How to Specify Gearboxes for Motion Control Systems
| By: Kristin Lewotsky, Contributing Editor
Gearboxes can be used to fine-tune the performance characteristics of a motion axis. They’re most commonly considered torque multipliers but actually serve several other functions, including speed matching, inertia reduction, and resolution increase. Properly specifying a gearbox for a servo motor or stepper motor involves taking into account machine parameters, application requirements, environmental conditions, mechanical factors, and, of course, budget. Here, we review the process of sizing and selecting a gearbox for a servo or stepper system with an eye toward achieving the required performance at a price that won’t break the bank.
Why Use Gearboxes?
Gearing can play a number of roles in motion systems. Let’s start by considering the gear ratio G, which is given by:
G = D2/D1
If we attach a motor with torque t1 and input speed w1, and the output of the gearbox will be
t2 = t1 G
w2 = w1 / N
In other words, the gearbox acts as a torque multiplier and a speed reducer. Torque multiplication makes it possible to drive a system with a much smaller motor, saving money and space.
For some applications, the role of the gearbox as a speed reducer is just as important as its function as a torque multiplier. Crystal growth, for example, requires the boule to be gradually raised out of a drum holding the melt. To keep the crystal as round, smooth and homogeneous as possible, the entire assembly must be rotated very gradually, at a rate of 15° per hour.
The servo system provides tight control of angular velocity, but servomotors don’t traditionally perform well or generate much torque at slow speeds. Adding the gearbox enables the servo motor to run at optimal speed from a controls standpoint while still generating a modest amount of torque, which increases to the required levels by the gear ratio.
Gearboxes are also very useful for inertia matching. It’s not enough for the motor to be able to start the load; it needs to control and decelerate it as well. If the load inertia is too much higher than that of the motor, the axis will be unable to position the load at the location and time required, and performance will suffer. This is where the gearbox can assist.
By multiplying motor torque, a gearbox also effectively scales the motor’s ability to control the load. The inertia reflected from the load, JR, is scaled by the gear ratio as:
JR= JL / G 2 + JG
where JG is gearbox inertia.
The gearbox scales the reflected inertia by the inverse square of the reduction ratio. This property equips a smaller motor to effectively control a larger load. The approach saves money, reduces the size, and enhances performance. However, it’s important to remember that the gearbox does contribute to overall inertia.
The gear ratio also increases the resolution of a stepper motor. “The steps are diminished directly by the ratio of the gearheads,” says Brien Shirey, Director of Engineering at CGI Gear (Carson City, Nevada). “You have a resolution that's much finer at the output shaft at the gearhead.”
Another less appreciated benefit to gearboxes is that they can reduce running noise in servo systems. “There's a misconception that servo gearboxes are loud,” says Joe Schneider, Application Engineering team lead at Wittenstein (Bartlett, Illinois). “However, the motor creates a lot of that noise itself. Especially when it's operating at higher utilization, you start getting winding noise. If the gearbox is properly sized, the noise is mitigated because you're not working the motor as hard. The gearbox is doing the work.”
Gearboxes do involve some trade-offs. They add size and weight to the system, although that can be offset, to some degree, by the accompanying reduction in the size of the motor. They increase cost, although the motor/gearbox combination may still be less expensive than a larger motor. In any case, gearboxes do add complexity and points of failure to the system. They increase maintenance and monitoring tasks. The latter issues can be mitigated to a large extent by properly specifying the gearbox for the application. Let’s take a look at how.
Specifying a Gearbox
Gather Application Requirements
Specifying a gearbox for a motion control system requires much more than just application torque or speed data. Before prospecting online or picking up the phone to call a vendor, assemble a detailed description of the application, with as much technical information as possible.
Key parameters include:
- Load inertia: Take advantage of the skills of your vendor. Most manufacturers offer sizing software, some of which is quite sophisticated. Work with the applications engineers, sending them CAD renderings of your system and whatever other information is available.
- Motion profile: Detail the full motion profile, including acceleration time (tacc), continuous run time (tcont), deceleration time (tdec), and dwell time (tdwell). These can be used to determine:
- Maximum continuous speed (Ncont): Calculate the maximum continuous speed required for the motion cycle, as this will be used to determine the gear ratio.
- Duty cycle: This quantifies the amount of time in each cycle spent moving, as opposed to dwelling. It can be used to identify the type of motion taking place, which will help determine the scale factors used during the sizing process.
- Layout: Although most applications can be served by multiple types of gearboxes, the configurations and space constraints of some applications require certain form factors; for example, a right-angle gearbox in an AGV steering solution.
- Environmental issues: These include temperature, pressure, moisture, contamination, etc.
The parameters above can be used to calculate:
- Acceleration torque (Tacc)
- Continuous run torque (Tcont)
- Deceleration torque (Tdec)
- Dwell torque (Tdwell)
We will use these two sets of data to determine root mean cube output torque and use that to calculate the gear ratio required for the application.
It’s not enough for the gearbox to generate enough torque to drive the load. It also needs to meet the lifetime requirements of the application. Material fatigue is one of the most common failure modes for gearboxes. For an improperly sized gearbox, repetitive stress can cause teeth to break and deform, or bearings to develop defects. The equipment underperforms and fails prematurely (and sometimes catastrophically). To minimize these issues, manufacturers use stress testing to determine ultimate tensile strength (fracture point), the yield strength (point of irreversible damage), and endurance limit (maximum stress that can be applied for unlimited cycles without damage) of the gearbox material. This data provides the foundation for gearbox ratings.
Certain conditions such as heavy usage, high shock loads, and extreme temperatures can intensify stress on the gearbox. As a result, gearboxes are de-rated under certain circumstances (using service factor and application factor, for example). This takes place more frequently for continuous-duty axes than for intermittent-duty systems, but the technique is still applied on occasion.
Sizing a gearbox for a single axis in a simple configuration can be straightforward, but for complex, multi-axis systems, the process becomes difficult in a hurry. Here, we will review the basics.
Start by determining the duty cycle D to confirm that the system is intermittent. We define duty cycle as
A motion is considered to be intermittent if the duty cycle is less than 60% and the sum of tacc, tcont, tdec is less than 20 minutes. Gearboxes for intermittent applications typically don’t require de-rating to address thermal factors because the start-stop nature of the motion allows time for the heat to dissipate each cycle.
The motion is considered continuous if the duty cycle is 60% or greater. These systems will need to be de-rated to compensate for heat buildup.
Calculate the Root Mean Cube output torque (Tmean):
Review potential gearheads and look for one that can deliver the following performance:
Tmean ≤ Tnomr
tacc and tdec ≤ taccr
where Tnomr is nominal rated torque and is rated acceleration.
Calculate maximum allowed gear ratio Gmax using
Gmax = Nmaxr / Ncont
where Nmaxr is maximum rated input speed for the candidate gearhead.
We can calculate mean input speed Nmeani and maximum input speed Nmaxi using
Nmaxi = G Ncont
Double-check that the operating speeds and accelerations all within the rated speeds and accelerations. In addition, gearboxes for servo/stepper axes operating with continuous or intermittent motion should be de-rated by a temperature factor KT and/or shock factor KS as shown in the table below1:
Table 1: De-rating guidelines for continuous and intermittent motion
Tmean KT KS
Tnomr > Tmean KT KS
Tnomr > Tmean KS
Courtesy of Parker Bayside
It’s also important to determine E stop torque and confirm that the gearbox can handle it. The immediate stop can cause teeth to slam together and in the worst-case scenario, break. “You have to take into consideration a crash or an e stop situation,” says Jason Hale, Sales Engineer at Nabtesco Motion Control (Farmington Hills, Michigan). “Can the gearbox handle the load moving at the speed you want to move it, and then stop on a dime? Or is it going to damage the gearbox? Do you need to go up a size? Now is the time to check that.”
Confirm that the gearbox can tolerate stresses involved. Ensure that operators understand that function should only be used in an emergency and not as a stopping mechanism during normal operations.
What are the Mechanical Considerations?
The next step is to check the mechanical design to ensure that both motor and gearbox are properly supported. It can be tempting to mount the motor on the gearhead rather than isolating the radial and axial loads using an outside bearing support. It may provide momentary savings but will very likely lead to premature failure of the gearhead.
In some cases, the moment load may be applied by an actuator such as a belt and pulley or rack and pinion. “those types of applications put a notable side load on the output shaft of the gearhead,” says Shirey. “If you're relying on the bearings of the gearhead to accommodate that, then you certainly have to size the gearhead so that it can accommodate that load. That might be a reason to go up in size in the gearhead even though it may not require much torque.”
In general, the frame sizes of motor and gearbox should be matched. Trying to mount a 75 frame motor on a 34 frame gearhead will apply a dangerous moment load to the front face of the gear, especially since units are usually attached by four bolts.
Consider Accuracy Requirements
Although every application is different, motion control systems typically use spur gears, worm gears, planetary gears, or one of the other more sophisticated high-performance gearboxes.
“For the vast majority of our applications, we use servomotors or stepper motors,” says Wally Logan, VP of Engineering at Motion Solutions (Alisa Viejo, California). “For the stepper applications, we typically go spur gearbox first and then step up to a planetary if we have to. For servo applications, we'll generally go the other way. We'll generally use a planetary gearbox and less there’s some reason we can go with a spur gearbox. For very high-end applications or those with tight packaging constraints, we sometimes use harmonic drive gearboxes.”
Gears need some finite amount of clearance between the teeth of matching gears in order to allow lubricant to work its way in between. When the input shaft or gear begins to turn, no actual motion of the output shaft or gear can occur until this clearance is taken up. As a result, every standard gearbox has some finite amount of backlash, which is the primary contributor to lost motion.
The amount of backlash varies depending on the tooth profile, the gearhead design, and the quality of the manufacturing. Spur gears, which are linear and make contact along the entire length of the gear teeth simultaneously, require the most clearance and have the greatest backlash. Helical gears, in which the teeth have a helical profile along their length so that the process of meshing is more gradual, demonstrate lower levels of backlash.
In terms of gearbox designs, planetary gearboxes have a very good backlash performance. A planetary gearbox consists of a central sun gear surrounded by three or more revolving “planet” gears, all enclosed by a ring gear (see. The increased contact area boosts stability. High-end planetary gearboxes can achieve backlash on the order of arc minutes. They are highly efficient and provide good power transfer levels. All of these factors make them extremely popular for use with servo, servo-and stepper-motion applications.
The next step up the performance ladder is the cycloidal gearbox. Cycloidal gearboxes are built around a pair of side-by-side elliptical plates enclosed by a ring gear. The plates rotate along a cycloidal path, alternating, so that one of the plates is meshing with the ring gear at all times. As a result, these gearboxes demonstrate backlash of between 0.3 and 0.5 arcmin, as tested under full load.
Cycloidal gearboxes are best suited to high-load applications with demanding positioning requirements, such as satellite dish steering systems or indexing tables for robotic welding. Particularly in the case of indexing tables, cycloidal gearboxes offer advantages. Worm gears, for example, are set to advance a predefined number of degrees per index, as defined by the number of starts on the worm gear. The design of the cycloidal gearbox enables it to be continuously positionable.
For high-end applications that require high torque in the smallest, lightest possible package, Logan points to harmonic drives. “They definitely take a little more engineering to use especially if you're going to design the gear into a custom application rather than just use an off the shelf gearbox,” says Logan. “There are also harmonic gearheads where you have a direct drive motor driving a harmonic gearbox, all in one package. We’ve been developing some of those here and they are pretty incredible. You can get a huge amount of torque out of a very small package.” He points to a turntable application for electronics manufacturing as an example combining high precision and high inertia.
Be sure to check with prospective vendors to determine how they measure backlash. Some companies calculated theoretically, while others actually test to confirm performance.
Plan for Efficiency
Gearbox efficiency is always important in real-world applications. Inefficient gearboxes dissipate energy and generate heat that needs to be managed. The most common gearboxes used in motion control, listed in order of increasing efficiency, are spur gears, helical gears, worm drives, and planetary gearboxes (see Figure 1). In particular, the efficiencies of worm gearboxes can be as low as 50%.
Low efficiency isn’t always a negative thing. In certain circumstances, a right-angle worm gear can be used as a reduced cost power-off brake. “Right-angle worm gears are self-locking above say 60:1 ratio, so some people use right-angle worm gearboxes because when the machine is off the gearcase prevents rotation of the shaft,” says Matt Hanson, General Manager of industrial markets at Bison Gear & Engineering (St. Charles, Illinois).
Right angle applications that require high efficiency typically require hypoid gearing. “These types of reducers use heat treated and ground hypoid gearing (85% efficient) that provide a quiet, robust gear solution,” Hanson adds.
Gearbox efficiency varies depending on speed, production ratio, and load. A gearhead operated no load will deliver good numbers but they won’t be meaningful in a real-world context. Once again, be sure to ask the vendor how they measure efficiency.
Determine the Right Form Factor
Performance is essential but the gearbox needs to fit into the system. Are there size and weight limitations? Does the layout require specific designs such as right-angle gearboxes rather than in-line gearboxes? Does the system need a phalange output for proper assembly or should it be shafted? Design engineers also have a broad selection of hollow-bore gearboxes available in different styles to provide paths for cabling and fiber optics. These designs are particularly useful for robotics.
Form factors are primarily considered a matter of convenience but they have a bearing on performance as well. A right-angle gearbox can’t transfer power as effectively as an in-line design. High-torque applications benefit from flanged mounts. That said, with careful specification and installation, flanged and flush-mount designs can work equally well.
Don’t Forget Environmental Concerns
Motion control systems operate in a wide variety of environments ranging from clean rooms to syrup bottling lines to sawmills. Environmental conditions should always be taken into account during gearbox selection. Gearboxes that will operate in hygienic environments will probably need IP-rated enclosures and anti-corrosion coatings. Devices destined for clean rooms will need specialty greases and seals. Be sure to bring up these factors during discussions with vendors.
What About Budget?
With the exception of certain aerospace and military applications, every project has budget realities. The choice of gearbox provides another degree of freedom for achieving performance goals while meeting budget.
For many cost-sensitive applications, designers choose lower-end versions of standard motion control gearboxes. “Typically on stepper applications, you're generally looking at cost [as a primary concern],” says Logan. “A limited budget is why we would be using a stepper motor in the first place, so that would narrow down our choices right away to either a low-cost planetary gearbox or a low-cost spur gearbox.”
Worm gearboxes tend to have fairly high gear ratios, delivering large torque multiplication in a fairly small package. There were other benefits, as well. “Worm gearboxes tend to be quite quiet,” says Logan, who points to a project building a patient bed for a treatment machine. “We started out with a relatively high ratio planetary gearbox. At the relatively high motor speeds we had to run, the gearbox was pretty noisy. We switched to a worm gearbox and the noise was much less. Even though the gearbox is probably a little less efficient, for us, the trade-off was less noise from a gearbox with a similarly high gear ratio.”
Gearboxes are essential tools in the arsenal of the OEM. They can be leveraged as torque multipliers, speed reducers, inertia matchers, or even tools to increase resolution. When properly selected, installed, and maintained, a gearbox can operate for decades without intervention. “We get gearboxes all the time that were installed in the '90s,” says Schneider. “We see that as long as a gearbox is sized correctly.”