BIZOMAT MAKEOS · Mechanics
Screw Jack and Power Screw Design
What torque and lever force raise this load, will the screw self-lock, and are the threads, nut and screw strong enough?
Complete check of a screw jack or power screw with Acme or trapezoidal thread: raising and lowering torque with collar friction, efficiency and self-locking, the force at the lever, nut bearing pressure from the engaged threads, combined direct and torsional stress at the screw root, and Euler buckling of the screw column.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load | kN | Axial load lifted. |
| Major diameter | mm | Major diameter of the screw. |
| Pitch | mm | Thread pitch. |
| Number of starts | Number of thread starts. | |
| Flank half-angle (15° for Acme/trapezoidal) | ° | Half the thread angle (15° for 29° Acme and 30° trapezoidal threads; 0 for square threads). |
| Thread friction coefficient | Thread friction coefficient (about 0.1–0.15 lubricated steel on bronze). | |
| Mean collar diameter (0 = none) | mm | Mean diameter of the thrust collar or bearing face. |
| Collar friction coefficient | Collar friction coefficient (about 0.01 with a thrust ball bearing). | |
| Lever arm length | mm | Length of the lever or handle. |
| Nut length | mm | Length of thread engaged in the nut. |
| Allowable thread bearing pressure | MPa | Allowable bearing pressure between screw and nut threads (low for slow-moving bronze nuts). |
| Screw yield strength | MPa | Yield strength of the screw. |
| Unsupported screw length | mm | Unsupported length of the screw acting as a column. |
| Effective length factor | Effective length factor (2 for a jack with a free top). | |
| Screw modulus | GPa | Elastic modulus of the screw. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load
- What it is
- Axial load the screw lifts or holds, acting along the screw axis.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All torques, lever force, nut pressure and stress rise in proportion.
- Get it right
- Include the weight of any platform or fixture lifted with the load.
What this means: Major diameter
- What it is
- Outside (major) diameter of the screw thread. The tool estimates the pitch and root diameters from it and the pitch.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the nominal major diameter, for example the 40 in Tr40×7, not the root.
What this means: Pitch
- What it is
- Axial distance between neighbouring thread crests. With the number of starts it gives the lead, the travel per turn.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A coarser pitch reduces the root diameter and raises the lead.
- Get it right
- For multi-start threads enter the pitch, not the lead; the tool multiplies by starts.
What this means: Number of starts
- What it is
- Number of separate thread helixes on the screw. Lead equals pitch times starts.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 6. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More starts raise lead and efficiency, but can lose self-locking.
- Get it right
- Count thread ends at the screw end face; most jack screws are single-start.
What this means: Flank half-angle (15° for Acme/trapezoidal)
- What it is
- Half the included thread angle, measured from a line square to the axis. It increases the effective thread friction.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter half the thread angle, not the full included angle; 0 means a square thread.
What this means: Thread friction coefficient
- What it is
- Friction coefficient between screw and nut threads under load.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.12 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher friction raises torque and lowers efficiency, but helps self-locking.
- Get it right
- Depends on materials and lubrication; take it from tests or reliable data for your pair.
What this means: Mean collar diameter (0 = none)
- What it is
- Mean diameter of the thrust collar or bearing face that carries the load as the screw turns. Friction there adds to the raising and lowering torque.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Collar torque rises in proportion to this diameter.
- Get it right
- Use the mean of inner and outer contact diameters; enter 0 when there is no collar friction.
What this means: Collar friction coefficient
- What it is
- Friction coefficient at the thrust collar or bearing face, which may differ from the thread friction.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.12 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Collar torque rises in proportion.
- Get it right
- A thrust ball bearing at the collar has far lower friction than a plain face.
What this means: Lever arm length
- What it is
- Distance from the screw axis to where the operator pushes on the handle or lever.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The lever force falls in proportion as the lever lengthens.
- Get it right
- Measure from the screw centre to the middle of the hand grip.
What this means: Nut length
- What it is
- Axial length of thread engaged in the nut. It sets how many threads share the load.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer nut lowers the thread bearing pressure in proportion.
- Get it right
- Use engaged length, not the overall nut length including chamfers.
What this means: Allowable thread bearing pressure
- What it is
- Highest contact pressure allowed between screw and nut threads, which governs wear of the nut.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 200 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from nut maker data or your design practice; slow-moving bronze nuts use low values.
What this means: Screw yield strength
- What it is
- Yield strength of the screw material. The tool checks the combined root stress against it divided by 1.5.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the minimum specified yield for the grade and condition, from the material standard or certificate.
What this means: Unsupported screw length
- What it is
- Length of screw acting as an unsupported column under compression, from the nut to the load point at full extension.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Buckling load falls with the square of this length.
- Get it right
- Use the length at the highest lift, where buckling is worst.
What this means: Effective length factor
- What it is
- Factor converting the unsupported length into the effective buckling length for how the screw ends are held.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Buckling load falls with the square of the factor.
- Get it right
- Pick it from the end conditions: a jack with a free, unguided top acts like a flagpole and needs a large factor.
What this means: Screw modulus
- What it is
- Elastic (Young’s) modulus of the screw material, used for the buckling check.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 206 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Buckling load rises in proportion.
- Get it right
- Enter gigapascals; 1 GPa = 1,000 MPa.
Method and formulas
- Pitch diameter d₂ ≈ d − p ÷ 2, root d₃ ≈ d − p; lead l = starts × p.
- Raise: T = W d₂ ÷ 2 × (l + π μ d₂ sec α) ÷ (π d₂ − μ l sec α) + W μ_c d_c ÷ 2; lower with the signs reversed (handbook jack formulas with collar friction).
- Self-locking when π μ d₂ sec α > l; efficiency = W l ÷ 2π T_raise.
- Nut pressure = W ÷ (π d₂ (p ÷ 2) n), n = nut length ÷ pitch; root stress by von Mises from W ÷ A₃ and the thread torque; buckling P_cr = π² E I ÷ (K L)².
- Example: 20 kN on a Tr40×7 screw needs 128.14 N·m to raise, or 427.15 N on a 300 mm lever.
Limitations
- Approximate thread diameters; use the thread standard for final dimensions.
- Static load; wear life of the nut depends on speed and lubrication.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a lifting screw or press screw
- Check a jack for self-locking and lever effort
- Size the nut length for wear
Who it is for
- Machine designers
- Automation engineers
- Design engineers
What you get
- Raising and lowering torque, efficiency and lever force
- Self-locking and nut bearing pressure
- Screw stress and buckling factor
Interpreting the result
- A thrust ball bearing at the collar can halve the raising torque.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 171, 2561. Topic reference; no source tables or recommended settings are reproduced.
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