Power Transmission Reference Guide 2020

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VOLUME 6 NUMBER 2

CONTENTS 6 8 14 18 22 27 30 35 37 40 46 48 52

Editorial Linear actuation + power transmission Linear bearings • slides • guides Bearings Belts Brakes + clutches Couplings Encoders Gearing Motors Wave springs + retaining rings Shock + vibration mitigation Ad index

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Automation in the time

of coronavirus WELCOME

to Design World’s special issue on Power Transmission. Each year our editors assemble this

special issue that focuses on the mechanical part of power transmission, the components responsible for keeping things moving, so to speak.

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These are the screws and actuators, the slides and rails and guide ways and the linear bearings that help bear the loads – and the belts, brakes, clutches, couplings, motors and gears, and the components that dampen shock and vibration.

Much continues to change in power transmission and motion control systems, with electronic controls adding smarts to systems and faster communication networks better able to handle large volumes of data enabling better and more precise control. But the mechanical components are changing too. For instance, newer materials extend useful life and durability of workhorse components such as bearings and guides. Also, improved lubrication materials help parts run smoother and more reliably in a range of environmental conditions.

Many of these components are central to the latest wave of automation, helping power robotic systems in warehousing and material handling applications, among a host of others. The rise in automation also takes on a new dimension in the midst of the COVID-19 pandemic. Now more than ever, manufacturers are turning to automating manufacturing processes and tasks as a way to reduce contact between workers and to keep them at safe distances from one another.

Automation also is central to critical medical and laboratory equipment. For instance, linear motion systems enable rapid, high-volume automated testing of the kind that is needed to deal with extraordinary events like the COVID-19 pandemic. These automation systems must perform an array of step-by-step tasks with a high level of precision and accuracy.

A typical large-scale test setup includes a number of different subsystems working together. For example, gantry robots with rotary end effectors are used to remove caps from sample tubes containing specimens to be tested, while separate Cartesian robots or gantry systems are used to extract samples and dispense fluids. Then, linear actuators or belt conveyors are used to move samples to different parts of a workstation.

Stories like this and many more are featured in a new section on the Design World web site (designworldonline.com) called “Hack the Crisis: Engineering through COVID-19.” There you’ll find the latest examples of engineering companies innovating to help in the battle against the coronavirus. And we’re always on the lookout for more success stories to share with our readers. So if you’ve got something to share, get in touch with me via email at mbudimir@wtwhmedia.com or on Twitter at @DW_Motion.

And remember that you can find all of the latest news and information about power transmission and motion control at our motion-specific sites motioncontroltips.com and linearmotiontips.com, as well as bearingtips.com and couplingtips.com.

MILES BUDIMIR • SENIOR EDITOR 6

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POWER TRANSMISSION REFERENCE

GUIDE

All about rigidity in

linear actuation THE

default method for increasing ballscrew rigidity is to increase the preload of the ball nut. However,

Fa

Fa

the ball nut is one of the most rigid components in the ballscrew assembly … so increasing ball nut rigidity has little effect on the overall system rigidity (except when upgrading from a ball nut with no preload to one that is preloaded). Also, higher preload causes higher frictional torque, which means more heat is generated and more torque is required to drive the screw.

A double ball nut is somewhat more rigid than a single nut but again, the effect is minimal due to the nut’s already high rigidity relative to the other components.

Ballscrew rigidity is calculated:

A double ball nut has higher rigidity than a single nut, but the overall effect on the ballscrew system’s rigidity is relatively small.

Where: Rtot = Rigidity of the screw system (N/μm) RS = Rigidity of the screw shaft (N/μm) RN = Rigidity of the ball nut (N/μm) RB = Rigidity of the support bearings (N/μm) RH = Rigidity of the ball nut and bearing housings (N/μm) The limiting factor for rigidity in a ballscrew assembly is typically the screw shaft. The rigidity of the screw shaft depends on its modulus of elasticity, diameter (which determines its crosssectional area), and unsupported length. The screw’s modulus of elasticity is dependent on the material (typically steel) and its diameter is primarily determined by the required thrust force and speed. The unsupported length of the screw shaft is determined by the stroke and the end bearing arrangement.

While the screw’s material and diameter are generally set by the application, the end bearing arrangement (and hence, its influence on unsupported length) is chosen based on factors such as speed, buckling load, and rigidity.

There are four common end bearing combinations for

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Nuts can help boost rigidity.

5 • 2020

ballscrew assemblies. From most to least rigid, they are fixed-fixed, fixed-floating, floating-floating, and fixed-free. A fixed end uses an angular contact thrust bearing, for support against both radial and axial loads, while a floating end uses a simple radial bearing, with no support for axial loads. A free end has no bearing support.

Using the stiffest bearing arrangement – fixed-fixed – increases the rigidity of the screw shaft by four times compared to the least rigid arrangement of fixed-free. This is due to two design advantages. First, using angular thrust bearings on both ends allows forces to be transmitted through the screw on both sides of the ball nut. In addition, with thrust bearings on both ends, the maximum distance between the ball nut and either one of the fixed bearings occurs when the nut is at the middle of the stroke, which means the unsupported length is one-half the length of the screw.

Another effective method to increase ballscrew rigidity is to change the way the assembly operates: hold the screw stationary and rotate the ball nut. In a rotating nut design, because the screw itself does not rotate, there is no need for support bearings on the motioncontroltips.com

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LINEAR ACTUATION + POWER TRANSMISSION The fixed-fixed end bearing arrangement provides the highest rigidity, while fixed-free is the least rigid arrangement.

L Lb

La

Fixed-fixed arrangements have the shortest unsupported lengths. ends of the screw shaft. Instead, the ball nut is supported by a large angular contact thrust bearing.

The screw shaft is rigidly mounted at both ends, which allows torsional moments to be transmitted to the mounts at each end of the screw. While a rotating nut assembly is very rigid, its construction can pose dimensional problems and interference issues for applications that were designed with standard rotating screw assemblies in mind.

RIGIDITY IN LINEAR ACTUATORS AND LINEAR STAGES Although there are no industry standards that define linear actuators and linear stages, generally accepted terminology indicates that: A linear actuator is typically constructed with an aluminum extrusion or base A linear stage is typically built on a flat, machined steel or granite base.

This distinction implies that linear actuators can provide longer strokes and use a variety of drive mechanisms (belt, screw, rack and pinion) while stages generally have higher rigidity and use highprecision linear guides and drive mechanisms (typically a ballscrew or linear motor) for excellent travel and positioning accuracies.

But one actuator design — the U-shaped linear actuator — defies these specifications ... using an extruded steel base to provide rigidity and travel accuracy specifications that rival some linear stages.

The use of a steel (rather than aluminum) profile makes the U-shaped design extremely rigid and allows manufacturers to offer a linear actuator with the high travel and positioning accuracies typically found in more precise (and more expensive) linear stages.

The steel base can also be machined to provide a reference edge for precise alignment with other machine components ... or with other actuators in a multi-axis system.

With their very high rigidity, U-shaped linear actuators can be better suited than other designs to applications where the actuator is supported only on one end.

These include two and three-axis Cartesian systems, for example.

In the U-shaped actuator design, the linear guide system is integrated — there is no guide rail. Instead, the raceways that would normally be found on the guide rail are ground into the inside of the

5 • 2020

DESIGN WORLD — MOTION

9

base. The carriage or table is analogous to a linear bearing block turned inside-out, with the balls riding on the outside.

This leaves the center portion of the carriage available to accommodate the ballscrew nut. This construction principle makes the entire actuator extremely compact, with a width-to-height ratio of approximately 2:1. For example, a U-shaped actuator with a width of 60 mm is only 33 mm high. The most common cross-sections (width x height) are 40 x 20 mm, 50 x 26 mm, 60 x 33 mm, and 86 x 46 mm … although other sizes are offered as well.

POWER TRANSMISSION REFERENCE

In a fixed-fixed end bearing arrangement, the maximum unsupported length is 1/2 the length of the screw (La=Lb).

GUIDE

Fixed-free arrangements provide the least rigidity.

Floating-floating support includes a simple radial bearing at each end.

A fixed-floating arrangement has bearings at both ball screw ends, but a thrust bearing only at one.

A fixed-fixed arrangement provides maximum rigidity.

Some manufacturers offer U-shaped linear actuators made from extruded aluminum profiles, with steel inserts for the linear guide raceways. Aluminum versions lack the rigidity of steel designs, but they offer a very compact profile. In addition, they are often dimensionally interchangeable with steel versions where an application might benefit from a lower-cost option. Note that the use of a steel (rather than aluminum) profile makes the U-shaped design extremely rigid and allows manufacturers to offer a linear actuator with the high travel and positioning accuracies typically found in more precise (and more expensive) linear stages.

While steel versions of U-shaped linear actuators use ballscrew drives almost exclusively, aluminum designs are more likely to be offered with both ballscrew and leadscrew drive options.

Originally developed for high-precision applications such as semiconductor wafer handling and medical diagnostic dispensing — for which space constraints don’t allow a typical linear stage — U-shaped linear actuators are now used in a wide variety of

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industries and applications. These include plasma welding, automated assembly, and optical inspection.

One of the driving factors behind the widespread adoption of U-shaped actuators is that they are the only linear actuator design with dimensional interchangeability between manufacturers.

However, it’s important to note that due to differing guideway and ballscrew designs, technical specifications (such as load capacity, speed, or rigidity) can vary between manufacturers and product lines — even for products with the same cross-sectional size and mounting dimensions.

MORE MECHANICAL PROPERTIES: STIFFNESS AND DEFLECTION Note that in most linear-motion contexts, stiffness is the rigidity of an assembly and the extent to which it resists deformation under loading. That’s in contrast with rigidity that we've just explained — the inability of a material to be to deformed by some force.

Recall from the classic stress-strain curve how various aspects of material strength 5 • 2020

(including tensile strength, yield strength, and fracture strength) relate. While we often think of materials and structures in terms of strength, technically strength is a measure of how much force a material can withstand before permanent deformation or failure occurs. For proper running of linear guides, actuators, and other motion components, it’s typically more important to know how much deflection the object will experience under a given load — in other words, the more important property is the object’s stiffness.

A material’s stiffness indicates its ability to return to its original shape or form after an applied load is removed.

When a material is subjected to a load — including its own unsupported weight, an external applied load, or both — it experiences stress and strain. Stress σ is an internal force on the material caused by the load, and strain ε is the deformation of the material that results from this stress. The ratio of stress (force per unit area) to strain (deformation per unit length) is referred to as the modulus of elasticity denoted E. This ratio of stress to strain is also referred to as a motioncontroltips.com

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POWER TRANSMISSION REFERENCE

Tubular linear motors see increased use in automation

GUIDE

This actuator design has various names depending on the manufacturer. We call it a U-shaped linear actuator in reference to its defining feature — a U-shaped extruded steel profile.

Matt Prellwitz | Motion control product manager ● Beckhoff Automation

Ironless tubular motors are suitable for an array of existing and new linear motion scenarios.

They usually replace pneumatic and hydraulic options for linear actuation. That’s in part because ironless tubular motors offer a compact design, easy integration, and high precision and dynamics … features that are useful in packaging, machine tool, paper, textile, and food industries.

In combination with the Beckhoff AX8000 or AX5000 servo drives, AA2518 ironless tubular motors is suitable for linear motion … especially in confined spaces. The AA2518 leverages water cooling to deliver a peak force of 1,050 N and acceleration to 8 m/sec.

The magnetic rods are 35 mm in diameter and available in lengths of 700 mm and 1,000 mm.

The absence of additional mechanical parts minimizes wear, resulting in lower maintenance costs than systems that use a spindle.

For more information, visit www.beckhoff.com/drivetechnology.

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material’s elastic modulus, tensile modulus, or Young’s modulus.

According to Hooke’s Law, the modulus of elasticity is the slope of the linear portion of the stress-strain curve, up to the proportional limit … also called the elastic limit.

A material that is strong can withstand high loads without permanent deformation. A material that is stiff can withstand high loads without elastic deformation. Another material property sometimes confused with strength or stiffness is hardness. Hardness defines a material’s ability to resist localized (surface) deformation often due to friction or abrasion.

Unlike strength, a material’s stiffness or modulus of elasticity is an inherent property of the material … and external factors such as temperature or material processing have very little effect on its value.

But in practical applications, the stiffness of a structure depends on both the material’s modulus of elasticity and the structure’s geometry in terms of planar moment of inertia (also referred to as second moment of area). Planar moment of inertia I expresses how the material’s area is distributed around the axis of motion.

The product of modulus of elasticity and planar moment of inertia is sometimes referred to as the material’s flexural rigidity EI. In equations for deflection, both stiffness factors — the modulus of elasticity E and the planar moment of inertia I — appear in the denominator. This makes sense because deflection is inversely related to stiffness. So the higher the material’s modulus of elasticity (and the higher the object’s planar moment of inertia) the less the structure will deflect under a given load.

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THINK INSIDE THE BOX Exceptional designs deserve superior components.

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POWER TRANSMISSION REFERENCE

GUIDE

Comparing options for

linear bearings, slides, and guides LINEAR-MOTION

devices incorporating ball and roller elements include plain

bearings, ball bushings, recirculating roller bearings. Confusing matters is the fact that industry uses many linear-motion terms interchangeably … and many terms such as linear guides are so generic that they can refer to any one of several different products.

While the plain-bearing guide taxonomy has less variability in terminology and specification, ball and roller linear guides have quite a lot. So let’s review all these terms that are used to identify, describe, and specify them.

In many though not all cases, the term linear guide indicates a standalone guide rod, ball slide, or mechanism solely for guiding loads. In contrast, many manufacturers use the terms linear slide and linear rail to indicate a linear-motion guide element that is incorporated into an integrated build complete with mechanical drive. The term linear stage generally implies a design has guided elements as well as some mode of mechanical linear actuation and reinforced body — often sans inclusion of the motor.

Plain bearing linear guides can be boxway, dovetail, or shaft and bushing design.

LINEAR-BEARING DESIGNS BASED ON SLIDING CONTACT

BOXWAY PLAIN BEARING

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DOVETAIL PLAIN BEARING

5 • 2020

BUSHING PLAIN BEARING

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LINEAR BEARINGS • SLIDES • GUIDES CIRCULAR ARC CONTACT VERSUS GOTHIC ARCH CONTACT

CIRCULAR-ARCH PROFILES HAVE TWO POINTS OF CONTACT.

Motorized rails (more commonly called linear actuators) abound — though the distinction here is that there are countless linear actuators sold sans any guided element. That’s useful for OEMs aiming to employ some specialized linear guide or omit it altogether.

Taxonomy variations don’t apply to just product descriptions: Design types and technical features are also called different names depending on the component manufacturer.

Plain bearings are the simplest type of linear guide, relying on sliding contact between two surfaces. Their construction can be boxway, dovetail, or shaft and bushing. Boxway bearings are able to carry the highest loads, while dovetail designs require less precise machining and assembly. Plain bearing bushings are simple to manufacture and install, but their unsupported shafts give them limited load capacities and make them vulnerable to deflection.

While metal surfaces provide the highest stiffness and load capacities, plain bearings can also be made of plastics or composites for high corrosion resistance and inherent lubricating properties. It’s important to note that sliding contact should always be between dissimilar materials, with one element being harder than the other. This allows wear to be concentrated in the softer element.

Plain bearings have a high coefficient of friction, typically 0.05 to 0.1, when 5 • 2020

GOTHIC-ARCH PROFILES HAVE FOUR POINTS OF CONTACT.

Profiled rail track geometries can be either circular arc or Gothic arch. compared to rolling-element bearings.

But unlike rolling elements, they can withstand shock loads and vibrations without significant damage to the surfaces.

Plain bearings are also less sensitive to contamination and rarely experience catastrophic failure.

In contrast, rolling-element linear guides add balls or rollers between the two bearing surfaces. Rolling-element bearings can be recirculating (profiled rail bearings or linear bushings or linear bearing guides) or non-recirculating linear bearings in the form of some cam roller guides or crossed-roller slides.

Recirculating designs allow unlimited motion along the length of the guide rail or shaft, where non-recirculating designs are limited in stroke by bearing length.

PROFILED RAIL TRACK GEOMETRIES A significant advantage of rolling-element linear guides is their low coefficient of friction, which is typically 0.005 to 0.01.

Because they’re made of bearing steel, they have high load capacities and can be preloaded for very high rigidity. One caveat is that preload increases friction and must be taken into account when sizing rolling element linear guides.

While plain linear bearings can be made from a wide variety of materials, DESIGN WORLD — MOTION

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POWER TRANSMISSION REFERENCE

GUIDE

RECIRCULATING AND NON-RECIRCULATING LINEAR BEARINGS

NON-RECIRCULATING ROLLING ELEMENTS

RECIRCULATING ROLLING ELEMENTS In non-recirculating linear guides the bearing housing contains rolling elements that move a finite distance along the base. In recirculating linear guides, the rolling elements recirculate through the bearing housing, so the bearing can travel an infinite distance (limited only by the length of the guide rail or shaft).

profile-rail rolling-element bearings come in the most diverse track geometries and raceway arrangements. Track geometry defines how the rolling elements make contact with the raceways. Profiled rail track geometries can be: • Circular arc — which provides lower friction or • Gothic arch — which gives higher moment capacities.

Circular arc geometry produces twopoint contact between the ball and the raceway. This gives the assembly a lower friction coefficient and smoother running characteristics.

Gothic arch geometry provides fourpoint contact between the ball and the raceways, resulting in higher moment load capacities … but also higher friction.

More specifically, the Gothic arch design provides two contact points on the ball and two contact points on the raceway.

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Determining the life of rolling element linear guides is done by calculating the L10 bearing life — a theoretical but statistically formulated prediction of the distance the bearing can travel before it reaches its fatigue life. The L10 life is based on the type and magnitude of loading, although environmental factors such as shocks, vibrations, and contamination can reduce the life of rolling element bearings.

While the construction of linear bearings that employ balls for friction reduction isn’t a technical specification, it is typically referenced in manufacturer catalogs. That’s in part because various linear-bearing construction options have a significant effect on performance.

the raceways point inward, making an X inside the profiled rail. This arrangement gives the assembly equal load capacity in all directions but reduces its ability to handle moment loads.

The back-to-back arrangement is also called the O arrangement because the contact lines point outward — making an O around the rail. This design gives a longer moment arm and allows the bearing to withstand high moment loads.

Raceway geometry determines the number of contact points between the ball and raceway and affects the bearing block’s friction and load capacity.

PROFILED RAIL ARRANGEMENTS To review, raceway arrangement refers to where and how the load-bearing balls sit on the profiled rail. There are two raceway arrangements ... face-to-face and backto-back.

The face-to-face arrangement is often called the X arrangement because the contact lines between the balls and 5 • 2020

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POWER TRANSMISSION REFERENCE

GUIDE

Sizing and selecting bearings

with software in 2020

By Travis Shive | Analytical tools expert • SKF USA Inc.

BEARINGS

are a fundamental part of any machine

— which is why the design of their moving elements can mean the difference between an efficient machine and one that continually wears out and breaks down. So now, some manufacturers offer bearing-simulation software tools to support everything from from entry-level design to complex machine designs necessitating internal analysis.

One SKF software tool that is somewhat more sophisticated than the bearing supplier’s SimPro Quick software is SimPro Expert.

SimPro Quick is targeted to single-shaft equipment; in contrast, SimPro Expert lets OEMs build more complex models — including multiple-shaft models as those of a gearbox. That in turn lets the engineers visualize the influence of one shaft on another … and to quantify the supporting properties of the housing, for example.

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5 • 2020

One engineer-facing software lets designers analyze singleshaft designs. This lets design engineers use the software themselves to modify the machine-axis shaft to existing dimensions … and then adjust the bearing arrangement and surrounding gears and spring spacers as well as other components nearby in the assembly. Engineers can then assess the performance of variations on a given design to predict bearing subsurface fatigue life as well as possible performance conditions that could spur a premature end of bearing life. Such software can warn of surface damage that may go unaccounted when bearing-life calculations are based on traditional catalog-calculation methods.

Such entry-level bearing-design software is relatively straightforward and easy to use … in some cases, with a drag-and-drop interface for adding in components. Such design software also lets users see bearing inner and outer-ring rotation as well as bearing stiffness represented in a matrix.

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SKF in-house bearing simulation tool (BEAST) software analysis yields more in-depth information than SimPro software. BEAST lets SKF investigate on a micro level the contacts between the bearing rolling element and the rings … as well roller deflection and skewing and other factors.

More sophisticated software goes beyond single-shaft equipment to let engineers build more complex models — such as multipleshaft models to virtualize a gearbox series, for example. That in turn allows: • Analysis of how one shaft in the assembly can affect other shafts • Quantify the supporting properties of any housing in the assembly • Importation of any OEM or end-user CAD components into the software for more realistic design confirmation • Sophisticated thermal analyses to predict the temperatures of components during operation Still more sophisticated are simulation services to help in bearing sizing and selection.

These are services executed by the bearing manufacturer; such simulation generates more in-depth profiling than any software

offered for engineers to use themselves. In many cases, the analysis of such programs yields in-depth information about micro-level contacts between the bearing rolling element and the rings — in addition to factors such as roller deflection and skewing.

Bearing manufacturers can also supply detailed information about the cage that holds the bearing’s rolling elements — including the way in which the cage and the balls or rolling elements interact.

VALUE-ADD ENGINEERING SUPPORT WITH SOFTWARE Consider how an OEM might notice vibration in their system on after an initial machine build.

Such OEMs can often measure the amplitude of vibration but not whether it’s acceptable for the bearings in the system. Here, a bearing manufacturer can intervene

with software analysis — virtually applying the vibration the OEM measures to a digital twin of the design at the bearing’s outer ring. Next comes an investigation of how everything inside the bearing moving as a function of this vibration. One potential problem here is the way the rolling elements impact the cage. The question ultimately becomes: Will the cage last? In this situation, cage examination to document force levels can yield a recommended vibration reduction for sufficiently long cage life and a longer machine-axis mean time before failure.

SOFTWARE TOOLS ARE CHANGING HOW DESIGN ENGINEERING IS DONE Bearing simulation software offers benefits to engineers in a wide range of industries — including off-highway, pumps and systems, pulp and paper, automotive, wind, mining, and aerospace. Some of the advantages that come with using this software are that design engineers have more insight into (and control

SimPro Expert allows thermal analyses so that engineers can have a realistic idea of how components temperatures will change during operation.

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5 • 2020

DESIGN WORLD — MOTION

19

Quality Bearings & Components QUALITY BEARINGS & COMPONENTS

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Features: Lightweight handheld design Push-button operation Color screen Intuitive graphical user interface Rated IP65 USB battery charging External or internal transducer VibChecker Machine vibration produces problems in industrial equipment. Add VibChecker to your predictive maintenance tool box to access vibration severity, reducing downtime and unplanned replacement of machine parts. VibChecker measures RMS vibration levels as units of velocity, displacement and acceleration, as well as vibration severity according to ISO 2372/10816.

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BEARINGS

Some software allows analysis of single shafts so engineers can investigate and modify assemblies on their own. Here such software lets design engineers visualize inner and outer-ring rotations.

over) the finer details of a given application … which can help them optimize their bearing selections.

Design engineering software also lets OEMs and end users work more quickly and with more power in their hands. It cuts down the amount of time spent in testing, which in turn reduces development expenses. With software, a design engineer might devise four different designs — and then simply identify which one is the most economical with the best technical attributes.

Consider a manufacturer of high-end textile machinery.

Here, the objective might be to design bearing arrangements that help increase machine speed and accuracy. The bearing running accuracy is critical … software can help such OEMs quicken their design process while evaluating optimal bearing arrangements without external help.

SKF SimPro Quick is easy-to-use software with a drag-and-drop interface for adding components to a virtual assembly. It outputs bearing stiffness in matrices.

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POWER TRANSMISSION REFERENCE

GUIDE

Using synchronous belt drives

for positioning NEOPRENE

or polyester urethane or

synchronous belts (also called timing belts) with reinforcing tensile cords are widely used on rotary motion axes and other power transmission applications. Recall that timing belts are constructed much like flat and V belts plus have arrays of evenly spaced teeth on their inner surface to work via positive engagement. This kind of operation (core to chain and gear drives as well) is defined by almost zero relative differential of motion between the pulley or sprocket driving the belt and the belt itself.

But besides their use for simple PT and rotary motion, the belts are also indispensable in two precision-motion application types: • Linear motion axes inside machinery necessitating servo-level motion control • Conveyors that need to position workpieces and other discrete items.

The reinforcing tensile cords embedded in these belts are usually made of steel or Kevlar to prevent stretch, even when transmitting large torques and propelling loads with high acceleration; that complements the way in which the belt teeth prevent creeping because of their positive-drive nature. That’s especially true for urethane belts, which exhibit minimal tooth deflection.

Left: The synchronous belt here is a Poly Chain GT Carbon belt from Gates Corp. These excel on axes on low-speed high-torque machine in industrial applications.

RIght: Shown is a small sampling of how the geometries of various synchronous belts differ. Some elements are tailored to English and metric designs; other features are industry-specific or even patented for improved power transmission and reliability on positioning axes.

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BELTS Such operation makes for a constant speed ratio and in some cases the ability to execute relative axis positioning with the belt — both useful in automated machinery that must execute predefined strokes.

The distance between belt teeth (from centerline to centerline) is the belt pitch; this in turn is measured at the belt pitch line defined by the belt’s tensile cords and neutral bending axis. The neutral axis is that plane of the synchronous belt that neither compresses or stretches so remains free of stress during operation. Pitch circle intersects with this pitch line.

Such definitions are key to properly specifying belts and pulleys that are compatible — and quantifying the dynamics of a synchronous belt employed in moving workpieces. For more on this topic and the specific case of driving a load-bearing carriage along a linear axis, visit linearmotiontips.com.

APPLYING SYNCHRONOUS BELTS Some general guidelines are applicable to all timing belts, including miniature and double-sided belts. First, engineers should always design these belt drives with a sufficient safety factor—in other words, with ample reserve horsepower capacity. Tip: Take note of overload

MORE DETAILS OF TIMING BELT PROFILES

service factors. Belt ratings are generally only 1/15 of the belt’s ultimate strength. These ratings are set so the belt will deliver at least 3,000 hours of useful life if the end user properly installs and maintains it. The pulley diameter should never be smaller than the width of the belt.

As mentioned, belts are quieter than other power-transmission drive options … but they’re not silent. Noise frequency increases proportionally with belt speed, and noise amplitude increases with belt tension. Most belt noise arises from the way in which belt teeth entering the pulleys at high speed repeatedly compresses the trapped pockets of air. Other noise arises from belt rubbing against the flange; in some cases, this happens when the shafts aren’t parallel.

Pulleys are metal or plastic, and the most suitable depends on required precision, price, inertia, color, magnetic properties and the engineer’s preference based on experience. Plastic pulleys with metal inserts or metal hubs are a good compromise.

Another tip: Make at least one pulley in the belt drive adjustable to allow for belt installation and tensioning. Also note that in a properly designed belt drive, there should be a minimum of six teeth in mesh and at least 60° of belt wrap around the drive pulley. Other tips: Pretension belts with the proper recommended tension. This

MXL with 0.080-in. PITCH Ø 0.005 in.

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DESIGN WORLD — MOTION

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POWER TRANSMISSION REFERENCE

Manufacturers of Power Transmission and Motion Control Components

GUIDE

Concentric Maxi Torque

Stock and Custom Keyless Hub-to-Shaft Connection System Email or call to get your CMT Stock Products Catalog Order today. Ships today!

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extends life and prevents belt ratcheting or tooth jumping.

Align shafts and pulleys to prevent belttracking forces and belt edge wear. Don’t crimp belts beyond the smallest recommended pulley radius for that belt section. Select the appropriate belt for the design torque.

SYNCHRONOUS BELT CONVEYOR BENEFITS AND USES

Timing Pulley Stock

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When designing a conveyor, one of the first considerations is the conveying media to be used, which depends on the size, shape, and weight of the product being handled and on the process requirements, such conveying distance and route, transport speed, and positioning accuracy. For assembly and automation applications, the most popular conveying media are belts, chains, flat-top chains, and powered rollers.

Of these media choices, belts are arguably the most versatile. They can be manufactured in virtually any width and can span long conveying

distances, and they operate with lower noise and less required maintenance than chains or rollers.

Belts and their mating rollers (or pulleys) are also available in many different materials and finishes to meet specific application requirements and environmental conditions.

Traditional belt-driven conveyors use flat belts that rely on friction between the belt and rollers to transmit power. They also rely on friction between the belt surface and the product to hold the product at a specific location on the conveyor. This friction-based design is flexible and economical, but it leads to a potentially variable product positioning and orientation. Case in point: Tthe belt can slip on its drive rollers if working conditions exceed rated load, speed, or acceleration, and the product can move, or slip, on the belt during starts and stops or any time there’s a change in acceleration.

When accurate product location and orientation is required, synchronous timing belt conveyors are typically the best choice.

American Engineering • American Made © 2017 Custom Machine & Tool Co., Inc.

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BELTS

SYNCHRONOUS (TIMING) BELT PROFILES

Timing belt conveyors typically use belts that are reinforced with steel or Kevlar tensile cords to provide increased load carrying capability and enable high acceleration rates (which result in high forces on the belt) without causing the belt to stretch.

To improve grip, the top (carrier) side of the belt can be coated to increase friction between the product and the belt surface and reduce the possibility of the product slipping on the belt. Belt and pulley materials and finishes can also be selected to meet specific application requirements and environmental conditions, such as ESD-compatible, food-grade, or clean environments.

When application requirements call for a very accurate product location with no loss of position, cleats or fixtures can be attached to the belt carrier surface to hold the product in a specific location and with the correct orientation.

Another option to ensure precise location and orientation is to transport the product on a pallet.

Locating the product on a fixed pallet, together with the accurate, no-slip conveying of the timing belt, provides the highest level of position accuracy and certainty.

A further benefit of timing belt conveyors is that the movements — and therefore the products being carried — of multiple conveyors can be synchronized.

This makes timing belt designs ideal for dual- or multipleline configurations and allows large, heavy loads to be transported, even when accurate positioning is required.

TRAPEZOIDAL

CURVILINEAR

MODIFIED CURVILINEAR CURVILINEAR TOOTH PROFILE PITCH (CIRCULAR PITCH) BELT PITCH LINE OUTSIDE DIAMETER PITCH DIAMETER SPROCKET PITCH CIRCLE

TRAPEZODIAL TOOTH PROFILE PITCH (CIRCULAR PITCH)

RATCHETING IN SYNCHRONOUS BELT DRIVES Synchronous belts (also referred to as toothed, cogged, timing, or high torque belts) use profiled teeth that mesh with a pulley or sprocket to deliver power transmission – most notably for applications that require high torque.

Where V-belts rely on friction between the sidewalls of the belt and the sides of the pulley to transmit power, synchronous belts rely on the engagement between pulley teeth and belt teeth to transmit power.

While synchronous belts can transmit high torque without slippage when properly tensioned, using a belt with insufficient tension for the required operating parameters can cause the belt to jump teeth – a condition known as belt ratcheting.

When belt tension is too low, the belt may begin to self-tension with the belt teeth riding out of the pulley and causing increased tension on the belt. When this tension becomes too high, it will force the belt back down into the pulley grooves, which results in a brief but pronounced period of bending that can damage the belt tensile cords in a manner referred to as crimping.

However, if the force of the “self-tension” does not

PULLEY PITCH CIRCLE

Curvilinear tooth profiles offer some distinct advantages in motion applications employing belt drives.

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CURVILINEAR BELT TEETH CONCENTRATE STRESS AT TOOTH CENTERS FOR MORE RELIABILITY.

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POWER TRANSMISSION REFERENCE

DW_LIE_halfpage 2020_X1a.pdf

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PRECISION, QUALITY AND VERSATILITY FOR THE

DESIGN ENGINEER

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cause the belt to slip back into the pulley grooves, the belt will ratchet, which can also cause crimping to the belt tensile cords and result in premature failure.

Proper tension of synchronous belts is the tension at which the belt will transmit the required power without ratcheting when the drive system experiences full load.

Synchronous belts have three general tooth profiles: trapezoidal, curvilinear, and modified curvilinear. Trapezoidal profiles are arguably the most common and provide good force capabilities with low backlash. Curvilinear (also called high torque drive) profiles have a geometry that is rounder and deeper than trapezoidal profiles, with a higher flank angle and greater contact area. This allows for better stress distribution and higher overall loading on the belt, but at the expense of higher backlash.

Modified curvilinear tooth profiles have a smaller tooth depth and an even greater flank angle, which provides the highest load carrying capacities of the three tooth profiles. But one of the primary advantages of this design is that the areas of the belt between teeth share loadcarrying duties with the teeth that are engaged in the pulley. This gives modified curvilinear belts the best anti-ratcheting properties, even under extremely high loads.

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DESIGN WORLD — MOTION

BRAKES & CLUTCHES

Brake and clutch basics ONE

of the unsung heroes of mechanical power transmission

are brakes and clutches. Often hidden away, these humble components are indispensable in many machines and systems.

Fundamentally, they’re used to stop, hold, or index a load. More specifically, brakes are used to stop a load, usually a rotating one. Brakes are used where accurate stopping of the load is a must, and typically the motor needs to stop as well.

Clutches, on the other hand, are typically used to transfer torque. So a clutch is used where it’s required to engage or disengage a load and motor while leaving the motor running. With a clutch, the load coasts to a stop.

Other application needs may call for a brake and clutch combination; for example, if the load must be stopped and started while the motor continues to rotate. Brakes and clutches can mount to a motor shaft or can even be basemounted with input from a belt drive, chain drive, or coupling.

Sizing and selecting the right brake or clutch for the job requires knowing a few parameters, specifically the horsepower and frame size of the motor. Manufacturers typically provide selection tools making it easy to pick the right component size by finding the intersection of the motor horsepower and speed at the clutch shaft.

These selection charts are constructed using the dynamic torque capacity for the specific clutch and the motor torque capacity plus an overload value. This method works well in most uses; for

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A new line of micro brakes from Ogura is designed specifically for servo motor applications, especially in robotics and medical equipment. Ogura micro holding brakes come in both square and round designs with the newest round design being 10 mm in diameter with length as short as 9 mm. Micro brakes can weigh 20 g or less allowing for reduced inertia on fast moving robotic arm applications.

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POWER TRANSMISSION REFERENCE

GUIDE

Design tips for dynamic clutch or brake applications The motor driving the load partially dictates the needed clutch or brake size. The required torque for an axis needing dynamic clutching or braking is defined by the motor horsepower (hp) and operational speed. So the required dynamic torque in lb-ft is: 5,250 x (hp/rpm) x (safety factor) where rpm is the rotational shaft speed that the brake must stop (or the speed difference between clutch output and input). The safety factor adjusts for the motor type and the typical torsional output during operation. Most electric motors have a safety factor near unity as their output is fairly consistent.

A key consideration is the time needed to change the axis speed. Another parameter is the duty cycle – if there are more than a few instances of engagement per hour, duty cycle becomes an influencing design factor. For instance, in high-cycle applications running to 300 cycles/min as in indexing applications using a clutch-brake, each clutch engagement transfers a torque spike to the connection between the motor shaft and the input shaft of the clutchbrake. Such high-cycle applications can cause severe hammering on the shaft connection of the motor to the clutch-brake.

C-face motor connections are the most common as they offer convenience and easy assembly. However, their loose fit can cause torque to transfer through the key and keyway, which may cause failure. Alternate connection options include clutches and brakes with shrink-fit or clamping couplings for a 360° connection.

A note about the dynamic torque calculation above; it’s based on the time to stop the load or bring it to speed and doesn’t account for the time needed for the clutch or brake to actuate. For electromagnetically engaged clutch-brakes, a coil generates an electromagnetic field for armature activation and friction-disk engagement. This process can take from 10 to 500 msec depending on size.

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Miki Pulley’s BXW springactuated electromagnetic brakes use internal compression springs to provide power-off, fail-safe braking. The primary moving part is the armature plate.

example, where the motor is sized correctly. However, other instances may not be suitable. For instance, where cycle rates are considered aggressive for the inertia of the load, it’s better to consult with others including the manufacturer, especially to get more information about heat dissipation capacity.

Another consideration in selecting brakes and clutches is the coil voltage. Common options include 6, 24, and 90 Vdc, where 90 V are more common in North America, whereas 24 V supplies are more common in Europe.

The main brake and clutch designs are mechanical, electrical, and fluid power models.

Mechanically actuated brakes and clutches use a lever for mechanical advantage to trigger engagement and disengagement. The lever works by squeezing friction disks together to transmit torque. Movement of the mechanism engages or disengages the brake or clutch, with some designs featuring a locking mechanism to maintain the state until repowering.

These brakes and clutches typically don’t have bearings, are available with optional one-position setups, and offer automatic overload release during over-torqueing or locking. On the downside, these types of brakes and clutches need adjustments to compensate for mechanical wear and they don’t automatically disengage in the event of a loss of power.

Electromechanical brakes and clutches, on the other hand, incorporate a magnetic coil to generate a magnetic flux, which is used to move an armature. Different designs mean they can be electrically activated or

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BRAKES & CLUTCHES

what are known as spring-applied electrically deactivated types, which also fail-safe during a loss of power.

Electromagnetic brakes and clutches are generally easy to control, are tolerant of high speeds, and have a long life cycle.

Most also come equipped with a selfadjustment mechanism to compensate for friction-disk wear. However, they do require a bearing to support the stationary coil and the engagement time may be a bit longer compared with other designs due to the need to generate the magnetic field for the coil.

Lastly, fluid-power based designs work by fluid shear action between friction disks and drive plates. The fluid in shear transmits torque as parts come together, eliminating direct friction-disk contact during highspeed slip. Oil-shear based technologies are suitable for applications that must rapidly stop, start, reverse or change speed.

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Don’t eat up valuable time searching for friction brakes, clutches and torque limiters. For more than 45 years, machine designers have relied on us for made-to-order products that meet their exact requirements.

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BRAKES • CLUTCHES • TORQUE LIMITERS DESIGN WORLD — MOTION

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POWER TRANSMISSION REFERENCE

GUIDE

Couplings for

power transmission COUPLINGS

connect rotating shafts

in equipment powered by electric motors and other drives.

All transmit torque and angular velocity. Flexible variations compensate for misalignment. Many of the latter even address vibration and improve system dynamics. Sesign considerations include machine or installation construction and backlash, torsional stiffness, damping, inertia, torque ratings, maximum rpm, size, misalignments, ease of installation, robustness, and cost.

Jaw (spider) couplings are suitable for an array of applications — and are one coupling type that (depending on the subtype) is suitable for either power transmission or servo designs. They come in an array of sizes to accommodate shaft diameters of 3 to 150 mm and beyond.

Jaw couplings from Martin Sprocket can be specified with bronze, Hytrel, rubber, or urethane spider inserts.

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Applications for motion control (such as axes to position loads) usually use disc, slit or beam, curved-jaw, bellows, and other zero-backlash couplings capable of precise transmission of torque.

In contrast, applications for power transmission (as in grinding machines, pumps, and material-handling machinery) commonly include disc, gear, chain, elastomer tire, grid, jaw, and Oldham couplings.

Such PT couplings transmit more torque on average than couplings designed for motion control … even to millions of lb-in. Plus they’re more rugged to withstand challenging environments.

Chain couplings — with typical maximum torques to 220,000 lb-in. at their largest — wrap lengths of chain around sprockets with clearances to impart flexibility. These powertransmission couplings excel in high-horsepower applications on axes needing correction of up to 2° and 0.01-in. angular and parallel misalignment.

Diaphragm couplings — with typical maximum torques to 500,000 lb-in. at their largest — transmit power through a metal membrane (sometimes of varying thickness or ganged in

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WHAT’S NEW RULAND

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• Vibration isolation mounts can be sandwiched between components to dampen shock loads.

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• Spring-loaded indexing plugers with or without lock-out.

• Designed to lock devices in-place for adjustable positioning.

from

POWER TRANSMISSION REFERENCE

GUIDE

COUPLINGS FOR POWER TRANSMISSION CHAIN COUPLINGS COURTESY IWIS DRIVE SYSTEMS

DIAPHRAGM COUPLINGS

These are just a few coupling types used for power transmission between shafts. Others include uni-lat, finger, K-flex, and fluid (hydraulic or hydrodynamic) couplings as well as flexible shafts and Hooke's joints, also called Cardan or universal or U joints.

ELASTOMERIC TIRE COUPLINGS TB WOOD’S DURA-FLEX COUPLING COURTESY ALTRA INDUSTRIAL MOTION

JAW COUPLINGS

FLEXIBLE JAW COUPLING MARTIN SPROCKET & GEAR INC.

JAW-IN-SHEAR (JIS) COUPLING LOVEJOY INC.

OLDHAM COUPLINGS

RULAND MFG. CO. INC.

In this CD coupling from Zero-Max, Composite Disc packs have high torsional stiffness. The flex elements also ensure zero backlash and low bearing loads. Specially sized and located holes can be drilled on the coupling’s hubs to allow addition of weight during final trim balancing … although the manufacturer prebalances the couplings at 4,000 rpm so that final assembly only requires fine-tune balancing.

TYPICAL TORQUE CAPACITY

arrays). Though often more costly than other options, diaphragm couplings mitigate and avoid problematic transmission of forces and moments t coupled equipment such as bearings. Profiles include straight-spoked diaphragms; tapered diaphragms; and convoluted diaphragms assembled in arrays. These correct up to 1° and 0.1-in. angular and parallel misalignment.

Elastomeric tire couplings — with typical maximum torques to 550,000 lb-in. at their largest — transmit power through a tire-shaped rubber element that bridges the coupling’s two hubs. These correct up to 1° and 0.2-in. angular and parallel misalignment.

Jaw couplings — with typical maximum torques to 550,000 lb-in. at their largest — include both straight and curved variations. Much like disc couplings, the design lends itself to adaptation to both power transmission and backlash-free motion control. The coupling hubs have jaws that lock into a spider made of bronze, elastomer, or other material. Power transmission is reliable even through 1° and 0.01 in. angular and parallel misalignment.

Oldham couplings — with typical maximum torques to 550,000 in. at their largest — include a metal or polymer disc with slots on each face 90° offset. Usually hub fins or tenons engage a slotted disc that’s free to slide even while transmitting torque. Oldham couplings for accommodation of angular misalignment might transmit through 6° and 0.05 in. Oldham couplings to primarily address parallel misalignment might address 0.15 in. or more and 0.5° or so.

Disc couplings — with typical maximum torques to 5,000,000 lb-in. at

DISC-ELEMENT COUPLINGS ROBA-DS DISC-PACK COUPLINGS MAYR POWER TRANSMISSION

BIBBY TURBOFLEX • ALTRA INDUSTRIAL MOTION

MORE

GRID COUPLINGS

GEAR COUPLINGS FALK GEAR COUPLING REXNORD CORP.

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Metal Bellows Experts

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GUIDE

FOR SPEED AND ACCURACY

BELLOWS COUPLING 9 Torsionally stiff 9 Well balanced 9 Low inertia

RW-AMERICA.COM THE COUPLING.

ABB’s Dodge Raptor elastomeric-tire couplings transmit up to 340,200 lb-in.

their largest — are one of a few coupling types that come in variations to satisfy motion-control or power-transmission applications. Single-disc couplings should perhaps be called single discpack couplings … because they include a single disc pack having many friction discs. In contrast, double-disc couplings have two disc packs — with an additional center hub between them. In some cases, this center spacer hub is of the same material as the two end hubs; otherwise the component supplier may offer center hubs made of something else — acetal for electrical isolation, for example. In representative designs, the discs impart flexibility to transmit torque even while addressing up to 2° and 0.05 in. angular and parallel misalignment.

Grid couplings — with typical maximum torques to 5,000,000 lbin. at their largest — include a heavy spring that weaves between slots on the coupling hubs. Compliant connection damps torsional vibration and shock loading — even through 0.3° and 0.30 in. angular and parallel misalignment.

Gear couplings — with typical maximum torques to 55,000,000 lb-in. at their largest — include a flexible joint on each hub. In most variations, a spindle joins the two. Each joint includes gearset that mates with a 1:1 ratio. The tooth flanks and external gearing’s outer diameter are crowned to allow rotating-spline action and accommodate misalignment of 3° and 0.04 to 0.4 in. on average.

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DESIGN WORLD — MOTION

ENCODERS

Encoders — on the front lines

of motion sensing ENCODERS are key components in motion systems,

providing information on position, distance, and speed. They’re differentiated a number of ways including as rotary or linear, incremental or absolute, or according to their operating principle as optical, magnetic, or capacitive.

While optical encoders were traditionally the primary choice for high-resolution applications, improvements in magnetic encoder technology now allow them to achieve resolutions down to one micron, competing with optical technology in many applications. Magnetic technology is also more robust than optical technology, making magnetic encoders more common in harsh industrial environments.

As for capacitive encoders, they offer resolution comparable to optical devices, with the ruggedness of magnetic encoders. Their suitability for applications requiring high precision and durability make them a good choice for the semiconductor, electronics, medical, and defense industries.

A critical performance parameter for encoders is resolution.

For incremental encoders, resolution is typically given in pulses per revolution Balluff’s BML absolute magnetic encoder with a DriveCliq interface easily integrates into Siemens controller environments. The linear measuring system measures lengths up to 48 m with an accuracy of up to ± 12 μm and a resolution of 1 μm.

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(PPR), or, in the case of linear encoders, pulses per inch (PPI) or pulses per millimeter (PPM). These square-wave pulses are precisely spaced, and the encoder determines its position by counting the number of pulses generated during movement.

Besides resolution, there are a few other specifications to consider when choosing an encoder, including the required accuracy. But one specification that is sometimes overlooked during sizing and selection is the maximum encoder speed.

Like any electrical component, delays in switching and processing time limit the speed at which an encoder can operate. This limitation in speed due to internal electronics is referred to as the encoder’s maximum electrical speed, and applies to both linear and rotary encoders with either magnetic or optical sensing technologies.

As an encoder moves — rotationally or linearly — internal electronics switch on-and-off in response to changes in light (for optical types) or magnetism (for magnetic types).

This electronic switching produces a digital signal (or a binary word, for absolute encoders) indicating the encoder’s position. The maximum speed at which its electronics can change state (from “on” to “off” or vice-versa) is known as the encoder’s frequency response.

The maximum electrical speed is directly proportional to the encoder’s frequency response and inversely proportional to the encoder’s pulses per revolution (PPR) for rotary encoders, or pulses per distance (typically pulses per millimeter, PPM) for linear designs.

In addition to the maximum electrical speed, rotary encoders are also limited by a maximum mechanical speed.

The maximum mechanical speed primarily depends on the speed capability and lifetime of the bearings that support the encoder as it rotates. Exceeding the encoder’s maximum mechanical speed (specified by the manufacturer) can result in physical damage to the encoder or a shortened service life.

HOW TO CALCULATE MAXIMUM ENCODER SPEED For rotary encoders, the maximum rotational speed is determined by dividing the encoder’s maximum frequency response by its pulses per revolution (PPR).

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POWER TRANSMISSION REFERENCE

GUIDE

For linear encoders, the maximum linear speed is determined by dividing the frequency response by the number of pulses per distance (typically PPM).

HOW QUADRATURE ENCODING AFFECTS ENCODER SPEED

X2 and X4 encoding can increase encoder resolution by a factor of 2 or 4, respectively. But increasing resolution decreases the maximum encoder speed. | Danaher

To improve resolution, incremental encoders often produce two signals in quadrature and count both the rising and falling edges of one signal — known as X2 encoding — or the rising and falling edges of both signals — known as X4 encoding. It’s important to remember that when X2 or X4 encoding is used, the encoder’s pulses per revolution (or per distance) must be multiplied by either “2” or “4” accordingly, since the electronics will have to switch two or four times as quickly.

As the equations above show, although increasing the pulses per revolution (or per millimeter) improves resolution, it reduces the encoder’s maximum speed.

Regardless of the resolution, sensing technology, output type, or encoder design, if the encoder’s maximum electrical speed is lower than the speed required by the application, an encoder with a higher frequency response will need to be selected.

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GEARING

Using gears to change the inertia ratio of a

motor-driven system LOAD

Adding a gear set or gearbox between the motor and the load can improve the load-motor inertia ratio.

GEARS

MOTOR

ANY

system using a motor to drive a load with precise positioning, velocity, or torque

requires consideration of inertia. That’s because the ratio of load inertia to motor inertia significantly impacts a motor’s ability to effectively and efficiently control attached loads. That’s especially true during the acceleration and deceleration portions of the motion profile.

In this context, the inertia to which we’re referring is mass moment of inertia, sometimes called rotational inertia — an object’s resistance to change in rotational speed. An object’s mass moment of inertia depends on its mass and geometry … usually the radius defined by the object’s center of mass and the point around which the object rotates.

If the load’s inertia significantly exceeds the motor’s inertia, that load will essentially “try” to “drive” the motor … and the motor will struggle to get the load to its target position, speed, or torque. That in turn will prompt the motor to draw higher current … which decreases efficiency and increases wear on the motor and electrical components.

On the other hand, if the motor’s inertia significantly exceeds the load’s inertia, it’s likely that the motor is oversized.

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That in turn has negative implications throughout the system — including higher initial cost, higher operating cost, larger footprint, and the need to oversize other components such as mounting hardware, couplings, and cables.

If the inertia ratio is too high, the load inertia is much higher than the motor inertia and will cause problems with positioning accuracy, settling time, or control of velocity or torque.

If this is the situation at hand, load inertia that is seen by (reflected to) the motor can be decreased by adding a gearset or gearbox between the motor and the load:

Where JL = Inertia of the load reflected to motor and JM = Inertia of the motor Adding a gearset or a gearbox to a motor-driven system reduces the load inertia by the inverse square of the gear ratio, meaning that even a relatively low gear ratio can have a significant effect on the inertia ratio.

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POWER TRANSMISSION REFERENCE

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Spur gear basics Spur gears are a type of cylindrical gearing with shafts that are parallel and coplanar ... and teeth that are straight and oriented parallel to the shafts. They’re arguably the simplest and most common type of gear – easy to manufacture and suitable for a wide range of applications.

Where JL = Inertia of load reflected to motor; JD = Inertia of drive — whether ball screw, belt, or rack-and-pinion set; JE = Inertia of external (moved) load; JC = Inertia of the coupling; JG = Inertia of gearset or gearbox; and i = Gear ratio Note that the inertia of the gearset or gearbox JG is added to the load inertia, but its effect is typically small compared to the reduction provided by the gear ratio.

In addition to optimizing the load-motor inertia ratio, gearboxes are often used in motion control applications to increase the torque delivered to the load from the motor, but they also decrease the rotational speed delivered to the driven component from the motor, by an amount equal to the gear ratio. This is why gearboxes are often called gear reducers or speed reducers.

In other words, if a motor running at 1,200 rpm is driving a load through a 3:1 gearbox, the rotational speed delivered to the load will be 1,200 ÷ 3 = 400 rpm. This reduction in speed can enable the system to operate at a more favorable location on the motor’s speed-torque curve.

Although it is possible to use a gearbox or gearset that is configured to reduce torque (and increase speed) in motion control applications, a more typical solution here is to choose a smaller motor.

Spur gears are a type of cylindrical gearing with shafts that are parallel and coplanar ... and teeth that are straight and oriented parallel to the shafts. They’re arguably the simplest and most common type of gear – easy to manufacture and suitable for a wide range of applications.

The teeth of a spur gear have an involute profile and mesh one tooth at a time. The involute form means that spur gears only produce radial forces (no axial forces), but the method of tooth meshing causes high stress on the gear teeth and high noise production. Because of this, spur gears are typically used for lower speed applications, although they can be used at almost any speed.

Involute gear teeth have a profile that is the involute of a circle. So as two involute gears mesh, they contact at a single point where the involutes meet. This point moves along the tooth surfaces as the gears rotate ... and the line of force (known as the line of action) is tangent to the two base circles. In this way, the gears adhere to the fundamental law of gearing — that the ratio of meshing gears’ angular velocities must remain constant throughout the mesh.

Spur gears can be made from metals such as steel or brass or from plastics such as nylon or polycarbonate. Plastic gears are quiet but at the expense of strength and loading capability. Unlike other gear types, spur gears don’t experience high losses due to slippage, so they generally have high transmission efficiency. Multiple spur gears can work in series (referred to as a gear train) to achieve large reduction ratios.

The two types of spur gears are external and internal. External gears have teeth that are cut on the outside surface of the cylinder. Two external gears mesh together INVOLUTE GEAR MESH FOR TRADITIONAL TOOTH GEOMETRY and rotate in opposite directions. In contrast, internal THINK OF THE INVOLUTE AS THE LINE gears have teeth cut on the inside surface of the TRACED BY A STRING PINNED TO A CIRCLE O.D. ... AND THEN WRAPPED AROUND THAT O.D. cylinder. An external gear sits inside the internal gear, and the gears rotate in the same direction. Because the shafts are positioned closer together, internal gear assemblies are more compact than external gear assemblies. Internal gears are primarily used for planetary gear drives.

Spur gears are generally best for applications needing moderate speed reduction and torque LINE OF multiplication — such as ball mills and crushing ACTION equipment. High-speed applications that use spur gears (despite their high noise levels) include consumer appliances such as washing machines and blenders. Though noise limits the use of spur gears INVOLUTE-SHAPED TEETH ALLOW SMOOTH TRAVEL OF CONTACT (MESHING) in automobiles, they’re common in aircraft engines, SO CONTACT POINTS TRACE THE INVOLUTE CURVES OF MATING TEETH trains, and even bicycles.

AND LIE ON A TANGENT COMMON TO THE MATING GEARS’ BASE CIRCLES.

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DESIGN WORLD — MOTION

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POWER TRANSMISSION REFERENCE

GUIDE

These outer-rotor brushless motors from Allied Motion Technologies are designed for hightorque, low-cogging applications like robotics, AGVs, and handheld power tools. The KinetiMax High Power Density (HPD) motor series feature an efficiency rating of over 85% coupled with a high power-to-weight ratio. They’re available in six frame sizes, with three stack-lengths per size and three windings per stack length.

All about

electric motors THERE

are many types

of electric motors used in power transmission. They vary from small brush dc motors for moving light loads to high horsepower ac motors powering conveyor lines in heavy duty mining applications.

For more precision applications, servomotors and stepper motors are the motors of choice. Here, compact size and high torque as well as greater controllability are common advantages.

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DESIGN WORLD — MOTION

Electric motors can be categorized in a number of different ways; as ac (alternating current) or dc (direct current) motors, or by the type of motion they produce, rotary or linear. Another common approach is to distinguish between commutation methods; for example, self-commutated or external, and by mechanical means (as brushes used in brushed dc motors) or electronic commutation (as in brushless dc motors.)

MOTORS – AC There are two fundamental types of ac motors; induction and synchronous motors.

5 • 2020

Induction motors run at constant speed across a wide range of load settings, from zero to full-load. With synchronous motors, their name indicates that they run synchronously with the frequency of the source. The motor speed is fixed and doesn’t change with changes to the load or voltage.

MOTORS – DC A dc motor works by generating a magnetic field via electromagnetic windings or permanent magnets. The most common industry naming conventions for dc motors recognize three subtypes: brush motioncontroltips.com

|

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ELECTRIC MOTORS This line of stepper motors from Applied Motion Products feature IP65 ratings that are dustproof and resistant to water pressure impact, making them suitable for use in wet and dusty applications. The motors feature sealed laminations, an oil shaft seal, internal corrosion-resistant film coating, gaskets for mechanical joints and an integral 10-ft. shielded cable that offers protection against the ingress of dust and resistance to low-pressure water jets.

motors, permanent-magnet (PM) motors, and universal motors. Many dc motors still employ brushes and wound fields, but PM motors dominate fractional and integralhorsepower applications below 18 hp.

For brushed dc motors, the magnet acts as the stator. The armature is integrated onto the rotor and a commutator switches the current flow. It does this by transferring current from a fixed point to the rotating shaft. Brushed dc motors generate torque straight from the dc power supplied to the motor by using internal commutation, fixed permanent magnets, and rotating electromagnets.

Brushless dc (BLDC) motors, on the other hand, do away with mechanical commutation. They use electronic commutation that eliminates the mechanical wear and tear involved with brushed dc motors. In BLDC motors, the permanent magnet is housed in the rotor and the coils are located in the stator.

These coil windings produce a rotating magnetic field because they’re separated from each other electrically, which enables them to be turned on and off. The rotor’s permanent magnet field trails the rotating stator field, producing the rotor field.

SERVOMOTORS Servomotors are one of the most common types of motors used in motion control applications. While there’s some disagreement over exactly what constitutes a servomotor, one factor is the presence of feedback for closed-loop control. Closedloop control gives servomotors precise positioning ability by greatly reducing motioncontroltips.com | designworldonline.com

error. That means they can accommodate complex motion patterns and profiles more readily. They offer precise control of torque and speed and they can also operate at zero speed while maintaining enough torque to maintain a load in a given position.

STEPPER MOTORS On par with servomotors, stepper motors find extensive use in motion systems.

They operate open loop without the need for tuning parameters as in closed-loop servo systems. They’re used mostly in positioning applications and have the advantage of being able to be accurately controlled down to fractions of a degree without the use of feedback devices such as encoders or resolvers.

Stepper motors are generally classified by the number of allowable steps they can be commanded to move.

For instance, a 1.8 degree step motor is capable of 200 steps/revolution (1.8 x 200 = 360 degrees, or one full revolution) in full-step mode. If operated in halfstep mode, each step becomes 0.9 degrees and the motor can then turn 400 steps/revolution. Another mode called microstepping subdivides the degrees per step even further, allowing for extremely precise movements.

LINEAR MOTORS For applications requiring linear motion, a viable option may be a linear motor. One way to think of a linear motor is essentially a rotary motor that has been unrolled. So instead of producing torque via rotation it generates a straight-line force along its 5 • 2020

DESIGN WORLD — MOTION

41

POWER TRANSMISSION REFERENCE

GUIDE

length. Like many rotary motors, linear motors consist of a coil and magnets. Although there are many types of linear motors, brushless iron core and ironless designs prevail in automation and positioning applications.

Linear motors offer a number of advantages over belts, screws, and other drive mechanisms, including low maintenance and higher accuracy and repeatability. There are no mechanicaltransmission components – such as pulleys, couplings, or gearboxes – to introduce elasticity and backlash. The system’s accuracy and repeatability are determined by the controls and don’t degrade over time. The lack of rotating or sliding components also means linear motors are almost maintenancefree, with only the support bearings, or linear guides, requiring periodic maintenance.

High-dynamic dc motors such as those offered by FAULHABER are seeing increased demand, particularly in medical applications such as ventilators and automated sample analysis in testing laboratories.

FOCUS: How stepper motors handle heat and vibration Depending on operating conditions and

STEP MOTORS REQUIRE SUFFICIENT LOADING 7

the job the motor does in a machine, heat and are most at risk of overheating when the application makes the motor draw more than its current rating. So here, avoid overdraw by sizing motors correctly upfront — and don’t operate stepper motors in areas with high ambient temperature or where an enclosure or surrounding machinery prevents good heat transfer away from the stepper motor. Use

Vpeak-to-peak VIBRATION

noise can be other problems. Stepper motors

heatsinks where space and design permits.

DESIGN WORLD — MOTION

Insufficient loading or damping

5 4 3 2 1 0

Bigger motors keep cooler than smaller equivalents for a given job. The main caveats here are that larger motors can be louder; can transmit higher EMI and RFI than smaller options; are costlier than compact alternatives; and can have torque-to-inertia ratios than are sometimes prohibitive to speed.

Complicating matters is that current overdraw can also overheat motors.

So when reading performance and torque curves, determine whether the curves represent

42

6

Damped • Loaded 200

400

600

800

SPEED (Hz) Overloaded stepper motors risk missing steps. However, unloaded or underloaded stepper motors exhibit excessive vibration. One common rule of thumb is that torque required for the driven axis should be between 25 to 75% of the step motor’s rated torque.

Otherwise, the “extra” torque from the motor induces vibration.

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POWER TRANSMISSION REFERENCE

GUIDE

STEPPER-MOTOR PERFORMANCE FALLS AT HIGH TEMPERATURES

The graph is a simplified representation of changes in motor performance at elevated temperatures, showing decreased performance as the motor gets hotter.

NO LOAD SPEED n0

Δn0

Room-temperature conditions allow top performance.

Elevated temperature degrades performance.

LOCKED ROTOR TORQUE TLR

behavior at room temperature or maximum rated temperature. After assembly, a motor’s theoretical torque constant KT and voltage constant KE (as well as terminal resistance Rm) are fixed. However, actual values vary with temperature.

As temperature increases, so does resistance — just as the torque constant and voltage constant decrease. So steppermotor performance changes at elevated temperatures according to set relationships: θr =

2 × Rm Rth × Irms 2 × Rm × 1−(Rth × Irms

0.00392 °C

)

and θm = θr + θa ∙ θr where θr is the rise in temperature and Rth = thermal resistance; Rm = motor terminal resistance; Irms = root mean square current; θa = ambient temperature; and θm = temperature of the motor.

Note that these equations report the increase in temperature internally. It’s impossible to tell how much hotter a stepper motor has become simply by feeling its surface. Not only can this be dangerous (because motor surfaces can get hot as well as pose electrical hazards) but it’s also a misleading technique — because motors are

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DESIGN WORLD — MOTION

ΔTLR

insulated to prevent them from becoming hotter than allowed by applicable safety standards. This means that a motor can either feel quite hot yet be running perfectly fine or (even more deceptively) insulation makes it feel as if nothing is wrong.

When in doubt, consult manufacturer documentation and ask motor-maker application engineers about allowable motor operating temperatures. See Understanding dc motor curves and temperature for more information on stepper-motor temperature ratings and effects.

Also note the relationship to stepping mode and motor heat. Full stepping a two-phase motor with the phases fully on together outputs more torque than running that same motor at the same maximum current per phase in half or microstepping.

That said, running the motor at higher peak current (×√2) with a half or microstepping waveform delivers the same torque for a given level of power consumption as full stepping — but for smoother output motion without any extra heat generation.

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POWER TRANSMISSION REFERENCE

GUIDE

Strain energy and resilience

in springs

WHEN

a compressive or tensile load is

Typical compression springs experience both shear and torsional stresses and store strain energy from both stresses. Wave springs, however, experience only shear stress (no torsion) and therefore, have lower strain energy, meaning they can exert higher forces — or resist higher loads — than standard compression springs.

Stress is the applied load on a material divided by the material’s cross-sectional area. Stress causes the material to change its shape, and strain is the deformation that occurs due to stress.

Materials that follow Hooke’s law — which include most compression springs and wave springs — experience deflection, or displacement, in proportion to the applied force.

Wave springs have relatively linear spring constants and provide consistent force over a range of deflections (or conversely, predictable deflection over a range of forces).

The behavior of a spring is often depicted in a force-deflection chart, which shows the amount of deflection the spring experiences for a range of forces. The slope of the force-deflection curve represents the spring constant, and the area under the curve is equal to the work done by the load to displace the spring. This work — force applied over a distance — represents the potential energy (strain energy) stored in the spring.

A note about work and energy: When work is done on an object, its energy is changed by an amount equal to the work done. In the case of springs, it’s the potential energy (referred to as strain energy) that is changed. In other words, a spring’s strain energy is Wave-spring images courtesy equal to the work done on the spring.

Smalley Steel Ring Co.

Where F = Applied force in N; k = Spring constant in N/m; and δ = Deflection in m.

From the spring equation above, substituting kδ for F…

applied to a spring (or any elastic

material), the load does work on the spring, causing the spring to undergo a change in shape (extension or compression). This change in shape creates a type of potential energy — referred to as strain energy — in the material.

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WAVE SPRINGS + RETAINING RINGS 60

MEASURED SPRING DEFLECTION

Force (lb)

50

Test curve

40 30

Theoretical calculation

20 10 0

Top: Typical wave springs show a slight difference between theoretical and measured deflection characteristics.

0.180

0.140

0.100

0.060

0.020

Working spring height (in.)

STRESS-STRAIN CURVE

Stress σ (psi)

Bottom: The stress-strain curve allows visualization of a spring material.

Ultimate strength

σty σel

Yield point

Fracture

Elastic limit

Yield strength

0.002 offset

Where U = Strain energy in Nm, J; δ = Deflection in m; F = applied force in N; and k = Spring constant in N/m.

Strain energy is elastic — that is, the material tends to recover when the load is removed. The ability of a material to return to its original length or shape by releasing strain energy when a load is removed is referred to as its resilience. A spring with high resilience can withstand greater deflections and produce higher forces. The best performance comes from springs that have high allowable deflection (resilience) and high permissible forces.

Resilience is typically expressed as the modulus of resilience, which is the amount of strain energy the material can store per unit of volume without causing permanent deformation. The modulus of resilience can be found by taking the area under the material’s stressstrain curve, up to the elastic limit (which is approximately equal to the yield point).

Where Ur = modulus of resilience in N/m2; σy = Yield stress in N/m2; εy = Yield strain (dimensionless); and E = Modulus of elasticity.

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εty

Strain

Modulus of resilience Ur

ε (in./in.)

POWER TRANSMISSION REFERENCE

GUIDE

Back to basics: What’s the difference between

a dashpot and a snubber?

DASHPOTS

and snubbers are two types of pneumatic

device used for controlling the movement of a load — typically for the purpose of controlled deceleration or motion damping.

Although they can be used to control rotary motion, the more common uses for dashpots and snubbers in industrial applications involve the control of linear motion mechanisms, such as solenoids or spring-loaded devices.

Both dashpots and snubbers contain two primary parts: a glass cylinder with a polished bore and a precision piston, often made of a low-friction material such as graphite. And both devices operate by forcing ambient air through an adjustable orifice at a controlled rate. But despite these similarities, dashpots and snubbers are designed for different applications. Case in point — a dashpot is best for applications that require accurately controlled force or velocity, whereas a snubber is best used for end-of-stroke damping where accurate control of impact is required.

A dashpot has a connecting rod that joins the load to the piston and provides control throughout the stroke, either by extending the connecting rod and piston (in pull mode) or by causing the connecting rod and piston to retract into the cylinder — in push mode. Dashpots can also control motion in both directions.

Both operating modes — push and pull — rely on the change in air pressure inside the cylinder. In push mode, as the piston moves farther into the cylinder, the air inside the cylinder is compressed, causing the pressure to rise. In pull mode, as the piston retracts out of the cylinder, the pressure inside the cylinder falls and creates a partial vacuum.

Dashpots in pull mode work best when the movement needs to be controlled for the entire stroke. This is because the air column is short when the motion begins and the damping force increases quickly, providing controlled motion after just a short amount of travel. It’s also important that a dashpot used in pull mode is returned to the starting position — otherwise, if the piston isn’t fully retracted, the air column inside the cylinder will be relatively long and the damping force will be slow to increase.

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DESIGN WORLD — MOTION

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A dashpot in push mode works best for applications that require a reduced impact at the end of travel. In this mode, the pressure inside the cylinder rises as the column of air becomes shorter.

With push damping, the damping effect is lower at the beginning of the movement. This is because the column of air is relatively long and requires some amount of movement to create sufficient pressure to provide damping. With push damping, there can be a noticeable effect of the load bouncing on the air column (sometimes referred to as an air spring) midway through the stroke, as the pressure rises and begins to dampen the movement.

Also referred to as pneumatic shock absorbers, snubbers differ from dashpots in two ways: The piston is not attached to the load being controlled, and damping occurs in compression only — as for push damping.

When the load contacts the piston rod of a snubber, the force of the load causes the piston to move, compressing the air inside the cylinder. This compression of air provides a controlled

SHOCK ABSORBER (SNUBBER)

DASHPOT

Vent path Mounting stud (airpot bottom) Adjustable orifice Precision cylinder Graphite piston Ball joint

Connecting rod Push rod

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SHOCK + VIBRATION MITIGATION deceleration, with the amount of deceleration depending on the magnitude and speed of the load and the adjustment of the orifice.

If the damping is too high, the load will bounce on the air column (air spring effect) or bounce on landing. If the damping is too low, the load will land with too much force, causing damage to it or to other equipment. Although snubbers provide only compression damping, their accuracy in controlling movement and reducing shock is better than that of dashpots.

OVERVIEW OF VIBRATION MITIGATION IN INDUSTRY Vibration in industrial machinery often originates from imbalances inherent to motors, gearboxes, and other turning component that excites natural frequencies.

Dampers in this context are components that counteract and often isolate the vibration source from the rest of the design or machine — to prevent its propagation of mechanical oscillation.

Passive vibration mitigation includes passive isolators — such as closed-cell foam slabs, metal coil or wave springs, wire rope isolators (common in military applications) and rubber machine mounts. These reduce system natural frequency to less than that of excitation frequency… though to be clear, traditional springs and rubber have near-zero damping capabilities.

Precision passive isolators include negative-stiffness isolators, which decrease system natural frequency upon loading via a kinematic linkage of beam columns and springs … typically stacked in series for tilt, horizontal, and vertical motion.

In fact, many isolators do impart a small amount of damping. Some (including wirerope isolators) also attenuate shock impact at sudden move ends, hard stops, and collisions without recoil — on conveyor e-brakes or axis stroke ends, for example.

In contrast with isolators, passive dampers (such as material slabs and mechanical

linkages) change the kinetic energy of vibration into heat. Passive damping usually employs viscous fluids, viscoelastic materials, piezo elements, or simple magnetics.

Active dampers include an array of electronically controlled force cancellers that employ a power source, sensors, and actuation to counteract vibration with disruptive interference … out of phase with the source vibration. These include shocks containing magnetorheological fluid that stiffen to solid with controllable yield strength under an applied magnetic field in milliseconds. These also include oowered piezoelectric elements affixed to the design frame at critical points to execute active countermotions and address vibration (usually detected by acceleration sensors) and under the control of a DSP. Regarding passive vibration damping ... those in mechanical formats include tuned mass dampers that affix to machinery or structures to damp narrow frequency bands

POWER TRANSMISSION REFERENCE

of vibration. Other options for passive mechanical damping are friction and piezoelectric action prompted by simple resistive shunt.

Passive vibration mitigation in fluidpower formats include hydraulic mounts, air springs, and bladders to isolate and damp industrial machines and other moving equipment. Passive air tables are another iteration, though increasingly displaced by other technologies. Gas springs (of the piston-type plunger design) act as kinematic holds.

Many pneumatic dampers have a similar structure — with a cylindrical chamber containing a piston and compressed air behind it — though work on moving axes. Oil dashpots employ a contained volume of fluid to resist

GUIDE

motion with viscous friction to damp (though not isolate) vibration.

Now consider passive vibration mitigation in elastomeric material formats — which offer simplicity in format and application. Foam slabs isolate well though lack durability. Rubber and neoprene excel at isolation but not damping. In contrast, another option is viscoelastic material that excels at vibration and shock control — absorbing up to 94.7% of the latter.

The material is classified as viscoelastic, as it exhibits both viscous and elastic characteristics when subject to deformation. A high delta tangent — also called the loss factor or damping coefficient — means an out-of-phase time relationship between shock impact

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or vibration and force transmission. The viscoelastic material absorbs more than half the energies at 1 to 30,000 Hertz for powerful vibration damping … shedding the energy as heat (through hysteresis) and directing remaining energy perpendicularly — 90° out of phase from the vibration or shock source.

Gas springs, also called gas dampers, tension springs, or gas-pressure springs depending on the setup and context, are compressed-air or oil cylinders that install in motion designs to damp forces and return kinematic linkages (and more complicated assemblies) to default positions. Gas springs work through a piston on the end of a rod that protrudes from a steel cylinder body; usually compressed gas (often nitrogen) within the cylinder exerts force on this piston to reassume and maintain set positions.

Nitrogen is common here because it’s inert and nonflammable. In such designs, oil or grease between the piston and other contacting parts minimize friction.

In fact, the small amount of oil in these gas springs serves another function — to further damp and gently decelerate gas springs during full extension or compression. Some setups even include a fine hole in the piston for damping that’s still slower than with other designs; such slow-damper springs are common on safety gates and doors.

In contrast, extended-reach gas springs usually leverage telescoping mechanisms pairing multiple cylinders on one rod; then the smaller cylinder extends from within the larger cylinder. Consider one particularly long-stroke application: Passive heave compensators — systems on ships or offshore oil-rig systems that reduce the effect of waves on engineered structures — use gas springs with strokes to many meters long.

Still other gas-spring applications include those for medical beds and hoists; industrial equipment such as machine-tool presses; off-highway and automotive equipment for hatches, hoods, and covers; office equipment and

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furniture; and general strut and support applications. Fast-acting gas springs find use in weaponry and aerospace design. Specific variations include gas springs with standard or fixed-height cylinders; spindle-only designs; and cable, return, adjustable autoreturn, nonrotating, stage, and multi-mode cylinders.

No matter the iteration, gas-spring extension force — a value that usually ranges from 1 to 5,000 N — depends on piston-rod cross-section multiplied by fill pressure. Manufacturers commonly express extension force with two values — for rod extension and rod retraction — at normal ambient temperature and with the piston rod pointing downward. (Note that typical ranges are only those most common; some gas-spring applications in heavy industries use gas springs delivering several hundredthousand Newtons cases.) Other gas-spring definitions include two pull-in forces — at rod extension and rod retraction — and overall friction force. These values depend on the gas spring’s gas and damping-oil volumes. Various nozzle orifices and oil quantity allow control of push-out and pushin speed.

If design parameters are unknown, look for manufacturers capable of prototyping — especially for designs requiring an exact force that’s hard to pre-estimate — as in lifting a frame in a set time, for example.

Here, some manufacturers sell prefilled 5 • 2020

cylinders sporting bleed valves. Then installers can bleed gas from the cylinders after system setup to get the correct forceacceleration actuation profile.

The only caveat here is that if too much gas is bled, the assembly will need a new spring. That’s why OEM-level quantities of gas springs justify pre-engineered cylinders with preset pressurization. Or gas springs can offer full in-design adjustability via bleed valves and movable-endstop pressurization mechanisms, Bowden cables, knobs, and more. Some emergency-use gas springs also employ gas-generator cartridges that resemble those in airbags.

Find, price and order the exact gas spring for your application in seconds!

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