How Do KHK Gears and Racks Convert Between Rotation and Linear Motion?

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  Key takeaways
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  How KHK gears and racks turn rotation into straight travel
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  Sizing a KHK gears and racks set before you cut metal
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  Setting backlash and preload on a rack drive
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  Machining the mounting features that hold rack alignment
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  Material and heat treatment choices for rack and pinion
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  Step by step: building a rack and pinion axis
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  Rack drive options compared

A rack is a gear blank rolled out flat. The teeth keep the same involute profile as the pinion, so the two mesh exactly like any spur gear pair. When the pinion turns, the contact point walks along the rack and the carriage moves in a straight line. Reverse the input and the rack drives the pinion.

The travel per pinion revolution equals the pitch circumference: π × module × tooth count. For a module 2 pinion with 20 teeth, that is about 125.66 mm per turn. Notice that the outside diameter never enters this number. Sizing off the outer diameter is the most common arithmetic error we see on drawings.

KHK publishes the pitch line, pressure angle, and tooth count for every catalog rack and pinion, so you can pick a set without recalculating the geometry. What you still have to decide is how the rack is held, how backlash is set, and how the axis is lubricated.

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  Pitch circumferenceπ × module × teeth = travel per pinion turn.
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  Pressure angle20° is the standard for KHK racks; it sets the thrust load on the pinion bearing.
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  Helical optionHelical racks run quieter and carry more load, but add axial thrust.
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  Rack jointButt two racks together and the tooth pitch must stay continuous across the seam.

Start with the load, not the tooth count. Add the carriage mass, the cutting or pressing force, and the friction of the guide rail. Multiply by a service factor of 1.5 to 2.0 for a reversing axis with shock. That number tells you the tangential tooth force the pinion must carry.

Convert tangential force into torque at the pinion: torque = force × pitch radius. Compare that to the motor torque after the gearbox ratio, then check the rack tooth bending stress at the same force. Skipping this step is how shops end up with a module 1.5 set on a 300 kg gantry.

Rack length follows from travel plus a safety margin. Add at least one tooth of overtravel at each end so the pinion never runs off the last tooth. If the axis needs more than roughly 2 m of travel, plan the rack as several sections with staggered joints.

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  Service factor1.5–2.0 for reversing or shock-loaded axes.
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  Pitch radiusmodule × teeth ÷ 2, in millimeters.
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  OvertravelAt least one full tooth beyond each travel limit.

Backlash is the gap between the non-working flanks of the meshing teeth. On a positioning axis it shows up directly as lost motion when the direction reverses. On a slow indexing axis it barely matters. Decide the number from the job, not from habit.

For most machine tool and automation axes, 0.02–0.10 mm of backlash at the pitch line is workable. Below that, thermal growth and imperfect mounting start to bind the teeth. Above it, a servo axis will hunt and the surface finish will show it.

Two ways to remove backlash properly. A split pinion with a spring or shim between halves pushes the two tooth rows against opposite flanks. A dual-pinion arrangement drives the same rack with two pinions loaded against each other. Both cost money and add setup time. Neither is needed if the axis only moves in one direction.

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  Measure at the pitch lineA dial indicator on the carriage, not on the tooth tip.
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  Watch the temperatureA 30 °C rise on a 1 m steel rack closes roughly 0.36 mm of length.
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  Lubrication gapLeave room for the oil film; dry teeth wear faster than tight teeth.

The rack only runs as straight as the surface it sits on. Machine the rack mounting face flat within 0.02 mm over its length, and keep the pinion axis parallel to that face. In practice this means cutting the face, the dowel holes, and the pinion bearing bores in one setup wherever the part size allows.

Our 5-axis centers hold ±0.005 mm on those bores, and we routinely finish locating faces to Ra 0.8–1.6 μm so the rack seats without rocking. A 4,000 mm maximum processing envelope covers long gantry beds and machine frames without re-fixturing.

Use dowel pins, not just bolts, to locate each rack section. Bolts clamp, dowels position. On a 2 m axis with three rack sections, the dowel pattern is what keeps the tooth pitch continuous across the joints. Ream the dowel holes in the same setup as the mounting face.

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  One setupFace, dowel holes, and bearing bores cut without re-clamping.
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  Dowel firstTwo dowels per rack section minimum, then tighten the bolts.
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  Check with a straight edgeFeeler gauge under a precision straight edge along the rack back.

Carbon steel racks such as S45C are the default for general machine axes. They machine cleanly, take a case-hardening treatment, and cost less than alloy grades. For higher tooth loads, alloy steel with carburizing gives a hard case over a tough core, which resists both wear and shock.

Stainless grades like 304 or 17-4PH suit food, medical, and wash-down equipment. They are softer than case-hardened carbon steel, so derate the tooth load or increase the module. For clean-room and medical builds, we machine 304 and 316L routinely and finish to Ra 0.8–1.6 μm.

Aluminum racks in 6061-T6 or 7075 work well in light automation and pick-and-place heads where inertia matters more than load. Anodize the teeth if the axis runs dry, but keep the coating thin. A hardcoat that builds 0.05 mm per flank changes the backlash you set at assembly.

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  S45CGeneral machine axes, case-hardened after cutting.
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  17-4PHCorrosion resistance with better strength than 304.
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  6061-T6Light, fast axes; anodize thin or leave bare and lubricate.