ISRI

ARC SPRING CALCULATOR MODULE

Arc Spring Calculator

Arc Spring (DMF Spring) is a mechanical mapping of helical compression spring on a curved axis. Core relation: M(α) = F(α) · r. Outputs Torque-Angle curve with hysteresis loop, supports single/dual-stage systems.

Design Rules (Geometry & Proportion)
Warn

Geometry is acceptable but outside recommended range

Auto-calculate enabled (300ms debounce)
N_total (total turns)
N_total（总匝数）
52.3 turns
p_free (arc turn spacing)
p_free（自由态弧长等效匝距）
5.086 mm
Rule: p_free > 1.05·d
规则：p_free > 1.05·d
p_work (arc turn spacing)
p_work（工作末端弧长等效匝距）
4.125 mm
Rule: p_work > 1.05·d
规则：p_work > 1.05·d
Estimated wire length
估算线长
2022.1 mm
⚠ Spring index is outside preferred range / 弹簧指数超出推荐范围
Spring index C=3.30 is outside preferred range (4~12).
弹簧指数 C=3.30 超出推荐范围（4~12）。
⚠ High coil count / 圈数偏大
High coil count (n=50.3) may increase wire length, cost, and packaging risk.
圈数偏大（n=50.3）可能增加线长/成本/包装干涉风险。
⚠ Estimated wire length is high / 估算线长偏大
Estimated wire length is high (2022mm). Check manufacturability/cost.
估算线长偏大（2022mm），请关注可制造性/成本。
i Trend: n affects stiffness and cost / 趋势：n 影响刚度与成本
Increasing n reduces stiffness and increases wire length, cost and handling risk.
n 增大会降低刚度并增加线长，从而提升成本与加工装配风险。
i Arc turn spacing is not axial pitch / 弧长等效匝距≠轴向节距
This module checks spacing along arc length (turn spacing). Axial pitch/coil-bind needs free-length model (not included).
当前模块检查沿弧长方向的匝距（等效匝距）。轴向节距/贴圈需要自由长度模型（当前未包含）。
Design rules evaluate geometric feasibility only. They do not guarantee engineering safety.
Real-World Samples
3D Preview Options
ARC PROFILE
Geometry
mm
0.510
mm
5120
130
Arc Layout

Current: 115.00°

Approx: 240.86 mm

mm
0200
mm
010
Engineering Audit Result
PLATFORM STANDARD V1.0

Engineering conditions not met. Design is geometrically valid but exceeds allowable limits.

Governing Failure Mode

Stress

Gov Variable: Δθ

RATIO

137.4%

S.F.

0.73
Geometry
Loadcase
Stress
Stability

Detailed: Governing Stress

Governing Stress ModelHelical Shear (Factory)
Max Stress
Allowable Stress
137.4%

Suggested Engineering Actions

  • MISSION: Quality OS serves as a decision-support system. It structures engineering judgment but does not replace factory-specific process expertise.
  • 系统定位：Quality OS 为决策支持系统。它系统化地辅助工程判断，不替代工厂特定的工艺经验。
  • Engineering Safety: Critical issue in Helical Shear (Factory). Immediate redesign required.
  • Deliverability: Design cannot be manufactured/delivered reliably. Manufacturing waiver may be required.
  • Decision Support: This system provides engineering recommendations. Final manufacturability and commercial commitment remain the responsibility of the manufacturer.
Material
25°C

Thermal Relaxation: 2.0% stiffness reduction

Hysteresis & System / 迟滞与系统
01
3D Preview / 三维预览
Per End / 单端圈数
k
σ
β

请先计算以生成 3D 预览

d=3.70mm, D=12.2mm, n=50.30, r=120.0mm, α₀=127.0°, dead=1.00×2, k=2.00, σ=0.08
k20.52
C 3.30
SF 0.73
Geometry & Rate / 几何与刚度
Spring Rate k
20.52 N/mm
Spring Index C
3.30
Wahl Factor Kw
1.513
Gohner Factor Kg
1.025
Arc Spring Stress Methodology
Core AlgorithmBeyond standard helical formulas, this calculator uses Curved Beam Theory to compute stiffness and stress, correcting for curvature effects on torsional stiffness and stress distribution.
Coefficient Audit
K_wahl (D/d):1.513
K_gohner (D/r):1.025
K_total:1.551
Friction Model
Mode:proportional
Peak Multiplier:Linear

Calculation Logic Verification:

  • Friction Surge: The Exponential Friction model predicts massive forces at the tab. This pushes the calculated "Peak Stress" above 1200 MPa.
  • Factory Reality: Factories use Hot Setting (Scragging) to boost the material limit to ~1300 MPa+. The generic standard limit (800 MPa) is too low for these high-performance parts.
Guidance
If "Elastic Stress" is safe but "Peak Stress" fails, it usually means the design is valid provided the factory uses correct Presetting/Hot Setting processes.
Results / 计算结果
Rotational Stiffness R / 旋转刚度 (核心参数)
5157.03 N·mm/deg
Tangential stiffness k_t
20.52 N/mm
Max Angle Δα
24.0°
Max Torque (Load)
138621 N·mm
Max Torque (Unload)
108916 N·mm
Geometry & Safety / 几何与安全
De (外径)
15.9 mm
Di (内径)
8.5 mm
Safety Margin
4.8°
Stress Analysis / 应力分析
Spring Index C
3.30
Wahl Factor K_W
1.513
τ_max (剪切应力)
1099 MPa
Damping / 阻尼
Hysteresis Work (阻尼能量)
356454 N·mm·deg
Damping Capacity (阻尼效率)
21.4 %
Torque–Angle Curve
Loading chart...

Hysteresis loop shows friction effect between loading and unloading

SEOSSpring Engineering Operating System
SAFETY
DELIVERABILITY

Redesign Required

Engineering limits exceeded. Physical design is unsafe.

Fatigue SF
-
Spring Index
3.3
Energy (J)
-
Full Coverage
0/0
Total Coverage
0/0
Design Rule Findings
Spring index is outside preferred range
DWARN
High coil count
nWARN
Turn spacing is tight in free state
nWARN
Turn spacing is tight at working state
nWARN
Estimated wire length is high
nWARN

Please adjust design parameters to resolve these issues.

Torque Rate
20.5192 Nmm/deg
Index C
3.30
Wahl Factor
1.513
CONCEPT

Engineering Assumptions

This analysis is for reference. Physical testing is mandatory before production.

Engineering Requirements / Deliverability
High Risk

Tolerances, assembly, surface, environment & lifespan (does not affect calculations)

Inspection & Gauge Strategy
OPTIONAL
FACTORY QUOTE STATUSMARGINAL

Profile not configured. Safe-to-Quote gate is inactive.

All capabilities verified.
QUALITY OS

Decision Board

Automated engineering audit for quote risk assessment.

✕DO NOT QUOTE
MARGINAL
Geometry & Tolerance

Can it be assembled?

PASS
Material & Heat Treatment

Is the material reliable?

FAIL
Engineering Safety

Will it perform safely?

  • • Stress: Critically High
PASS
Manufacturing

Can factory produce it?

PASS
Compliance & Delivery

Can we deliver?

Quality OS is a decision-support system for spring manufacturers. It structures your engineering judgment but does not replace your factory-specific process expertise.

Engineering Specifications (SEC)

Standard Compatibility

Calculations align with EN 13906-1 physical principles for helical compression springs, mapped to an arc axis. All material data follow EN 10270 standards.

Stiffness Relation

The rotational stiffness R (N·mm/deg) is derived from axial stiffness k (N/mm) and working radius r: R = k · r² · (π/180).

Manufacturing Limits

  • Spring Index (D/d): 4 - 20 recommended.
  • Min Free Pitch: 1.1 * d.
Frequently Asked Questions (FAQ)