The ball screw is the high-performance standard for precision linear drives. With efficiencies of 90–98% and accuracies in the hundredths-of-a-millimeter range, it is a key component of modern machinery. This guide explains sizing per ISO 3408/DIN 69051.
Understanding Ball Screws
A ball screw is a highly efficient mechanical conversion of rotary motion into linear motion. Unlike a trapezoidal thread (which relies on sliding friction), a ball screw uses rolling ball elements in helical grooves.
Key Advantages at a Glance
- High efficiency: 90–98%, significantly better than trapezoidal threads (25–50%)
- Zero-backlash: With preload, play can be completely eliminated
- Precision positioning: Repeatability of ±0.05–0.1 mm achievable
- Long service life: Hundreds of thousands of operating hours possible
- No self-locking: Not suitable for loads that can back-drive without a brake
Construction and Components
A ball screw consists of:
1. The Screw (Ball Screw Shaft)
A steel cylinder with a precision-ground helical groove in which balls roll. The groove geometry is precisely defined per DIN 69051. Standard diameters: 8–80 mm, lead: 1–20 mm/revolution.
2. The Nut (Ball Screw Nut)
It sits on the screw and carries the load. Inside, it also has grooves that form a ball circuit with the screw groove. Variants exist with recirculation tube and without (open nut).
3. The Balls
Hardened steel balls in precision diameters (typically 4–10 mm). They roll between the screw and nut and are held at even spacing by retainer cages.
4. The Retainer Cage
Made of plastic or sheet metal, it holds the balls at constant spacing and prevents them from rubbing against each other.
Practical Tip from TEA:
Store ball screws dry and protected from contamination. A single particle of dust can significantly impair running accuracy.
For complete linear system design, combining the ball screw with suitable roller guides (LinRol/LinTrek) is recommended — they absorb lateral forces and moments while the ball screw handles axial force exclusively.
Key Sizing Parameters
Lead (P)
The lead defines the linear travel per screw revolution. Smaller leads produce higher torque; larger leads produce higher speed.
- P = 1–3 mm: High-torque design, e.g. for precise positioning
- P = 5–10 mm: Standard design, balanced between torque and speed
- P > 10 mm: High-speed design, requires higher motor power
Screw Diameter (d)
Determines load capacity and stiffness. Larger diameters handle higher loads but also require higher torques for rotation.
Rule of thumb for load rating: The dynamic load rating Ca approximately doubles when the diameter grows by about 25%.
Accuracy Classes per ISO 3408
| Class | Lead deviation | Typical application |
|---|---|---|
| C1 (highest) | ±0.006 mm/300 mm | Metrology, optics, robotics |
| C5 | ±0.023 mm/300 mm | Standard industrial equipment |
| C7 | ±0.050 mm/300 mm | Robust machinery and equipment |
| C10 (basic) | ±0.210 mm/300 mm | Cost-effective mass production |
Service Life Calculation per ISO 3408
The nominal service life L10 is a statistical measure indicating how long 90% of all identical screws can be operated before fatigue occurs.
Formula
Ca = dynamic load rating [N] (from catalog)
F = operating load [N]
To obtain the service life in hours:
n = speed [rpm]
For shock or variable loading, the operating load is multiplied by a load factor fw before inserting it into the formula (F = fw · Fm; fw ≈ 1.0–1.5 depending on running smoothness per ISO 3408). If the load varies across multiple phases, the equivalent mean load Fm must first be derived from the load spectrum.
Sample Calculation
Given:
Ball screw 16 mm × 5 mm, Ca = 4,200 N (from catalog)
Operating load F = 800 N, speed n = 600 rpm
Calculation:
L10 = (4200 / 800)³ × 10⁶ = 5.25³ × 10⁶ = 144.7 × 10⁶ revolutions
T10 = 144.7 × 10⁶ / (600 × 60) ≈ 4,020 hours ≈ 1.9 years (8 h/day, 5 days/week)
Critical Speed and Buckling Load
Two stability limits constrain long, fast-rotating screws: buckling under compressive load and critical bending resonance speed. Both depend strongly on the unsupported length and the bearing arrangement.
Buckling Load (Compressive Loading)
A slender screw under compressive load can buckle. The permissible buckling load follows from the Euler approach:
I = π · d_r⁴ / 64 (d_r = root diameter)
E = 210,000 N/mm² (steel) · L_k = unsupported length [mm]
n (bearing arrangement): fixed–fixed 4 · fixed–supported 2 · supported–supported 1 · fixed–free 0.25
The operating load should not exceed 50% of F_k. Example: d_r = 14 mm, L_k = 1,000 mm, fixed–supported arrangement (n = 2) → I ≈ 1,885 mm⁴, F_k ≈ 7,800 N → permissible operating load ≈ 3,900 N.
Critical Speed (Bending Resonance)
At high rotational speeds, the screw enters bending resonance. The critical speed in the common catalog form:
d_r = root diameter [mm] · L_k = unsupported length [mm]
f_n (bearing arrangement): fixed–fixed 21.9 · fixed–supported 15.1 · supported–supported 9.7 · fixed–free 3.4
The operating speed should not exceed 80% of n_krit. Example: d_r = 14 mm, L_k = 1,000 mm, fixed–supported (f_n = 15.1) → n_krit ≈ 2,100 min⁻¹ → permissible ≈ 1,700 min⁻¹.
Bearing Arrangement: Fixed Bearing / Floating Bearing
The bearing arrangement determines both limits. A fixed–fixed arrangement (axially restrained at both ends) allows the highest speed and buckling load, but requires preload and provision for thermal expansion. The fixed–floating arrangement (one fixed bearing carries the axial load, one floating bearing allows longitudinal expansion) is the robust standard. A fixed–free cantilevered end is only suitable for short, slow-running screws.
Standards Reference
Load ratings, accuracy, and testing of ball screws are governed by ISO 3408 (Parts 1–5) and DIN 69051. The buckling and speed factors are guideline values from common catalog practice — binding values are the manufacturer's specifications for the specific bearing arrangement and overall length.
Preload and Zero-Backlash
Manufacturing tolerances always result in a small amount of play between ball and grooves. Preload is an additional axial pre-tension force that eliminates this play.
Preload Levels
- C0 (none): For simple positioners, accepts play
- C1, C2, C3: Increasing preload force, typically 3–8% of the dynamic load rating
Effect of preload:
- Higher stiffness (less deflection under load)
- Eliminates play (backlash-free movement)
- Higher wear rate (friction forces increase)
- Shorter service life (L10 decreases with high preload)
Practical Tip from TEA:
Choose preload C2 or C3 only when zero-backlash is truly critical. For simple positioners, C0 or C1 is sufficient and more economical.
Lubrication and Maintenance
Ball screws are relatively low-maintenance. Nevertheless, proper lubrication is essential:
Lubrication Schedule
- Lubricant: Lithium complex grease (DIN 51825 K2K-30), or specialty greases for high speed
- Frequency: Every 100–200 operating hours
- Quantity: Small amounts; over-greasing worsens efficiency and thermal behavior
- Cleanliness: Use only clean tools, prevent contamination
Inspection Intervals
- Monthly: Visual inspection for contamination or damage
- Semi-annually: Functional check, verify positioning accuracy
- Annually: Cleaning, lubrication, wear check
TEA Selection Recommendations
Ball screws are indispensable for highly accurate and efficient linear drives. Sizing per ISO 3408 requires careful consideration of lead, diameter, preload, and expected service life. For critical applications (robotics, metrology), we recommend a detailed sizing review by experts. Use our online sizing tools or contact our application engineering team for your project.
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