Ball Spline

What is a Ball Spline

A ball spline is a rolling-element linear-motion device that does two jobs at once: it lets a nut slide freely along a shaft, and it transmits rotational torque between that nut and shaft with the rolling balls acting as the engaging teeth. Structurally it has two parts. The spline shaft is a hardened, precision-ground round bar carrying axial load-bearing grooves along its length. The spline nut, sometimes called the spline outer cylinder, surrounds the shaft and contains rows of steel balls that recirculate through return passages, a retainer or cage that guides them, and end rings that close the circuits. When the nut moves along the shaft the balls roll in the grooves, and when a torque is applied to the nut those same balls are trapped between the groove flanks and react the load against the shaft.

The behavior is best understood by comparison to two familiar parts. A plain linear bushing also runs balls on a round shaft, but its balls sit in straight raceways with no groove engagement, so it carries only radial load and cannot resist rotation; the nut spins freely on the shaft. A keyed or conventional splined shaft does transmit torque, but through sliding metal contact, which means friction, wear, and a few thousandths of an inch of rotational lash. The ball spline merges the two ideas: it carries radial and moment load like a bushing and transmits torque like a spline, but on rolling contact. Engineering references summarize it directly, calling the ball spline to splines what the ball screw is to the lead screw.

The practical consequences are large. The rolling friction coefficient is roughly 0.002 to 0.003, low enough that a servo can stroke the axis quickly and reverse without stick-slip. Because rolling contact distributes load across many balls in hardened grooves, a ball spline reaches an allowable load well above that of a sliding bush; THK states its ball spline can achieve a rated load more than ten times that of a linear bushing of the same shaft diameter. Rotational lash, which on a sliding spline might be several thousandths of an inch measured at the ball-circle diameter, can be driven to near zero by applying a preload, so the nut and shaft turn as a rigid unit. This is why the ball spline is the default for axes that must rotate while they translate.

The element traces to THK of Japan, which commercialized the ball spline as a companion to its ball screw and LM (linear motion) guide families and still holds the broadest catalog. Today the device is mainstream across automation: SCARA robot Z-theta axes where the shaft moves vertically while the nut indexes the gripper, automatic tool changers, pick-and-place and packaging machinery, honing and grinding spindles, indexing tables, oil-and-gas and downhole tools, medical positioning, and even helicopter rotor driveshafts where a cantilever load must rotate and slide. A hollow spline shaft variant lets electrical cables, air lines, or vacuum lines pass straight through the rotating axis, a feature that simplifies cable management on SCARA and gantry robots.

Four engineering attributes determine whether a ball spline is the right joint and which model fits: the torque type and load rating that set capacity, the accuracy grade that sets rotational true running, the preload and rotational-clearance class that set backlash and rigidity, and the shaft material and hardness that set corrosion behavior and life. The chapters that follow take each in turn, then close with a selection sequence that turns the attributes into an order.

Ball Spline Types and Classification

Ball splines are classified two ways: by how much torque the groove arrangement can carry, and by what the nut does at its outer surface. The torque axis runs from medium-torque types, through high-torque types, to caged-ball high-torque types, while the nut-function axis separates ordinary translating nuts from rotary nuts that add their own bearing so the nut can rotate as well as slide. The table below summarizes the THK family, the most complete in the market and a useful reference frame for any maker.

Medium-torque types such as models LT and LF use a shaft with two to three crests around the circumference. Along both sides of each crest two rows of balls are arranged, giving four or six rows in total, set up so a reasonable preload holds the crests. The rows are positioned to take load in opposing directions, so the nut resists radial and moment loads from any angle while still transmitting torque. Medium-torque models span the widest size range, from miniature 4 mm shafts up to 100 mm, and are the workhorse where torque is present but not dominant: general slide axes, feed mechanisms, and light indexing.

High-torque types such as models LBS, LBST, LBF, LBR, and LBH redesign the shaft with three crests positioned equidistantly at 120 degrees. On both sides of each crest two rows of balls run, for six rows in total, holding each crest between them. The symmetric three-crest layout packs more contacts onto the shaft and balances the load, which raises both torsional and flexural rigidity and lifts the torque rating sharply over a medium-torque shaft of the same diameter. These are the models reached for in robot joints, automatic tool changers, and machine-tool spindle drives, where a large reversing torque must pass through a sliding joint without lash.

Caged-ball high-torque types such as models SLS, SLS-L, and SLF take the three-crest idea further. The shaft is reshaped to be more circular, which improves torsion and flexural rigidity, and a ball cage keeps the balls evenly spaced so they no longer collide as they recirculate. The cage cuts noise, smooths motion, allows higher speed and faster cycle times, and extends grease life by maintaining oil films between balls. Caged-ball splines are chosen where the axis runs fast and continuously, for example in high-throughput assembly cells, and where quiet running matters.

Rotary types change the nut rather than the shaft. Models such as LBG and LBGT are based on a high-torque ball-spline nut but add radial and thrust bearings inside the housing so the whole nut assembly can rotate, and many carry gear teeth on the flange so a motor can drive that rotation. The result is a single compact unit in which the spline shaft strokes linearly (the Z axis) while the geared nut spins (the theta axis). This is the canonical SCARA robot wrist solution and the basis of many indexing heads and tool changers. THK rotary ball spline shaft diameters in the LBG line run 20, 25, 30, 40, 50, 60, and 85 mm. A related family, the precision ball screw spline, machines ball-screw grooves and ball-spline grooves onto a single shaft so one shaft gives both vertical thrust and rotational holding, the densest way to build a Z-theta column.

Two construction choices cut across all families. Ball contact geometry is either a gothic-arch profile, where each ball touches the groove at four points for higher rigidity and precision on larger sizes, or a circular-arc profile, where each ball touches at two points for lower friction on smaller or friction-sensitive sizes. Groove count ranges from two to six, with four grooves the most common on general nuts. And shaft bore can be solid or hollow; a hollow spline shaft routes cables, air, or vacuum through the rotating axis, which is why it appears so often on SCARA and gantry robots.

Accuracy Grades and Preload

Two independent settings govern how precisely a ball spline runs: the accuracy grade, which is a manufacturing tolerance on how true the nut runs as the shaft rotates, and the preload or rotational-clearance class, which is a fit choice that sets how much lost motion exists before the nut and shaft turn together. They are specified separately, and confusing them is a common selection error.

Accuracy grades are defined by the radial run-out of the spline nut outer diameter measured relative to the shaft support, the areas the maker marks on its accuracy drawings. THK divides ball splines into three grades: normal grade with no symbol, high accuracy grade marked H, and precision grade marked P. As the grade tightens, the permitted run-out falls, the straightness of the shaft improves, and the maximum allowable shaft length for that grade shortens, because a longer shaft is harder to hold true. The grade matters most when the spline itself drives something that must run concentric, such as a grinding spindle, a precision indexing head, or a measuring axis, and matters least when the spline is only a sliding guide and the torque is incidental. The table below frames the grades.

Preload and rotational clearance are about backlash, not run-out. Clearance in the rotation direction is how far the nut can twist on the shaft before the balls seat against the groove flanks and torque starts to transmit. THK offers a normal grade with a small positive clearance for smooth motion under a small force, suited to cases where torque is always applied in the same direction so the joint never reverses through the gap. Where the load reverses, oscillates, or must hold position precisely, a preload is applied instead: the balls are sized to sit slightly oversize so they are always in compression, removing the gap entirely. THK labels rotational-clearance and preload selections with class symbols such as CL and CM, with the applied preload raising the seated torque the joint can carry before any further motion. The trade is real: preload raises torsional rigidity and removes backlash, but it also increases rolling friction and reduces nominal life, so it should be sized to the duty rather than maximized.

The rigidity gain from preload is worth quantifying in principle. Under a light preload, the nut and shaft behave as a single rigid body up to the seated-torque limit, after which deflection follows the spring rate of the balls and grooves. A normal-clearance joint, by contrast, must first cross the clearance band before it stiffens, which appears in a servo as lost motion on every reversal and as positioning error in bidirectional moves. For a reversing servo axis the choice is therefore almost always a preload class; for a one-way feed or a simple slide a normal clearance is cheaper, runs cooler, and lasts longer.

Two practical rules follow. First, set accuracy grade from the rotational true-running requirement and preload class from the backlash and rigidity requirement; they are not substitutes, and a high accuracy grade with normal clearance still has rotational lash. Second, do not over-specify. A precision grade with heavy preload costs far more, runs hotter, and wears faster, and it is wasted on an axis that only needs to slide under a unidirectional load. Match each setting to the function the spline actually performs in the machine.

Shaft Materials, Hardness and Standards

The material and heat treatment of the spline shaft and the load-bearing parts of the nut decide load capacity, fatigue life, and corrosion behavior. The standard choice is a through-hardening bearing steel, and the load surfaces are ground to a hard, smooth track so the balls roll without brinelling the grooves or fatigue-spalling the surface.

SUJ2 high-carbon chromium bearing steel is the default. SUJ2 is the JIS designation, and it is equivalent to AISI 52100 in the United States and 100Cr6 (EN 31) in Europe, the same family used for ball-bearing rings and balls. It is heat treated so the raceway surfaces reach roughly 58 to 62 HRC, then precision ground. Published engineering references quote the inner race (the splined shaft) at about 56 to 60 HRC and the outer race at about 58 to 60 HRC, which keeps the contact hard enough to resist plastic indentation under the high local pressures at the ball contacts. SUJ2 is suited to clean, dry, or oiled environments and gives the highest published load and torque ratings.

Corrosion-resistant variants are offered where the axis sees moisture, washdown, or clean-room duty. Stainless martensitic grades and surface treatments such as black chrome or specialty coatings protect the shaft, at the cost of some load rating and sometimes a lower attainable hardness. For food, pharmaceutical, or semiconductor service the corrosion grade is mandatory despite the capacity penalty, and the maker datasheet will derate the load and torque ratings accordingly. Always confirm both the hardness and the surface finish on the datasheet before sizing for life, because a softer or rougher track changes the contact behavior the life formula assumes.

On standards, ball splines sit between two reference frames. The conventional splined-shaft world is governed by involute-spline standards: DIN 5480 covers involute splines on reference diameters at a 30 degree pressure angle for sliding and fixed shaft-hub connections, while ISO 4156 (with ANSI B92.2M) covers involute splines at 30, 37.5, and 45 degree pressure angles, and the two are not interchangeable. A ball spline does not use involute teeth, so those standards describe the alternative it replaces rather than the ball spline itself. For the rolling-element side, the JIS B 1192 ball-screw framework (aligned with ISO 3408) defines the accuracy-grade system THK extends across its linear products by linearity and travel-distance error, and bearing-steel practice follows the SUJ2 / AISI 52100 / 100Cr6 material standards. In practice, a ball-spline datasheet is the governing specification: it states the torque type, accuracy grade, preload class, ratings, and material, and the engineer verifies the duty against those numbers rather than against a single ISO part.

The table below maps common operating environments to a recommended shaft material choice. It is for initial selection only; before purchase, obtain the maker corrosion and derating data for the specific medium, temperature, and lubrication.

Key Specification Parameters

A ball spline datasheet lists many dimensions, but a handful of ratings drive the selection: the basic dynamic load and torque ratings that set life, the basic static ratings and permissible moment that set the strength limit, the nominal shaft diameter and nut envelope that set fit, and the accuracy and preload classes covered in Chapter 3. Each is explained below, with a representative high-torque LBS-style rating table for the Key Specifications comparison.

Basic dynamic load rating (C) is the radial load under which a population of splines reaches a nominal life basis, expressed in kilonewtons. Basic dynamic torque rating (Ct) is the analogous figure for a torque duty, in newton-metres. These are the numbers that enter the life formula. Basic static load rating (C0) and basic static torque rating (C0t) are the static limits, the load or torque at which the permanent deformation at the most heavily loaded ball contact reaches a defined fraction of the ball diameter; the maximum applied load must stay below these through a static safety factor. The static permissible moment (for example MA for a single nut, and the higher value for two nuts in contact) bounds the moment load the nut can carry without overload.

The table below lists representative ratings for a high-torque ball spline across four sizes, drawn from the THK LBS-family catalog, to show how the numbers scale with shaft size. Use it to read the shape of a spec sheet, not as a substitute for the exact model page.

Nominal life (L10) follows the rolling-bearing model. It is the travel distance that 90 percent of a population reaches before the first signs of material fatigue, and THK expresses it as a distance in kilometres against a 50 km basis. For a radial-load duty the nominal life L10 equals 50 km multiplied by the cube of the ratio C divided by Pc, where Pc is the applied radial load; for a torque duty the same form uses Ct divided by Tc, the applied torque. The cube exponent is the value used for ball contact, so life is highly sensitive to load: doubling the applied load cuts life to roughly one eighth, which is why getting the load and range right dominates life prediction. Temperature, contact, and load (vibration) factors then derate the basic result, and the maximum applied load is separately checked against the static rating through a static safety factor.

Critical and dangerous speed matter when the shaft rotates. As rotational speed rises, the rotation cycle nears the natural frequency of the spline shaft, and at resonance the shaft can whirl and seize, so the maker publishes a dangerous-speed limit that depends on shaft diameter, unsupported span, and end fixity. A long, slender rotating shaft must be checked against this limit just as a long ball screw is checked for whip. Stroke and shaft length are bounded by the accuracy grade, since a longer shaft is harder to hold straight at a tight grade. Finally, the mass of the nut and the shaft (per metre) feeds the dynamics of a fast servo axis and should be read from the same table when sizing the motor.

Selection Decision Factors

To turn the knowledge of the previous five chapters into a specific model, follow the decision sequence below. Most selection mistakes come not from a single wrong number but from deciding a downstream detail before an upstream one is fixed, so work the list in order. The eight steps double as a fixed RFQ template.

1. Confirm the duty: decide whether the axis must transmit torque while it strokes, or only guide a linear load. If torque is incidental and one-directional, a medium-torque type and normal clearance suffice; if torque reverses or is large, move to a high-torque type with a preload class. If the nut must also rotate, you need a rotary type.
2. Torque type and shaft diameter: pick medium torque (LT, LF), high torque (LBS, LBF, LBR, LBH), caged-ball high torque (SLS, SLF), or rotary (LBG, LBGT) per Chapter 2, then size the nominal shaft diameter (about 4 to 150 mm across the range) so the dynamic torque rating Ct and load rating C give the required L10 life with margin.
3. Accuracy grade: choose normal, high (H), or precision (P) from the rotational true-running requirement. Reserve precision for spindle drives, indexing, and metrology; use normal for plain guidance. Remember the grade bounds the maximum shaft length.
4. Preload and rotational clearance: choose normal clearance for smooth, one-way, low-force motion, or a preload class (for example CL or CM) for reversing servo axes, oscillating loads, and high positioning accuracy. Size the preload to the duty, since excess preload shortens life and adds friction.
5. Loads and life check: verify the maximum applied radial load, moment load, and torque against the basic static ratings (C0, C0t, static permissible moment) through a static safety factor, then compute L10 against C and Ct with temperature, contact, and load factors. Confirm the operating point leaves life margin for vibration and shock.
6. Speed and span: for a rotating shaft, check the rotational speed against the dangerous-speed limit for the chosen diameter, unsupported span, and end fixity, and check linear velocity and acceleration against the nut rating. Add intermediate support or a larger diameter if the shaft is long and slender.
7. Material and environment: default to SUJ2 / AISI 52100 bearing steel hardened to about 58 to 62 HRC for clean or oiled duty; specify stainless or a surface treatment for humid, washdown, food, pharma, or clean-room service, and accept the load derating. Decide solid or hollow shaft, the latter where cables or air must pass through the axis.
8. Mounting, sealing and lubrication: fix the nut mounting (cylindrical, flanged, or keyed body), the housing bore tolerance, the seal type for the contamination level, and the lubricant and relubrication interval. For a rotary type, confirm the gear and bearing arrangement matches the drive.

One last dimension is often overlooked: manufacturer serviceability. Match the torque type, accuracy grade, and preload class across every brand you cross-quote so the comparison is like for like, and check local stock of spline shafts and nuts, lead time for cut-to-length shafts, the availability of replacement nuts that fit the same shaft, and field support for relubrication and alignment. THK, which originated the ball spline, holds the widest catalog (medium-torque LT and LF, high-torque LBS, LBF, LBR, LBH, caged-ball SLS and SLF, rotary LBG and LBGT) with diameters from about 4 to 150 mm; Nippon Bearing offers the SSP, SSPF, and rotary SPR and SPB families; and Thomson, Tsubaki, NSK, and IKO supply ball-spline shafting and related linear-motion components. For a long-running production axis, the maker that can deliver a matching replacement nut and a straight cut shaft on short notice often outweighs a small unit-price difference at purchase.