# Planetary Units in Dynamic Linear Axis Applications

##### by Patrick Stöber

We often use a timing belt to transfer rotating movement into linear movement for a highly dynamic linear axis. In this type of application, a servomotor/planetary gear unit combination drives the timing belt. The planetary gear unit's main functions are increasing the system's torque capacity and reducing its mass moment of inertia to an acceptable level. What follows is an explanation of how planetary gear units can be applied to such systems.

The question we need to ask is this: Is a gear unit, as a part of a highly dynamic system (used for applications that need high-speed positioning), a contradiction in itself or an absolute must?

These are the requirements for a gear unit in such applications:

• Fast acceleration and, consequently, high acceleration torque
• High travel speeds and, therefore, high output speeds
• Precise positioning, which means very low backlash when a gear unit is used
• Harmonic interaction between the load inertia and the mass moment of inertia

Looking at these requirements, we see that optimizing such an application means our goal is to eliminate the gear unit because its backlash negatively influences precise positioning, and its gear reduction reduces (comparatively speaking) the motor's output speed. At this point, it seems logical to solve the problem by using a larger servomotor.

However, if we take a closer look and consider the high acceleration requirements, we'll find that a bigger servomotor also has a tremendously higher mass moment of inertia. Such a servomotor uses most of its torque capacity for its own acceleration, leaving only a small portion to accelerate the load. The motor's main task becomes running and stopping itself.

Consequently, we have to choose an even bigger servomotor. It's unlikely such a motor can accelerate and stop in the time required by the application.

We can take care of these problems by using a gear unit. It's true that a gear unit reduces the motor's output speed by whatever gear ratio we select; however, at the same time, it reduces the load inertia quadratically in relation to that ratio. The formula that describes this relation is

where

 JD = drive inertia i = gear ratio JZ = load inertia

This is why gear units play a very important role in high dynamic positioning applications.

Gear Unit Requirements

A gear unit for our example application must have the following features:

• Low backlash
• Constant backlash over the full range
• Low noise
• High efficiency (low efficiency loss means low temperature)
• High-speed capacity
• High torsional stiffness
• High-quality gearing
• Gear ratios starting at 3:1
• Small overall package
• Easy mounting to a servomotor

Planetary gear units match these requirements perfectly. As applications have developed increasingly shorter time intervals, higher productivity, and speeds, they've created a demand for even more sophisticated gear units in the future. Today, not every planetary gear unit satisfies industry's demands. Spur gear units, especially, create too much noise and (due to planetary units' compact design) heat, which often leads to leakage problems because the seals frequently can't tolerate the temperature levels that can be achieved. Thus, we use grease to lubricate planetary units, eliminating the seals. Grease's disadvantage, however, is that once the unit runs for a while, it accumulates in the corners of the housing rather than staying on the gears, where it's really needed.

Today's manufacturing processes, combined with a gear selection process, allow backlash ratings of less than 3 arc-minutes in planetaries. It's important that the backlash is constant over the full range, enabling control over the application from a positioning standpoint.

Helical gearing allows us to have three gears in contact at any one time, compared with spur geared units, where the number of teeth in contact is 1.5–1.7 maximum. By having almost double the standard tooth contact, the pressure between the tooth flanks is cut in half. This reduces tooth wear and provides constant backlash over the full range. In addition, contrary to some theories, helical gears (as well as spur gears) do allow the necessary axial movement needed for thermal expansion caused by gears in motion.

Furthermore, the helical gearing and a highly sophisticated manufacturing process make possible a noise level that, compared with conventional planetaries, is approximately 12 dB A lower. This is quite impressive, considering a noise level reduction of 3 dB A means cutting the intensity by half. In other words, 16 highly sophisticated planetary gear units create the same noise level as one conventional unit, as shown in Figure 1.

Another feature of today's state of the art planetary units is that they're very efficient. An efficiency greater than 97% is possible by decreasing friction loss on the unit's input side, where the servomotor shaft is turning at very high speeds. Rather than sealing the input bearing in an oil bath, which means the inner seal diameter has to match the servomotor's shaft diameter, the input bearing is outside the oil bath and grease-packed. This decreases the seal's requisite diameter, resulting in much lower friction. Compared with lower-efficiency units, these planetary gears experience only a third of the efficiency loss. Testing has shown that the temperature decrease for an average-sized unit can be more than 50°F. Ergo, a high-efficiency planetary gear unit can, at the same temperature, be driven with up to 30% higher input speeds (Figure 2).

To correctly mount the motor, it's critical to have a coupling system that allows no room for shaft misalignment. Conventional units often have double- or even single-split couplings, which don't permit concentric clamping of the motor shaft. Hence, in these cases the user is limited to mounting the motor to the gear unit only when the latter is in a vertical position. The solution to this problem is Figure 3's triple-split coupling, which uses the same principle as a chuck in a lathe: The coupling clamps the motor concentrically, permitting mounting with the gear unit in any position. This can be a big advantage, especially in situations where space restrictions apply.

You may find that today's market has room for an increasing number of planetary gear unit suppliers. However, not all of them offer the same packages. Only a few offer matching products for all of today's increasingly demanding applications. Only the best products will have a chance to fulfill these requirements, and they too will need to stay current to best cope with tomorrow's needs. MC

## Author Information

Patrick Stöber is vice president and general manager of Stöber Drives, Inc., a German manufacturer of gear reducers and planetary gear heads. Patrick has been in charge of Stöber's U.S. operations since May 1999. Contact him at 1781 Downing Drive, Maysville, KY 41056; tel: (606) 759-5090; fax: (888) 4-STOBER (478-6237); www.stober.com.