ISO 3408-4:2006

Overview

ISO 3408-4:2006, "Ball screws - Part 4: Static axial rigidity," defines the terminology and mathematical relations for determining the static axial rigidity of ball screws. The standard explains how axial stiffness is produced by the screw shaft, ball nut(s) and the ball/balltrack contacts, and it gives a simplified calculation method suitable for practical engineering use. It also provides symbols, subscripts and example calculations (Annex A) plus corrections for load application (Annex B).

Key topics and technical requirements

• Scope and definitions: Uses terms from ISO 3408‑1 and a complete list of symbols and subscripts for consistent calculation.
• Non‑linear rigidity: Highlights that ball screw rigidity is load‑dependent and must be evaluated at a specific axial load since the system behaves like a combination of linear and non‑linear spring elements.
• Component decomposition: Static axial rigidity is composed of contributions from:
  • Ball screw shaft rigidity (depends on shaft geometry and mounting - one‑end or both‑end rigid mounting),
  • Ball nut body and shaft radial deformation under normal loads,
  • Ball/balltrack contact deflection calculated using Hertz contact theory.
• Preload and backlash: Distinguishes between ball nuts with backlash and preloaded (symmetrical or otherwise) systems. It describes common preloading methods (oversize balls, shifted threads, double‑start, double nuts) and provides formulae to account for preload effects.
• Mathematical relations: Provides expressions for rigidity R (N/µm), rigidity characteristic k, contact geometry parameters (ρ, Y, τ), and correction factors for accuracy and load application (f_ar, f_al).
• Worked examples: Includes informative annexes with example calculations and correction procedures for practical application.

Practical applications and users

ISO 3408‑4:2006 is essential for anyone involved in precision linear motion design and validation, including:

• Mechanical and design engineers sizing ball screws for CNC machines, robotics, semiconductor equipment and precision actuators.
• Machine tool designers optimizing positioning accuracy and stiffness.
• Test laboratories and quality assurance teams calculating acceptance criteria for static axial rigidity.
• OEMs and suppliers specifying preloads, life estimates and stiffness requirements for ball screw assemblies.

Using this standard helps ensure predictable stiffness, improved positioning performance, and consistent specification language across suppliers and users.

Related standards

• ISO 3408‑1: Vocabulary and designation
• ISO 3408‑2: Nominal diameters and leads - Metric series
• ISO 3408‑3: Acceptance conditions and tests
• ISO 3408‑5: Static and dynamic axial load ratings and operational life

Keywords: ISO 3408-4:2006, ball screws, static axial rigidity, preload, Hertz contact, ball nut, positioning accuracy, machine tools, rigidity calculation.