The Rail That Developed a Groove After Six Months
We used a 15 mm profile rail on an X-Y gantry. The carriage carried a 10 kg load moving at 1 m/s. The rail was the smallest in the series (15 mm). On the catalog, the dynamic load rating seemed adequate. After six months, the carriage had a noticeable groove in the rail — the balls were wearing into the raceway. The problem was the moment load. The load wasn’t centered over the carriage; it was 100 mm forward (the tool hung off the front). The moment load created an uneven load on the four ball tracks. The front two tracks carried 3× the rated load. The rail wasn’t sized for the moment — only for the vertical force. We upgraded to a 25 mm rail (higher moment rating) and added a second carriage. The groove didn’t return.
Linear guide sizing isn’t just matching a rail to the vertical load. The moment loads (pitch, yaw, roll) and the equivalent dynamic load determine the L10 life. This article walks through the numbers.
The Loads on a Linear Guide
A carriage on a rail sees six load components:
- Radial force (Fr): Vertical load (weight). Downward on the rail.
- Lateral force (Fl): Sideways force (cutting, belt pull).
- Axial force (Fa): Force along the rail (thrust).
- Moment pitch (Mp): Tipping forward/backward (like a seesaw). Load offset in the travel direction.
- Moment yaw (My): Twisting around the vertical axis. Load offset sideways.
- Moment roll (Mr): Rolling around the rail axis. Load offset above/below.
Most designers check only the radial force. The moments are the killers. A load offset from the carriage center creates moments that load one end of the carriage more than the other.
The Equivalent Dynamic Load
Like bearings, linear guides use an L10 life formula. The catalog gives a dynamic load rating C. The actual load (equivalent dynamic load P) determines the life.
L₁₀ = (C / P)³ × 50 km (for ball rails)
Where C is the basic dynamic load rating (kN) from the catalog, and P is the equivalent load (kN). For profile rails, life is in kilometers (not revolutions, like rotary bearings).
Step 1: Calculate the Forces and Moments
For our gantry example: carriage carries 10 kg (98 N) of load. The tool hangs 100 mm forward of the carriage center.
- Radial force Fr = 98 N (downward, at the load center).
- Pitch moment Mp = Fr × offset = 98 N × 0.1 m = 9.8 N·m (tipping forward).
- Lateral force Fl = 0 (no side load in this example).
- Yaw moment My = 0 (load centered sideways).
Step 2: Convert Moments to Equivalent Load
The catalog gives allowable moment ratings (Mp, My, Mr) for each carriage size. If the applied moment is within the allowable, the load is OK. If not, the equivalent load P increases.
For a 15 mm rail carriage, the allowable pitch moment is about 10 N·m. Our Mp = 9.8 N·m — just under. But the catalog also says the dynamic load rating C is about 10 kN. The equivalent load P isn’t just the vertical force (98 N). The moment adds to it.
The equivalent load for a single carriage under a moment is approximately:
P ≈ |Fr| + k₁ × |Mp| + k₂ × |My| + k₃ × |Mr|
Where k₁, k₂, k₃ are factors from the catalog (convert moment to equivalent force). For a 15 mm rail, k₁ (pitch) is about 1,500 N per N·m. So the pitch moment adds Pₘₚ = 1,500 × 9.8 = 14,700 N = 14.7 kN. That’s the equivalent load from the moment alone! Combined with the 98 N vertical load, P ≈ 14.8 kN.
The dynamic rating C is 10 kN. P (14.8 kN) exceeds C. The L10 life is (10/14.8)³ × 50 = 0.31 × 50 = 15.5 km. That’s only 15 km of travel. At 1 m/s, that’s 15,000 seconds = 4 hours. No wonder it wore in six months.
Step 3: Use Two Carriages (or a Bigger Rail)
With two carriages on the same rail, the moment is shared. The pitch moment Mp acts between the two carriages, and each sees half the moment load. If the carriages are spaced 200 mm apart, the effective k₁ drops (the moment is resisted by the carriage separation, not the single carriage length).
With two carriages spaced 200 mm apart: the equivalent load per carriage drops to about 2 kN (the moment is split). L10 = (10/2)³ × 50 = 125 × 50 = 6,250 km. That’s over 1,700 hours at 1 m/s — about 2 years of 8-hour days. Still not great, but much better.
Upgrading to a 25 mm rail: C ≈ 28 kN. With two carriages, P ≈ 2 kN. L10 = (28/2)³ × 50 = 2,744 × 50 = 137,000 km — over 15 years. That’s the right answer.
| Configuration | Equivalent Load P | Dynamic C (15 mm) | L10 Life |
|---|---|---|---|
| Single carriage, no moment | 0.1 kN | 10 kN | 500,000 km (fine) |
| Single carriage, 9.8 N·m pitch | 14.8 kN | 10 kN | 15 km (wears fast) |
| Two carriages, 200 mm spacing | 2 kN | 10 kN | 6,250 km (~2 years) |
| Two carriages, 25 mm rail | 2 kN | 28 kN | 137,000 km (~15 years) |
Step 4: Preload and Stiffness
Profile rails come in preload classes (clearance, light preload, medium preload, heavy preload). The preload removes internal clearance and increases stiffness.
- Clearance (Z0): No preload. For light loads, low friction. Not for precision.
- Light preload (Z1): Slight preload. General automation. Good stiffness, moderate friction.
- Medium preload (Z2): Higher stiffness. For precision axes. More friction (more drive torque).
- Heavy preload (Z3): Maximum stiffness. For machine tools, high cutting forces. Very high friction.
For a pick-and-place axis (light load, need accuracy), Z1 or Z2. For a machining axis (cutting forces, need rigidity), Z2 or Z3. More preload = more stiffness but more friction and shorter life (the preload adds to the equivalent load).
Step 5: Mounting and Parallelism
Two rails must be parallel within tight tolerance. If they’re not, the carriages bind.
- Parallelism between rails: Within 0.02–0.05 mm over the travel. Mount them to a flat, machined surface.
- Height difference (level): The two rails must be at the same height. A height difference loads one rail more than the other.
- Reference edge: One rail is the reference (against a machined edge). The other rail is shimmed or adjusted to match. Don’t mount both to un-machined extrusion.
A machine frame that flexes under load also causes binding. The rail mounting surface must be rigid. If the frame deflects 0.1 mm under load, the carriages fight it.
Step 6: Speed and Acceleration
Profile rails have speed and acceleration limits. Standard rails handle 5 m/s and 50 m/s². For higher speeds (high-speed packaging), use a rail with end-cap recirculation (the balls recirculate smoothly without banging). For very high acceleration, check the dynamic load rating (C) — the acceleration forces add to P.
The guide sizing workflow: 1) Calculate vertical force Fr. 2) Calculate moments from load offset (Mp, My, Mr). 3) Convert moments to equivalent load P using catalog factors. 4) Check P against C (dynamic rating). 5) L10 = (C/P)³ × 50 km. 6) If life is too short: bigger rail, more carriages, or reduce load offset. 7) Select preload class (Z1/Z2/Z3). 8) Verify mounting surface rigidity and parallelism.
Mounting the Carriages: How Many Per Rail?
Each rail can have one or two carriages. The number affects the moment capacity.
- One carriage per rail: Simple, but the carriage sees the full moment. For light loads, no offset.
- Two carriages per rail: The moment is resisted by the carriage spacing. Higher moment capacity. Standard for gantries and X-Y tables.
- Four carriages (two rails × two): The highest rigidity. For heavy loads, machining, or large tables.
The carriage spacing matters. Wider spacing = more moment resistance. A 200 mm spacing is standard. A 500 mm spacing resists moments better but needs a longer rail.
Lubrication
Profile rails need lubrication (grease). The balls recirculate through the raceways. Without grease, they wear fast.
- Grease fitting (zerk): Most carriages have a grease zerk. Add grease every 3–6 months (or per the manufacturer’s schedule).
- Lubrication unit: For 24/7 machines, an automatic lubricator (a small grease dispenser on the rail) feeds grease continuously.
- Seals: The carriage has end seals that keep dirt out. Check them periodically. A damaged seal lets dust in and the rail wears.
A Linear Guide Sizing Checklist
- What is the vertical load Fr? (N or kN)
- What are the moments from load offset? (Mp, My, Mr in N·m)
- Convert moments to equivalent load P (catalog factors).
- What is the rail’s dynamic rating C?
- L10 = (C/P)³ × 50 km. Does it meet required life?
- How many carriages per rail? (1 or 2?)
- Carriage spacing? (Moment resistance.)
- Preload class? (Z1/Z2/Z3 based on stiffness need.)
- Is the mounting surface flat and rigid? (Parallelism.)
- Speed and acceleration within rail limits?
- Lubrication schedule (grease every X months)?
- Is the environment dirty? (Seals, bellows?)
The Bottom Line
Linear guide sizing calculation isn’t matching a rail to the vertical load. The moments from load offset are what kill rails. A 10 kg load centered on a carriage is nothing. The same 10 kg load hanging 100 mm forward creates a pitch moment that multiplies the equivalent load by 100×. Calculate the moments, convert to equivalent load, and check L10. The rail that grooved wasn’t under-sized for weight — it was under-sized for the moment. Add carriages, space them out, and upsize the rail. The guide that rolls smoothly for years wasn’t chosen for the static load; it was chosen for the moments.
