Motion Control Resources
by Kristin Lewotsky, Contributing Editor
Motion Control & Motor Association Posted 07/28/2009
Gearboxes are of the workhorses of motion control systems. They can turn RPMs into muscle for a conveyor belt moving heavy boxes or convert the torque of a wind turbine into sufficient speed to drive a generator. They can completely change the direction of motion. The technology is powerful, with sufficient options to satisfy virtually every occasion - when used properly, that is. Let's take a look at some of the options in today's market and some of the pitfalls to avoid.
A gearbox is a mechanical device that transfers power from one element to another in a system. Typically, a gearbox is integrated with a motor to convert the raw motion of the motor into the speed and torque necessary for the application. We define the gear ratio G for two gears as the ratio of their diameters, D1 and D2:
G = D2/D1
If we attach a motor producing torque t1 at speed w1, our output torque t2 and angular velocity w2 are given by:
t2 = tiG
w2 = wi /G
In other words, a gear box with a reduction ratio of greater than one yields increased output torque and decreased speed.
There are a wide range of types of gearboxes. We can class the gears themselves by the characteristics of the teeth. A spur gear features teeth that are parallel to the axis of rotation of the gear and tend to produce rolling motion rather than sliding motion (see figure 1). This type of gear is economical and can provide a lot of power. The surface area in contact on meshing teeth is limited, however, which can lead to faster wear. When the teeth of spur gears mesh, they slip into place all at once over the length of the tooth. Depending on how the gear is used, this can cause some unevenness of motion. It can also cause backlash, in which is essentially the delay between motion of the input shaft and motion of the output that occurs during reversals of motion. Backlash is caused by the space between the teeth on two meshing gears when contact is re-established.
A helical gear features teeth that are slanted with respect to the axis of rotation (see figure 2). The gradual meshing of the teeth provided by the angled design yields smoother motion. The greater amount of surface area in contact at all times also increases lifetime compared to basic spur gears and can reduce backlash. “With a spur gear you always have 1:1 tooth contacts,” says Chris Ball, Product Sales Manager at Lenze-AC Technology (Uxbridge, Massachusetts). “With a helical gear you get 1:1.5 so you can transmit 10 to 15% more torque.” The trade-off is more complex machining, and hence, higher price.
To be useful, gears must be combined into gear sets and gearboxes. The engagement of an inline gear set is parallel to the rotational axis. The engagement of a bevel gear set is typically at a 45 deg angle and redirects the rotational axis by 90 deg (see figure 3). Although the orientation of the teeth can be vertical, as in a straight bevel gear, they are more commonly slanted, as in a helical bevel gear. The angled face can also be curved, for spiral or even hypoidal gears, which combine a rolling and sliding motion for high efficiency and low noise.
The teeth can also be spiraled around in a cylinder like screw threads to form a worm gear (see figure 4). A worm gear typically provides sliding motion. It suffers very low efficiency but it can stand up to large loads and provides an economical solution for low performance applications.
The various types of individual gears can be combined together in gearboxes. In addition to the in-line and bevel designs, there are planetary gearboxes, harmonic gearboxes, and cycloidal gearboxes.
A planetary gear gets its name from the arrangement of the central gear (the sun), the orbiting gears (the planets), and the outer ring (the annulus). Because of the number of teeth interfacing, planetary gears tend to offer very smooth, accurate motion with long lifetime, low wear, and extremely low backlash. They can also accommodate very large loads and torques.
The downside is that because of the complexity they are often larger and heavier than the alternatives, as well as more expensive than simple in-line or bevel gears. The sheer number of surfaces meshing can reduce efficiency. Particularly in high-torque applications, shear forces can cause exert uneven pressure on the individual planet gears, triggering axial misalignments. This compromises efficiency and causes wear that reduces lifetime.
One solution to this problem is substituting the fixed bearing pins of the planet gears with flexible cantilevers that allow the individual planet gears to adjust position to equalize loading (click here for the Flexdrive Animation Video courtesy of Timken). “Because of the flexibility of the system, it ensures uniform contact with the gear so that it doesn’t need to be as wide,” says Doug Lucas, Manager of Application Engineering in the wind-energy business unit at the Timken Co. (Canton, Ohio). “It can be narrower because you don’t have to account for any stress concentration factors.” That opens up the potential for compact, lighter planetary gearboxes.
The approach offers other advantages. The torque of each planetary gear is affected by the load-sharing factor, Kg. As its name suggests, Kg describes how the torque on the gearbox is shared among the various planet gears. Conventional planetary designs with fixed bearing pins tend to consist of three planets because that configuration yields a load-sharing factor of Kg = 1 which indicates the load is shared evenly. If we change our configuration to n = 7, the configuration becomes less deterministic, with Kg rising as high as 1.4 or 1.5. The flexible-pin approach reduces the Kg opening up the possibility of using larger numbers of planet gears to distribute force and increase both lifetime and efficiency. “We’ve actually found through testing that we are able to get that load sharing factor are down to 1.2 for seven planets,” says Lucas. “We’re now more able to understand and predict how load sharing goes through the system.”
Another option is a cycloidal gearbox, which features a pair of side-by-side elliptical plates enclosed by a ring gear. The plates rotate along a cycloidal path so that one of the plates is meshing with the ring gear at all times (click here for the cycloidal gearbox video courtesy of Nabtesco Motion Control). As a result, backlash can drop as low as 1.5 arcmin. Because the design uses the entire casing of the gearbox design efficiently, it reduces wear to yield a 2000-hour cycle life. Designs include a central aperture that allows cabling to be passed through.
For the best performance, engineers turn to harmonic gearboxes. They consist of three nested elements: a solid steel outer ring with internal teeth, a flexible inner ring with external teeth and a slightly smaller diameter than the outer ring, and an elliptical cam nested inside that. The cam is driven by a shaft. As it turns, it deforms and rotates the flexible inner ring so that it precesses around the outer ring, the teeth remaining always in contact at two points (click here to view a harmonic gearbox courtesy of Harmonic Drive).
The devices achieve transmission accuracy of less than 1 arcmin, with high torque and repeatability of ± 5 arcsec. They are light, compact, and efficient while offering reduction ratios as high as 320:1. There is a price penalty to pay but for demanding applications, it may be worth it.
All mechanical systems suffer to some degree from what is known as lost motion: rotation of the input shaft or gear that does not translate to rotation of the output shaft or gear. The causes of lost motion include hysteresis, torsional elasticity or stiffness, and backlash. The latter, mentioned earlier, gets an unfair rap as an undesirable phenomenon. In reality, if gearing systems did not have some degree of backlash - some gap between the teeth of meshing gears -- there would be no room for lubricants and the gear train would seize up. Backlash is designed into every gearbox. The problem arises when backlash interferes with the positional accuracy required for an application.
“Part of the reason backlash is a problem is because people try to use the input encoder attached to the motor to give them output positioning," says Clyde Hancock, Director of Electro-mechanical Research at MicroMo (Clearwater, Florida). “If you have backlash built into the system and you go in one direction all the time, it probably won't be a problem. It's when you reverse direction that the backlash gets taken up. You lose a little bit of accuracy because now you have a movement at the motor that doesn't result in a movement at the output.”
For many applications, backlash is not a serious issue, in part because the accuracy gets a boost from the same gear ratio effect that reduces speed. For example, if a motor with a 100 line per revolution input encoder is attached to a 10:1 gear box, the resolution at the output is effectively 1000:1. For all but the most demanding applications, or systems with reduction ratios of less than one, this is typically enough. For systems that require better performance, a number of options exist.
Helical gears can give reasonably good backlash performance at an economical price point. If better performance is required, it's possible to configure a pair of parallel inline spur gear trains, both connected to the output shaft, to greatly reduce backlash. Essentially, a pinion gear sits between the two gear trains, which are preloaded such that the pinion gear teeth are always pressed against the surface of the opposing gear (see figure 5). If the pinion gear turns to the left, its teeth are pressed against the teeth of the gear train on the left. If the pinion gear turns to the right, its teeth are again pressed firmly against the teeth of the gear train on the right.
Of course, in the real world, nothing comes for free. Because the pinion gear is in contact with both gear trains at all times, the design requires more current to run, which should be considered if the application must be battery powered. In addition to being larger and heavier, this type of design suffers increased wear because of the constant contact of the gear teeth; moreover, the wear can be inconsistent depending on whether motion tends to involve full revolutions of the larger gears or just small increments. Once wear occurs, the “zero backlash" effect is compromised. The degradation is gradual, of course, and only manifests over time and duty cycle, but users should be aware of the issue.
An alternative is to turn to one of the more sophisticated gearbox designs - planetary, cycloidal, and harmonic. The trade-off, of course, is cost. Depending on the gearbox design, size can also be a factor. For applications that simply cannot tolerate error, the best solution is an output encoder that will monitor output position exactly.
Sizing a gearbox
Now that we’ve reviewed gearbox basics and new developments, let’s tackle the most important part: How do you choose a gearbox and what are the pitfalls? As with most motion control design, you should first know your application. What are you trying to accomplish? How well do you need to do it and how much money do you have to spend? “Typically an application is sized on a speed/torque basis,” says Ball. “After that, you have to study the application to make sure that you size the motor and gearbox properly. If the application has severe shock loads, certain running styles, changing loads, and so on, the gearbox needs to be oversized to make sure you compensate. You want your gearing to last a long time.”
Although gearboxes can significantly increase torque, they can only go so far. It is important to get a motor that provides enough torque to start with. Inertia mismatch between load and motor can be a problem, especially in the case of high acceleration rates. If you have very rapid start and stop application, every bit of mass plays a big role, inertially speaking.
“I think people trying to use a really small motor with 100:1 ratio can sometimes lead to a bad situation,” says Mike Anselmo, Application Engineering Manager at Wittenstein Inc. (Bartlett, Illinois). “It takes a certain amount of torque to get the gearbox moving -- internal friction, seals, oil churning, the bearings, etc. We call this no-load running torque. Sometimes, we have users who can't even turn the gearbox because their motor is too small - all the torque is used up in turning the gearbox and there's none left for the application.”
Too high of an inertia mismatch and you can’t turn your gearbox or control the servo axis properly. Too low and you're not utilizing the motor to its full capability which means that the motor is now the biggest load in the system and you're spending the majority of the energy just to accelerate it. Anselmo’s advice is to work from the load back. “Start with the load and all the mechanisms in between and then add the motor,” he says. “That way you know what you're dealing with because if you don't include that extra mechanism (the mechanical component that does have inefficiencies or losses in it), you could run into that case we just talked about.”
The load helps determine gearbox sizing but you also need to take into account where that load is positioned. “If you have a good balance in your center of gravity, the overall life of the product is guaranteed to be a lot longer,” says Jim Gruszczynski, Sales Engineer at Nabtesco Motion Control Inc. (Novi, Michigan). Depending on the load, offsetting the center of gravity by a matter of inches can make a big difference. “We can say our gearboxes can do 27,000 lbs but if you throw in a 4 in. offset, now we have to go back and calculate the mass on the output bearing to make sure there are no extra radial forces that will cause that bearing to fail.”
Performance is not the only consideration. The solution has to fit in your available space, especially if it’s a retrofit, and cost is always a factor. Above all, you need to prioritize your requirements. If pricing is most important, for example, a spur gear or a worm gear might work. If torque is more of a priority, perhaps a helical gear is a good fit. If performance trumps all, then one of the more sophisticated gearbox designs are your best bet.
Of course, the highest precision gearbox is useless if it is not properly integrated into the system as a whole. “When you assemble something with a precision gearbox, you should also do it with high precision,” says Gruszczynski. “If a tech in the shop is out there working and can’t get something to fit together so he takes a mallet to it or grinds something off, it's a problem.”
With the range of gearbox technologies available, if you take time to understand your application and watch out for the pitfalls in working with gearboxes, your solution will be a success.