Backlash (engineering)
Encyclopedia
In mechanical engineering
, backlash, sometimes called lash or play, is clearance between mating components, sometimes described as the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established. For example, in a pair of gear
s, backlash is the amount of clearance between mated gear teeth.
Theoretically, the backlash should be zero, but in actual practice some backlash must be allowed to prevent jamming. It is unavoidable for nearly all reversing mechanical couplings, although its effects can be negated. Depending on the application it may or may not be desirable. Reasons for requiring backlash include allowing for lubrication
, manufacturing errors, deflection
under load and thermal expansion
.
Backlash due to tooth thickness changes is typically measured along the pitch circle and is defined by:
where:
Backlash, measured on the pitch circle, due to operating center modifications is defined by:
where:
Standard practice is to make allowance for half the backlash in the tooth thickness of each gear. However, if the pinion
(the smaller of the two gears) is significantly smaller than the gear it is meshing with then it is common practice to account for all of the backlash in the larger gear. This maintains as much strength as possible in the pinion's teeth. The amount of additional material removed when making the gears depends on the pressure angle of the teeth. For a 14.5° pressure angle the extra distance the cutting tool is moved in equals the amount of backlash desired. For a 20° pressure angle the distance equals 0.73 times the amount of backlash desired.
As a rule of thumb the average backlash is defined as 0.04 divided by the diametral pitch; the minimum being 0.03 and the maximum 0.05.
In a gear train
, backlash is cumulative. When a gear-train is reversed the driving gear is turned a short distance, equal to the total of all the backlashes, before the final driven gear begins to rotate. At low power outputs, backlash results in inaccurate calculation from the small errors introduced at each change of direction; at large power outputs backlash sends shocks through the whole system and can damage teeth and other components.
tuning dial where one may make precise tuning movements both forwards and backwards. Specialized gear designs allow this. One of the more common designs splits the gear into two gears, each half the thickness of the original. One half of the gear is fixed to its shaft while the other half of the gear is allowed to turn on the shaft, but pre-loaded in rotation by small coil spring
s that rotate the free gear relative to the fixed gear. In this way, the spring tension rotates the free gear until all of the backlash in the system has been taken out; the teeth of the fixed gear press against one side of the teeth of the pinion while the teeth of the free gear press against the other side of the teeth on the pinion. Loads smaller than the force of the springs do not compress the springs and with no gaps between the teeth to be taken up, backlash is eliminated.
s. Again, as with the gear train example, the culprit is lost motion when reversing a mechanism that is supposed to transmit motion accurately. Instead of gear teeth, the context is screw thread
s. The linear sliding axes (machine slides) of machine tool
s are an example application.
Most machine slides for many decades, and many even today, were simple-but-accurate cast iron linear bearing surface
s, such as a dovetail slide or box slide, with an Acme leadscrew drive. With just a simple nut, some backlash is inevitable. On manual (non-CNC
) machine tools, the way that machinists compensate for the effect of backlash is to approach all precise positions using the same direction of travel. This means that if they have been dialing left, and now they want to move to a rightward point, they move rightward all the way past it and then dial leftward back to it. The setups, tool approaches, and toolpaths are designed around this constraint.
The next step up from the simple nut is a split nut, whose halves can be adjusted and locked with screws so that one side rides leftward thread faces, and the other side rides rightward faces. Notice the analogy here with the radio dial example using split gears, where the split halves are pushed in opposing directions. Unlike in the radio dial example, the spring tension idea is not useful here, because machine tools taking a cut put too much force against the screw. Any spring light enough to allow slide movement at all would allow cutter chatter at best and slide movement at worst. These screw-adjusted split-nut-on-an-Acme-leadscrew designs cannot eliminate all backlash on a machine slide unless they are adjusted so tight that the travel starts to bind. Therefore this idea can't totally obviate the always-approach-from-the-same-direction concept; but backlash can be held to a small amount (1 or 2 thou), which is more convenient and in some non-precise work is enough to allow one to ignore the backlash (i.e., act as if there weren't any).
CNCs can be programmed to use the always-approach-from-the-same-direction concept, but that is not the normal way they are used today, because hydraulic anti-backlash split nuts and newer forms of leadscrew other than Acme/trapezoidal, such as recirculating ball screws
or duplex worm
gear sets, effectively eliminate the backlash. The axis can move in either direction without the go-past-and-come-back motion.
The simplest CNCs, such as microlathes or manual-to-CNC conversions, use just the simple old nut-and-Acme-screw drive. The controls can be programmed with a parameter value entered for the total backlash on each axis, and the machine will automatically add that much to the program's distance-to-go when it changes directions. This [programmatic] "backlash compensation", as it's called, is a useful trick for capital-frugal applications. "Professional-grade" CNCs, though, use the more expensive backlash-eliminating drives mentioned above. This allows them to do 3D contouring with a ball-nosed endmill, for example, where the endmill travels around in many directions with ease and constant rigidity.
In mechanical computers a more complex solution is required, namely a frontlash gearbox. This works by turning slightly faster when the direction is reversed to 'use up' the backlash slack.
Some motion controllers include backlash compensation. Compensation may be achieved by simply adding extra compensating motion (as described earlier) or by sensing the load's position in a closed loop control scheme
. The dynamic response of backlash itself, essentially a delay, makes the position loop less stable and prone to oscillation
.
Difference between the maximum and minimum backlash occurring in a whole revolution of the larger of a pair of mating gears.
Backlash is undesirable in precision positioning applications such as machine tool tables. It can be minimized by tighter design features such as ball screw
s instead of leadscrew
s, and by using preloaded bearings. A preloaded bearing uses a spring or other compressive force to maintain bearing surfaces in contact despite reversal of direction.
There can be significant backlash in unsynchronized transmissions because of the intentional gap between dog gears (also known as dog clutch
es). The gap is necessary so that the driver or electronics can engage the gears easily while synchronizing the engine speed with the driveshaft speed. If there was a small clearance, it would be nearly impossible to engage the gears because the teeth would interfere with each other in most configurations. In synchronized transmissions, synchromesh solves this problem.
Mechanical engineering
Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the...
, backlash, sometimes called lash or play, is clearance between mating components, sometimes described as the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established. For example, in a pair of gear
Gear
A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine....
s, backlash is the amount of clearance between mated gear teeth.
Theoretically, the backlash should be zero, but in actual practice some backlash must be allowed to prevent jamming. It is unavoidable for nearly all reversing mechanical couplings, although its effects can be negated. Depending on the application it may or may not be desirable. Reasons for requiring backlash include allowing for lubrication
Lubrication
Lubrication is the process, or technique employed to reduce wear of one or both surfaces in close proximity, and moving relative to each another, by interposing a substance called lubricant between the surfaces to carry or to help carry the load between the opposing surfaces. The interposed...
, manufacturing errors, deflection
Deflection
Deflection or deflexion may refer to:* Deflection , the displacement of a structural element under load* Deflection , a technique of shooting ahead of a moving target so that the target and projectile will collide...
under load and thermal expansion
Thermal expansion
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.When a substance is heated, its particles begin moving more and thus usually maintain a greater average separation. Materials which contract with increasing temperature are rare; this effect is...
.
Gears
Factors affecting the amount backlash required in a gear train include errors in profile, pitch, tooth thickness, helix angle and center distance, and runout. The greater the accuracy the smaller the backlash needed. Backlash is most commonly created by cutting the teeth deeper into the gears than the ideal depth. Another way of introducing backlash is by increasing the center distances between the gears.Backlash due to tooth thickness changes is typically measured along the pitch circle and is defined by:
where:
 |
= backlash due to tooth thickness modifications |
 |
= tooth thickness on the pitch circle for ideal gearing (no backlash) |
 |
= actual tooth thickness |
Backlash, measured on the pitch circle, due to operating center modifications is defined by:
where:
 |
= backlash due to operating center distance modifications |
 |
= difference between actual and ideal operating center distances |
 |
= pressure angle |
Standard practice is to make allowance for half the backlash in the tooth thickness of each gear. However, if the pinion
Pinion
A pinion is a round gear used in several applications:*usually the smallest gear in a gear drive train, although in the case of John Blenkinsop's Salamanca, the pinion was rather large...
(the smaller of the two gears) is significantly smaller than the gear it is meshing with then it is common practice to account for all of the backlash in the larger gear. This maintains as much strength as possible in the pinion's teeth. The amount of additional material removed when making the gears depends on the pressure angle of the teeth. For a 14.5° pressure angle the extra distance the cutting tool is moved in equals the amount of backlash desired. For a 20° pressure angle the distance equals 0.73 times the amount of backlash desired.
As a rule of thumb the average backlash is defined as 0.04 divided by the diametral pitch; the minimum being 0.03 and the maximum 0.05.
In a gear train
Gear train
A gear train is formed by mounting gears on a frame so that the teeth of the gears engage. Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, this provides a smooth transmission of rotation from one gear to the next.The transmission of...
, backlash is cumulative. When a gear-train is reversed the driving gear is turned a short distance, equal to the total of all the backlashes, before the final driven gear begins to rotate. At low power outputs, backlash results in inaccurate calculation from the small errors introduced at each change of direction; at large power outputs backlash sends shocks through the whole system and can damage teeth and other components.
Anti-backlash designs
In certain applications, backlash is an undesirable characteristic and should be minimized.Gear trains where positioning is key but power transmission is light
The best example here is an analog radioRadio
Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
tuning dial where one may make precise tuning movements both forwards and backwards. Specialized gear designs allow this. One of the more common designs splits the gear into two gears, each half the thickness of the original. One half of the gear is fixed to its shaft while the other half of the gear is allowed to turn on the shaft, but pre-loaded in rotation by small coil spring
Spring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...
s that rotate the free gear relative to the fixed gear. In this way, the spring tension rotates the free gear until all of the backlash in the system has been taken out; the teeth of the fixed gear press against one side of the teeth of the pinion while the teeth of the free gear press against the other side of the teeth on the pinion. Loads smaller than the force of the springs do not compress the springs and with no gaps between the teeth to be taken up, backlash is eliminated.
Leadscrews where positioning and power are both important
Another area where backlash matters is in leadscrewLeadscrew
A leadscrew , also known as a power screw or translation screw, is a screw designed to translate turning motion into linear motion...
s. Again, as with the gear train example, the culprit is lost motion when reversing a mechanism that is supposed to transmit motion accurately. Instead of gear teeth, the context is screw thread
Screw thread
A screw thread, often shortened to thread, is a helical structure used to convert between rotational and linear movement or force. A screw thread is a ridge wrapped around a cylinder or cone in the form of a helix, with the former being called a straight thread and the latter called a tapered thread...
s. The linear sliding axes (machine slides) of machine tool
Machine tool
A machine tool is a machine, typically powered other than by human muscle , used to make manufactured parts in various ways that include cutting or certain other kinds of deformation...
s are an example application.
Most machine slides for many decades, and many even today, were simple-but-accurate cast iron linear bearing surface
Bearing surface
A bearing surface is a mechanical engineering term that refers to the area of contact between two objects. It usually is used in reference to bolted joints and bearings, but can be applied to a wide variety of engineering applications....
s, such as a dovetail slide or box slide, with an Acme leadscrew drive. With just a simple nut, some backlash is inevitable. On manual (non-CNC
Numerical control
Numerical control refers to the automation of machine tools that are operated by abstractly programmed commands encoded on a storage medium, as opposed to controlled manually via handwheels or levers, or mechanically automated via cams alone...
) machine tools, the way that machinists compensate for the effect of backlash is to approach all precise positions using the same direction of travel. This means that if they have been dialing left, and now they want to move to a rightward point, they move rightward all the way past it and then dial leftward back to it. The setups, tool approaches, and toolpaths are designed around this constraint.
The next step up from the simple nut is a split nut, whose halves can be adjusted and locked with screws so that one side rides leftward thread faces, and the other side rides rightward faces. Notice the analogy here with the radio dial example using split gears, where the split halves are pushed in opposing directions. Unlike in the radio dial example, the spring tension idea is not useful here, because machine tools taking a cut put too much force against the screw. Any spring light enough to allow slide movement at all would allow cutter chatter at best and slide movement at worst. These screw-adjusted split-nut-on-an-Acme-leadscrew designs cannot eliminate all backlash on a machine slide unless they are adjusted so tight that the travel starts to bind. Therefore this idea can't totally obviate the always-approach-from-the-same-direction concept; but backlash can be held to a small amount (1 or 2 thou), which is more convenient and in some non-precise work is enough to allow one to ignore the backlash (i.e., act as if there weren't any).
CNCs can be programmed to use the always-approach-from-the-same-direction concept, but that is not the normal way they are used today, because hydraulic anti-backlash split nuts and newer forms of leadscrew other than Acme/trapezoidal, such as recirculating ball screws
Ball screw
A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical raceway for ball bearings which act as a precision screw. As well as being able to apply or withstand high thrust loads, they can do so with...
or duplex worm
Duplex worm
Contrary to standard toothing of worm gear sets, the two flanks of duplex or dual lead worms and wheels are manufactured with slightly different modules and/or diameter quotients....
gear sets, effectively eliminate the backlash. The axis can move in either direction without the go-past-and-come-back motion.
The simplest CNCs, such as microlathes or manual-to-CNC conversions, use just the simple old nut-and-Acme-screw drive. The controls can be programmed with a parameter value entered for the total backlash on each axis, and the machine will automatically add that much to the program's distance-to-go when it changes directions. This [programmatic] "backlash compensation", as it's called, is a useful trick for capital-frugal applications. "Professional-grade" CNCs, though, use the more expensive backlash-eliminating drives mentioned above. This allows them to do 3D contouring with a ball-nosed endmill, for example, where the endmill travels around in many directions with ease and constant rigidity.
In mechanical computers a more complex solution is required, namely a frontlash gearbox. This works by turning slightly faster when the direction is reversed to 'use up' the backlash slack.
Some motion controllers include backlash compensation. Compensation may be achieved by simply adding extra compensating motion (as described earlier) or by sensing the load's position in a closed loop control scheme
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
. The dynamic response of backlash itself, essentially a delay, makes the position loop less stable and prone to oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
.
Minimum backlash
Minimum backlash is the minimum transverse backlash at the operating pitch circle allowable when the gear tooth with the greatest allowable functional tooth thickness is in mesh with the pinion tooth having its greatest allowable functional tooth thickness, at the tightest allowable center distance, under static conditions.Difference between the maximum and minimum backlash occurring in a whole revolution of the larger of a pair of mating gears.
Applications
Gear couplings use backlash to allow for angular misalignment.Backlash is undesirable in precision positioning applications such as machine tool tables. It can be minimized by tighter design features such as ball screw
Ball screw
A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical raceway for ball bearings which act as a precision screw. As well as being able to apply or withstand high thrust loads, they can do so with...
s instead of leadscrew
Leadscrew
A leadscrew , also known as a power screw or translation screw, is a screw designed to translate turning motion into linear motion...
s, and by using preloaded bearings. A preloaded bearing uses a spring or other compressive force to maintain bearing surfaces in contact despite reversal of direction.
There can be significant backlash in unsynchronized transmissions because of the intentional gap between dog gears (also known as dog clutch
Dog clutch
A dog clutch is a type of clutch that couples two rotating shafts or other rotating components not by friction but by interference. The two parts of the clutch are designed such that one will push the other, causing both to rotate at the same speed and will never slip.Dog clutches are used where...
es). The gap is necessary so that the driver or electronics can engage the gears easily while synchronizing the engine speed with the driveshaft speed. If there was a small clearance, it would be nearly impossible to engage the gears because the teeth would interfere with each other in most configurations. In synchronized transmissions, synchromesh solves this problem.