Precision line shafts transmit torque across longer distances while maintaining mechanical synchronization. Here we review their basics, as well as speed considerations. Line shafts span long distances: in palletizing robots, screw jacks, printing presses, conveyors, and woodworking and packaging machinery. These mechanical devices perform in temperatures -30 to +120° C.

They’re lightweight with straightness and lateral stiffness that boost stability at higher speeds. Line shafts, also known jackshafts and torque tubes, span long distances to connect other power transmission shafts. Conventional designs require an intermediate bearing or a pillow block in the drive system for supporting purposes. In contrast, newer high-precision line shafts run smoothly and can operate without intermediate support — even to 6 m. Line-shaft structure is similar to that of precision couplings: The main components are hubs in various designs, and a metal bellows or an elastomer insert, plus an intermediate tube made of aluminum, steel, or carbon fiber.

First point: Minimize vibration

Let’s review some physics here: If a body is deflected in one direction by an acting force (for example, by an imbalance force at a high rotational speed) the body will recoil and deflect in the opposite direction as soon as the force is removed. This deflection’s amplitude leads to flexural body vibration, which settles at a rate that depends on the body’s specific spring constant — so settling time is different in each case. However, if the excitation frequency periodically corresponds with the natural resonant frequency, the vibration will build instead — or more technically, will continuously increase in amplitude. The speed that causes vibrations to build is sometimes called the critical speed. Worst-case scenario, increasing amplitude can cause the line shaft to break — and any system not resistant to vibration has such resonant frequencies.

In the case of line shafts, vibration-inducing forces can be generated in two different ways: by an imbalance in attached rotating masses, or by the fact that the intermediate tube itself is never absolutely straight, but always deviates from its centerline slightly. Total line shaft deflection, and thus the difference between the ideal and actual axis of rotation, can be calculated by adding these two deviations — more on this in a moment.

Another consideration is maximum operating speed. Maximum operating speed, defined by manufacturers, is normally about 60 to 80% of critical speed, though line shafts manufactured with very precise concentricity can operate quite safely at 80% of critical speed. Keeping below this guarantees that the line shaft is never operated within the critical speed range.

Running the gauntlet

What if a design requires a speed higher than a certain line shaft’s critical speed? Is that particular line shaft unusable in that application, even if it’s appropriate in all other ways? In special cases, and after consulting the coupling manufacturer, line shafts can be operated at more than 20% above the critical speed, in what’s called the super-critical range, provided that the entire application is highly dynamic.

In these situations, operating speed should be reached within one or two seconds at most. This short period gives no prolonged opportunity for excitation, and thus prevents axial amplitude growth.

The line shaft should also be very rigid. Operating a line shaft at critical speed puts an additional load on the intermediate tube and the entire line shaft, so this additional load should be taken into account during design.

Design and selection

Determining critical speed is an important calculation when selecting line shafts. At this rotational speed, vibration continuously builds because of two things: deflection from specific weight fE and deflection resulting from the fact that the tube is never absolutely straight — fR. To calculate total line shaft deflection fm, these two factors are added:

fm = fE + fR

A fixed clearance prevents maximum admissible compensation angle from being exceeded.

Total deflection prevents the line shaft from rotating exactly on the ideal axis of rotation. This creates an additional centrifugal force that stresses the line shaft.

An explicit calculation of critical speed that takes all influencing factors into account, is very sophisticated and complicated. So here, we give a very rough formula. The critical speed (nkb) for axes and shafts, taking the bearing into account, is calculated:

Where k = Bearing correction factor

Rotationally borne axes or shafts that are not clamped (which are most common) have a non-adjusting correction factor of k = 1; in comparison, fixed axes clamped at the ends or with rotating discs, wheels, and similar components on them are calculated with a correction factor of k = 1.3. For line shafts, the correction factor k = 1 is normally used. As explained, the maximum deflection of the shaft is determined by two criteria. The second criterion, tube straightness, can be actively improved by using special ball bearing sets and test devices. But deflection caused by the specific weight is a constant value that cannot be changed: It depends on wall thickness, line shaft length, the elasticity modulus of the intermediate tube material, and other factors:

qo = Intermediate tube’s specific weight
E = Material’s elasticity modulus
I = Area moment of inertia with cylindrical hollow bodies
l = Intermediate tube length, mm

As with the last formula, this only yields rough results. For precise data on critical speed and the corresponding total deflection in a specific application, coupling manufacturers often have special calculation programs to simulate operations.