The Shaft That Sagged in the Middle
We used a 20 mm diameter hardened linear shaft for a 1 m long axis. A plastic carriage slid on the shaft. The shaft was supported at both ends (bare shaft, no intermediate supports). On the bench, it slid fine. On the machine, the carriage moved smoothly at the ends but wobbled in the middle. The shaft had sagged. At 1 m unsupported, a 20 mm steel shaft deflects about 0.5 mm under the carriage’s weight. The carriage rocked. We added a support rail (the shaft sits in an aluminum extrusion with a continuous support). The sag went away. The mistake was using a bare unsupported shaft for a span longer than the manufacturer’s recommended maximum.
Linear shaft and support rail selection is about the shaft diameter, the support spacing, and whether the shaft needs continuous support. This article covers the choices.
Bare Shaft vs. Supported Shaft
Bare (Unsupported) Shaft
A hardened steel shaft, mounted at both ends. The middle spans freely. Simple, cheap. But the shaft sags (deflects) under the carriage weight. For short spans (under 500 mm), it’s fine. For longer spans, it deflects.
Best for: Short travel (under 500 mm), light loads, low precision.
Supported Shaft (Shaft in Rail)
The shaft is mounted inside an aluminum extrusion (a support rail). The shaft is supported along its entire length (no sag). The rail bolts to the machine frame. This is standard for longer axes.
Best for: Long travel (over 500 mm), heavy loads, precision linear motion.
| Type | Max Span | Sag | Cost |
|---|---|---|---|
| Bare shaft (Ø16) | Up to 400 mm | Visible over 500 mm | Low |
| Bare shaft (Ø20) | Up to 600 mm | Visible over 800 mm | Low |
| Bare shaft (Ø30) | Up to 1000 mm | Minimal | Medium |
| Supported rail (any length) | Unlimited | Zero (continuous support) | Medium |
Shaft Diameter Selection
The shaft diameter depends on the load and the span. A larger diameter is stiffer (less deflection). But it’s heavier and more expensive.
Standard diameters: 8, 10, 12, 16, 20, 25, 30, 40 mm. The linear bearing (the carriage that slides on the shaft) is sized to the shaft diameter.
Deflection Check (Bare Shaft)
For a bare shaft supported at both ends with a point load in the middle:
δ = F × L³ / (48 × E × I)
Where F is the load (N), L is the span (mm), E is Young’s modulus (206,000 N/mm² for steel), and I is the moment of inertia (π × d⁴ / 64 for a solid shaft).
For a Ø20 mm shaft (I = π × 20⁴ / 64 = 7,854 mm⁴), L = 1,000 mm, F = 50 N (carriage + load): δ = 50 × 1000³ / (48 × 206,000 × 7,854) = 50 × 10⁹ / (7.75 × 10¹²) = 0.64 mm. That’s visible sag. For a Ø30 mm shaft (I = π × 30⁴ / 64 = 39,794 mm⁴): δ = 50 × 10⁹ / (48 × 206,000 × 39,794) = 50 × 10⁹ / 3.93 × 10¹⁴ = 0.13 mm. Better. But still, a supported rail eliminates the sag entirely.
Hardened Ground Shaft vs. Soft Shaft
Hardened Ground Shaft
The shaft is hardened (HRC 60+) and ground to a precise diameter (h6 or h9 tolerance). The linear bearing balls roll on the hardened surface. Wear-resistant. This is the standard for linear motion.
Soft (Cold-Drawn) Shaft
Unhardened, not ground. Cheaper. But the linear bearing will wear a groove into it quickly. For low-cycle or hand-adjustable axes (not continuous motion).
For any axis that moves continuously (automated), use hardened ground shaft. Soft shaft is for static adjustments (a sliding block that moves once per day).
The shaft selection rule: For spans under 500 mm, a bare hardened shaft is fine. For longer spans, use a supported rail (shaft in aluminum extrusion). The shaft that sagged in the middle was a bare Ø20 mm shaft over 1 m — too long unsupported. Either go to a Ø30 mm bare shaft or, better, use a supported rail. The rail costs more but eliminates sag entirely.
Linear Bearings (Carriages)
The carriage slides on the shaft. Two types:
- Ball bushing (closed): A cylindrical bearing with recirculating balls. Fits over the shaft. Standard for supported rail axes.
- Open ball bushing: For shafts that are supported along the length (the rail has a slot for the carriage to wrap around the shaft). The bearing opens to slide over the supported shaft.
- Plain (bushed): A polymer bushing (no balls). Cheaper, but higher friction. For slow, light-duty axes.
Parallel Shafts (Two Shafts)
For a carriage that carries a load (a plate with a workpiece), use two parallel shafts (not one). Two shafts prevent the carriage from rotating (the load doesn’t twist). The shafts must be parallel (aligned during installation).
Two shafts are mounted in a support rail (or on two blocks). The carriage has two linear bearings (one on each shaft). This is the standard for a slide table.
Shaft End Supports
For bare shafts, the ends need support blocks. The block holds the shaft concentrically.
- End support block: A round block that clamps the shaft end. Available in shaft diameters.
- Set screw vs. clamp: Set screws mark the shaft. Clamp blocks (split collar) hold without marring.
For a supported rail, the rail itself is the support — no end blocks needed (the rail bolts to the frame).
A Linear Shaft Checklist
- What is the travel length? (mm)
- What is the carriage load? (kg, N)
- Is the span under 500 mm? (Bare shaft OK.)
- For longer spans: supported rail? (No sag.)
- What shaft diameter? (Check deflection.)
- Is the shaft hardened and ground? (For continuous motion.)
- One or two shafts? (Two for a load plate.)
- What bearings? (Ball bushing or open?)
- Are the end supports clamped? (No set screws?)
- Is the rail mounted flat? (Alignment.)
- Is there lubrication? (For ball bushings.)
- What is the precision requirement? (TIR?)
The Bottom Line
Linear shaft and support rail selection is about the span. A bare shaft works for short spans. For longer travels, the shaft sags. The shaft that wobbled in the middle was a bare Ø20 mm shaft over 1 m — too long unsupported. Use a supported rail (shaft in extrusion) for spans over 500 mm, or go to a larger diameter bare shaft. Two parallel shafts prevent rotation on load plates. The slide that moves smoothly over long travel wasn’t the thickest shaft — it was supported along its length.
