (ZDWE\/ZDWF) \u2014 wider due to bevel gear stage contribution. Values calculated from E = R \u00d7 tan(\u03b8), where \u03b8 = backlash in radians.<\/p>\n

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Reading this table for a real application<\/div>\n

A collaborative robot wrist joint with a 400 mm arm radius, using an EP-ZDWE-80 at <25 arcmin<\/a>, will have a maximum backlash-induced positioning error at the end-effector of approximately 400 mm \u00d7 tan(25\/60 \u00d7 \u03c0\/180) = 2.91 mm<\/strong>. For a robot controlled by a servo drive in closed-loop position mode, this 2.91 mm is not a permanent error \u2014 it is the dead band at direction reversal. The servo controller compensates for this through position feedback from the motor encoder. However, any external disturbance during a hold position (after the encoder confirms position) can produce up to 2.91 mm of drift if the load torque causes the output shaft to move within the backlash dead band without the motor encoder detecting it.<\/p>\n<\/div>\n<\/section>\n

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Four Backlash Precision Classes \u2014 Matching Grade to Application Requirement<\/h2>\n

The standard industry precision class structure for precision planetary gearboxes maps backlash ranges to application categories. Choosing the right class is as important as not over-specifying: a <1 arcmin ultra-precision unit costs 3\u20135 times more than a <8 arcmin standard precision unit of the same frame size. If your application’s accuracy requirement is met by <8 arcmin, spending on a <1 arcmin unit adds no measurable performance benefit.<\/p>\n

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<1<\/div>\n
buemin<\/div>\n<\/div>\n
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Ultra-Precision \u2014 Semiconductor, Optical Alignment, Direct-Drive Robotics<\/div>\n

At 100 mm radius, <1 arcmin produces only 0.029 mm of backlash-induced dead band. Required for semiconductor wafer handling robots (silicon die positioning to \u00b10.01 mm), precision optical mounts, and research-grade direct-drive robotics where any dead band is unacceptable. Not typically available as a standard EP series product \u2014 requires contact with Korea Ever-Power application engineering for custom specification.<\/p>\n<\/div>\n<\/div>\n

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1\u20133<\/div>\n
buemin<\/div>\n<\/div>\n
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High Precision \u2014 CNC Machining Axes, Laser Cutting Heads, Precision Positioning Stages<\/div>\n

At 200 mm radius, <3 arcmin produces 0.175 mm maximum dead band. Appropriate for CNC feed axes where part dimensional tolerance is \u00b10.01\u20130.1 mm, laser cutting head positioning where kerf width is 0.2\u20130.5 mm, and multi-axis servo-driven positioning stages in Korean electronics assembly equipment. The servo position feedback loop readily compensates for backlash at this level in normal operation.<\/p>\n<\/div>\n<\/div>\n

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3\u20138<\/div>\n
buemin<\/div>\n<\/div>\n
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Standard Precision \u2014 EP-ZDE\/ZDF\/ZDS: General Industrial Automation, Robot Joints, AGV Drives \u2605 Most Common<\/div>\n

This is the specification range of the EP-ZDE, EP-ZDF, and EP-ZDS series (frames 60\u2013190 at single stage). At 100 mm radius, <8 arcmin means 0.233 mm maximum dead band \u2014 completely adequate for industrial robot positioning, general automation indexing, and conveyor servo drives. The standard class represents the best value for the vast majority of Korean servo automation applications. For applications where cost matters and positioning requirements are moderate, this grade delivers consistent performance without the premium of tighter-tolerance alternatives.<\/p>\n<\/div>\n<\/div>\n

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8\u201330<\/div>\n
buemin<\/div>\n<\/div>\n
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Economy \/ Right-Angle Input \u2014 EP-ZDWE\/ZDWF, EP-ZDE-40, Multi-Stage Units<\/div>\n

The EP-ZDWE and EP-ZDWF right-angle input series fall into this range due to the bevel gear input stage adding angular clearance. The <25\u201330 arcmin specification is not a quality deficiency \u2014 it is an inherent characteristic of bevel-gear input designs across all manufacturers. For servo-controlled axes where the position loop compensates for gearbox backlash, this range is fully functional. Where it is not appropriate: open-loop stepper motor systems, where the backlash directly becomes a positioning error with no feedback compensation.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n

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\"Korea<\/p>\n
The EP series covers standard precision (<8 arcmin, EP-ZDE\/ZDF), right-angle input (<25\u201330 arcmin, EP-ZDWE\/ZDWF), and high-stiffness IP65 (<8 arcmin at 1,800 N\u00b7m, EP-ZDS).<\/div>\n<\/div>\n

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Backlash vs Torsional Stiffness \u2014 Two Different Causes of Positioning Error That Engineers Frequently Confuse<\/h2>\n

One of the most persistent misunderstandings in precision planetary gearbox specification is treating backlash and torsional stiffness as the same phenomenon. They are not. They affect positioning accuracy through completely different physical mechanisms, they are specified in the same units (arcminutes at the output shaft), and confusing them leads to incorrect gearbox selection. Buying a tighter-backlash unit does not solve a torsional stiffness problem, and vice versa.<\/p>\n

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Modreaktion<\/div>\n
Angular dead band at zero load<\/strong>, measured when load direction reverses. Purely geometric \u2014 caused by clearance between gear teeth in mesh. Present even when no torque is applied.<\/div>\n
When it appears: At direction reversal, before load is reapplied. Output shaft “free-travels” through the backlash angle.<\/div>\n<\/div>\n
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Torsionsstivhed<\/div>\n
Elastic deflection of gearbox components under applied load<\/strong>. Caused by material elasticity of gear teeth, shafts, and housings. Increases proportionally with applied torque \u2014 the higher the torque, the larger the elastic angular error.<\/div>\n
When it appears: Under any applied load, proportional to torque magnitude. Disappears when load is removed (elastic, not permanent).<\/div>\n<\/div>\n
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Total Angular Error<\/div>\n
In real servo applications, total positioning error is the sum of both contributions plus encoder and controller contributions. For dynamic axes (rapid reversals, variable loads), the torsional stiffness contribution can exceed the backlash contribution at high torque levels.<\/div>\n
\u03b8_total \u2248 \u03b8_backlash + \u03b8_elastic = \u03b8_backlash + T\/Ct \u00a0where Ct = torsional stiffness [N\u00b7m\/arcmin]<\/div>\n<\/div>\n<\/div>\n

Quantified Comparison: EP-ZDE-160 vs EP-ZDS-190 Elastic Deflection Under Variable Load<\/h3>\n

The following table uses the formula \u03b8_elastic = T \/ Ct to show how the same applied torque creates very different elastic angular errors in the standard precision series vs the high-stiffness series. This is the actual data relevant for CNC rotary table and heavy robot joint specifications, where peak cutting or handling torques can reach 200\u2013800 N\u00b7m.<\/p>\n

\n\n\n\n\n\n\n\n\n\n
Applied Torque<\/th>\nEP-ZDE-160<\/a>
\nCt = 38 N\u00b7m\/arcmin<\/span><\/th>\n		EP-ZDS-190<\/a>
\nCt = 130 N\u00b7m\/arcmin<\/span><\/th>\n		Stiffness Ratio<\/th>\nZDE-160 linear error
\nat R=200mm<\/span><\/th>\n		ZDS-190 linear error
\nat R=200mm<\/span><\/th>\n<\/tr>\n<\/thead>\n
50 N\u00b7m<\/td>\n1.32 arcmin<\/td>\n0.38 arcmin<\/td>\n3.4\u00d7<\/td>\n0.077 mm<\/td>\n0.022 mm<\/td>\n<\/tr>\n
100 N\u00b7m<\/td>\n2.63 arcmin<\/td>\n0.77 arcmin<\/td>\n3.4\u00d7<\/td>\n0.153 mm<\/td>\n0.045 mm<\/td>\n<\/tr>\n
200 N\u00b7m<\/td>\n5.26 arcmin<\/td>\n1.54 arcmin<\/td>\n3.4\u00d7<\/td>\n0.306 mm<\/td>\n0.089 mm<\/td>\n<\/tr>\n
380 N\u00b7m
\n(heavy CNC cut)<\/span><\/td>\n		10.00 arcmin<\/td>\n2.92 arcmin<\/td>\n3.4\u00d7<\/td>\n0.582 mm<\/td>\n0.170 mm<\/td>\n<\/tr>\n
800 N\u00b7m<\/td>\n21.05 arcmin<\/td>\n6.15 arcmin<\/td>\n3.4\u00d7<\/td>\n1.225 mm<\/td>\n0.358 mm<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
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Critical insight: at 380 N\u00b7m, the EP-ZDE-160 elastic deflection alone equals 10 arcmin<\/div>\n

An engineer who specifies an EP-ZDE-160 with <8 arcmin backlash for a heavy CNC rotary table application has the backlash specification correct \u2014 but under 380 N\u00b7m peak cutting torque, the torsional elastic deflection adds another 10 arcmin. The total angular error at the output under load is 18 arcmin \u2014 more than twice the specified backlash. This is why heavy-load precision applications (large CNC rotary tables, heavy robot joints, servo press drives) require the EP-ZDS series with Ct = 130 N\u00b7m\/arcmin, not merely a tighter-backlash EP-ZDE unit. The EP-ZDS-190 under the same 380 N\u00b7m load produces only 2.92 arcmin elastic deflection \u2014 a 3.4\u00d7 improvement in dynamic accuracy.<\/p>\n<\/div>\n<\/section>\n

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How Backlash Grows Over the Gearbox Service Life \u2014 and What Accelerates It<\/h2>\n

A precision planetary gearbox does not maintain its initial backlash specification indefinitely. Angular dead-band increases over time as gear tooth flanks wear and planet carrier bearings accumulate running clearance. The rate of increase depends heavily on operating conditions \u2014 a correctly loaded, correctly lubricated gearbox running at recommended duty cycles will show only modest backlash increase over 20,000 hours. An overloaded or contaminated unit can double its backlash in under 5,000 hours.<\/p>\n

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Service Hours<\/th>\nApproximate Backlash
\nEP-ZDE-80, correctly loaded<\/span><\/th>\n		Linear Error at R = 300 mm<\/th>\nNotes<\/th>\n<\/tr>\n<\/thead>\n
0 h (new)<\/td>\n7.5 arcmin<\/td>\n0.654 mm<\/td>\nFactory-certified at \u00b13% rated torque test<\/td>\n<\/tr>\n
2,000 h<\/td>\n8.0 arcmin<\/td>\n0.698 mm<\/td>\nNormal run-in completed; initial surface conditioning<\/td>\n<\/tr>\n
5.000 timer<\/td>\n8.8 arcmin<\/td>\n0.768 mm<\/td>\nSteady-state wear rate; record baseline at 5,000 h inspection<\/td>\n<\/tr>\n
10.000 timer<\/td>\n10.2 arcmin<\/td>\n0.890 mm<\/td>\nStill within acceptable range for most standard applications<\/td>\n<\/tr>\n
15,000 h<\/td>\n12.5 arcmin<\/td>\n1.091 mm<\/td>\nApproaching replacement threshold for high-precision applications<\/td>\n<\/tr>\n
20,000 h (L10)<\/td>\n15.1 arcmin<\/td>\n1.318 mm<\/td>\nL10 rated life; schedule gearbox replacement<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Illustrative progression based on industry longitudinal data for correctly specified and loaded precision planetary reducers. Actual values depend on specific loading conditions, duty cycle, and ambient environment. The EP-ZDE\/ZDF series lifetime lubrication significantly slows gear flank wear vs. improperly lubricated units.<\/p>\n

Four Conditions That Accelerate Backlash Growth<\/h3>\n
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\u2460 Operating above rated torque (no service factor)<\/div>\n

Planet gear tooth flanks experience Hertzian contact stress above their designed surface fatigue limit. Pitting initiates and accelerates. Backlash can double within 3,000\u20135,000 hours rather than 20,000. This is the most common accelerant of backlash growth in Korean servo automation applications.<\/p>\n<\/div>\n

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\u2461 Lubricant contamination or degradation<\/div>\n

Water ingress (particularly in IP54 units subjected to direct washing) emulsifies the lifetime grease, reducing its film strength. Metal wear debris from early overload creates abrasive conditions. The resulting three-body abrasive wear acts on all gear mesh surfaces simultaneously, compounding the backlash growth rate.<\/p>\n<\/div>\n

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\u2462 Excessive input speed<\/div>\n

Operating consistently above the recommended input speed (3,000 rpm for most EP series) increases planet gear centrifugal stress and generates heat that accelerates lubricant oxidation. Higher temperature reduces grease viscosity and film thickness, increasing metal-to-metal contact on gear tooth flanks.<\/p>\n<\/div>\n

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\u2463 High-frequency impact loading<\/div>\n

Servo press main drives and robot collision-stop axes subject planet carrier bearings to repeated impact loads that exceed the steady-state fatigue design. Planet carrier bearing races develop micro-pitting, which adds to output shaft radial play \u2014 eventually contributing to measurable backlash increase beyond the gear tooth wear component.<\/p>\n<\/div>\n<\/div>\n<\/section>\n

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\"Precision<\/p>\n
All EP series gear components are case-hardened alloy steel with ground tooth profiles \u2014 the primary factor in backlash precision and long-term backlash stability. Korea Ever-Power \u2014 precision planetary gearbox manufacturer \u2192<\/a><\/div>\n<\/div>\n

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EP Series Complete Backlash Specifications \u2014 All Frame Sizes and Stages<\/h2>\n

The following specifications are the factory-certified backlash values for all Korea Ever-Power EP series precision planetary gearboxes, measured at \u00b13% of rated output torque per standard test protocol. The wider backlash of the ZDWE\/ZDWF series is a direct consequence of the bevel gear input stage \u2014 this is consistent with all right-angle input planetary gear reducers regardless of manufacturer.<\/p>\n

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Serie<\/th>\nFrame Size<\/th>\n1-trins<\/th>\n2-trins<\/th>\n3-Stage<\/th>\nConfiguration<\/th>\n<\/tr>\n<\/thead>\n
EP-ZDE<\/strong><\/td>\n40 mm<\/td>\n<12 arcmin<\/td>\n<15 arcmin<\/td>\n<18 arcmin<\/td>\nInline, round flange<\/td>\n<\/tr>\n
EP-ZDE<\/strong><\/td>\n60\u2013160 mm<\/td>\n<8 arcmin<\/td>\n<12 arcmin<\/td>\n<15 arcmin<\/td>\nInline, round flange \u2014 standard precision<\/td>\n<\/tr>\n
EP-ZDF<\/a><\/td>\n40\u2013160 mm<\/td>\n<8\u201312 arcmin<\/td>\n<12\u201315 arcmin<\/td>\n<15\u201318 arcmin<\/td>\nInline, square flange \u2014 identical to ZDE by frame<\/td>\n<\/tr>\n
EP-ZDS<\/strong><\/td>\n115\u2013190 mm<\/td>\n<8 arcmin<\/td>\n<12 arcmin<\/td>\nN\/A<\/td>\nInline, square flange, IP65 \u2014 same backlash as ZDE, higher Ct<\/td>\n<\/tr>\n
EP-ZDWE<\/strong><\/td>\n60 mm<\/td>\n<30 arcmin<\/td>\n<35 arcmin<\/td>\n<40 arcmin<\/td>\nRight-angle, round flange \u2014 bevel stage adds clearance<\/td>\n<\/tr>\n
EP-ZDWE<\/strong><\/td>\n80\u2013160 mm<\/td>\n<25 arcmin<\/td>\n<30 arcmin<\/td>\n<35 arcmin<\/td>\nRight-angle, round flange \u2014 wider but servo-compensatable<\/td>\n<\/tr>\n
EP-ZDWF<\/a><\/td>\n60\u2013160 mm<\/td>\n<25\u201330<\/td>\n<30\u201335<\/td>\n<35\u201340<\/td>\nRight-angle, square flange \u2014 identical to ZDWE by frame<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/section>\n

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When Backlash Does Not Affect Accuracy \u2014 The Unidirectional Exception<\/h2>\n

Angular dead-band only produces positioning error at direction reversal. If your application positions in one direction only \u2014 the load always approaches the target from the same angular direction, and the drive always maintains a positive torque in that direction during positioning \u2014 backlash contributes zero positioning error regardless of its magnitude.<\/p>\n

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Applications where backlash = zero accuracy impact<\/div>\n