Bearing Torque Calculation for Constant-Section Bearings: What Changes After Mounting?

Introduction

Why does a constant-section bearing rotate smoothly before installation but require noticeably more torque after mounting?

This is a common engineering concern in precision rotary tables, robotic joints, semiconductor equipment, medical devices, and compact motion-control systems.

Constant-section bearings, often categorized as thin-section bearings, maintain a fixed radial cross-section across a range of bore diameters within the same dimensional series. Their compact design helps reduce weight and installation space. However, their relatively thin rings also make them sensitive to mounting conditions.

Even when the bearing itself has been manufactured correctly, changes in shaft interference, housing geometry, preload, lubrication, or operating temperature can significantly influence its installed friction torque.

According to the technical guidance published by Kaydon Bearings, an SKF Group brand, thin-section bearings are particularly sensitive to shaft and housing fits because their rings can conform to the geometry of surrounding components. Improper mounting can increase friction, alter internal clearance, and affect bearing performance.

This article explains how bearing torque is estimated, what changes after installation, how to measure actual running torque, and what application information should be provided when requesting a bearing quotation.

Understanding the Three Different Types of Torque

Before performing any calculation, engineers must distinguish between three quantities that are frequently confused: bearing friction torque, motor output torque, and overturning moment.

Although all three can be expressed in newton-meters (N·m), they describe different physical effects.

Bearing Friction Torque

Bearing friction torque is the rotational resistance generated inside a bearing during motion.

It results from rolling and sliding contact, lubricant shear, seal friction, and other internal resistance mechanisms.

Bearing friction torque directly affects:

• Motor power consumption

• Starting and running resistance

• Heat generation

• Positioning accuracy and motion stability

• Low-speed control performance

• Overall system efficiency

For precision constant-section bearings, friction torque may be an important selection criterion, especially when the application requires smooth movement or a low-torque drive system.

Motor Output Torque

Motor output torque is the torque delivered by a motor or actuator to drive a mechanical system.

Unlike bearing friction torque, it must account for all relevant loads acting on the drivetrain.

For a direct-drive rotary system, a simplified torque balance is:

An overturning moment is not the same as friction torque. Instead, it changes the load distribution within the bearing, potentially influencing contact stress, deflection, and friction.

A four-point contact thin-section bearing may accommodate combinations of radial, axial, and moment loads, but its suitability must be verified against the manufacturer's application limits.

Comparison of the Three Torque-Related Quantities

These quantities should never be treated as interchangeable, even though they share the same unit.

How Is Friction Torque Calculated in a Constant-Section Bearing?

Bearing friction torque depends on more than applied load and bearing diameter.

A realistic estimate should consider contact mechanics, lubrication, seals, operating speed, and the installed internal condition.

SKF's Frictional Moment Model

SKF provides a detailed friction model that separates different sources of resistance within rolling bearings.

A published SKF formulation is:

This formulation illustrates why bearing torque cannot be predicted accurately from radial load alone. It also shows that the contribution of each mechanism changes with bearing design and operating conditions.

Engineering limitation: SKF's model is a manufacturer-specific engineering methodology. Its coefficients, bearing-specific parameters, and calculated results should not be transferred directly to LILY bearings without validation. The equation is presented here to explain the physical sources of friction, not as a published LILY torque calculation or test result.

Rolling Friction

Rolling friction is associated with the rolling elements moving through loaded contacts and the deformation and lubrication behavior of those contacts.

Its magnitude depends on:

• Bearing geometry and ball diameter

• Contact angle

• Internal load distribution

• Radial and axial loads

• Preload

• Lubricant properties

• Operating speed and temperature

Increasing the effective load on the rolling elements generally increases rolling resistance, although the overall torque response can be more complex.

Sliding Friction

Sliding friction can arise from relative sliding within rolling contacts and between rolling elements and cage surfaces.

The amount of sliding depends on the bearing's internal geometry, contact conditions, operating load, and speed.

For applications requiring exceptionally low running torque, bearing configuration and internal contact conditions deserve particular attention.

Seal Friction

Contact seals can introduce additional rotational resistance.

Seal friction depends on factors such as lip geometry, contact pressure, material, temperature, lubrication, and speed.

Non-contact shields or labyrinth arrangements can reduce direct seal-contact resistance, although their contamination protection and lubricant-retention characteristics differ from those of contact seals.

A bearing with contact seals should not be assumed to have the same running torque as an otherwise comparable open bearing.

Lubricant-Related Drag

Lubricant-related losses can result from fluid shear, churning, and other lubricant movement.

Relevant parameters include:

• Base oil viscosity

• Grease formulation

• Grease fill quantity

• Lubrication method

• Operating temperature

• Rotational speed

• Internal bearing geometry

The friction behavior of grease-lubricated bearings may also change during initial running as the grease redistributes.

For this reason, starting torque, initial running torque, and stabilized running torque should be evaluated separately when the application requires tight torque control.

Why Does Bearing Torque Change After Mounting?

A constant-section bearing may exhibit low friction when tested as an individual component but develop greater rotational resistance after installation.

This difference is not necessarily evidence of a defective bearing.

Mounting changes the mechanical boundary conditions surrounding the bearing. In particular, it can alter ring geometry, internal clearance, preload, alignment, and load distribution.

The following factors should be investigated.

Shaft and Housing Fits

One of the most important factors is the fit between the bearing rings and their mating components.

An interference fit can deform a thin bearing ring and reduce internal radial clearance.

If the clearance reduction is excessive, the bearing may develop unintended preload, increasing friction torque.

Conversely, excessive clearance between a bearing ring and its mounting surface may permit movement, creep, or unstable support.

Because constant-section bearings have relatively flexible rings, their mounting requirements can differ from those of conventional deep groove ball bearings.

Kaydon specifically emphasizes the importance of selecting appropriate shaft and housing fits to prevent thin-section bearings from becoming radially tight after installation.

The appropriate fit depends on bearing design, rotating-ring arrangement, load direction, mounting materials, temperature, and the manufacturer's dimensional recommendations.

Shaft and Housing Roundness

Thin-section bearing rings can conform to the shape of the shaft or housing.

If the shaft is out of round or the housing bore is distorted, the installed bearing may no longer maintain its intended raceway geometry.

Potential consequences include:

• Uneven rolling-element loading

• Localized increases in contact stress

• Higher and more variable friction torque

• Increased vibration

• Reduced rotational accuracy

Housing distortion can also result from uneven clamping, insufficient structural stiffness, or machining inaccuracies.

Kaydon's mounting guidance highlights shaft and housing roundness, as well as bearing-seat flatness, as critical installation parameters.

Preload

Preload is an intentionally applied internal load that reduces or eliminates clearance and increases bearing stiffness.

In precision applications, preload may improve positional stability and reduce unwanted movement.

However, preload also increases the load carried by rolling-element contacts.

Consequently, higher preload generally results in higher friction torque.

This creates an important design trade-off:

Higher preload can improve stiffness, but it can also increase friction, heat generation, and motor torque requirements.

For torque-sensitive applications, preload should be selected according to the required stiffness and operating loads rather than maximized unnecessarily.

Kaydon's technical guidance confirms this relationship between preload, stiffness, and friction torque.

Operating Temperature and Thermal Expansion

Temperature can change both bearing internal geometry and lubricant behavior.

The effect is particularly important when the shaft and housing are manufactured from materials with different coefficients of thermal expansion.

For example, an aluminum housing and steel bearing rings may expand at different rates.

This can change the effective fit and internal clearance during operation.

A simplified thermal expansion relationship is:

This equation describes free thermal expansion. It does not independently predict installed bearing clearance because constrained components and temperature gradients must also be considered.

Temperature additionally changes lubricant viscosity, which can alter rolling, sliding, and lubricant-related resistance.

Therefore, a torque value measured at room temperature may not represent the bearing's performance at its actual operating temperature.

Lubrication Conditions

Two identical bearings can exhibit different friction torque when different lubricants or fill quantities are used.

Grease-lubricated bearings may exhibit elevated initial resistance, particularly when excess grease must redistribute during early operation.

Oil lubrication also influences torque through viscosity, film formation, and fluid drag.

SKF explains that friction varies with speed and lubrication regime, including boundary lubrication, mixed lubrication, and full-film lubrication.

For meaningful torque comparisons, the lubricant type, viscosity, quantity, and conditioning history must be controlled.

Seals and External Contact

Seals can be a significant source of resistance in low-torque bearing assemblies.

The total torque of an installed system may include both integral bearing seal friction and external sealing components.

Engineers should distinguish between these contributions to avoid double-counting or incorrectly attributing external resistance to the bearing.

Clamping Force and Mounting Alignment

Improper tightening procedures can distort the bearing support structure.

For thin-section bearings, uneven clamping may produce nonuniform ring deformation and changes in internal loading.

Recommended installation practices include using properly designed face clamps, controlling mounting-surface geometry, and tightening fasteners evenly.

Kaydon recommends a star-pattern tightening sequence to distribute clamping force more uniformly.

How Do Bearing Type and Contact Configuration Affect Torque?

Constant-section bearings are available in different internal contact configurations.

The appropriate configuration depends on the direction and magnitude of the application loads.

Radial Contact Bearings — Type C

Primarily intended for radial loading. Depending on the design and internal clearance, they may also accommodate limited axial loading. Torque depends on the actual load and mounting condition.

Angular Contact Bearings — Type A

Designed to accommodate combined loading with axial load in one direction per bearing. Often installed in matched or opposed pairs, where preload and arrangement influence torque.

Four-Point Contact Bearings — Type X

Can support combinations of radial, bidirectional axial, and overturning moment loads. Their contact behavior and friction characteristics differ from those of radial or angular contact designs.

The selection of a contact configuration should be based on the complete application load case, not friction torque alone.

Kaydon notes that four-point contact bearings generally exhibit higher friction than comparable radial or angular contact configurations under relevant conditions. However, this is not a universal numerical comparison and should not be used to predict a specific LILY bearing's torque.

What Information Is Required to Estimate Bearing Torque?

A meaningful torque estimate requires accurate operating information.

The following table summarizes the most important engineering inputs.

Incomplete inputs can lead to an estimate that does not represent the installed bearing.

For example, a calculated torque value based on nominal radial load and speed cannot fully represent an application with significant overturning moment, uncontrolled mounting distortion, and temperature-dependent preload.

A Practical Step-by-Step Bearing Torque Estimation Method

For preliminary engineering work, the following process provides a structured approach.

Step 1: Identify the Bearing Geometry and Contact Type

Record the bearing dimensions and internal configuration.

The bearing's contact geometry determines how applied loads are distributed among rolling elements.

For paired angular contact bearings, include the arrangement, bearing spacing, and preload method.

Step 2: Establish the Complete Load Case

Determine the radial load, axial load, and overturning moment acting on the bearing assembly.

Where possible, provide the actual force vectors and their points of application.

The most demanding torque condition may not correspond to the highest radial load alone.

Step 3: Determine the Installed Internal Condition

Review the nominal bearing clearance or preload together with the shaft and housing fits.

Consider ring deformation, clamping, and thermal expansion.

The installed internal condition may differ substantially from the bearing's free-state condition.

Step 4: Define Lubrication and Operating Speed

Specify the actual lubricant and operating viscosity.

Use the intended operating speed and temperature, not only catalog maximum values.

Where applicable, calculate multiple operating points to capture low-speed and high-speed behavior.

Step 5: Estimate the Friction Contributions

Use a bearing-specific, validated friction model where available.

As an engineering accounting framework:

This simplified expression identifies the main resistance mechanisms. It is not a substitute for a validated model with the appropriate contact mechanics and operating corrections.

SKF's detailed methodology can be used to understand the structure of a friction model, but SKF-specific coefficients must not be presented as LILY product data.

Step 6: Calculate Power Loss

Once the friction torque has been estimated, rotational power loss can be calculated:

This means that approximately 6.28 W of mechanical power is dissipated through the modeled rotational resistance.

This is an illustrative calculation only. The 0.20 N·m torque value is assumed and is not a measured or guaranteed value for any LILY bearing.

Step 7: Review the Estimate With the Supplier

Before using the estimated value for final motor selection or acceptance criteria, request a technical review from the bearing supplier.

The supplier should confirm whether the proposed bearing configuration and installation conditions are suitable for the application.

How Can Bearing Torque Be Measured After Mounting?

The most reliable way to determine installed friction torque is to measure it under controlled, representative operating conditions.

However, the test method must be selected carefully.

Starting Torque Measurement

Starting torque describes the torque required to initiate rotation from rest.

A suitable test setup may use a calibrated torque transducer or a controlled force applied at a known radius.

When using a tangential force measurement:

For accurate results, the measurement must exclude or separately account for fixture resistance and other external loads.

Starting torque should be recorded under a defined temperature, rest period, lubrication condition, and direction of rotation.

The peak breakaway value should not be confused with stabilized running torque.

Running Torque Measurement

Running torque is measured while the bearing rotates at a defined speed.

A typical test arrangement includes:

• A controlled drive source

• A calibrated torque transducer

• A representative bearing mounting fixture

• A defined radial and axial loading arrangement

• Temperature monitoring

• Speed measurement and data acquisition

The measured torque may fluctuate during rotation.

Therefore, useful reporting parameters include mean torque, maximum torque, minimum torque, and torque variation over a defined interval.

Free-State Versus Installed Torque Testing

To identify the effect of mounting, compare the bearing under two conditions.

A free-state test still requires a controlled fixture that supports the bearing without introducing uncontrolled deformation or parasitic resistance.

To isolate the effect of mounting, other test variables should remain consistent.

Recommended Test Sequence

A controlled test plan should also define rotational direction, acceleration, dwell time, running-in procedure, sampling rate, and whether the reported torque is a peak or average value.

Motor current alone is generally insufficient to establish bearing friction torque unless the motor and drivetrain have been appropriately calibrated and other losses accounted for.

Why Can Starting Torque and Running Torque Be Different?

Starting torque and running torque describe different operating states.

At rest, lubricant distribution and contact conditions differ from those during continuous rotation.

Once rotation begins, lubricant films develop and grease may redistribute.

As a result, torque can vary during the transition from rest to steady operation.

The SKF friction model discusses different lubrication regimes and their relationship with rotational speed and viscosity. It also specifies conditions under which its reference calculations are applicable.

For grease lubrication, the cited SKF document identifies steady-state operating conditions as an important assumption.

Therefore, a steady-state model should not automatically be used to predict cold-start torque or initial grease churning.

For applications such as robotic joints and precision positioning systems, engineers should consider:

• Breakaway torque after a defined rest period

• Running torque at minimum operating speed

• Running torque at rated speed

• Peak torque during acceleration

• Torque after thermal stabilization

• Torque variation during reversal or oscillation

A single torque value may not adequately characterize the bearing's performance.

Troubleshooting Excessive Torque After Installation

When installed torque exceeds expectations, engineers should investigate the system systematically rather than immediately replacing the bearing.

These are diagnostic possibilities, not definitive fault diagnoses.

For thin-section bearings, shaft and housing geometry should be checked early because ring deformation can strongly affect installed behavior.

What Should Be Verified With the Bearing Supplier?

An engineering estimate is useful for initial selection, but it should not be treated as a guaranteed installed torque value.

The most effective approach is to verify the application in a defined sequence.

• First: Confirm bearing suitability.

  Verify the bearing dimensions, contact type, load capacity, speed capability, and basic application compatibility.

• Second: Review the installed internal condition.

  Confirm shaft and housing fits, materials, operating temperatures, internal clearance, preload, and mounting geometry.

• Third: Review the preliminary torque estimate.

  Identify the calculation methodology, assumptions, missing inputs, and expected uncertainty.

• Fourth: Define a representative test method.

  Agree on the measurement equipment, test fixture, operating conditions, and reporting requirements.

• Finally: Establish acceptance criteria.

  Determine whether maximum starting torque, average running torque, torque ripple, or another measurable characteristic is required.

Where a guaranteed torque limit is necessary, the supplier and customer should agree on the acceptance method before placing the order.

This is particularly important for customized bearings and applications with strict motion-control requirements.

Frequently Asked Questions About Constant-Section Bearing Torque

Q1. Why does a constant-section bearing become harder to rotate after installation?

The most common areas to investigate are shaft and housing fits, mounting distortion, unintended preload, and changes in alignment. Because constant-section bearings have thin rings, their internal geometry can be sensitive to the surrounding structure.

Q2. Can bearing friction torque be calculated using only radial load and rotational speed?

Not reliably for a precision application. Lubrication, seals, bearing geometry, axial load, preload, temperature, and mounting conditions can all affect torque. A simplified calculation may be useful for initial screening but should not be treated as an installed-torque guarantee.

Q3. Does increasing preload always increase bearing friction torque?

Increasing preload generally increases contact loading and friction torque, but the exact relationship depends on bearing geometry, lubrication, temperature, and operating conditions. Preload must be optimized together with stiffness and life requirements.

Q4. Is overturning moment the same as bearing friction torque?

No. Overturning moment is an external load that tends to tilt the bearing assembly. Bearing friction torque is the resistance to rotation. Overturning moment can indirectly influence friction by changing internal load distribution.

Q5. Can SKF bearing friction coefficients be used for LILY bearings?

SKF's published models can be studied as professional engineering references, but manufacturer-specific coefficients and results should not be assumed to apply to LILY bearings. Product-specific calculations require appropriate design information and validation.

Q6. Should bearing torque be measured before or after mounting?

Both measurements can be valuable. A controlled pre-installation measurement provides a baseline, while installed testing evaluates the effects of fits, preload, clamping, and the surrounding structure. For critical applications, testing under representative loads and temperatures is recommended.

Q7. How can engineers reduce excessive installed bearing torque?

Possible measures include correcting shaft and housing geometry, reviewing fits, optimizing preload, selecting suitable lubrication, and avoiding unnecessary seal contact resistance. Changes should be reviewed against bearing life, stiffness, accuracy, and contamination-protection requirements.

Q8. What is the best way to specify a low-torque constant-section bearing?

Define a measurable torque requirement together with the exact operating and test conditions. For example, specify the maximum permissible running torque at a particular speed, temperature, load, lubrication condition, and installed preload.

A torque limit without defined test conditions is difficult to verify consistently.

Conclusion: Installed Torque Matters More Than Free-State Torque Alone

Bearing torque calculation for constant-section bearings requires more than selecting a coefficient and multiplying it by an applied load.

The installed friction torque depends on bearing geometry, load distribution, lubrication, seals, preload, operating temperature, and the mechanical conditions imposed by the shaft and housing.

Because constant-section bearings have relatively thin rings, installation quality can have a substantial influence on their rotational behavior.

For reliable engineering results, the recommended approach is to:

1. Distinguish bearing friction torque from motor output torque and overturning moment.

2. Establish the complete operating load and speed conditions.

3. Evaluate the effects of mounting fits, preload, temperature, lubrication, and sealing.

4. Use a suitable bearing-specific calculation method for preliminary estimation.

5. Measure starting and running torque under controlled, representative conditions.

6. Confirm application suitability and acceptance criteria with the bearing supplier.

For engineers selecting constant-section bearings for robotics, precision machinery, automation, or other demanding applications, the key question is not simply how much torque the bearing generates before mounting, but how much rotational resistance the complete assembly will exhibit under actual operating conditions.

Request Technical Support From LILY Bearing

Selecting the appropriate constant-section bearing requires balancing load capacity, stiffness, rotational accuracy, friction torque, and installation requirements.

LILY Bearing can be contacted to discuss bearing selection and application requirements. When requesting a quotation, provide the bearing dimensions, load conditions, operating speed, mounting details, lubrication requirements, and target torque limits.

A complete technical inquiry helps establish which bearing configurations and verification requirements should be reviewed before final selection.