The Parameter That Dominates Accuracy Under Load — and Rarely Appears in Selection Guides
Backlash is the accuracy specification that every gearbox selector knows. It is the angular dead band at direction reversal — measurable with no load applied, listed prominently on every datasheet, and typically the first (and sometimes only) precision criterion applied when comparing planetary gearboxes. Torsional stiffness, designated Ct and measured in N·m/arcmin, is the parameter that determines how much the output shaft rotates elastically under an applied load. It appears in fewer than one in five published planetary gearbox selection guides — and it is entirely absent from most application-specific sizing tools.
This creates a systematic blind spot: engineers specify backlash carefully, select a low-backlash unit, and then discover that at their actual operating torque, the elastic deflection from torsional compliance produces an angular error two to four times larger than the backlash they specified. The two phenomena are completely independent in origin — and a gearbox with tight backlash can have poor torsional stiffness, and vice versa.
The angular dead band between input and output when drive direction reverses. Purely geometric — caused by clearance between gear teeth. Present at zero load. Fixed once manufactured (until wear increases it). Specified in arcmin.
Occurs when: direction reverses
Depends on: manufacturing tolerance
The elastic “wind-up” of gear teeth, shafts, and planet carrier under applied torque. Proportional to load. Occurs at any torque level. Disappears when load is removed (elastic). Grows with every N·m of applied torque beyond zero.
Occurs at: any applied torque
Depends on: gearbox stiffness Ct
In real servo applications, total positioning error includes both contributions simultaneously. At low torques, backlash dominates. At high torques — above a crossover point that depends on Ct — elastic deflection exceeds backlash and becomes the primary accuracy limit.
= BL + T/Ct (arcmin)
Linear: E = R × tan(θ_total/60 × π/180)
The Complete EP Series Torsional Stiffness Table — All Frame Sizes and Series
The following specifications are the certified torsional stiffness values for all Korea Ever-Power EP series precision planetary gearboxes. Torsional stiffness Ct is defined as the output torque required to produce one arcminute of elastic angular deflection at the output shaft under load, with the input shaft fixed. Higher Ct means less elastic deflection under the same applied torque — and therefore better dynamic positioning accuracy.
| مسلسل | Frame (mm) | Ct — 1-Stage (N·m/arcmin) |
Ct — 2-Stage (N·m/arcmin) |
Max Torque (N·m) |
Ct Class |
|---|---|---|---|---|---|
| EP-ZDE / EP-ZDF | 40 mm | 0.7 | — | 6 | Light-duty |
| EP-ZDE / EP-ZDF | 60 mm | 1.8 | — | 16 | Standard |
| EP-ZDE / EP-ZDF | 80 mm | 4.5 | — | 50 | Standard |
| EP-ZDE / EP-ZDF | 120 mm | 12 | — | 110 | Moderate |
| EP-ZDE / EP-ZDF | 160 mm | 38 | — | 450 | Standard-High ★ |
| EP-ZDWE / ZDWF | 60–160 mm | 1.5 – 38 | 2.5 – 43 | 16 – 450 | Same as ZDE by frame |
| EP-ZDS | 115 mm | 20 | 22 | 210 | High |
| EP-ZDS | 142 mm | 44 | 46 | 910 | High (1.16× ZDE-160) |
| EP-ZDS | 190 mm | 130 | 140 | 1,800 | Highest (3.4× ZDE-160) ★★ |
★ EP-ZDS-115 Ct (20 N·m/arcmin) is lower than EP-ZDE-160 (38 N·m/arcmin) because ZDS-115 is a smaller frame — compare within frame class, not across. ★★ EP-ZDS-190 achieves 130 N·m/arcmin through a larger output shaft (Φ55h7 vs Φ40h7), stiffer planet carrier, and preloaded output bearings. 2-stage Ct exceeds 1-stage because additional planet stages increase carrier rigidity in ZDS design.
The Crossover Point — Where Torsional Deflection Overtakes Backlash as the Dominant Error
At low torque levels, backlash dominates total angular error because the elastic deflection is small. As applied torque increases, elastic deflection grows linearly with T/Ct while backlash remains constant. There is a crossover torque beyond which elastic deflection becomes the larger of the two error sources — and this crossover point differs dramatically between the EP-ZDE and EP-ZDS series.
This is the calculation that most selection guides omit entirely — and it fundamentally changes how torsional stiffness should be weighted in the specification process for high-torque applications.
EP-ZDE-160 crosses over at 304 N·m — well within its rated range of 450 N·m. For the upper half of its torque range (304–450 N·m), elastic deflection is already larger than backlash. Tightening the backlash specification from 8 arcmin to 3 arcmin in this torque range saves only 5 arcmin of dead band while the elastic deflection at 380 N·m is 10 arcmin — an error that a tighter backlash cannot address at all. EP-ZDS-190 does not cross over until 1,040 N·m — beyond its rated 1-stage range — so backlash remains the dominant error for its entire operating range, which is why the EP-ZDS achieves better total accuracy than EP-ZDE even with the same (<8 arcmin) backlash specification.
| Applied Torque | ZDE-160 رد فعل عنيف (أركمين) |
ZDE-160 Elastic θ (arcmin) |
ZDE-160 Total (arcmin) |
ZDS-190 Elastic θ (arcmin) |
ZDS-190 Total (arcmin) |
Accuracy Gain |
|---|---|---|---|---|---|---|
| 50 N·m | 8.0 | 1.3 | 9.3 | 0.4 | 8.4 | 1.1× better |
| 100 N·m | 8.0 | 2.6 | 10.6 | 0.8 | 8.8 | 1.2× better |
| 200 N·m | 8.0 | 5.3 | 13.3 | 1.5 | 9.5 | 1.4× better |
| 304 N·m ← Crossover | 8.0 | 8.0 ← elastic = BL | 16.0 | 2.3 | 10.3 | 1.6× better |
| 380 N·m | 8.0 | 10.0 > BL | 18.0 | 2.9 | 10.9 | 1.7× better |
| 800 N·m | 8.0 | 21.1 | 29.1 | 6.2 | 14.2 | 2.0× better |
Both units specified at <8 arcmin backlash. Ct: ZDE-160 = 38 N·m/arcmin; ZDS-190 = 130 N·m/arcmin. θ_elastic = T/Ct. Total = backlash + elastic. The ZDS-190 improvement grows with torque because Ct is the only differentiator — backlash is identical for both.
From Arcminutes to Millimetres — Dynamic Positioning Error at Your Load Radius
As established in the backlash guide, the conversion from angular error to linear error at a specific load radius is: E_linear = R × tan(θ/60 × π/180). The following table applies this conversion to the elastic deflection component alone — showing the millimetre-level dynamic positioning error from torsional compliance at four representative load radii. This is the error that tighter backlash specification cannot address.
| Torque | ZDE-160 elastic error (Ct=38) | ZDS-190 elastic error (Ct=130) | ZDS improvement | ||
|---|---|---|---|---|---|
| Applied torque | R=100mm | R=300mm | R=100mm | R=300mm | at R=300mm |
| 100 N·m | 0.077 mm | 0.230 mm | 0.022 mm | 0.067 mm | 3.4× better |
| 200 N·m | 0.153 mm | 0.459 mm | 0.045 mm | 0.134 mm | 3.4× better |
| 380 N·m (heavy cut) | 0.291 mm | 0.873 mm | 0.085 mm | 0.254 mm | 3.4× better |
| 800 N·m | 0.613 mm | 1.839 mm | 0.179 mm | 0.538 mm | 3.4× better |
Critical insight for CNC rotary table specification: A CNC B-axis rotary table with a 300mm workpiece mounting radius and a peak cutting torque of 380 N·m will accumulate 0.873mm of elastic positioning error from torsional compliance alone if fitted with EP-ZDE-160. This error changes with every variation in cutting force — it is dynamic, not static, and servo feedback cannot compensate for it because the motor encoder measures the motor position, not the tool position. The same table fitted with EP-ZDS-190 has only 0.254mm of elastic error under identical cutting conditions — a 3.4× improvement that directly translates to tighter part tolerances.
Torsional Stiffness and Resonant Frequency — The Servo Tuning Implication
The torsional stiffness of a precision planetary gearbox directly sets the mechanical resonant frequency of the gearbox-load system. This resonant frequency determines the upper limit of the servo velocity loop bandwidth — the speed at which the controller can respond to position errors without exciting structural resonance. A gearbox with higher Ct pushes the resonant frequency higher, allowing more aggressive servo tuning and therefore better dynamic positioning performance.
| Gearbox | Ct (N·m/arcmin) | f_resonant CNC table J=5 kg·m² |
f_resonant Robot J2 J=97 kg·m² |
Servo Kv limit | Tuning assessment |
|---|---|---|---|---|---|
| ZDE-160 | 38 | 25.7 Hz | 5.8 Hz | Limited | CNC table: OK. Robot J2: below servo BW — risk of oscillation |
| ZDS-115 | 20 | 18.7 Hz | 4.2 Hz | Low | Lower Ct than ZDE-160 — correct only for smaller-frame applications, not direct upgrade |
| ZDS-142 | 44 | 27.7 Hz | 6.3 Hz | Good | Modest improvement over ZDE-160 — preferred for heavy-load CNC and robot J2/J3 |
| ZDS-190 | 130 | 47.6 Hz | 10.8 Hz | Highest | Best dynamic response — recommended for large CNC tables and robot J1/J2 |
The EP-ZDS-115 (Ct=20 N·m/arcmin) has lower torsional stiffness than the EP-ZDE-160 (Ct=38 N·m/arcmin) because it is a smaller frame. Do not assume “ZDS = stiffer than ZDE” — the comparison is valid only within the same or comparable frame size. ZDS-142 (44) marginally exceeds ZDE-160 (38). ZDS-190 (130) vastly exceeds it. For the ZDS series to deliver its stiffness advantage, the application must require the 115–190mm frame range that ZDS covers.
Counterintuitively, the EP-ZDS 2-stage Ct exceeds the 1-stage (ZDS-190: 140 vs 130 N·m/arcmin). This is because the additional planet stage in ZDS contributes structural rigidity to the planet carrier assembly — the carrier becomes effectively stiffer with the secondary stage clamped in place. This is specific to ZDS design and does not apply to the ZDE series, where multi-stage adds compliance rather than stiffness.
When to Specify Torsional Stiffness as the Primary Selection Criterion
Torsional stiffness should be the primary accuracy specification — ahead of backlash — in four application categories. In all other categories, backlash specification alone is adequate and the EP-ZDE/ZDF series delivers correct performance at lower cost.
Peak cutting torques of 200–800 N·m in large horizontal machining centres. At these torques, elastic deflection dominates total angular error. Part dimensional tolerance on large workpieces (bore roundness, face perpendicularity) directly reflects gearbox dynamic stiffness. Specify: EP-ZDS-142 or EP-ZDS-190 by torque class.
Structurally high inertia ratio at J1/J2 means servo bandwidth must be limited to avoid resonance. Higher Ct raises the resonant frequency, allowing wider servo bandwidth and better path-tracking accuracy. Additionally, peak dynamic torques during acceleration of large robot arms exceed the ZDE-160 crossover point.
Impact forming operations subject the gearbox to impulse torques of 2–3× the sustained rated value at the moment of part contact. Under impulse load, elastic deflection is instantaneous and the tool tip position deviates from the commanded position. Higher Ct reduces this deviation and improves press forming dimensional consistency. Service factor 2.5+ plus stiffness specification is the correct approach for press drives.
Laser cutting gantries and high-speed pick-and-place systems execute direction reversals at 50–200 times per minute with significant axis inertia. At each reversal, the gearbox must both eliminate backlash dead band and simultaneously absorb the torque transient from decelerating and re-accelerating the load. A stiffer gearbox damps the torque transient faster and reduces position error during the reversal interval. For gantries operating above 3m/s with sub-0.1mm positioning requirements, consider EP-ZDS-142 even at moderate torque levels.
When EP-ZDE/ZDF at Ct=38 N·m/arcmin is sufficient: For applications where the peak applied torque is below the crossover point of 304 N·m for ZDE-160 — light robot joints (J3–J6), packaging servo axes, AGV drive wheels, solar tracker drives, and conveyor indexers — backlash is the dominant accuracy parameter and EP-ZDE/ZDF is the correct and more cost-efficient choice. The higher Ct of ZDS is not needed and the additional cost is not justified by any measurable improvement in application performance.
A Practical Three-Step Method for Including Torsional Stiffness in Your Selection
Most engineers apply service factor and backlash grade but omit torsional stiffness from the selection process entirely. The following three-step method integrates Ct into the standard five-step selection process without adding significant complexity.
T_crossover = BL × Ct. For EP-ZDE-160: 8 × 38 = 304 N·m. Compare this to your actual peak operating torque (after applying service factor). If peak torque > T_crossover, torsional stiffness is already the dominant accuracy limit and Ct must be increased to improve positioning performance — tighter backlash specification will not help.
Determine your machining or positioning tolerance (e.g. ±0.1mm at your specific load radius R). Calculate the maximum acceptable elastic deflection: θ_max = arctan(tolerance / R) in arcmin. Then calculate the required Ct: Ct_required = T_peak / θ_max. Select the EP series unit with Ct ≥ Ct_required.
θ_max = arctan(0.3/300) × 3438 = 3.44 arcmin
Ct_required = 380/3.44 = 110 N·m/arcmin → specify ZDS-190 (Ct=130)
Calculate f_resonant = (1/2π) × √(Ct[N·m/rad] / J_load). Compare to your servo control bandwidth. For safety, f_resonant should be at least 3× the servo Kv gain frequency. If f_resonant is below 3× servo BW even with the stiffest appropriate EP series unit, reduce servo bandwidth (accept slower response) or consider reducing load inertia at the output.
Korea Ever-Power application engineering provides crossover torque calculation, Ct requirement analysis, and resonant frequency verification for specific applications — including dimensional tolerance and load radius inputs. Provide your peak operating torque, load radius, and dimensional accuracy requirement to receive a complete stiffness specification recommendation in Korean or English.
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