Design the power screw (lead screw) that turns rotary motion into a powerful linear thrust. Adjust the nominal diameter, pitch, number of starts, axial load and thread friction to see the lead angle, raising torque, efficiency and self-locking verdict update in real time.
Parameters
Nominal diameter (outer) d
mm
Thread pitch p
mm
Axial spacing between adjacent thread crests
Number of starts
Travel per revolution = pitch x starts
Axial load W
N
Load the screw lifts or presses
Thread friction coefficient µ
About 0.1-0.2 for lubricated steel on steel
Results
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Lead (mm)
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Mean diameter d_m (mm)
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Lead angle λ (deg)
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Raising torque (N·m)
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Efficiency (%)
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Self-locking verdict
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Power screw & inclined-plane model — rotation animation
Left: the screw, nut and load. Right: one thread turn "unwrapped" into an inclined plane. The load climbs the slope at the lead angle λ, showing whether the screw raises (green), holds (orange) or overhauls (red).
Raising torque T_raise and raising efficiency η. W: axial load, d_m: mean diameter. λ is the lead angle, φ the friction angle (φ = arctan µ); the screw is self-locking when the lead angle λ is smaller than the friction angle φ.
$$\lambda=\arctan\!\frac{l}{\pi d_m},\qquad l = p\cdot z,\qquad d_m = d-\frac{p}{2}$$
Lead angle λ, lead l (axial travel per revolution) and mean diameter d_m (square thread). p: pitch, z: number of starts, d: nominal (outer) diameter.
$$T_{lower}=W\frac{d_m}{2}\tan(\phi-\lambda)$$
Lowering torque T_lower. It is positive when φ>λ, meaning force is needed even to back the screw off — the screw is self-locking.
What is the Power Screw Efficiency Simulator?
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A "power screw" or "lead screw" — is that different from an ordinary fastening screw?
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Yes, it is. A fastening screw's job is to clamp parts together; a power screw's job is to convert rotation into linear motion. Turn the handle of a vice and the jaws close; turn a jack and a car rises — those are power screws. It helps to picture a screw as a long, gently sloped inclined plane wrapped helically around a cylinder. It is exactly that gentle slope that turns a small input torque into an enormous axial thrust.
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I see. So the "lead angle" is the steepness of that slope. When I change the number of starts from 1 to 2 on the left, the lead angle jumps up.
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Exactly. The lead angle λ is the arctangent of the lead (the axial travel per turn) divided by the mean circumference. Adding starts doubles or triples the lead, so the lead angle climbs sharply. A screw with a large lead angle advances a lot per turn — it is "fast" — but it tends to lose self-locking, which we'll get to. That is the core design trade-off here.
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The efficiency reads about 31%. Isn't that really low? I've heard gears reach 98%.
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Yes — a power screw is strikingly inefficient. An ordinary single-start square-thread screw is only 20-40%. Most of the input torque goes into rubbing the thread faces against each other, and only a small part actually lifts the load. To raise efficiency you increase the lead angle (multi-start or coarser pitch) or lower the friction coefficient. Look at the "Efficiency vs lead angle" chart below: the curve rises, then falls — a hump shape.
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If it's that inefficient, why do we keep using power screws?
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Because of one extremely useful property: self-locking. When the lead angle is smaller than the friction angle, the load on the nut cannot drive the screw backwards on its own. Lift a car with a jack, let go of the handle, and it does not come down — the screw holds its position with no brake and no power. That is enormously valuable for safety. But pushing efficiency above 50% forces the lead angle past the friction angle, and self-locking is lost. Efficiency and self-locking are a tug-of-war.
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So what do you do when you need fast, precise travel, like on a machine tool?
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Then you use a ball screw. By rolling balls instead of sliding threads, friction drops sharply and efficiency exceeds 90%. The catch is that a ball screw does not self-lock, so when you need to hold position you do it separately with a motor brake. Conversely, for a jack or vice where load-holding safety comes first, you choose a self-locking sliding screw and accept the low efficiency. Picking the right one for the application is the heart of the design.
Frequently Asked Questions
The raising efficiency of a power screw is computed as eta = tan(lambda)/tan(lambda+phi), where lambda is the lead angle and phi is the friction angle (phi = arctan of the friction coefficient). An ordinary single-start square-thread screw has a small lead angle, only a few degrees, while the friction angle is close to 8-10 degrees, so most of the input torque is spent overcoming thread friction. Only the small remainder does the useful work of lifting the load, which is why efficiency stays at 20-40%. You raise it by increasing the lead angle (a coarser or multi-start thread) or by reducing friction.
Self-locking means the load on the nut alone cannot drive the screw backwards. The check is very simple: the screw is self-locking when the lead angle lambda is smaller than the friction angle phi. In that case the lowering torque is positive, and the screw holds its position with no brake and no power. This property is critical for the safety of a jack or a vice. If the lead angle exceeds the friction angle, the screw overhauls — it turns itself backwards under the load.
The raising torque is needed to turn the screw in the direction that lifts the load: T_raise = W*(d_m/2)*tan(lambda+phi). The friction angle adds to the lead angle, so this torque is large. The lowering torque applies when descending: T_lower = W*(d_m/2)*tan(phi-lambda). It is positive when phi > lambda, meaning force is needed even to back the screw off — that is, the screw is self-locking. When phi < lambda the lowering torque is negative and the screw runs back down on its own.
Not in principle. The self-locking condition is lead angle lambda < friction angle phi, but raising the efficiency eta = tan(lambda)/tan(lambda+phi) above 50% requires the lead angle to exceed the friction angle — the two requirements are exact opposites. Mathematically, once the efficiency just passes 50% self-locking is lost. For jacks and vices, where load-holding safety comes first, designers accept the low efficiency and choose a self-locking screw. For machine-tool lead screws that need fast traverse, a ball screw is used to reach over 90% efficiency, and holding is provided separately by a brake.
Real-World Applications
Jacks and lifting devices: Automotive scissor jacks, screw-type bottle jacks and stage or camera-rig lifts are the most typical uses of a power screw. They must hold a load suspended for a long time, so self-locking is essential. The lead angle is kept below the friction angle, and the low efficiency is absorbed through handle length or gear ratio so that "a person can still turn it without it feeling heavy".
Vices, clamps and presses: A machinist's vice, a C-clamp and a benchtop hand press are classic examples of a power screw turning a small hand torque into an enormous clamping force. The fact that a clamped joint does not loosen under vibration is also thanks to self-locking. Trapezoidal (Acme/metric trapezoidal) threads are widely used, balancing nearly square-thread efficiency with ample strength.
Machine tools and linear actuators: Lathe and milling-machine table feeds, the Z-axis of a 3D printer and many electric actuators also use power screws. Where positioning accuracy or feed speed matters, the sliding screw is replaced by a ball screw with over 90% efficiency, and holding is provided separately by a motor brake. The choice between a sliding screw and a ball screw comes down to the priority of efficiency versus self-locking.
Design study and education: In machine-element design courses, the power screw is a favourite topic that teaches inclined planes and wedges, friction and efficiency all at once. Visualizing the relationship between lead angle, friction angle, efficiency and self-locking — as this tool does — makes it intuitive why efficiency and self-locking cannot coexist. Detailed design also checks the bearing (contact) pressure and shear strength of the thread.
Common Misconceptions and Pitfalls
The most common pitfall is thinking "low efficiency means bad design". A power screw being only 20-40% efficient is not a design mistake; that property is the price paid for self-locking, a safety function. If you raise the lead angle too far chasing efficiency, the jack can overhaul under load and drop. When the application demands load-holding safety, low efficiency is in fact the correct design. Do not judge by the efficiency number alone — first decide whether the application needs self-locking.
Next, assuming the friction coefficient is a single fixed number. The friction coefficient in this tool is a representative value for lubricated steel on steel, but the real µ varies widely with lubrication state, surface roughness, material pairing (steel on bronze, for example), load, operating temperature and sliding speed. In particular µ is higher at start-up (static friction) than during running (kinetic friction), so a screw with a lead angle right at the friction angle can behave differently — it may not overhaul while running yet still hold once stopped. Estimate the friction coefficient conservatively, or leave margin in the lead angle.
Finally, the misconception that the square-thread model applies directly to trapezoidal or V-threads. This tool assumes a square thread. Trapezoidal and V-threads have a flank angle on the thread, which increases the force normal to the surface and raises the effective friction. In practice the same formulas are applied with an "equivalent friction coefficient" µ/cos(half the flank angle). Bear in mind that this tool's results are ideal square-thread values; for a trapezoidal thread the raising torque comes out somewhat higher and the efficiency somewhat lower.
How to Use
Enter nominal screw diameter (M8–M36 range) and pitch (0.5–4 mm for metric screws)
Set number of starts (1 for single-thread, 2–4 for multi-start designs) and axial load (100–50000 N)
Simulator calculates lead angle λ, mean diameter d_m, raising torque, efficiency percentage, and self-locking status
Worked Example
M16 steel power screw with 2 mm pitch, single start, 5000 N axial load: Lead = 2 mm, d_m ≈ 14.93 mm, λ ≈ 2.44°, raising torque ≈ 28.5 N·m, efficiency ≈ 23%. Self-locking occurs (λ < friction angle ~14°). Increasing to 4 mm pitch with 2 starts yields λ ≈ 4.85°, efficiency ≈ 41%, still self-locking under typical oil-lubricated conditions (μ ≈ 0.12).
Practical Notes
Lead angle < friction angle (typically 12–16° for lubricated steel) ensures self-locking; critical for vertical load holding in jacks without brake
Multi-start threads (2–4 starts) increase lead and efficiency but reduce torque multiplication; M10×2 single-start produces higher torque than M10×4 double-start for same rotational speed
Efficiency drops sharply below λ = 2°; acme or buttress profiles improve efficiency 5–10% over square threads due to reduced contact stress
Lubrication type (dry, oil ISO VG 32, grease) changes friction coefficient by ±0.03–0.08, directly affecting both torque and self-locking margin