Review of general gear operation

Review of general gear operation

Gears mesh with other gears to transmit altered torque and rotation. In fact, gearing can change the speed, torque and direction of motion from a drive source. When two gears with an unequal number of teeth engage, the mechanical advantage makes their rotational speeds and torques different.

In more complex setups, parallel-axis gearsets have helical gears that engage at an angle between 90° and 180° for more tooth contact and higher torque capacity. Helical reducers are suitable for higher-horsepower applications where long-term operational efficiency is more important than initial cost. Helical gear teeth engage gradually over the tooth faces for quieter and smoother operation than spur gearsets. They also tend to have higher load capacities. One caveat: Angled tooth contact generates thrust that the machine frame must resolve.

No matter the subtype, most parallelaxis gearsets have gear teeth with tailored involute profiles — customized versions of the rolled trace off a circle with an imaginary string. Here, mating gears have tangent pitch circles for smooth rolling engagement that minimizes slipping. A related value, the pitch point, is where one gear initially contacts its mate’s pitch point. Involute gearsets also have an action path that passes through the pitch point tangent to a base circle.

Besides parallel-axis gearsets, there are non-parallel and right-angle gearsets. These have input and output shafts that protrude in different directions to give engineers more mounting and design options. The gear teeth of such gearsets are either bevel (straight, spiral or zerol), worm, hypoid, skew or crossed-axis helical gears. The most common are bevel gearsets with teeth cut on an angular or conical shape. Hypoid gears are much like spiral-bevel gearsets, but the input and output shaft axes don’t intersect, so it’s easier to integrate supports. In contrast, zerol gearsets have curved teeth that align with the shaft to minimize thrust loads.

Basics of strain-wave gearing

This example of strain-wave gearing is the HIWIN DATORKER — a gearing set specifically for robotic applications.

Tooth-engagement kinematics of strain-wave gears is different than that of planetary or spur gearing. Strain-wave gearing uses the metal elasticity (deflection) of a gear to reduce speed. Benefits of strain-wave gearing include high torque, compact size, positional accuracy, and zero backlash. Recall that backlash is the difference between the tooth space and tooth width ... and this difference is zero in strain-wave gearing.

A strain-wave gearset consists of a wave generator, flexspline, and circular spline. The wave generator is an assembly of a bearing and a steel disc called a wave-generator plug. The outer surface of the wave generator plug has an elliptical shape machined to precise specification. A specialty ball bearing is pressed around this plug to cause conformity to the same elliptical shape of the wave-generator plug. Designers typically use the wave generator as the input member, usually attached to a servomotor.

The flexspline is a thin-walled steel cup. Its geometry lets the walls of the cup be radially compliant but remain torsionally stiff (because the cup has a large diameter). Manufacturers machine the gear teeth into the outer surface near the open end of the cup (near the brim). The flexspline is usually the output member of the mechanism.

The cup has a rigid boss at one end to provide a rugged mounting surface. The wave generator is inserted inside the flexspline so the bearing is at the same axial location as the flexspline teeth. The flexspline wall near the brim of the cup conforms to the same elliptical shape of the bearing. This conforms the teeth on the outer surface of the flexspline to the elliptical shape. That way, the flexspline effectively has an elliptical gearpitch diameter on its outer surface.

The circular spline is a rigid circular steel ring with teeth on the inside diameter. It is usually attached to the housing and does not rotate. Its teeth mesh with those of the flexspline. The tooth pattern of the flexspline engages the tooth profile of the circular spline along the major axis of the ellipse. This engagement is like an ellipse inscribed concentrically within a circle. Mathematically, an inscribed ellipse contacts a circle at two points.

However, the gear teeth have a finite height. So there are actually two regions (instead of two points) of tooth engagement. Roughly 30% of the teeth are always engaged ... 60 teeth for a 100:1 gear ratio. This contrasts with maybe six teeth for a planetary gear and one or two teeth for a spur gear.

The pressure angle of the gear teeth transforms the output torque’s tangential force into a radial force acting on the wave-generator bearing. The teeth of the flexspline and circular spline engage near the ellipse’s major axis and disengage at the ellipse’s minor axis.

Note that the flexspline has two less teeth than the circular spline, so every time the wave generator rotates one revolution, the flexspline and circular spline shift by two teeth. That means the gear ratio = number of flexspline teeth ÷ (number of flexspline teeth - number of circular spline teeth).

Gearboxes, specialty gearheads, and servogear sets

GAM Enterprises now offers SSP Series washdown servo gearboxes for food, medical or sanitary applications. The precision inline planetary gearboxes include a 300-series stainless steel housing. Shown here is the SSP-W gearbox with a stainless KG-VA coupling.

Servo systems are precision-motion setups that demand servogear reducers with good torsional stiffness, reliable output torque and minimal backlash. OEMs tasked with integrating servo systems should look for quiet reducers that easily mount to the motor and require little or (if possible) no maintenance. In fact, a lot of advanced machinery integrates servogears into application-specific electromechanical arrangements, and several of these arrangements are common enough to have specific labels. Here is a look at some of the most widespread.

Gearmotor: This complete motion component is a gear reducer integrated with an ac or dc electric motor. Usually the motor includes the gears on its output (typically in the form of an assembled gearbox) to reduce speed and boost available output torque. Engineers use gearmotors in machines that must move heavy objects. Speed specifications for gearmotors are normal speed and stall-speed torque.

Gearbox: This is a contained gear train … a mechanical component consisting of a series of integrated gears. Planetary gears are common in integrated gearboxes.

Planetary gears: Particularly common in servo systems, these gearsets consist of one or more outer planet gears that revolve about a central, or sun, gear. Typically, the planet gears mount on a movable arm or carrier that rotates relative to the sun gear. The sets often use an outer ring gear, or annulus, that meshes with the planet gears.

The gear ratio of a planetary set requires calculation, because there are several ways they can convert an input rotation to an output rotation. Typically, one of these three gear wheels stays stationary; another is an input that provides power to the system, and the last acts as an output that receives power from the driving motor. The ratio of input rotation to output rotation depends on the number of teeth in each gear and on which component is held stationary.

Planetary gearsets offer several advantages over other gearsets. These include high power density, the ability to get large reductions from a small volume, multiple kinematic combinations, pure torsional reactions and coaxial shafting. Another advantage of planetary gearbox arrangements is efficiency. Losses are typically less than 3% per stage, so rather than waste energy on mechanical losses inside the gearbox, these gearboxes transmit a high proportion of the energy for productive motion output. Planetary gearbox arrangements distribute load efficiently, too. Multiple planets share transmitted load between them, which greatly increases torque density. The more planets in the system, the greater load ability and the higher the torque density. This arrangement is also very stable due to the even distribution of mass and increased rotational stiffness. Disadvantages include high bearing loads, inaccessibility and design complexity.

In servo systems, besides boosting output torque, gearboxes impart another benefit — reducing settling time. Settling time is a problem when motor inertia is low compared to load inertia … an issue that’s the source of constant debate (and regular improvement) in the industry. Gearboxes reduce reflected inertia by a factor equal to the gear reduction squared.