A linear guide on a pick-and-place axis was rated for 100,000 km of travel. The machine ran 20 hours a day, 30 cycles per minute, 150 mm per cycle. The catalog life worked out to over 10 years. The carriage started showing play at 15 months, and the guide was loose at two years. The travel math: 30 x 2 x 0.15 m x 60 x 20 = 10,800 m per day, about 3,900 km per year. Two years is 7,800 km. The guide lost 93% of its rated life. The L10 calculation was done with catalog numbers. No hardness factor, no contamination factor, no load factor. The real world applied all three.
The L10 formula
L10 = (C/P)^3 x 50 km for ball-type guides, where C is the dynamic load rating and P is the equivalent load. For roller guides, the exponent is 10/3.
The pick-and-place used a 25 mm ball guide with C = 20 kN. The applied load was 2000 N, the carriage plus a 15 kg payload at 1 g with a 3x impact factor during the fast moves. P = 2000 N. L10 = (20000/2000)^3 x 50 = 1000 x 50 = 50,000 km. That’s the catalog number. But the machine’s moves were fast, and the load during deceleration hit 6000 N momentarily. The equivalent load isn’t the static 2000 N. It’s the RMS over the cycle.
The equivalent load nobody computes
For a cycle with 2000 N for 0.3 s and 6000 N for 0.05 s, the deceleration, the equivalent load is the cube-root of the time-weighted mean of P^3:
P_eq = [(2000^3 x 0.3 + 6000^3 x 0.05) / 0.35]^(1/3) = [(8e9 x 0.3 + 2.16e11 x 0.05) / 0.35]^(1/3) = [(2.4e9 + 1.08e10) / 0.35]^(1/3) = [1.32e10 / 0.35]^(1/3) = [3.77e10]^(1/3) = about 3350 N.
L10 = (20000/3350)^3 x 50 = (5.97)^3 x 50 = 213 x 50 = 10,650 km. The real calculated life is 10,650 km, not 50,000. Still more than the 7,800 km the guide actually delivered. More factors are in play.
The hardness and contamination factors
The catalog C rating assumes the rail is hardened to 58 HRC or above. If the rail is 55 HRC, the rating drops by 10%. The pick-and-place rail was a standard rail at 58 HRC, so that factor was fine.
The contamination factor is the big one. The catalog life assumes clean, sealed, lubricated operation. The pick-and-place ran in a dusty shop with no wipers on the carriage and grease that wasn’t re-applied. The contamination factor for a dusty, unsealed environment is 0.1-0.2. Apply 0.15: L10 = 10,650 x 0.15 = 1,600 km. The guide should have failed at five months. It lasted 15 months before play appeared. The factory grease gave some margin.
The fix: sealed carriages. The wipers keep dust out, and re-grease every three months. The replacement guide with sealed carriages and a quarterly grease schedule is projected to reach 10,000 km, six times the unsealed life.
The mounting factors
Misalignment also kills linear bearings. If the two rails of the gantry aren’t parallel, the carriage binds and the effective load doubles or triples. The pick-and-place’s rails were aligned to 0.05 mm over 600 mm, which is good, but the carriage preload was C0, no preload, and the play appeared quickly. A light preload (C1) would have held the play out longer, at the cost of slightly higher friction.
The selection path that matches field life
Write down the real load cycle, including the acceleration peaks. Compute the RMS equivalent load. Apply the hardness factor (1.0 for 58 HRC), the temperature factor (1.0 below 100C), and the contamination factor (1.0 for sealed, 0.3 for wipers without seals, 0.1 for nothing). Multiply the catalog life by the product. If the answer is shorter than the required life, pick a bigger guide or seal it better. Sealing and greasing are cheaper than up-sizing.
The 100,000 km catalog life assumes clean, sealed, ideal load. The pick-and-place ran dusty, unsealed, with load peaks three times the average. The real life was 1,600 km, not 100,000. Compute the RMS load, apply the contamination factor, and seal the carriage. The guide wasn’t defective. The calculation was done on catalog assumptions.
