Designing Spindle Jacks Step by Step
Designing a spindle jack requires five input parameters: force [N], stroke [mm], travel speed [mm/s], duty cycle [%], and mounting orientation. From these, spindle type, spindle diameter, buckling check, and motor power follow directly.
Correct sizing is essential for reliability and service life. This guide walks you through all five critical design steps – with formulas, examples, and practical notes from TEA application engineers.
Spindle Jack Design Types
Spindle jacks (also called screw jacks or machine screw actuators) convert rotary motion into linear motion using a lead screw. They are available in two fundamental configurations:
Fixed Spindle (Translating Screw)
The spindle (screw) does not rotate – the gear nut rotates in the housing and drives the spindle axially. Advantages: the spindle can be attached to the load, anti-rotation is built in, compact gearbox. Clearance for the retracted spindle must be kept free on the opposite side of the gearbox.
Rotating Spindle (Translating Nut)
The spindle rotates but stays axially fixed in the gearbox. A travelling nut moves along the spindle and carries the load; the nut must be secured against rotation, usually by the guided load. Advantages: the installation height stays constant because the spindle does not extend, which suits long strokes. Points to check: critical speed of the rotating spindle on long strokes and protection of the exposed spindle, e.g. by bellows. The rated lifting force of the gearbox depends on spindle and gearbox size. Under compressive load, however, the buckling load of the spindle can limit the permissible lifting force – and it depends on the free spindle length and the end bearing arrangement, and therefore also on the design type (see the design steps and the worked example).
Trapezoidal vs. Ball Screw
Single-start trapezoidal screws with a small lead angle are self-locking under static conditions (catalogues state about 3° as the safe limit; not reliable under shock and vibration — fit a brake for suspended loads), simple, and robust; steep and multi-start screws do not self-lock. Efficiency 30–50%. Ball screws have efficiency 90–98%, allow higher speeds and duty cycles, but are not self-locking (require brake) and more expensive.
| Feature | Trapezoidal screw (DIN 103) | Ball screw (ISO 3408) |
|---|---|---|
| Efficiency | 0.30–0.50 | 0.90–0.98 |
| Friction | sliding friction | rolling friction |
| Self-locking | only at small lead angle, static (manufacturer's statement) | no — holding brake required |
| Backlash / accuracy | backlash, limited | preloadable, high precision |
| Wear / maintenance | higher | low, defined lubrication intervals |
| Speed | low to medium | high |
| Cost (relative) | € (low cost) | €€–€€€ (higher) |
5 Design Steps
Step 1: Determine Effective Force
The effective force Feff includes static load, dynamic forces (acceleration), and safety factor (typically S = 1.5–2.0):
Feff = (Fstatic + Fdynamic) × S
Step 2: Determine Required Speed
The required motor speed n results from the travel speed v [mm/s] and the spindle pitch P [mm/revolution]:
n = v / P × 60 [rpm]
Step 3: Check Spindle Diameter
The minimum spindle diameter results from the compressive stress check and the buckling analysis (Euler). The compressive stress check is only a lower limit: in actual screw jacks, surface pressure and heating in the nut thread usually limit the load. Standard series assign, for example, Tr 40 × 7 to a lifting force of 50 kN and Tr 60 × 9 to 100 kN (root stress approx. 50–60 N/mm²). Euler applies only to slender spindles: the governing parameter is the slenderness ratio λ = Lk / i, using the buckling length Lk (= L for pinned-pinned mounting, = 2L for fixed-free mounting) and the radius of gyration i = d₃/4 of the root cross-section. Euler applies above the limit slenderness (rule of thumb: mild steel approx. 105, high-strength steel approx. 85–90; use the higher value if unsure). For shorter, stocky spindles the buckling case lies in the inelastic range (Tetmajer); use the Tetmajer method or the manufacturer's buckling chart. For pinned-pinned mounting (both ends pivoted):
dmin = [64 × SB × Feff × Lk² / (π³ × E)]0.25
With dmin = minimum root diameter d₃, Lk = buckling length (= L for pinned-pinned mounting), E = Young's modulus (steel: 210,000 N/mm²), SB = buckling safety factor (see FAQ)
Note on Euler end conditions:
The formula above assumes pinned-pinned (both ends pivoted) mounting. For fixed-free (cantilever) mounting, the effective buckling length doubles, significantly reducing the critical buckling load. Always verify the actual end conditions in the application.
For applications requiring high positioning accuracy and frequent load-direction reversals, the companion guide Ball Screw Selection covers preload, stiffness, and service life in detail.
Step 4: Calculate Drive Torque
M = F × P / (2π × η) [N·mm] (F in N, P in mm)
Where η = efficiency (trapezoidal screw: 0.3–0.5; ball screw: 0.90–0.98)
This is the torque required at the spindle. The power at the spindle follows from P = M × n / 9,550 (M in N·m, n in rpm); for the motor power, additionally account for the efficiency of the worm gear stage (approx. 0.45–0.9 depending on size and ratio, catalogue value) as well as the no-load torque and the starting torque. It is simpler to use the torque formula from the screw jack catalogue, plus a margin as specified by the manufacturer.
Observe the permissible duty cycle: it depends on the screw type and size and is stated in the catalogue of the series, usually referred to 10 minutes. The limiting factor is the heating of the screw nut and the worm gear stage, not just the motor. Screw jacks with a trapezoidal screw are designed for intermittent duty; with a ball screw roughly twice the duty cycle is possible. Agree higher values with the manufacturer.
Steps 1–4 can be performed directly in the Spindle Jack Sizing Calculator.
Step 5: Verify Self-Locking
A trapezoidal screw is self-locking when the lead angle φ ≤ friction angle ρ (static friction). In practice catalogues are stricter than the bare friction calculation and state about 3° as the safe limit for self-locking; common single-start jack screws lie at roughly 3° to 6° – right in the borderline range. Shock and vibration can cancel self-locking; steep and multi-start screws do not self-lock. The statement in the catalogue of the series used is binding; without the manufacturer's assurance, provide a holding brake. For ball screws, a brake is always required.
Worked Example: Press Drive
Application: Vertical press for forming operations
- Static pressing force: F = 80 kN
- Stroke: h = 200 mm
- Travel speed: v = 20 mm/s
- Impact loading → safety factor S = 1.5
- Free spindle length: L = 400 mm (given)
Calculation:
- Feff = 80 kN × 1.5 = 120 kN
- dmin = √(4 × 120,000 / (π × 150)) ≈ 31.9 mm (σperm = 150 N/mm²)
- Trapezoidal screw by calculation at least Tr 40 × 7 (DIN 103), root diameter d₃ = 32.0 mm (nominal) ≥ 31.9 mm – marginal; because of manufacturing tolerance, recheck with the manufacturer's minimum root diameter; σ = 120,000 / 804 mm² ≈ 149 N/mm² ≤ 150 N/mm² ✓ (Tr 32 × 6: 245 N/mm², Tr 36 × 6: 182 N/mm² – too small). Lower limit only: standard series assign Tr 40 × 7 to a lifting force of 50 kN (50,000 / 804 ≈ 62 N/mm²) and Tr 60 × 9 to 100 kN (100,000 / 1,963 ≈ 51 N/mm²); n = 20 mm/s ÷ 7 mm/rev ≈ 171 rpm
- Calculation shown for Tr 40 × 7 (it is ruled out for 120 kN, see result); η = 0.36 (catalogue value for this screw): M = 120,000 × 7 / (2π × 0.36) ≈ 371,400 N·mm = 371.4 N·m; P = 371.4 × 171 / 9,550 ≈ 6.65 kW
- Slenderness λ = L / (d₃/4) = 400 / 8 = 50 – below the Euler limit for steel (approx. 90–105) → Euler does not apply here (it would overestimate the load capacity). Buckling safety ≥ 3: required Fcrit = 3 × 120,000 N = 360,000 N → Tr 40 × 7 would need σk ≥ 360,000 / 804 ≈ 448 N/mm² – more than the yield strength of common spindle steels (S235: 235, S355: 355 N/mm²) ✗ → at least d₃ ≥ 35.9 mm (S355) or 44.2 mm (S235) is necessary; select the spindle with the manufacturer's buckling chart (inelastic range, e.g. Tetmajer).
Result: The compressive stress check requires by calculation at least Tr 40 × 7 – this is only a lower limit: standard series assign Tr 40 × 7 to a lifting force of 50 kN and Tr 60 × 9 to 100 kN; for 120 kN, therefore, no standard size with Tr 40 × 7 is an option, only an individual design with the manufacturer. The buckling check with a safety factor ≥ 3 requires a considerably larger spindle at 120 kN and a free length of 400 mm (given) – determine the final size with the manufacturer's buckling chart, or shorten the free length or improve the bearing arrangement. Calculated power required at the spindle for Tr 40 × 7 approx. 6.65 kW at approx. 171 rpm; a larger spindle changes lead, efficiency and speed. Motor power follows from this using the gearbox stage's efficiency, the duty cycle, and a margin (manufacturer's rating). All checks are carried out with the root diameter, not the nominal diameter. The low trapezoidal-thread efficiency and its self-locking are two sides of the same cause — the small lead angle; a ball screw would need about 37–40 % of the drive power but is never self-locking and needs a brake.
Lubrication and Maintenance
Spindle jacks require regular lubrication depending on the spindle type:
- Trapezoidal screw jack: Relubricate every 50–100 operating hours with lithium complex grease (DIN 51825 K2K-20)
- Ball screw jack: Relubricate every 100–200 operating hours with lithium or multi-purpose grease (DIN 51825 K3-30)
Practical Tip from TEA:
In our application support we see lubrication failures almost always where the spindle runs outdoors or in dusty environments – the DIN 51825 lithium grease then often lasts only a fraction of the catalogue interval (50–100 h for trapezoidal, 100–200 h for ball screws), because dirt acts as a grinding paste. For dusty or damp duty, state the environment and duty cycle (ED) in your enquiry right away, so we can plan for a protective bellows/wiper and a suitable K3 grease. And do not over-grease: on ball screws what counts is the thin lubricant film in the ball track, not the quantity – too much grease churns, raises the friction torque, and drives up temperature.
Use an online sizing calculator for precise spindle jack dimensioning:
Open Online Calculator →TEA Recommendation
TEA offers spindle jacks in various designs – from single-unit jacks through synchronized multi-unit systems. We also handle complete system design including motor, gearbox, coupling, and control. Standard spindle jacks in various lifting force classes are available in the TEA screw jacks range.
Request Spindle Jack ConsultationFrom design to enquiry: procurement notes
- Cost driver: Ball screws cost significantly more than trapezoidal screws. The price premium pays off at high duty cycles, tight positioning tolerances, or long strokes – for simple lifting tasks a trapezoidal version is usually sufficient.
- Standard vs. custom design: Standard spindle jacks are available for compressive forces up to approx. 100 kN in defined load classes. Custom variants (non-standard pitch, extended spindle, flange interface) become economical at medium quantities – for single units, check whether a standard size fits first.
- Inquiry specification: State lifting force [N], stroke [mm], travel speed [mm/s], duty cycle [%], mounting orientation (vertical/horizontal), and preferred spindle type. TEA can then propose a sizing directly.
- Total cost of ownership: Ball screws have longer relubrication intervals and lower energy consumption due to higher efficiency. At continuous operation or high switching frequency, the more expensive ball screw can be more economical in the long run.
- Further information: Inquiries and sizing consultations via our contact page.
Frequently Asked Questions about Spindle Jack Design
For slender spindles, use the Euler formula: F_crit = π²·E·I / L². For steel, E = 210,000 N/mm² and I = π·d₃⁴/64 with the root diameter d₃ (to DIN 103). Euler applies only above the Euler limit slenderness (rule of thumb, mild steel approx. 85–105 depending on the material); for short, stocky spindles use the calculation for the inelastic range (e.g. Tetmajer) or the manufacturer's rating. The buckling safety factor should be at least 3 (rule of thumb; higher where personal safety is at risk; the manufacturer's rating is binding). The applicable Euler case depends on the actual end conditions.
Single-start trapezoidal screws (DIN 103) for screw jacks have leads of about 3 to 9 mm, depending on diameter (for example Tr 20 × 4, Tr 30 × 6, Tr 40 × 7, Tr 60 × 9). More travel per revolution requires multi-start trapezoidal screws or ball screws (leads of 5 to 50 mm); neither is self-locking. A small lead gives fine positioning but low speed. Whether a screw is self-locking depends on the lead angle, not on the pitch alone: single-start trapezoidal screws with a small lead angle are self-locking under static conditions (catalogues state about 3° as the safe limit; shock and vibration can cancel self-locking). Steep and multi-start screws do not self-lock and require a brake or holding device. Ball screws are never self-locking – they always need a brake.
First calculate the torque at the spindle (M = F·P/(2π·η), η = screw efficiency) and from it the power at the spindle (P = M·n/9,550, n = spindle speed in rpm). For the motor, add the efficiency of the worm gear stage (approx. 0.45–0.9 depending on size and ratio, catalogue value) as well as the no-load torque and the starting torque. It is simpler to use the torque formula from the screw jack catalogue, plus a margin as specified by the manufacturer.
That depends on the screw type and size and is stated in the catalogue of the series, usually referred to 10 minutes. The limiting factor is the heating of the screw nut and the worm gear stage, not just the motor. Screw jacks with a trapezoidal screw are designed for intermittent duty; with a ball screw roughly twice the duty cycle is possible. Agree higher values with the manufacturer.
Use lithium or multi-purpose grease to DIN 51825 K3-30, with a relubrication interval of every 100–200 operating hours. Trapezoidal screws are lubricated with lithium complex grease DIN 51825 K2K-20 every 50–100 hours.
About the Author
Senior Sales & Application Engineer · Technical Sales
Specializes in linear systems and spindle jack design for industrial automation and special machine building.