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Mechanically Generated Friction Fits in Power Transmission Couplings 

In the world of electric motors and power transmission coupling products, torque is increasingly being transferred between directly coupled shafts by means of purely mechanically generated friction rather than by positive drive connections like keys and keyways or splines. Mechanical friction fits evolved into modern standardized dimensions during the twentieth century as machine tools and cutting tooling evolved into their present states of precision and accuracy. For many decades power transmission component design lagged behind the machining world when it came to the use of mechanically generated frictional clamping, with a large portion of connecting elements still relying on keyways and interference fits to guarantee transmission.

Interference fits, wherein the diameter of the male component is actually slightly larger than the diameter of the mating female component, do have their merits when it comes to ensuring reliable backlash free transmission.  But they can be difficult to assemble, as the shaft must be cooled with a cryogenic such as liquid nitrogen, or the bore needs to be expanded with heat. If either high heat or extreme cold are used, safety is a key concern during the assembly process. Heating a metal component will also often change its mechanical properties such as temper, so cooling the male fitting part is preferred when maintaining the material properties is a concern. Due to the inconveniences associated with interference fits, most newly designed frictional clamping coupling hubs are made using compression by means of screw thread fasteners instead. 

This type of mechanical connection is very predictable and can be made by applying a set amount of torque to radial or axial screws. For easy assembly the fit between the male and female part typically should not have overlapping diametrical tolerances, but should also not allow for excessive clearance. When the fits can be made by hand, proper tightening of the fasteners is all that is necessary to create a friction fit which will reliably and predictably transmit torque for the life of the machine.  A shrink disk style fit on a female member of a coupling will maintain concentricity and will compensate for tolerances on a male shaft while maintaining the ability to transmit torque across a range of diameter dimensions and torque values. This type of conical clamping hub can be manufactured in different styles to promote modularity, ease of assembly and concentricity between shafts, often allowing for easier balancing for high speed applications. 

The fastener assisted friction fit has streamlined design of couplings as it allows for the use of smooth shafts which are not subject the imbalance and complications shaft key or spline tolerances can cause. The next time you are sizing and selecting rotating components, consider going with keyless frictional fits and reap the benefits of modern machine construction.

Balanced High Speed Precision Couplings

As a manufacturer of precision couplings, we spend quite a bit of time on high speed applications. Here are a few basic tips about coupling balance.

A properly balanced drive component should not induce excessive vibration into the drive line. This means that the mass of the component rotating about the axis of the shaft must be evenly distributed in such a manner as to maintain an even centrifugal force about the axis of rotation. The magnitude of the centrifugal force generated by a rotating component varies with the location of the center of mass of the drive component versus the axis of rotation and orientation of the moment of inertia. 

A simple way to think of static balance about an axis is to imagine playing on a see-saw in a playground.  Two people of equal mass can sit at an even distance apart from each other and maintain balance. Or one person of a heavy mass can sit close to the pivot point and a person of a light mass can sit far away from the pivot point and maintain balance. A rotating mass works essentially the same way. As an object with constant mass moves away from the axis of rotation, the centrifugal force increases exponentially. In physics, this is simply illustrated with a moment of inertia calculation (I=mr^2).

In practical manufacturing, rotating parts are made with evenly spaced jaws, spokes, etc.  Balancing comes into play when manufacturing processes cause imbalance or additional parts such as clamping screws or shaft keys are added. Adding or subtracting mass in one area of a part causes an imbalance. This must be corrected by adding or subtracting mass on the opposite side of the part. Manufacturers most often do this by drilling holes into the part near the outside diameter so that less material will need to be removed resulting in a more structurally sound part versus removing a lot of material near the axis of rotation.

Precision parts such as machined coupling hubs are designed with the balancing holes in a location so they can be produced in quantity in a numerically controlled process without balancing each part individually. This provides cost savings and consistency to customers. Quality small to medium sized machined hubs should come with a speed rating of about 10,000 RPM. Many of these hubs can be finely balanced for speeds between 30-80,000 RPM depending on size. The larger in diameter and more massive a hub becomes, the lower the practical balance speed will be.

Other considerations such as torque transfer at high speed need to be examined as well. Centrifugal forces at high speeds will begin to open clamping hubs for example. Since the screws of clamping hubs are normally tightened to a torque which takes them near their tensile yield, the effects of centrifugal forces applying additional screw tension as the clamp opens must be considered. This is why in medium to large sized hubs, conical clamping rings are often favored, since they offer better symmetry and better stress distribution as a result of the forces applied to them at high speed.

R+W makes a lot of standard and custom couplings for high rotational speeds, some of which rated to handle speeds in excess of 150,000 rpm.

The coupling shown at left is one of our miniature designs. Higher torque versions are available on request.  Contact us with your high speed coupling requirements and get the ultimate connection.

CALCULATING MOMENT OF INERTIA

As a manufacturer of safety couplings and torque limiters, we are often asked to provide some assistance in calculating the moment of inertia of various loads, in order to aid in selecting the appropriate disengagement torque settings.  Once the driving and driven inertia values are known, acceleratin and deceleration rates are used to estimate safety coupling torque adjustment ranges. 

Moment of inertia can be described as a mechanical property of the mass of a solid object that quantifies the required torque needed to change the angular velocity of the object about an axis. This inertia is also known as the mass moment of inertia, first moment, or, rotational inertia.  This moment can be used to calculate how much energy it takes to get an object rotating which is especially useful in mechanical drive lines with motors and engines.  When sizing a torque limiter or safety coupling, it is important that the disengagement torque value be set to a value higher than what is required to accelerate the load up to speed.  It is also helpful to be aware of the torque levels resulting from abruptly decelerating a rotating mass, which is where torque limiters and safety couplings come into play, protecting driveline components from the excessive torques resulting from an unintended blockage stopping a machine too rapidly.  Moment of inertia often denoted as (I) is a unit of mass multiplied by area squared (M*A²). In the case of a two inch diameter rotating shaft with a mass of one hundred pounds, moment of inertia can be calculated per the example below.  

Calculating the moment of inertia for a 0.1 meter diameter shaft with a mass of 1000 kg is done in the exact same manner.

Finding the moment of inertia for a tube or hollow shaft is very similar. In the next example, we will find the value for a 0.5 meter outside diameter tube with a 0.3 meter inside diameter. The mass of the tube is 500 kg. 

The calculation for a moment of a square or rectangular shaft or shape can also be useful. In this example, the moment of a one inch by one inch square shaft with a mass of 1000 pounds will be found.

The examples above are handy for calculations involving sizing of mechanical drive components, and not just safety couplings. Inertia ratios of rotating shafts and motor rotors are critical to proper operation of many drives. These calculations are all done about the axis of typical shaft rotation and cannot be used for a different axis.  It is important to note that this is the mass moment and the calculation gives us a property of mass at a distance from the axis of rotation. As with all rotating objects, the moment increases exponentially as a mass moves away from the axis of rotation.  These basic facts of physics are critical for machine design and have been a primary guiding principle for centuries of mechanical engineering.

Proper Shaft Fits for Precision Drive Components

When sizing high performance drive components, proper shaft fit is an important consideration in helping to maintain concentricity and balance in the rotating equipment. In v-belt drives, chain drives and other low-cost / low-speed systems, designers often give little thought to shaft fit. Many manufacturers of these types of low cost drive components are simply relying on a shaft key and set screw to transmit torque and retain the hub on the shaft, and other types of misalignment absorbing elements help to take up any eccentricity resulting from a relatively large clearance between the shaft and the bore.  But when it comes to high-performance / high-speed drives and “smart” motors, such as servo and steppers, shaft fit becomes increasingly important.

When researching a possible vendor for zero backlash components with engineered clamping systems that can be assembled by hand, it is imperative that they are able to provide a shaft tolerance as well as a published chart which verifies the shaft and bore fits required. As a general rule of thumb, the overall diametrical clearance between the shaft and the bore should be around 10-50 µm (.0004-.0019”) for smaller diameter shafts, and as shaft diameters increase beyond 80mm (3.150”), larger clearances become allowable, and more annulus is required around the ID of the bore to ensure easy installation. If the fit is correct, a bit of oil is all that is required to easily slide a hub onto a shaft. 

 Many engineers are inclined to specify interference fits for high performance drives, which in a solid hub design would require either sub-zero cooling of the shaft and / or, more commonly, heating of the bored and keyed hub. This type of fit dates back to times before frictional clamping systems became well established in the power transmission industry, and is intended to eliminate problems associated with loose shaft fits and backlash.  Requiring this type of work can create a maintenance and installation problem, and is not necessary in most modern applications incorporating engineered clamping systems. But the importance of precision shaft fit remains when it comes to frictional clamping style hubs. 

Frictional Clamping Hubs

In the case of clamping collarstyle hubs, which offer the advantage of very easy installation and removal, if the fit clearance is too large between the shaft and bore, once clamped, the hub can become eccentric to the shaft.  This can cause an imbalance and or misalignment issue in addition to the potential for failure of the driveline. In self centering clamping systems, often used for high speed / high power systems, excessive fit clearance can reduce the transmittable torque of the shaft hub connection.  But with proper shaft fits and screw tightening torques applied, they offer superior performance to simple keyway hubs, and far easier handling than interference fit hubs. 

 (clamping collar)        (self-centering clamping system)

Manufacturing Standards

There are several standardized shaft tolerance charts commonly used in industry such as ANSI B4.1-1967 (R2004) for imperial units and ISO tolerance system per DIN 7160 (8.65) for metric units.  Precision drive components should have a clearance fit which is just out of range of a transition fit such as an H7/h6 fit per DIN 7160 (8.65) chart. For example on a 32 mm diameter shaft, this would mean that the shaft could be 0-16 µm under 32mm.  The bore could be 0-25 µm over 32 mm. This would result in a diameter difference of 0-41 µm (.0000-.0016”).

If the shaft and bore were both the same size, assembly would be difficult. In practical manufacturing, this would almost never happen. A good machinist would normally use a H7 go/no-go plug gauge and an h6 go/no-go ring gauge. The go portion of the plug gauge would not practically fit into the bore by hand unless the bore was slightly larger than 12 mm exactly. Vice-versa, with the ring gauge and shaft, when checking a turned part with a ring gauge, it would not fit by hand unless the shaft was a bit smaller. If either no-go plug or ring gauge fits, the parts are scrapped. This method of machining/checking shafts and hubs results in parts with a precise fit which can be assembled by hand. 

For more information on proper shaft fits and precision couplings for high performance drive applications, contact applications@rw-america.com.

Angular Acceleration and Moment of Inertia in Machine Design 

As a provider of flexible drive couplings and ball detent safety clutches, we are often asked to provide a bit of assistance in calculating application torques, especially for customers looking to retrofit existing equipment.  In order to aid in the process of estimating torques, we'll review one of the basic calculations used to estimate the torque required to accelerate a rotating mass to a certain speed over a given time.  

Angular acceleration (α) can be defined as angular velocity (ω) divided by acceleration time (t). Alternatively, pi (π) multiplied by drive speed (n) divided by acceleration time (t) multiplied by 30. This equation yields the standard angular acceleration SI unit of radians per second squared (Rad/sec^2). The equation below defines the rate of change of angular velocity.

ω = angular velocity in the standard SI unit of radians per second (Rad/sec), 1 radian = 57.3 degrees

t = acceleration time in seconds

π = 3.1416

n = drive speed in revolutions per minute RPM

In the next example, angular velocity will be calculated for acceleration from 0 to 60 RPM in one second. Note that 2π radians per second = 60 RPM.

This calculation is very useful in machine design because angular acceleration multiplied by rotational moment of inertia equals torque.  Keep in mind that the exact moment of inertia can be difficult to calculate based on complex geometries in real drive lines, and other variables such as friction are not considered in the next calculation.  Nonetheless it is still very helpful in approximating torque requirements or establishing baseline minimum values for component sizing purposes. 

J = moment of inertia in kg∙m²

T= torque in N∙m

N= force in Newtons

kg= mass in kilograms

m= lever arm radius in meters

In the final example below we will use the angular acceleration we found above to calculate torque on a flywheel with a 1 meter radius and 1000 kg mass. 

As we can see, if a flywheel with a 1 meter radius and 1000 kg mass were to be accelerated to 60 RPM in one second, it would require 3141.59 Newton meters of input torque.

I hope you found this refresher on calculating angular acceleration to be helpful.  If you have questions pertinent to the sizing and application of shaft couplings or safety clutches, feel free to contact our applications engineering department.

applications@rw-america.com

Configurable coupling systems save time and money

Many machine builders are well aware of the advantages of using configurable components in the design stages. As projects progress, specifications often change and builders must adapt components to fit new constraints. Drive and electrical components must be flexible to adapt to new operating parameters or machine chassis dimensions. Electrical designers often make use of DIN rail mounted devices which can be interchanged quickly on the production floor or in the field. Circuit breakers, fuses, and power supplies can be easily changed out in the event that a different motor or sensor is installed. From the mechanical perspective it is usually coupling elements which need to be changed to adapt to new dimensions.  This is why QD or similar bushings are typically used with V-Belt sheaves.  If drive speeds change, a fairly quick sheave swap is all that is required. If a new gearbox or actuator needs to be installed, drive couplings in various lengths and bore diameters are often required in order to help get everything tied together.  Finding direct drive couplings with compact dimensions and creative mounting configurations is normally fairly easy.  But in some cases layout changes involve longer distances between mechanically connected equipment, requiring something a little more specialized.

 Belt drive or direct drive

With longer distances between rotating components, designers are often in a position to choose between belt or chain driving, and using a direct drive line shaft system.  A direct drive line shaft coupling typically provides for stiffer power transmission than belts, which can be especially advantageous in applications that require precision timing and positioning or frequent changes in rotational direction. Line shaft couplings are also low maintenance compared with belts which need to be changed at regular intervals, just like car tires for optimal performance. But in the past there were occasionally major drawbacks to using direct drive line shafts over belts in some applications.  Assembly with steel shafting and standard couplings generally requires intermediate support bearings and is not very well suited to higher drive speeds over long distances.  Most preassembled torque tube styles of line shaft couplings are also built to order rather than being stocked by many large industrial supply companies. In the past a typical prefabricated torque tube style line shaft would need to be rebuilt if length or shaft sizes changed. 

New configurable line shaft couplings

In more recent years, prefabricated, variable length, telescoping line shaft couplings have been brought to the industrial market in order to address the growing trend toward designing with direct drives. A variable length line shaft with removable hubs solves the issue of shaft sizes and lengths changing (within adjustment range) as a machine is built or upgraded. With a variable length line shaft, the overall length can be changed in minutes by simply loosening and tightening a couple of machine screws. Jaw style hubs or flange mounted bellows coupling hubs can be swapped out with stock parts in less time than it takes to change a v-belt sheave and re-tension belts. Additionally, common size adjustable line shaft couplings are stocked by many distributors and ready to ship with hubs just like sheaves and belts.

This new take on configurable coupling component technology ultimately saves cost in labor and/or materials over time. While newer components produced in smaller quantity can have higher pricing up front, they can actually lower the cost of maintenance and overhaul down the road. Making use of a more precision product can also help to increase the rate at which a product is manufactured. As we all know, increased productivity and lower service costs ultimately decrease the time over which a return on initial investment is seen. This makes money for our employers, which is something I’ve found they enjoy universally.  

Elastomer Jaw Couplings:  not all are created equal

Today’s mechanical drive components market is flooded with a wide variety of direct drive couplings. Many folks working with or designing drives are not familiar with the different technologies or differences in quality and precision between manufacturers. One prime example is with elastomeric jaw couplings. Elastomer jaw couplings have been around for 100 years or more. Most of these couplings use two hubs and an elastomeric spider between the jaws to transmit torque. Although they look essentially the same, the applications can vary greatly.

Traditional Jaw Couplings

Much of the market by volume of units sold consists of low manufacturing cost cast hub couplings with a rubber spider element.  These hubs are used in drives such as conveyors and centrifugal pumps turning in one direction where precise shaft position is not important.  Torque is usually transmitted accross the hubs by means of a keyway locked down with a set screw.  Many of the machine frames are formed and welded to loose tolerances.  The coupling design has plenty of play between the spider insert and jaws to accomodate shaft misalignment.  This design is optimal for producing machinery where labor time to align shafts is cost prohibitive, and they are ideal for less demanding applications. 

Precision Jaw Couplings

A somewhat smaller part of the market volume is precision backlash free or low backlash elastomeric couplings. The hubs of these couplings are generally machined from solid stock with clamping features incorporated into them for wear free and play free frictional connections to the shafting.  This can eliminate the need for keys and keyways and also enhance performance while improving longevity.  

 

The machined hubs typically also come with curved jaws held to a very tight level of concentricity in reference to the bore. Measuring concentricity from the jaw to the bore is what ensures smooth transfer of rotation from one jaw set to the next. 

       

 

 

 

 

 

Wear resistant polyurethane inserts are then put through a secondary “match molding” process to smooth out any inconsistencies on the driving lugs, before being press fit into the hubs for a preloaded zero backlash assembly. 

 

 

 

 

  

Being based on the same principle of mounting a resilient element between the jaws of two metallic hubs, they look similar, but are quite different in some key characteristics.  Because the hubs are precision machined from solid bar stock, they are naturally more expensive than a cast or sintered hub.  But considering that both coupling styles are relatively inexpensive, the cost differences are often far outweighed by the benefits in situations where high torques or shock loads must be transmitted through a small space envelope, as can happen in many pumping, conveying, crushing and grinding applications to name a few, or in cases where dynamic motion needs to be transmitted smoothly, like in servo and stepper motor driven machines.  In the latter situations the precision concentricity and backlash free characteristics, and not only the stronger material condition of the hub benefit the user and the process.  

    

Shaft alignment

One of the assumptions being made with this design concept is that that a higher value will also be placed on the overall quality of the drive line assembly, which always includes precision alignment.  It is not uncommon for someone to switch to a precision elastomer jaw coupling and hear an audible clicking as the equipment runs. Because the elastomeric spider element is preloaded in the hubs and is a slightly harder material, it will rub on the metal surfaces audibly if there is significant shaft misalignment. Although lubricant can be used to address the clicking, eventually the elastomer segment may need replacement.  But when alignment is addressed they can be wear-free for a theoretically infinite service life.  

 

 

 

Many motors, gearboxes, linear actuators and pumps have precision centering features already incorporated into their mounting frames by the manufacturer for this very reason. When the coupling is installed inside a housing or bracket which takes advantage of a centering feature on both pieces of coupled equipment, then alignment is normally within the allowable limits for the precision variety of elastomer coupling.  

 

 

 

 

When no such feature exists, then alignment must be checked manually.  There are several approaches which can be taken to address this potential issue. For a single elastomer element coupling the shafts need to be precisely aligned with dial indicators or laser alignment systems in case the shaft alignment is not inherent to the mechanical assembly.  

 

 

 

    

For situations where space is tight, split hub couplings are available to be installed laterally after the manual alignment check has been performed and any necessary adjustments have been made. 

 

 

     

Then, in cases where precision manual alignment is just not practical, there are other options.  Many manufacturers make the urethane elastomer segment available with a convex tooth geometry, which allows for a rolling action as the coupling hubs rotate under angular misalignment. 

 

 

 

 

 

When two are used in series with a coupling spacer, the ability to compensate for parallel shaft misalignment is magnified to many times greater than with the single element version, allowing for simple visual shaft alignment, while at the same time maintaining the benefits of relatively low inertia, zero backlash and high torque density.  

 

 

 

 

 

While these two different shaft coupling styles may look more or less the same, small differences in materials and manufacturing processes can mean big differences in terms of the end result.  When considering making the switch from traditional to precision varieties of elastomer insert jaw couplings, consider discussing your requirements with the manufacturer, and make sure to check all of the specifications to get the best coupling for your unique situation.

  

Vibration damping couplings:  sometimes bigger is better

A customer sizing an elastomer insert coupling recently asked us if using a larger body size would provide better vibration damping.  In a word, the answer was, yes.  Vibrations in machine shafts come from a wide variety of sources. Machines that crush and shred materials can impart quite a bit of vibration into the drive line and prime mover. These types of machines can cause motors and mechanical driveline components to fail prematurely if proper damping measures are not in place.  Conversely, driving components, especially internal combustion engines, can impart severe vibration down the driveline.  While R+W specializes in vibration damping couplings for electric motor drives, the concept of increasing driving inertia for smooth continuous rotation is most easily explained and widely understood in terms of internal combustion engines.

One of the oldest methods mechanical designers have used to damp vibrations is employing a flywheel. This device is still widely in use, in many parts of industry. Using laws of basic classical mechanics, “a body in motion tends to stay in motion, while a body at rest tends to stay at rest,” designers know that it is difficult to change the rotating velocity of a massive, high inertia flywheel easily. This is why a flywheel is used on the output shaft of many combustion engines, since they tend to continue rotating smoothly rather than jerking severely every time a cylinder fires. A large drive coupling or belt pulley would have the same effect. Piston air compressors often have massive cast iron sheaves driving them for this reason. 

In situations where inertia, space and power consumption are not of concern, it can be beneficial to use shaft couplings with larger and heavier hubs than are necessary to simply transmit the torque.  At R+W we have machined flywheel features directly into steel coupling hubs on many occasions in order to assist customers with torsional vibration damping, especially in pump coupling applications. Another reason to consider upsizing for vibration damping is that in the case of elastomer insert couplings, the vibration is spread over a larger area which can also provide damping. In general, using the “bigger is better” concept is often a good policy when the priority is to make a robust and smooth running machine more so than a quick moving, light or compact machine. For many folks this concept is basic common sense, however in this day and age of making everything more compact, this principle can be overlooked when it might make a lot of sense. 

What is a ball detent torque limiter?

A ball detent torque limiter is essentially a mechanical circuit breaker designed to release the load when it senses an overload condition. This type of device is not to be confused with a shear pin which is basically a mechanical fuse designed to break the circuit and be replaced.  A ball detent torque limiter is also not to be confused with a slip clutch which will “slip” to maintain a constant peak torque value when an overload is sensed.

What are the advantages of ball detent torque limiters?

A Quick Refresher on Converting Torsional Stiffness Values 

Customers often ask us for a bit of assistance in comparing torsional stiffness values between flexible couplings made by manufacturers using Imperial versus SI units.  This may be considered rudimentary to some but a quick refresher never hurts.  

Any drive component which transmits torque will twist a bit when torque is applied. For example, if a shaft was marked on each end very precisely notched on the same plane along its axis, the notches would move apart as torque is applied.

The amount they move apart is proportional to the applied torque. Therefore, torsional stiffness is called out in units of torque applied per angular unit of twist. North American manufacturers tend to use a variety of different units while Europeans typically use Newton meters per radian.  

The Conversion

I've provided an example conversion below.  In this example calculation, we are converting a given stiffness value of 76000 N*m/Rad  to in*lb/Deg , this will require a bit of unit conversion. As many of us may remember from college chemistry, we are allowed to multiply ratios of different units that mathematically equal 1 to cancel unwanted units and convert to the desired ones. Below, we can see that the units in red cancel. In just a couple of steps the desired units emerge.

Or conversely, converting a value given in in*lb/Deg to N*m/Rad:

Coupling Stiffness

As we see in the example, if we we’re comparing flexible couplings, the top one would be more torsionally stiff. Having a high level of torsional stiffness is not always desirable, especially if someone wanted to use the flexible coupling to damp vibration.  However in many cases machine builders need to maximize torsional stiffness in order to reduce settling times in highly dynamic applications or to maximize rotational positioning accuracy.  In the case of flexible shaft couplings, elastomeric (elastic) couplings are typically used for vibration damping, and metallic couplings are used for maximizing torsional stiffness. 

This example can be used for comparing any multitude of different units as long as the correct conversion ratios are employed.