Bearing Preload and Axial Play Calculator

Q: What is residual clearance and why does it matter?

It is the radial internal clearance a bearing actually has once it is mounted and up to temperature, and it matters because it can be negative. Three terms: the clearance class it came with, minus the clearance the interference fit eats as the inner ring expands on the shaft (about eighty per cent of the effective interference), minus the clearance the temperature difference between the rings eats (α·ΔT·D_e). If the answer is negative the bearing is preloaded, which means contact stress and heat before any external load arrives.

Q: How much clearance does a temperature difference cost?

About α·ΔT·D_e, which is roughly 0.9 micrometres per degree on a 40 × 80 mm bearing and about 2.2 on a 100 × 180 mm one. Ten degrees of difference between the rings therefore eats between half and four-fifths of the whole width of a CN clearance band at any size from 20 to 100 mm. Note that it is the DIFFERENCE between the rings that costs clearance, not the operating temperature — a bearing uniformly hot loses nothing, because all three parts grow together.

Q: Is C3 clearance a heavy-duty upgrade?

No. C3 is the normal clearance class for an interference fit or a hot inner ring, and it is normal because the arithmetic makes it so: an ordinary interference fit plus an ordinary ten-degree difference between the rings puts a CN bearing into preload at both ends of its band. Electric motors, fans and pumps handling warm product are C3 applications as a matter of course. The suffix costs nothing and the bearing is otherwise identical. Treating CN as the good one and C3 as heavy duty is the commonest way this calculation goes wrong.

Q: Why does the thermal formula use the OUTER raceway diameter when the INNER ring is the hot one?

Because the clearance loses the inner ring's growth and the rolling elements' growth together, and those add up to exactly the outer raceway diameter. Radial clearance is D_o − d_i − 2·B_d; warm the inner ring and the balls by ΔT and the loss is α·ΔT·(d_i + 2·B_d), and d_i + 2·B_d = D_o identically. So the published formula is right and it only looks wrong. The assumption inside it is that the rolling elements are at the inner ring's temperature, which is reasonable because they roll on it.

Q: Back-to-back or face-to-face?

Back-to-back (DB, O) if there is moment load or the shaft will grow axially; face-to-face (DF, X) if the two seats may be out of square. The mechanism is where the two load lines meet: back-to-back diverges them outside the pair, giving a longer effective spread between the pressure centres, which takes tilting moments better and tolerates misalignment worse. Face-to-face is the reverse. And the temperature behaviour differs: axial growth increases a face-to-face preload directly, while in a back-to-back pair the radial and axial effects can cancel.

Q: Does a rigid preload always increase with temperature?

No, and the flat version of that claim is wrong. In a face-to-face pair it does: the shaft grows, the inner rings are pushed together, the preload rises, and the extra heat causes more growth, so it can run away. In a back-to-back pair SKF's own preload publication says the radial and axial expansions can cancel so that the preload is independent of operating temperature. That needs the spacing and materials to suit, so treat it as something to design for rather than assume. A spring preload genuinely is temperature-independent, because the spring takes up the movement at constant force.

Q: Can I just fit a looser class and forget about it?

Not quite, because too much clearance has its own costs. A bearing with a large residual clearance carries its load on fewer rolling elements — the load zone shrinks towards the bottom of the bearing — so the contact stress on those elements rises and the effective capacity falls. It is also noisier, it allows more shaft runout, and at speed the unloaded elements can skid through the unloaded arc. The aim is a small positive residual clearance at the tight corner of the stack, not the largest class that fits.

Residual radial clearance after mounting: the clearance class, less what the interference fit eats, less what the temperature difference between the rings eats — with the back-to-back against face-to-face comparison that decides what a preload does when it warms.

Last updated 24 Sep 2026

Bearing residual clearance and preload

Class, fit, ΔT → residual clearance

Bearing bore d (mm)

Bearing outside diameter D (mm)Needed for the thermal term, which uses the OUTER raceway diameter and not the bore — see the note below the formula, because that looks like a misprint and is not.

Radial internal clearance classISO 5753 groups. CN is normal; C3 is what you specify for an interference fit or a hot inner ring, and it is not an upgrade. The values come from SKF’s and NTN’s published tables, which agreed exactly.

Interference on the shaft seat (µm)The measured (apparent) interference. Get it from the bearing fits page, which computes it from the shaft class and the bearing’s own bore tolerance. Use the mean for a probable answer and the maximum for a worst case.

Shaft seat finishRoughness flattens on assembly, so the effective interference is d/(d+2) of the measured one for a ground seat and d/(d+3) for a turned one.

Inner ring hotter than the outer by (°C)The TEMPERATURE DIFFERENCE between the rings, not the operating temperature. 5 to 10 °C is typical for a bearing cooled through its housing; 15 to 20 °C where the shaft brings heat in from a coupling, a hot product or a motor rotor.

Bearing typeOnly changes the estimate of the outer raceway diameter the thermal term uses. A roller bearing’s raceway sits closer to the mean diameter than a ball bearing’s.

Arrangement, if this is a preloaded pairChanges none of the numbers above — it selects the guidance below, because what happens to a preload as the machine warms up depends entirely on which of these three it is.

Not a circuit: the clearance budget as three bars down to a residual, all at the same scale of eighty micrometres across. The top bar is what the bearing came with — the maximum of its clearance class. The second is how much of it the interference fit takes, because the inner ring expands with the shaft. The third is how much the temperature DIFFERENCE between the rings takes, which is α·ΔT·D_e and is usually the one nobody budgeted for. The fourth bar is what is left at the TIGHT end of the clearance class, and when it reaches zero it keeps going: the block below the axis is negative clearance, which is preload. Each bar is built from twenty or forty narrow tiles rather than one rectangle, because a wire in this renderer is stroked and never filled, so a single rectangle would read as an outline rather than as a length. Watch the third bar as you raise the temperature difference: on a 40 × 80 mm bearing it grows by about 0.9 micrometres per degree, so ten degrees eats as much as a whole clearance class is wide.

-9.24µmExample

A 40 × 80 mm C3 ball bearing with 20 µm of interference on a ground shaft seat, running with the inner ring 10 °C hotter than the outer

Residual clearance: what you started with, less the fit, less the temperature

G_residual = G_initial − δ_fit − δ_thermal · δ_fit ≈ 0.80·Δd_a·d/(d+2) · δ_thermal = α·ΔT·D_e · D_e = (4D+d)/5 (ball), (3D+d)/4 (roller) · α = 12.5 × 10⁻⁶/°C

G_initial: the bearing’s radial internal clearance before mounting, a RANGE from its ISO 5753 class (C2, CN, C3, C4, C5). Mounting shifts the range; it does not narrow it
δ_fit: clearance lost because the inner ring expands with the shaft. About 80 per cent of the effective interference, and the effective interference is the measured one less two micrometres of roughness for a ground seat
δ_thermal: clearance lost to the temperature DIFFERENCE between the rings — not to the operating temperature. About 0.9 µm per degree on a 40/80 bearing
D_e: the OUTER raceway diameter, which is what the thermal term uses even though the inner ring is the hot one. Because the clearance loses the inner ring’s growth AND twice the rolling elements’ growth, and those add to exactly D_e
G_residual < 0: preload. Not a clearance at all: the rolling elements are squeezed, the contact stress is there before any load is applied, and the bearing generates heat that makes it worse

Worked example

A 40 × 80 mm C3 ball bearing with 20 µm of interference on a ground shaft seat, running with the inner ring 10 °C hotter than the outer
Start with what the bearing has to spend. A C3 bearing at a 40 mm bore has a radial internal clearance of 15 to 33 µm before it is mounted. That is a class, not a number, and the width of the band is the bearing maker's tolerance — mounting shifts the band but does not narrow it
TERM ONE, the fit. The measured 20 µm of interference becomes 20 × 40/42 = 19.05 µm effective once the seat roughness has flattened, and the inner ring's expansion removes about 0.80 of that from the internal clearance: 15.24 µm. NSK gives the range as 70 to 90 per cent, which here is 13.3 to 17.1 µm, and both bounds are printed above
TERM TWO, the temperature difference, and this is the one nobody budgets for. The clearance falls by α·ΔT·D_e, where D_e is the outer raceway diameter — estimated as (4D+d)/5 = 72 mm for a ball bearing. So 12.5 × 10⁻⁶ × 10 × 72 = 9.0 µm. Ten degrees. Nine micrometres. That is more than the whole minimum clearance of a CN bearing at this size
Why the OUTER raceway diameter, when it is the INNER ring that is hot? Because the radial clearance is the outer raceway diameter less the inner raceway diameter less twice the ball diameter, and warming the inner ring and the balls together by ΔT loses α·ΔT·(d_i + 2B_d) — and d_i + 2B_d IS the outer raceway diameter, identically. The published formula is right and it looks wrong
Add them up: 15.2 + 9.0 = 24.2 µm of clearance gone, of which 63 per cent is the fit and 37 per cent is the temperature. Residual clearance runs from -9.2 µm at the tight end of the C3 band to 8.8 µm at the loose end
So at the tight end this bearing is PRELOADED — negative clearance, contact stress before any load is applied, and heat generated by it. Not necessarily fatal at 9 micrometres, but not intended either, and it will run warmer than the calculation upstream assumed. The same mounting with CN clearance would be preloaded at BOTH ends of the band (-18.2 to -4.2 µm), which is exactly why C3 is the normal choice for an interference fit and not an upgrade
The two break-even questions the page answers. At this interference the temperature difference that would just close the minimum clearance is -0.3 °C — which is below zero, confirming the fit alone has already done it. And at this temperature difference the interference that would just close it is 7.9 µm, against the 20 µm you have. Those two numbers are how you decide whether to loosen the fit or loosen the class

Internal clearance classes at a 40 mm bore, and what each is for

The last column is the page’s whole argument in one place: with a very ordinary 20 micrometres of interference and a very ordinary ten degrees of difference between the rings, C2 and CN are preloaded at the tight end of their bands and C3 is marginal. Note that the classes are not evenly spaced, and note what C3 actually is — the class for an interference fit or a hot inner ring, which describes most electric motors, most fans and most pumps. Calling it a heavy-duty option gets it exactly backwards: a bearing specified CN where the conditions want C3 is a bearing that will run hot. The published values are ISO 5753 groups, read from SKF’s table 3 and NTN’s table 8.8, which agreed at every bore step from 6 to 120 mm. These dimensions come from a published standard’s table, not from a formula. The standard itself is cited below and the printed values are attributed to the catalogue they were taken from; a different publisher may round differently in the last digit. This page sizes a part; it does not certify one. Where the answer carries a consequence — a load path, a lifting duty, a pressure boundary, a fastener holding something that can fall — confirm it against the design code that governs the application, and against the manufacturer’s own rating, before relying on it.
Class	Clearance (µm)	As % of CN’s maximum	What it is for	Residual after 20 µm fit and 10 °C (µm)
C2	1–11	55%	Reduced. Where running accuracy and quiet running matter more than heat: light loads, small temperature differences, precision spindles. Unforgiving of a tight fit	-23.2
CN (CN, normal)	6–20	100%	Normal. The default, and correct for a point load on the inner ring, a light interference fit and rings at much the same temperature	-18.2
C3	15–33	165%	NOT an upgrade — the normal choice for an interference fit, a hot inner ring, or both. Electric motors, fans, pumps with hot product, anything driven through a hot coupling	-9.2
C4	28–46	230%	Heavy interference fit, large temperature difference, or a shaft that misaligns. Also where the housing squeezes the outer ring	3.8
C5	40–64	320%	Very large temperature differences and very heavy fits. Kiln trunnions, hot fans, rolls	15.8

The term that surprises people: clearance lost per 10 °C between the rings

Ten degrees of difference between the inner and the outer ring eats between fifty and eighty per cent of the ENTIRE width of the CN clearance band, at every size in the table. Nobody expects that, and it is the reason a bearing arrangement that works on a cold test rig runs hot in service. The mechanism is worth understanding because the published formula looks wrong: the loss is α·ΔT·D_e where D_e is the OUTER raceway diameter, even though it is the INNER ring that is hot. The reason is that the radial clearance is the outer raceway diameter less the inner raceway diameter less twice the rolling element diameter — and warming the inner ring AND the rolling elements by ΔT loses α·ΔT·(d_i + 2·B_d), and d_i + 2·B_d is exactly D_e. The two empirical estimates (4D+d)/5 for a ball bearing and (3D+d)/4 for a roller bearing reproduce the real outer raceway diameter of a published bearing geometry to better than half a per cent. For a fit whose two parts are different materials and both change temperature, see the thermal effect on fit calculator. These dimensions come from a published standard’s table, not from a formula. The standard itself is cited below and the printed values are attributed to the catalogue they were taken from; a different publisher may round differently in the last digit.
Bearing	D_e (mm)	Lost per 10 °C (µm)	CN clearance (µm)	As % of CN’s whole band	°C to eat the whole band
20 × 47	41.6	5.20	5–20	35%	28.8
30 × 62	55.6	6.95	5–20	46%	21.6
40 × 80	72.0	9.00	6–20	64%	15.6
60 × 110	100.0	12.50	8–28	63%	16.0
80 × 140	128.0	16.00	10–30	80%	12.5
100 × 180	164.0	20.50	12–36	85%	11.7

Back-to-back against face-to-face: what actually differs

The flat claim that a rigid preload always rises with temperature and runs away is wrong, and this table is why it is worth getting right. In a face-to-face pair, axial growth of the shaft relative to the housing pushes the two inner rings together and the preload rises — and because a rising preload generates more heat, which causes more growth, it can run away. In a back-to-back pair the axial growth pulls the inner rings apart while the radial growth of the inner rings pushes the contacts together, and SKF’s publication says those two effects can cancel so that the preload is independent of temperature. That is a design condition rather than a guarantee — it needs the spacing and the materials to suit — but the direction is not automatic and the arrangement decides it. A SPRING preload sidesteps the question entirely: the force is set by the spring rate and stays put, which is why a lightly loaded motor bearing that must never lose contact gets a wavy washer rather than a ground spacer. This page sizes a part; it does not certify one. Where the answer carries a consequence — a load path, a lifting duty, a pressure boundary, a fastener holding something that can fall — confirm it against the design code that governs the application, and against the manufacturer’s own rating, before relying on it.
	Back-to-back (DB, O arrangement)	Face-to-face (DF, X arrangement)
Where the load lines meet	Outside the bearing pair, so the effective spread between the pressure centres is LONGER than the physical distance between the bearings	Inside the pair, so the effective spread is SHORTER than the physical distance
Moment (tilting) load	Better, and that is the main reason to choose it. SKF: back-to-back bearings “can accommodate relatively large tilting moments even if the distance between the bearing centres is relatively short”	Worse, for the same reason reversed. Avoid where there is significant overhung load
Misalignment of the two seats	Less tolerant: a longer effective spread means a given angular error produces a larger relative displacement at the contacts	More tolerant, which is why it is used where the two seats are made separately or the housing is less rigid
Shaft growing axially relative to the housing	Tolerated. SKF’s own finding, and the one that upsets the usual summary: radial and axial thermal expansion “can cancel each other out so that preload remains unchanged … independent of operating temperature”	NOT tolerated. Axial expansion INCREASES the preload directly. GlobalSpec: face-to-face “should be avoided in applications … prone to shaft thermal expansion”
Setting the preload	By grinding the spacer or the ring faces, or by buying a matched set with the preload built in	Same, and the same sensitivity — a micrometre of spacer is a real change in preload

Three terms down to a residual, and what a preload does when the machine warms up

Residual clearance is what you started with, less the fit, less the temperature — and the temperature term is the one nobody budgets for. A bearing’s radial internal clearance is a CLASS, a range: C3 at a 40 mm bore is 15 to 33 micrometres. Mounting shifts that range down twice. The interference fit expands the inner ring and removes about eighty per cent of the effective interference. Then the temperature difference between the rings removes α·ΔT·D_e, which for a 40 × 80 mm bearing is about 0.9 micrometres per degree. Ten degrees of difference between the inner and outer rings therefore eats nine micrometres — more than the entire minimum clearance of a CN bearing at that size, and between half and four-fifths of the whole width of the CN band at every bore size from 20 to 100 mm.

The thermal formula looks like a misprint and is not. Every catalogue prints δ = α·ΔT·D_e with D_e the OUTER raceway diameter, for a temperature difference driven by the INNER ring. The reason falls out of the geometry once you write the clearance down: it is the outer raceway diameter, less the inner raceway diameter, less twice the rolling element diameter. Warm the inner ring AND the rolling elements by ΔT and you lose α·ΔT·(d_i + 2·B_d) — and d_i + 2·B_d is exactly D_e. So the outer raceway diameter is the right length to use, and the assumption buried in it is that the rolling elements are at the inner ring’s temperature. The empirical estimates (4D+d)/5 for a ball bearing and (3D+d)/4 for a roller bearing reproduce the real outer raceway diameter of a published bearing geometry to better than half a per cent.

C3 is not an upgrade. It is the class for an interference fit or a hot inner ring. Which between them describe most electric motors, most fans, most pumps handling warm product and anything driven through a hot coupling. Treating the clearance class as a quality grade — CN as the good one, C3 as heavy duty — is the commonest way this calculation goes wrong, and the arithmetic on this page shows why: an ordinary 20 micrometres of interference and an ordinary ten degrees of difference put a CN bearing into preload at BOTH ends of its band. The suffix costs nothing. The opposite error exists too: too much clearance shrinks the load zone to a few rolling elements and raises the contact stress on those, so C5 is not a safe default either.

Why an angular contact or taper pair is preloaded on purpose, and what DB against DF actually decides. A preload removes the axial play, makes the shaft’s position definite, and raises the stiffness — which is why a machine tool spindle has one. It also guarantees that every rolling element stays in contact, which matters at speed. The choice between back-to-back (DB, O) and face-to-face (DF, X) is about where the two load lines meet. Back-to-back diverges them outside the pair, so the effective spread between the pressure centres is longer than the physical distance between the bearings: better against moment load, less tolerant of the two seats being out of square. Face-to-face converges them inside: worse against moment load, more tolerant of misalignment.

And the temperature effect on a rigid preload depends on which of those two it is. The usual summary — a rigid preload rises with temperature and can run away — is right for a FACE-TO-FACE pair, where axial growth of the shaft pushes the inner rings together and increases the preload directly, with the heat that generates causing more growth. For a BACK-TO-BACK pair, SKF’s own preload publication says the radial and axial expansions “can cancel each other out so that preload remains unchanged … independent of operating temperature”. That is a design condition and not a guarantee, but it means the direction is not automatic and the arrangement decides it. A SPRING preload avoids the question altogether, because the force is set by the spring rate and the spring simply takes up the growth — at the cost of being axially soft, which defeats the purpose if the reason for the preload was stiffness.

Frequently asked questions

What is residual clearance and why does it matter?

It is the radial internal clearance a bearing actually has once it is mounted and up to temperature, and it matters because it can be negative. Three terms: the clearance class it came with, minus the clearance the interference fit eats as the inner ring expands on the shaft (about eighty per cent of the effective interference), minus the clearance the temperature difference between the rings eats (α·ΔT·D_e). If the answer is negative the bearing is preloaded, which means contact stress and heat before any external load arrives.

How much clearance does a temperature difference cost?

About α·ΔT·D_e, which is roughly 0.9 micrometres per degree on a 40 × 80 mm bearing and about 2.2 on a 100 × 180 mm one. Ten degrees of difference between the rings therefore eats between half and four-fifths of the whole width of a CN clearance band at any size from 20 to 100 mm. Note that it is the DIFFERENCE between the rings that costs clearance, not the operating temperature — a bearing uniformly hot loses nothing, because all three parts grow together.

Is C3 clearance a heavy-duty upgrade?

No. C3 is the normal clearance class for an interference fit or a hot inner ring, and it is normal because the arithmetic makes it so: an ordinary interference fit plus an ordinary ten-degree difference between the rings puts a CN bearing into preload at both ends of its band. Electric motors, fans and pumps handling warm product are C3 applications as a matter of course. The suffix costs nothing and the bearing is otherwise identical. Treating CN as the good one and C3 as heavy duty is the commonest way this calculation goes wrong.

Why does the thermal formula use the OUTER raceway diameter when the INNER ring is the hot one?

Because the clearance loses the inner ring’s growth and the rolling elements’ growth together, and those add up to exactly the outer raceway diameter. Radial clearance is D_o − d_i − 2·B_d; warm the inner ring and the balls by ΔT and the loss is α·ΔT·(d_i + 2·B_d), and d_i + 2·B_d = D_o identically. So the published formula is right and it only looks wrong. The assumption inside it is that the rolling elements are at the inner ring’s temperature, which is reasonable because they roll on it.

Back-to-back or face-to-face?

Back-to-back (DB, O) if there is moment load or the shaft will grow axially; face-to-face (DF, X) if the two seats may be out of square. The mechanism is where the two load lines meet: back-to-back diverges them outside the pair, giving a longer effective spread between the pressure centres, which takes tilting moments better and tolerates misalignment worse. Face-to-face is the reverse. And the temperature behaviour differs: axial growth increases a face-to-face preload directly, while in a back-to-back pair the radial and axial effects can cancel.

Does a rigid preload always increase with temperature?

No, and the flat version of that claim is wrong. In a face-to-face pair it does: the shaft grows, the inner rings are pushed together, the preload rises, and the extra heat causes more growth, so it can run away. In a back-to-back pair SKF’s own preload publication says the radial and axial expansions can cancel so that the preload is independent of operating temperature. That needs the spacing and materials to suit, so treat it as something to design for rather than assume. A spring preload genuinely is temperature-independent, because the spring takes up the movement at constant force.

Can I just fit a looser class and forget about it?

Not quite, because too much clearance has its own costs. A bearing with a large residual clearance carries its load on fewer rolling elements — the load zone shrinks towards the bottom of the bearing — so the contact stress on those elements rises and the effective capacity falls. It is also noisier, it allows more shaft runout, and at speed the unloaded elements can skid through the unloaded arc. The aim is a small positive residual clearance at the tight corner of the stack, not the largest class that fits.

Related calculators

References

ISO 5753-1, Rolling bearings — Internal clearance — Part 1: Radial internal clearance for radial bearings. Cited by number. The C2/CN/C3/C4/C5 clearance groups used here were read from SKF’s published table 3 for deep groove ball bearings and from NTN’s table 8.8 in its technical section on bearing internal clearance and preload; the two agreed exactly at every bore step from 6 to 120 mm, which is why the numbers are used.
SKF, Radial internal clearance of deep groove ball bearings (table 3 of the published deep groove ball bearing technical section). Used as the second, independent printing of the ISO 5753 clearance groups; it agreed with NTN’s table exactly over the range this page covers. Its rows above 250 mm contain one gap that NTN’s does not (C4 ending at 237 µm where C5 starts at 255), which is why this page stops at 120 mm rather than transcribing the whole column.
NTN, Ball and Roller Bearings, catalogue 2203-E, technical section 8, “Bearing internal clearance and preload”. The source for the radial internal clearance table (cross-checked against SKF’s), for the effective clearance relation Δ_e = Δ₀ − (δ_f + δ_t), and for the thermal term δ_t = α ΔT D_e with α = 12.5 × 10⁻⁶/°C.
NSK, Rolling Bearings catalogue E1102, section 9, “Fits and internal clearances”. The source for the effective-interference correction Δd = Δd_a d/(d+2) for a ground shaft and d/(d+3) for a machined one, for “the amount of this decrease is approximately 70 to 90 % of the interference”, for D_e = (4D+d)/5 for ball bearings and (3D+d)/4 for roller bearings, and for the recommended shaft and housing classes. NOTE: two readings of table 9.2 returned its condition headings SWAPPED — one put g6 under “rotating outer ring load” and the interference classes under the same heading in the other. Only the classes both readings agreed on are used here, the diameter steps are kept coarse, and the decision rule — which is the part that matters — is taken from Schaeffler’s own wording instead.
NSK, Internal clearance — types and norms, and the NSK bearing-doctor chapter “Fits and internal clearance”. The source for “generally, the decrease in radial clearance is calculated to be approximately 80 % of the interference”, which is the figure this site uses, and for the residual-clearance bookkeeping.
SKF, Bearing preload (published technical publication). The source for the back-to-back against face-to-face comparison in its own words: “the distance L between the pressure centres is longer when the bearings are arranged back-to-back compared with bearings arranged face-to-face”, and that back-to-back bearings “can accommodate relatively large tilting moments even if the distance between the bearing centres is relatively short”. It is ALSO the source for the finding that upsets the usual summary: in a back-to-back arrangement “thermal expansion in both the radial and axial directions can cancel each other out so that preload remains unchanged … independent of operating temperature”, while in a face-to-face arrangement axial expansion INCREASES preload. The direction of the temperature effect therefore depends on the arrangement, and a flat claim that a rigid preload always runs away with temperature is wrong.
GlobalSpec/Engineering360, Bearing preload: what is it and why is it important? The source for the rigid against spring preload comparison — a rigid preload varies with thermal expansion, while with a spring “the force applied by the spring is relatively constant throughout its compression” — and for the statement that a face-to-face arrangement “should be avoided in applications with high moment loading or that are prone to shaft thermal expansion”, which is the second source agreeing with SKF on the direction of the temperature effect.
ISO 15243:2017, Rolling bearings — Damage and failures — Terms, characteristics and causes. Cited by number. It is the document that gives the failure modes this batch keeps naming — surface-initiated and subsurface fatigue, smearing, fretting corrosion, false brinelling — their agreed names, which matters because a defect frequency identifies a LOCATION and not a cause.