The static performance of a ball screw is not represented by one catalog value. It describes how the ball screw and the complete feed system behave when they carry a stationary, slowly changing or peak axial load.
The main parameters are the basic static axial load rating Coa, the axial static stiffness K, and the axial clearance or preload condition. These parameters answer different engineering questions and should not be substituted for one another.
A complete static check must also include screw-shaft buckling, tensile or compressive stress, support-bearing capacity, nut-housing rigidity, mounting bolts and the deformation of the surrounding machine structure.
What Does "Static Performance" Include?
"Static performance" is a useful engineering description rather than one standardized catalog parameter. It normally covers the following characteristics.
| Parameter | What It Describes | Main Design Question |
|---|---|---|
| Basic static axial load rating Coa | Resistance of the balls and raceways to permanent contact deformation | Will the peak axial load damage the rolling-contact surfaces? |
| Axial static stiffness K | Relationship between axial force and elastic axial displacement | How far will the axis deflect under the working force? |
| Axial clearance | Free axial movement before the opposite contact side carries load | How much lost motion may occur during direction reversal? |
| Preload | Internal force applied to reduce clearance and increase contact stiffness | Is greater rigidity required at the cost of higher torque and heat? |
| System static capacity | Combined limit of the nut, screw shaft, support bearings, housing and mounting structure | Which component becomes the first static limit? |
What Is the Basic Static Axial Load Rating Coa?
The basic static axial load rating, written as Coa or C0a, is the axial load at which the combined permanent deformation of the steel balls and the ball-track surfaces at the most heavily loaded contact point reaches 0.0001 times the ball diameter.
Coa is therefore a reference contact-deformation rating. It is not the recommended working load, machine payload or load that should be applied repeatedly without a safety factor.
DLY SFU2010-3/2 has a model-specific static load rating and stiffness. These values should not be inferred only from its 20 mm diameter.
Calculate the Static Safety Factor
The basic static load rating should be compared with the maximum axial load using a static safety factor:
| Symbol | Meaning | Unit |
|---|---|---|
| fs | Static safety factor | No unit |
| Coa | Basic static axial load rating | N, kN or kgf |
| Fmax | Maximum axial load including gravity, acceleration, process force, impact and emergency conditions | Same unit as Coa |
The required safety factor depends on shock, vibration, load uncertainty, machine type and the consequence of permanent deformation.
The following values are useful initial references from a TBI-type ball screw selection system. They are not universal guaranteed limits for every DLY application.
| Application | Normal Operation | Impact or Vibration |
|---|---|---|
| Machine tool | 1.0–1.3 | 2.0–3.0 |
| Industrial machine | 1.0–1.5 | 2.5–7.0 |
Worked Example: DLY SFU2010-3/2
DLY SFU2010-3/2 has the following catalog values:
- Nominal diameter: 20 mm
- Lead: 10 mm
- Static load rating Coa: 1,680 kgf, approximately 16.48 kN
- Nut stiffness K: 20 kgf/μm
Assume the maximum calculated axial load, including acceleration and process force, is 400 kgf:
The ball-and-raceway contact check gives a static safety factor of 4.2. The designer must still verify screw buckling, shaft stress, support-bearing capacity and total elastic displacement.
How to Calculate Axial Static Stiffness
Axial static stiffness describes how strongly the ball screw resists elastic axial deformation:
- K = axial stiffness
- F = axial force
- δ = elastic axial displacement caused by the force
When the catalog stiffness is given in kgf/μm, the ideal elastic displacement can be estimated as:
Using the SFU2010 example, a 400 kgf axial force and a catalog nut stiffness of 20 kgf/μm give:
This 20 μm value represents an ideal estimate based on the catalog nut stiffness. It is not the total displacement of the machine axis.
Catalog Nut Stiffness Is Not Complete-System Stiffness
The axial load path passes through more than the ball nut. The screw shaft stretches or compresses, the support bearings deflect, and the nut housing and machine structure deform.
The stiffness of components connected in series can be estimated as:
Because the component compliances are added, the complete-system stiffness is always lower than the stiffness of the nut alone.
| Deformation Source | Main Influencing Factors | Possible Improvement |
|---|---|---|
| Screw-shaft deformation | Root diameter, effective shaft length, nut position and shaft material | Increase root diameter, reduce unsupported length or change support arrangement |
| Ball-and-raceway deformation | Ball diameter, loaded circuits, groove geometry and preload | Select a higher-stiffness nut structure or suitable preload |
| Support-bearing deformation | Bearing type, arrangement, preload and support-unit rigidity | Use an appropriate fixed-side bearing arrangement and confirm bearing preload |
| Nut-housing deformation | Housing material, wall thickness, flange contact and bolt layout | Increase housing rigidity and improve flange support |
| Machine-structure deformation | Base, table, brackets, bearing seats and mounting interfaces | Improve the load path and structural stiffness |
Screw-Shaft Elastic Deformation
For a uniform shaft section carrying axial tension or compression, a simplified elastic calculation is:
- L = effective loaded shaft length
- A = effective shaft cross-sectional area based on the root diameter
- E = elastic modulus of the shaft material
Shaft deformation changes with the nut position. On a long axis, the stiffness measured near the fixed support may differ significantly from the stiffness measured near the opposite end.
Preload Increases Stiffness but Does Not Automatically Increase Coa
Preload creates internal contact force to reduce axial clearance and increase stiffness during direction reversal.
It should not be assumed that a preloaded or double-nut ball screw has a higher basic static load rating than the corresponding single-nut version.
DLY's 16 mm SFU and DFU data illustrate the difference:
| Model | Nut Structure | Coa | Stiffness K | Main Difference |
|---|---|---|---|---|
| SFU1605-4 | Single nut | 1,790 kgf | 20 kgf/μm | Standard rigidity and normal axial-clearance configuration |
| DFU1605-4 | Preloaded double nut | 1,790 kgf | 43 kgf/μm | Higher rigidity and reduced reversal clearance |
In this comparison, the two structures have the same Coa but different stiffness. The double-nut preload improves rigidity and reversal behavior; it does not double the basic static load rating.
Excessive preload can also increase:
- Starting and running torque
- Heat generation
- Sensitivity to mounting misalignment
- Internal rolling-contact load
- Motor and support-bearing requirements
Diameter and Lead Do Not Determine Static Performance Alone
A larger nominal screw diameter often provides greater shaft area and may improve buckling resistance and axial stiffness. However, the nut's Coa and catalog stiffness also depend on ball diameter, groove geometry, contact angle, number of loaded circuits and nut structure.
| DLY Model | Diameter × Lead | Circuits | Coa | K |
|---|---|---|---|---|
| SFU1604-4 | 16 × 4 mm | 4 | 1,270 kgf | 35 kgf/μm |
| SFU1605-4 | 16 × 5 mm | 4 | 1,790 kgf | 20 kgf/μm |
| SFU2005-4 | 20 × 5 mm | 4 | 2,380 kgf | 25 kgf/μm |
| SFU2010-3/2 | 20 × 10 mm | 3 | 1,680 kgf | 20 kgf/μm |
These examples show why the complete model suffix and catalog values must be checked. A smaller lead does not automatically provide a higher Coa, and a higher Coa does not automatically provide the highest stiffness.
A 2510 designation defines the nominal diameter and lead, but ball size, loaded circuits, nut structure, Coa and stiffness must still be confirmed.
Check Screw-Shaft Buckling Separately
A long ball screw subjected to compression may buckle before the ball nut reaches its basic static load rating.
The theoretical Euler buckling load can be expressed as:
For an approximately circular screw-root section:
- E = elastic modulus of the screw-shaft material
- I = second moment of area
- dr = screw-root diameter rather than nominal outside diameter
- Le = effective length determined by unsupported length and support arrangement
Buckling capacity changes strongly with unsupported length because the theoretical value is inversely proportional to the square of the effective length.
It also changes with the fourth power of the root diameter. A modest increase in effective shaft diameter can therefore have a large effect on buckling resistance.
The Support Bearing May Be the Static Limit
The fixed-side support bearing carries the axial thrust transmitted through the screw shaft. Its static capacity and axial stiffness must be checked separately from the ball nut.
The complete axis may be limited by:
| Limit | Main Failure or Performance Risk | Data Required |
|---|---|---|
| Ball nut Coa | Permanent ball-and-raceway contact deformation | Coa and maximum axial load |
| Shaft buckling | Lateral instability under compression | Root diameter, unsupported length and support method |
| Shaft stress | Excessive tensile or compressive stress at the screw-root section | Root area, material and maximum force |
| Support-bearing capacity | Permanent bearing deformation, preload loss or axial play | Bearing arrangement and static rating |
| Nut housing and bolts | Housing deformation, flange separation or bolt overload | Housing geometry, material, bolt grade and tightening condition |
Determine the Real Maximum Axial Load
The maximum axial load is not always equal to the machine payload.
For a horizontal axis, the load may include:
- Acceleration and deceleration force
- Cutting, pressing or pushing force
- Guideway and seal resistance
- Emergency-stop force
- Impact caused by machine collision or process variation
For a vertical lifting axis, the load may be estimated as:
A counterweight or balancing cylinder may reduce the normal drive force, but the static check must still include failure, braking and emergency conditions.
Static Performance Is Not the Same as Lead Accuracy
Lead-accuracy grades such as C3, C5 and C7 describe travel deviation. They do not directly state the ball screw's static load rating or complete-system stiffness.
A C5 ball screw may provide more accurate travel than a C7 screw but still have a lower Coa if it uses a smaller diameter, smaller balls or fewer loaded circuits.
Similarly, selecting a larger ball screw can improve shaft stiffness and buckling resistance, but it does not eliminate the need to check the nut stiffness, support bearings and mounting structure.
| Parameter | What It Controls | What It Does Not Prove |
|---|---|---|
| Accuracy grade | Lead and travel deviation | Static capacity, rigidity or backlash |
| Coa | Permanent contact-deformation reference | Fatigue life or total axis deflection |
| Stiffness K | Elastic force-to-displacement relationship | Permanent-deformation safety or lead accuracy |
| Preload | Clearance, reversal behavior and rigidity | Higher Coa or unlimited rigidity |
Does Lubrication Increase Static Load Capacity?
Correct lubrication is necessary for smooth movement, wear control, corrosion protection and fatigue life. It does not raise the published Coa value of an existing ball screw.
Similarly, adding more grease does not increase static stiffness. Excess grease may instead increase running torque and temperature.
Lubrication still matters indirectly because corrosion, contamination and wear can damage the raceways, change preload and reduce the actual performance of the ball screw over time.
How to Measure Static Performance on an Installed Axis
Measure Axial Lost Motion
- Secure the screw shaft against unintended rotation.
- Place a dial indicator or displacement sensor in the axial direction.
- Apply a controlled axial force in one direction and set the indicator reference.
- Reverse the force without rotating the screw.
- Record the displacement between the two load directions.
The measured result may include ball nut clearance, support-bearing play, coupling movement, housing deformation and mounting looseness. Isolate each component before concluding that the ball nut is the only source.
Measure Static Axial Stiffness
- Use a calibrated axial load cell or force application device.
- Measure axial displacement with a dial indicator, electronic probe or laser displacement sensor.
- Apply the load gradually within a safe elastic range.
- Record force and displacement at several load levels.
- Calculate K = ΔF ÷ Δδ over the selected load range.
- Unload the axis and check whether it returns to its original position.
Permanent residual displacement after unloading may indicate contact damage, bearing movement, bolt slip or structural yielding.
Compare Different Nut Positions
Test the axis near the fixed support, at the center of travel and near the opposite end. A significant change in stiffness may be caused by the changing effective screw-shaft length.
Common Static-Performance Selection Mistakes
| Mistake | Why It Is Incorrect |
|---|---|
| Treating Coa as the recommended working load | Coa is defined by a permanent-deformation criterion and must be divided by a suitable safety factor |
| Using machine mass directly as axial force | Orientation, acceleration, process force, friction and impact must be included |
| Checking Coa but ignoring buckling | A long screw under compression may buckle far below the nut's contact limit |
| Treating catalog K as complete-axis stiffness | Shaft, bearings, housing and machine structure add further elastic deformation |
| Assuming a double nut doubles Coa | Preload mainly changes clearance and stiffness; the exact Coa must be checked from the model data |
| Selecting only by nominal diameter | Ball diameter, groove geometry, loaded circuits, lead and nut structure also affect the ratings |
| Assuming a higher accuracy grade gives higher Coa | Lead accuracy and static contact capacity describe different product characteristics |
Ball Screw Static-Performance Selection Procedure
- Calculate the maximum axial load. Include gravity, acceleration, process force, braking, impact and emergency conditions.
- Check Coa and the static safety factor. Confirm that Coa ÷ Fmax meets the selected design requirement.
- Check screw-shaft buckling. Use the root diameter, maximum unsupported length and actual support arrangement.
- Check shaft tensile or compressive stress. Compare the root-section stress with the allowable material stress.
- Calculate total axial deformation. Include the screw shaft, nut, support bearings, nut housing and machine structure.
- Select axial clearance or preload. Match reversal accuracy and rigidity without creating unnecessary torque and heat.
- Check support bearings and mounting parts. Confirm their static capacity, stiffness and bolt security.
- Verify the assembled axis. Measure lost motion, load-displacement behavior and positioning stability under real operating conditions.
For the difference between static load rating and dynamic fatigue-life rating, see What Is the Dynamic Load Rating of a Ball Screw? .
Information Needed for a Static-Performance Check
- Complete ball screw model
- Nominal diameter and lead
- Ball circuit configuration
- Screw length and maximum unsupported length
- Screw-end support arrangement
- Horizontal, vertical or inclined installation
- Moving mass
- Acceleration and deceleration
- Maximum cutting, pressing or process force
- Impact and emergency-stop conditions
- Required axial stiffness or permitted deformation
- Required backlash or preload
- Support-bearing model
- Nut-housing and mounting drawing
View the DLY SFU ball screw specifications for model-specific Coa and stiffness data.
Frequently Asked Questions
Is Coa the maximum load a ball screw can carry?
No. Coa is a reference load defined by a specified permanent contact-deformation criterion. The allowable working load should be lower after applying a suitable static safety factor and checking buckling, bearings and structural limits.
Does a higher Coa mean higher axial stiffness?
Not necessarily. Coa and stiffness are affected by related but different geometric and contact conditions. Always check both catalog values.
Does a double nut increase static load capacity?
A double nut mainly provides preload, reduced backlash and greater rigidity. It does not automatically double Coa. Confirm the model-specific static rating.
Why is the complete axis less rigid than the catalog nut value?
The screw shaft, support bearings, nut housing, bolts and machine structure all deform under load. Their compliances are added to the nut's elastic deformation.
Does a smaller lead always provide better static performance?
No. Lead affects speed, torque and lead angle, but Coa and stiffness also depend on ball diameter, number of loaded circuits, groove geometry and nut design.
When is the static load rating especially important?
It is especially important during standstill, very-low-speed movement, pressing, clamping, emergency stops, impacts, collisions and vertical-axis holding conditions.
Contact DLY
Send DLY your ball screw model, screw length, support arrangement, moving mass, acceleration, maximum process force, mounting direction, required backlash and permitted axial deformation. We can help compare the Coa, stiffness and structural limits of suitable SFU, DFU and other ball screw configurations.
Email: dlyexport2@dlybearing.com | WhatsApp: +86 16605788856
