Rack and pinion drives move gantries, transfer axes, lifting axes and long-travel machines. Sizing one comes down to a simple question, asked carefully: what force does the pinion have to push on the rack, and which rack and pinion can carry that force for the life of the machine? This guide walks through the calculation our RackPro sizing calculator uses.
Step 1: the force on the pinion
Start with the moved mass m, the maximum speed v and the time to reach it, tb. The acceleration is:
a = v / tb
The tangential force on the pinion is then the force to accelerate the mass, plus friction in the guides, plus gravity on a lifting or inclined axis, plus any process force:
Fu = m · (g · sin θ + μ · g · cos θ + a) + process force
where θ is the axis angle (0° horizontal, 90° vertical) and μ the friction coefficient of the linear guides. If two pinions drive the axis and share the load, divide by two.
Example. A horizontal gantry moves 500 kg at up to 2 m/s, accelerating in 0.5 s, on guides with μ = 0.1. Then a = 4 m/s² and Fu = 500 × (0.1 × 9.81 + 4) ≈ 2,490 N, or 2.49 kN.
Step 2: apply the service factors
A rack's load rating assumes smooth, uniform running. Real machines are harsher, so the required force is multiplied by:
- Load factor KA (1.00 to 2.25): how much shock there is, from the drive (servo or electric motor, medium or heavy impact) and from the driven load.
- Safety factor SB (typically 1.1 to 1.4).
- Service-life factor Fn: rises with speed and with longer lubrication intervals. Automatic lubrication keeps it low; monthly manual greasing raises it a lot.
- Load-distribution factor LKHβ (1.1 to 1.5): how well the pinion is supported. A gearbox output with preloaded bearings holds the pinion straighter than one with standard bearings.
Step 3: reversing axes
If the axis is driven or braked in both directions, both tooth flanks carry load. For a reversing axis the rack's load-table force is reduced to two thirds, the same reduction JGMA 401-01 applies. Most gantries and transfer axes reverse; choose "one direction" only if the rack is never driven or braked the other way.
Step 4: compare with the load table
A rack and pinion fits when its load-table force, after the reversing reduction, divided by KA · SB · Fn · LKHβ, is at least Fu.
Example, continued. With a servo drive and uniform load (KA = 1.0), SB = 1.2, automatic lubrication at 2 m/s (Fn = 1.05) and a gearbox with preloaded bearings (LKHβ = 1.2), the combined factor is about 1.51. The gantry reverses, so the rack needs a load-table rating of at least 2.49 × 1.51 ÷ (2/3) ≈ 5.7 kN. The calculator lists every rack and pinion that meets it, smallest first.
Step 5: torque and speed for the gearbox
Once a pinion is chosen, its pitch diameter d gives the gearbox requirements:
- Torque: T = Fu · d / 2
- Speed: n = v / (π · d)
More pinion teeth means more load capacity and smoother running, but also more torque and a lower speed at the gearbox.
Step 6: choose the rack
- Helical or straight. Helical racks run more smoothly and quietly and carry more load for the same module; straight racks suit lifting axes, simple handling and cost-sensitive axes.
- Ground or milled. Ground racks (DIN quality 5 to 7) give the best positioning accuracy and smoothness; milled racks (quality 8 to 10) suit handling, lifting and long-travel axes.
- Material. C45 with induction-hardened teeth is the standard. 42CrMo4 is made to order and is taken as about 30% stronger than C45.
- Length. Standard lengths of 500, 1,000, 1,500 and 2,000 mm, with matched ends so racks join into a continuous axis; installation gauges set the pitch across each joint.
Treat it as a selection guide
Every rack manufacturer calculates load ratings slightly differently, so a calculation like this is a starting point, not a guarantee. Lubrication, mounting stiffness and alignment all matter as much as the numbers. Our engineers confirm every application before we quote.
Try the RackPro sizing calculator, browse the RackPro rack range, or tell us the rack you use today, from Güdel, Atlanta, GAM or another brand, and we will match it.