Design: Drive, worm gearbox, lead screw
A lifting system with a screw jack is a modular solution consisting of several components: an electric motor, a worm gearbox that provides a high reduction ratio and high torque, a trapezoidal or ball screw that converts the torque into lifting force, as well as guide rails that stabilize the load during the stroke. The gear system in the strict sense consists of the worm gear stage and the lead screw; the motor and guides are part of the lifting system. This modularity allows the motor size, gear reduction ratio, lead screw, and guides to be selected independently for each specific application. The required drive torque is the decisive factor for the motor, not a general power rating.
Two designs are common: In the non-rotating screw design, the spindle nut is permanently mounted in the gearbox—it also serves as the worm gear. The spindle is secured against rotation and extends axially from the gearbox; it bears the load at its head. In the rotating screw (travelling-nut design), the axially fixed spindle rotates, and a travelling nut moves along it, absorbing the load. The travelling nut must be secured against rotating with the spindle, usually via the guided load. Because the spindle does not extend in this case, the installation height remains constant—which is advantageous for long strokes. The rated lifting force of the gearbox depends on the spindle and gearbox size. Under compressive loads, however, the buckling load of the lead screw may limit the permissible lifting force—and this depends on the free lead screw length and the bearing arrangement, as well as the design (see Unit 2). For screw jacks, manufacturers often assume a buckling safety factor of 3; for ball screw units, S ≥ 2 is the standard rule of thumb listed in catalogs, though the manufacturer’s specifications are binding.
Stroke Speed and Drive Torque
The stroke speed is determined from the drive speed n, the lead Ph, and the gear ratio i; the required drive torque is determined from the axial force F, the lead, the gear ratio, and the efficiency η:
v = n · Ph / (i · 60)
M = (F · Ph) / (2π · i · η)
v = stroke speed (mm/s) · n = drive speed (min⁻¹) · Ph = lead (mm) · i = gear ratio · F = axial force (kN; 1 kN = 1,000 N) · η = total efficiency of the screw jack (worm gear stage and spindle combined) · M = drive torque in steady-state operation (Nm). The starting torque is significantly higher due to static friction. Catalogs list an idle torque and, in some cases, a starting efficiency; if this information is missing, inquire with the manufacturer about the safety margin—catalog formulas are often explicitly stated without a safety factor.
Unlike the ball screw formula in this module (where F is given in N), the axial force F is expressed here in kN: The constant in the denominator is therefore 2 instead of 2,000 (2,000 : 1,000 = 2); in addition, the gear ratio i of the worm gear stage of the screw jack is included there.
Trapezoidal or ball screw?
The type of lead screw determines efficiency, self-locking capability, and cost: The trapezoidal screw (DIN 103) features sliding friction, has an efficiency of approximately 0.30–0.50, and is self-locking at small lead angles—it is less expensive but more susceptible to wear. These two characteristics are interrelated: The smaller the lead angle, the lower the efficiency and the more reliable the self-locking. If the spindle’s efficiency during operation is around 0.5, self-locking can no longer be expected. The ball screw (ISO 3408) utilizes rolling friction, achieves an efficiency of 0.90–0.98, and can be preloaded to eliminate backlash; however, it is more expensive and not self-locking—it requires a holding brake.
These values apply to the lead screw alone. In the complete screw jack, the efficiency of the worm gear stage is added. The overall efficiency is therefore significantly lower—as a rough guide (manufacturer’s specifications), for example, 0.1–0.45 with a trapezoidal screw and 0.3–0.8 with a ball screw, depending on the size, reduction ratio, and speed. The torque formula always includes the catalog value of the gearbox—for startup, this is the startup efficiency or the reserve specified by the manufacturer.
Whether a trapezoidal screw is actually self-locking depends on the lead angle relative to the coefficient of friction. In simple terms, self-locking occurs when tan(lead angle) ≤ μ′ (μ′ = apparent coefficient of friction; for trapezoidal threads, μ′ = μ / cos 15°, μ = static coefficient of friction). Screw jack manufacturers use fixed limits; for example: no self-locking above a lead angle of approximately 4.5°, static self-locking only between about 2.4° and 4.5°, and dynamic self-locking below that (in each case without vibrations). Other catalogs are more stringent and specify self-locking only at lead angles below 3° or state efficiency limits—for example, static self-locking only at total efficiency below approximately 0.3. Standard single-start lifting screws range from approximately 3° to 6°—that is, exactly within the borderline range. These are rough estimates and depend on the manufacturer—the specifications in the catalog for the specific series used are decisive; in case of doubt, the stricter limit applies, and a holding brake must be provided unless otherwise specified by the manufacturer.
Mnemonic
Self-locking is not a safety device
Safety Note: Holding brakes, fall protection systems, and other safety functions are designed and tested based on a risk assessment and the relevant standards (e.g., DIN EN ISO 13849). This learning unit explains the fundamentals; it does not serve as a basis for such design and testing.
Worked example
Given
A screw jack with a trapezoidal screw and an overall efficiency of η = 0.30 (catalog value, including both the worm gear stage and the screw) has a gear ratio of i = 20 and a lead of Ph = 6 mm. Drive speed: n = 1,000 min⁻¹; required lifting force: F = 15 kN.
Calculation
- Stroke speed: v = n · Ph / (i · 60) = 1,000 · 6 / (20 · 60) = 5.0 mm/s
- Drive torque: M = (F · Ph) / (2π · i · η) = (15 · 6) / (2π · 20 · 0.30) ≈ 2.39 Nm
This is the torque in steady-state operation. When selecting a motor, also consider the no-load torque and the starting torque (starting efficiency or reserve, as specified by the manufacturer).
For verification: Spindle stroke design (opens in a new tab)
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