The Linear Shaft That Sagged Under the Load
We used two linear round shafts (Ø20 mm, hard chrome) with linear bearing blocks (ball bushings) to support a moving axis. The span between supports was 1.2 m. At mid-span, the shaft sagged 0.5 mm under the load. The axis position was off (the slide dropped in the middle). The problem: a round shaft, supported at two ends, sags under load (it’s a beam). We had undersized the shaft (Ø20 for a 1.2 m span). We switched to a profile rail (rectangular rail with recirculating ball blocks, article 52). The rail is mounted to the extrusion along its full length (not just at the ends). No sag. The mistake was using a round shaft on a long, un-supported span.
Linear shaft vs profile rail is about span and rigidity. Round shafts are simple; profile rails are rigid. This article covers when to use which.
Round Shaft (Linear Shaft + Ball Bushing)
A round shaft (hardened, chrome-plated) with a ball bushing (a recirculating ball bearing) slides on it. Simple, cheap, easy to install. The shaft is supported at two ends (or intermediate supports).
Pros: Cheap, simple, corrosion-resistant (chrome), easy to source.
Cons: Sags under load (it’s a beam between supports). Lower rigidity. Lower accuracy. Only handles radial loads (not moment loads).
Profile Rail (Linear Guide)
A rectangular steel rail (ground) with a recirculating ball block (carriage). The rail is bolted to the machine frame along its full length (not just at the ends). The block rides on the rail.
Pros: Very rigid (mounted along the full length, no sag). Handles moment loads (the block is wide). High accuracy. Long life (preloaded balls).
Cons: More expensive. Requires a flat, machined mounting surface (article 107).
| Type | Rigidity | Sag | Cost | Best For |
|---|---|---|---|---|
| Round shaft + bushing | Low | Significant (long span) | Low | Light loads, short spans, simple motion |
| Profile rail (guide) | High | None (full-length mount) | High | Precision, long spans, moment loads |
Step 1: Sag Calculation (Round Shaft)
A round shaft, supported at two ends, sags under a center load. The deflection (sag) is:
δ = F × L³ / (48 × E × I)
Where F is the center load (N), L is the span (mm), E is the modulus of elasticity (steel, 206,000 N/mm²), and I is the shaft’s moment of inertia (π × d⁴ / 64).
For d = 20 mm, I = π × 160,000 / 64 = 7,854 mm⁴. L = 1,200 mm. F = 200 N (the load at mid-span): δ = 200 × 1,200³ / (48 × 206,000 × 7,854) = 200 × 1.728e9 / (48 × 206,000 × 7,854) = 3.456e11 / 7.77e10 = 4.4 mm. That’s huge — the shaft sags 4.4 mm.
For d = 30 mm, I = π × 810,000 / 64 = 39,794 mm⁴ (5× stiffer). δ = 200 × 1.728e9 / (48 × 206,000 × 39,794) = 3.456e11 / 3.93e11 = 0.88 mm. Better, but still sagging.
For L = 500 mm (short span), d = 20 mm: δ = 200 × 125e6 / (48 × 206,000 × 7,854) = 2.5e10 / 7.77e10 = 0.32 mm. Acceptable.
The shaft vs rail rule: For spans over 500 mm, use a profile rail (mounted full-length). For short spans (under 500 mm) and light loads, a round shaft is fine. The shaft that sagged had a 1.2 m span on Ø20 mm. Switch to a profile rail.
Step 2: Moment Loads
A round shaft + bushing only handles radial loads (the load points down, through the shaft). It can’t handle a moment load (a load offset from the shaft, creating a tipping moment). The bushing tilts on the shaft.
A profile rail block is wide (it spans the rail). It handles moment loads (pitch, roll, yaw) because the block is wide. For a load that overhangs (a camera, a gripper mounted off to the side), use a profile rail (or two parallel round shafts).
Step 3: Mounting Surface
A profile rail needs a flat mounting surface (article 107). The rail is bolted to a machined pad (or an extrusion). If the surface isn’t flat, the rail binds.
A round shaft needs two end supports (or intermediate supports). It’s more forgiving (the shaft is held at the ends; it doesn’t need a flat surface along its length).
Step 4: Speed and Accuracy
A profile rail runs faster and more accurately (preloaded balls, no play). For a high-speed pick-and-place, use a profile rail. For a slow, light axis (a sensor slide), a round shaft is fine.
A Linear Guide Selection Checklist
- What is the span? (Between supports?)
- What is the load? (And where is it applied?)
- Is there a moment load? (Overhanging?)
- What accuracy is needed? (0.05 mm or 0.5 mm?)
- What speed? (Fast or slow?)
- For round shaft: is the sag acceptable? (Calculate δ = F L³ / 48EI?)
- Is the mounting surface flat? (For profile rail?)
- Is cost a factor? (Round shaft is cheaper?)
- Is corrosion an issue? (Chrome shaft or stainless?)
- Is the application dirty? (Sealed blocks?)
The Bottom Line
Linear shaft vs profile rail is span and rigidity. The shaft that sagged had a 1.2 m span on Ø20 mm (δ = 4.4 mm). For long spans and moment loads, use a profile rail (full-length mount, no sag). For short spans (under 500 mm) and light loads, a round shaft is cheaper and simpler. Calculate the sag before choosing. The axis that doesn’t sag wasn’t the thickest shaft — it was a profile rail.
