Guide to Gear Mesh Transmission Backlash - Factors, Types, Measurements & Calculations

Date: April 10, 2024

Gear backlash in precision applications is a critical element of gear system performance. Too much backlash can result in inefficiencies of motion in the gear train, and will ultimately damage a gear’s teeth. Too little can mean the gears bind up and cause excessive wear to the tooth’s surface and the root of the gear, or even the fracturing of a tooth. Establishing and setting the appropriate amount of backlash is essential in gear design and manufacturing.

backlash in spur gears

Backlash Topics in this Guide

Jump to a section:

What Is Backlash in Gears?

Gear backlash is a mechanical engineering term referring to the lost motion resulting from spaces occurring between gear teeth during the mesh process of bidirectional gears. Backlash is seen in the mating gears at the pitch circle diameter. In motors, it is a specification used to indicate mechanical precision of a transmission component between the power plant and the load of a gear train. In common usage, the term can refer to the spaces themselves or the loss of motion resulting from the spaces when a gear direction is reversed.

In other words, backlash can be defined as the excess wideness of a space between teeth of one gear compared to the thickness of the tooth of its mating gear. Both the resulting gap and wasted motion occurring when the gap is closed can be considered backlash.

While some gaps are required between mating gear parts to prevent jamming and promote proper lubrication, excessive gaps can add unexpected load forces, creating slippage between teeth, gear wear and eventual failure of entire gear systems.

Factors in Gear Backlash

As a gear designer, there are numerous factors to consider when accommodating a gear system’s optimal amount of backlash.

Accuracy Standard of Gears - How Well They Mesh

Spur and helical gear accuracy is measured according to AGMA precision standards and is grouped according to 13 different grades ranging from 3-15 (3 is highest, 15 is the lowest). This standard assigns values for the accuracy of several gear measurements including:

  • Single pitch deviation
  • Total pitch deviation
  • Total profile deviation
  • Total helix deviation
  • Total radial composite deviation
  • Runout

Measuring Backlash Due to Teeth Inaccuracies:

A gear’s accuracy standard has a negative relationship to the amount of backlash - the more accurate the gear tooth profile, the lower the backlash.

Backlash equation when measured along the pitch circle:

gear backlash equation for tooth thickness

Where:

gear backlash equation values for tooth thickness at ideal pitch circle

Center Distance Tolerance

Referring to the distance between the center of a pair of meshing gears, center distance tolerance is the amount of variance in the mating gear’s center distance that will allow for an optimized point of intersection. Natural variations of the gear’s pitch occur during a single gear rotation, resulting in some mesh inconsistencies. Compensating for center distance tolerance of ±25~30 µm in parallel gears is optimal for achieving the appropriate amount of backlash.

Center distance errors affect the drive’s running efficiency:

  • Increases in center distance increase the backlash & gear contact ratios
  • Decreases in center distance decrease backlash up to the point of gear binding

Measuring Backlash Due to Pitch Circle Variance:

A gear’s center distance has a positive relationship to the amount of backlash - more distance increases backlash, while less reduces it.

NOTE: Changes in the machine’s speed or the gear’s material composition can affect this distance, despite making no other changes.

Backlash equation when measured along the pitch circle:

gear backlash equation when measured along pitch circle

Where:

gear backlash equation values for center distance changes and pressure angle

Types of Fit Between Gears, Shafts & Bearings

  • Shaft fit - certain errors in shaft alignment can occur, particularly in instances where a coupling is integrated into the system
  • Bearing fit - clearance & flexibility are at play here: a bearing’s inner ring is subjected to contact force of the rotor, which can change the gear’s center distance
  • Gear type - a spur gear running parallel to another spur gear will have different backlash characteristics than helical & worm gear systems, which introduce a sliding motion into the process

How Much Gear Mesh Backlash Is Acceptable

How much backlash to aim for depends on the scenario, but a common rule is to set backlash in between 0.03 to 0.05 divided by the diametral pitch.

Minimum Backlash & Variation

Gear engineers consider the minimum backlash to be the least amount of transverse backlash allowable (measured at the operating pitch circle) when the gear with the greatest allowable tooth thickness is meshed with the smallest of the paired gears (the pinion) - configured with its greatest allowable tooth thickness - at the point of the smallest allowable center distance. This measurement is taken while the gears are not in motion.

Backlash variation is found in the difference between the minimum and maximum backlash occurring in the bigger of a pair of mated gears.

Backlash & Lost Motion

While backlash inevitably results in lost motion, not all lost motion is a byproduct of backlash. Certain geared motor setups implement gear configurations that eliminate backlash. In these cases, lost motion is the term of choice, and describes the total displacement occurring in bidirectional gears as well as mechanical hysteresis loss

Lost Motion Factors

  • Backlash
  • Gear teeth play
  • Transmission strength - the permissible torque & shaft output speed
  • Mechanical hysteresis loss - material deformations that lead to inefficient torque transmission

Classes of Backlash in Gears & Their Measurements

Normal Backlash

The appropriate amount of backlash may vary, but is normally considered to be the minimum distance between the flanks of meshed teeth in a gear pair when they’re in contact.

How It’s Measured

Taken when the leading edges of the meshing flank are in contact, this measures the gap between the meshed flanks on the opposite side.

Gear types affected:

Gear mesh types affected:

  • Parallel
  • Intersecting
  • Non-parallel & non-parallel axis gears

Circumferential Backlash

This refers to the length of the gear’s arc at the pitch circle and its travel before teeth make contact.

How It’s Measured

This measurement is taken at the pitch circle, accounting for how far the gear rotates before the meshed tooth makes contact with the stationary mated gear.

Gear types affected:

  • Spur gears
  • Helical gears
  • Straight bevel
  • Spiral bevel
  • Screw gears
  • Worm gears

Gear mesh types affected:

  • Parallel
  • Intersecting
  • Non-parallel & non-parallel axis gears

Angular Backlash

Measures the angle at which a meshed gear moves when the mating gear is stationary.

How It’s Measured

This value must be specified to each specific gear’s center.

Gear types affected:

  • Spur gears
  • Helical gears
  • Straight bevel
  • Spiral bevel
  • Screw gears
  • Worm gears

Gear mesh types affected:

  • Parallel
  • Intersecting
  • Non-parallel & non-parallel axis gears

Radial Backlash

The amount of displacement in the stated center distance when paired gears’ teeth are in contact

How It’s Measured:

Measures the difference in stated center distance vs. observed center distance when the meshed tooth flanks are in contact with each other.

Gear types affected:

  • Spur gears
  • Helical gears
  • Screw gears
  • Worm gears

Gear mesh types affected:

  • Parallel
  • Non-parallel & non-parallel axis gears

Axial Backlash

Indicates the amount of displacement of the stated center distance in bevel gears as the paired gears’ teeth are meshing.

How It’s Measured:

In bevel gears only: Measures difference in stated center distance vs. observed gear centers when the paired gears are in contact with each other.

Gear types affected:

  • Straight bevel
  • Spiral bevel

Gear mesh types affected:

  • Intersecting axes gears

Setting Backlash in Gears

Producing Backlash

When gear systems begin to underperform and increase in vibration and noise, too little backlash can be the culprit. Sub-optimal backlash can result in added wear and reduced lubrication, which will further contribute to gear tooth wear. In these cases, it may be necessary to find ways to increase backlash for smoother operation.

Two common methods for producing backlash include:

  • Widening the center distance - by lengthening the center distance, the gear mesh will loosen & pressure on the teeth will be reduced, allowing more “play” in the gear mesh upon the drive direction.
  • Reduce the tooth thickness - this involves changing out or modifying the gears in the mesh which can be time consuming & potentially expensive. As a result, enlarging the center distance is often the first & preferred method of producing backlash.

Reducing or Eliminating Backlash

Certain applications demand near-total position control accuracy, which requires reducing the amount of backlash or eliminating it completely. There are several options available to minimize or remove all backlash from a gear system, from using higher quality gear material to swapping spur gears for other types. These methods have been shown to mitigate backlash to varying degrees, and are often best used in combination:

Using Precision Gears

Improving the quality of the gear’s manufacture and material (and AGMA quality level) will allow for smooth tooth contact even in smaller tolerances and less backlash. This can be a costly option, as high-precision gears are more difficult to produce and may not be appropriate for all applications.

Adjusting Gear Clearance

Shortening the center distance between two gears is a simple way to reduce backlash. It will result in a tighter meshing between the teeth, and minimizes the effect of center distance variation, differences in tooth dimensions, and other gear set up or bearing inconsistencies. However, the added friction between gear teeth may result in wear which will begin to produce increasing levels of backlash over time.

Modifying Gears

  • Using spring-loaded split gearing
  • Switching to tapered spur or helical gears
  • Using plastic shims
  • Preloading gear train with springs or weights
  • Using dual-path gear trains - this is considered a “zero backlash” option

Using Special Drives

  • Harmonic drives
  • Cycloidal drives - “zero backlash” option
  • Epicyclic drives

Contact Berg technical support with questions, or shop precision gearing from WM Berg.

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