Gear failure mechanism

Gear failure mechanisms are several and can occur based on the rotational speed and the load applied to the gear. It is possible that more than one of them occur at the same time. These mechanisms are: wear, scuffing, pitting, micro-pitting, tooth flank fracture and tooth root fatigue fracture.^[1][2][3]

Gear Failure mechanism according to load and rotational speed ^[1]

These mechanisms are due to several phenomena: friction, contact (Hertzian pressure, sliding/rolling), bending fatigue and lack of lubrication.

In order to understand the failure on tooth flanks, it's necessary to study the kinematics of gear meshing. When the point of contact is on the pitch diameter, the contact is purely rolling. As we move away from this point, sliding starts. It increases moving to the external point of contact or the internal point of contact. Several tests have shown that, when sliding is in the same direction as rolling, it has a more severe effect on the flank surface. This condition occurs below the pitch diameter of the driving gear. This is a condition that causes failure mechanisms of tooth flanks such as wear, scuffing, macropitting, micro-pitting.^[2]

Moreover, the failure at the tooth root are caused by cyclic bending loads that are applied to the teeth during the meshing, hence the phenomenon is strictly related to bending fatigue.

ISO 10825^[4] is the standard that provides a classification system for the general modes of gear tooth wear and failure. It classifies and identifies the most common types of failure, providing information to identify them.

ISO 6336^[5] and AGMA 2001^[6] provide information regarding this failure mechanism and define a calculation method to verify if a gear is subjected to such phenomena.

Wear

Wear is the phenomenon of material removal from two sliding surfaces. In gears, it is present on the tooth flank and it is produced by the combination of sliding and rolling. It can be accelerated by significant metal-to-metal contact due to lack of lubricant, presence of abrasive particles in the lubricant or corrosion related to additives in the lubricant.^[2][3]

Wear includes polishing, scratches and abrasive wear. It can be categorized as mild, moderate or severe.^[4]

The principal effect of this failure mode is the modification of the tooth profile, hence a change of the contact area. Thus, wear can alter contact stresses and load distributions and, as a consequence, accelerate the occurrence of other failure modes.

Wear has a detrimental effect on noise, vibration and harshness. It also negatively affects dynamics and efficiency performance of the meshing gear.^[7][8][9]

This phenomenon, in some applications, can be exploited in the run-in of gear couples to improve their contact area.

Scuffing (or scoring)

Scuffing on tooth flank

Scuffing is a phenomenon that is related to the failure of the lubricant that allows metal-to-metal contact at high spots on the flank surfaces. Scuffing is a terminology used prevalently in the automotive industry, while the term scoring is used in aerospace industry instead.

In the area of contact, the peaks of roughness of the two flanks touch and, due to the small contact area (which creates a high pressure), a local temperature increase occurs. This increase in temperature can create microweldings between the peaks which immediately break due to the moving contact point. This breakage removes material which ends up moving inside the gearbox, causing other damages.^[10]

The scuffing marks appear as streaks or scratches with sharpened bottoms and sides. They also frequently appear as bands of variable depth and width, oriented in the sliding direction. They can affect either isolated zones or the whole width of the face.^[4]

This form of damage is most relevant when surface velocities are high. However, scuffing can also occur for relatively low sliding velocities when tooth surface pressures are high enough or due to uneven surface geometry and loading.

This phenomenon leads to a modification of the profile, an increased vibration and, usually, to the complete failure of the gearbox.

There are two calculation methods:

• ISO 6336-20 flesh temperature^[11]
• ISO 6336-21 integral temperature method^[12]

Calculation method according to ISO 6336-21 integral temperature method

The integral temperature method is based on the assumption that scuffing is likely to occur when the mean value of the contact temperature (integral temperature θ_int) is equal to or exceeds a corresponding critical value (the permissible integral temperature θ_int,P) derived from a gear test for scuffing resistance of lubricants.^[12]

The mean weighted surface temperature is calculated as:

${\textstyle \theta _{int}=\theta _{m}+\theta _{fla,int}}$

where θ_m is the mean temperature and θ_fla,int is the mean flash temperature during the engagement. Hence, the safety factor is:

${\displaystyle S_{s}=\theta _{int,P}/\theta _{int}}$

If the safety factor is higher than 1, the gear is safe from scuffing.

Macropitting

Stress distribution in contacting surfaces due to rolling/sliding^[13]

Stress by Hertzian pressure and the rolling/sliding motion leads to crack nucleation near the surface, then it propagates in the surface of the flank with an increasing rate. Pieces break away from the surface progressively, producing larger cavities. This condition is known as pitting or macropitting. The material is torn away from the flank by the relative motion of the contacting part.

The initial stage of pitting is confined mostly to three areas along the profile of a gear tooth^[13]:

• the pitchline, where only pure rolling contact is present
• the area immediately above or below the pitchline, where there is a combination of rolling and sliding contact
• the lowest point of single tooth contact, which is the point that receives the tip of the mating tooth. Tip contact will produce high pressures even if the load transmitted is low.

  

  Macropitting on tooth flank

The damage increases progressively with the noise and the vibrations during the meshing.^[9][14]

At low rotational speed, pitting is the predominant flank failure mode.^[2]

Calculations method according to ISO 6336-2

As the standard^[15] states:

Hertzian pressure, which serves as a basis for the calculation of the contact stress, is the basic principle used in this document for the assessment of the surface durability of cylindrical gears. It is a significant indicator of the stress generated during tooth flank engagement. However, it is not the sole cause of pitting, and nor are the corresponding subsurface shear stresses. There are other contributory influences, for example, coefficient of friction, direction and magnitude of sliding and the influence of lubricant on the distribution of pressure. Development has not yet advanced to the stage of directly including these in calculations of load‑bearing capacity; however, allowance is made for them to some degree in the derating factors and the choice of material property values.

The calculation method consists of comparing the pressure that occurs on the flank during the contact σ_G (calculated using the contact pressure), and the admissible flank pressure σ_HG.

Hence the safety factor is calculated as:

${\displaystyle S_{H}=\sigma _{HG}/\sigma _{G}\geq S_{H,min}}$

Here, some typical values for different applications are reported:

• normal cases S_H=1 - 1.2
• high reliability and high cases (ship transmission, aircraft transmission) S_H=1.2 - 1.6

Micropitting

It is a fatigue damage on the surface of the tooth flank caused by high sliding/rolling load with insufficient lubricant film thickness. This damage produces a wear-like scouring which modifies the profile shape, moreover it increases the noise and the vibration and can lead to a reduction of the pitting load capacity.

It is typically present in case hardened, high tempered and nitrided gears in form of microcracks and fractures.

Calculations method according to ISO 6336-22

As the standard^[16] states:

The basis for the calculation of the micropitting load capacity of a gear set is the model of the minimum operating specific lubricant film thickness in the contact zone. Many parameters can influence the occurrence of micropitting. These include surface topography , contact stress level, and lubricant chemistry.(...) Although the calculation of specific lubricant film thickness does not provide a direct method for assessing micropitting load capacity, it can serve as an evaluation criterion when applied as part of a suitable comparative procedure based on known gear performance.

The calculation of the relative lubricant film thickness λ_GF takes in account the minimum local film thickness h_min and the roughness R_a:

${\displaystyle \lambda _{FG}=h_{min}/R_{a}}$

The safety factor is obtained by comparing the relative lubricant film thickness λ_GF and the minimum required relative lubricant film thickness λ_GFP:

${\displaystyle S_{\lambda }=\lambda _{GF}/\lambda _{GFP}}$

If S_λ>2 microppitting is not expected, on the other hand if S_λ<2 the tooth flank is at risk of micropitting.

Tooth flank fracture

Tooth flank fracture is a sub-surface failure mechanism observed on case hardened gears. The initial crack can be found below the loaded surface, in correspondence of non-metallic inclusions, which act as notches increasing locally the stress and promoting the nucleation of cracks. Tooth flank fracture leads to the complete failure of the gear, hence the failure of the gearbox.

Calculations method according to ISO 6336-4

As the standard^[17] states:

This document provides principles for the calculation of the tooth flank fracture load capacity of cylindrical involute spur and helical gears with external teeth. The method is based on theoretical and experimental investigations (...) on case carburized test gears and gears from different industrial applications.

Tooth flank fracture is characterized by a primary fatigue crack in the region of the active contact area, initiated below the surface due to shear stresses caused by the flank contact. Failures due to tooth flank fracture are reported from different industrial gear applications and have also been observed on specially designed test gears for gear running tests. Tooth flank fracture is most often observed on case carburized gears but failures are also known for nitrided and induction hardened gears. Most of the observed tooth flank fractures occurred on the driven partner.

The basis for the calculation of the tooth flank fracture load capacity are sophisticated calculation methods based on the shear stress intensity hypothesis (...) which were transferred to a calculation method in closed form solution. With only a small set of parameters concerning gear geometry, gear material and gear load condition, a calculation of the local material exposure can be performed in order to calculate the tooth flank fracture load capacity.

The procedure was validated only for case carburized gears and the formule are only applicable to gears with specifications inside the following limits:

• — Hertzian stress: 500 N/mm² ≤ p_H ≤ 3 000 N/mm²;
• — Normal radius of relative curvature: 5 mm ≤ ρ_red ≤ 150 mm;
• — Case hardening depth at 550 HV in finished condition: 0,3 mm ≤ CHD ≤ 4,5 mm.

Tooth root fatigue fracture

Tooth root bending fracture

This failure mechanism is related to fatigue, in particular a crack nucleates in the tooth root and then propagates. The propagation direction depends to the gear geometry, in particular by the rim thickness. This mechanism is the most detrimental because it leads to a sudden interruption of the power flow in the gearbox.

The tooth root stress can be calculated analytically according to ISO 6336^[5] and AGMA 2001^[6] both are based on the tangential force Ft and factors given by the standard or by using numerical methods (FEM).^[5][6]

Calculations method according to ISO 6336-3

The calculation method is based on the nominal bending stress and factors. These factors are determined from equations and diagrams present in the standard and take in account the gear geometry and the increase in external forces.^[18]

The tooth root stress is calculated as:

${\displaystyle \sigma _{F}={F_{t} \over {b\cdot m_{n}}}\cdot Y_{S}\cdot Y_{F}\cdot Y_{\beta }\cdot K_{A}\cdot K_{V}\cdot K_{F\beta }\cdot K_{F\alpha }}$

The tooth root limit strength is calculated as:

${\displaystyle \sigma _{FG}=\sigma _{Flim}\cdot Y_{ST}\cdot Y_{NT}\cdot Y_{\delta relT}\cdot Y_{RrelT}\cdot Y_{X}}$

Here are reported the factors:

• Ft: Nominal tangential force at the pitch circle
• b: Tooth width
• m_n: Normal module
• Y_F: Tooth form factor (influence of the tooth form)
• Ys: Stress correction factor
• Y_β: Helix angle factor (influence of helix angle)
• K_A: Application factor
• K_V: Dynamic factor
• K_Fβ: Face load load factor
• K_Fα: Transverse load load factor
• σ_Flim: Fatigue strength value for bending stress at the tooth root
• Y_ST: Stress correction factor for dimensions of the reference test
• Y_NT: Life factor: Higher load capacity for limited load cycles
• Y_δrelT: Relative support factor: Notch sensitivity of material
• Y_RrelT: Relative surface factor: Surface quality at the tooth root
• Yx: Size factor: Tooth dimensions

The safety factor is calculated as:

${\displaystyle S_{F}={\sigma _{FG} \over \sigma _{F}}\geqslant S_{Fmin}}$

Here are reported some typical values for different application:

• normal cases S_F=1.2 - 1.5
• high reliability and high cases (ship transmission, aircraft transmission) S_F=1.4 - 2.0

• 
  Gear FEM simulation
• 
  Tooth root stress calculation method according to AGMA 2001^[6]
• 
  Tooth root stress calculation method according to ISO 6336.^[5]

Testing

Schenk pulsator for STBF (Single tooth bending fatigue) test ^[19]

The standard ISO 6336^[5] and AGMA 2001^[6] provide informations regarding the material and the geometry of gears but they cannot take in account all the possible combinations, hence experimental test are strongly suggested.

As mentioned above, the failure mechanism can happen simultaneously, thus to avoid this phenomena the tested gears are designed in order to isolate the specific failure mechanism to study.^[2]

Test rig for the transmission error

All the aforementioned failure mechanism can be studied using running ger tests, which consist in two gears that mesh together and the torque and speed are setted according to the test specifications.

The tooth root fatigue fracture can be also studied through pulsator test. This test methodology consist in loading one or two teeth at the time using two anvils on which the load is applied. Due to the different test configuration, it provides different result with respect to the running gear test but they are still accepted.^[20][21]

There are several testing rig in different dimensions and configurations to properly test gear of a large variety of shape.^[19]

See also

• Gear
• Wear
• Contact mechanics