ISO/TC 60/SC 2/WG 6 - Gear calculations

This document presents the basic principles of, an introduction to, and the general influence factors for the calculation of the load capacity of spur and helical gears. Together with the other documents in the ISO 6336 series, it provides a method by which different gear designs can be compared. It is not intended to assure the performance of assembled drive gear systems. It is not intended for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting reasonable values for the factors in these formulae based on the knowledge of similar designs and the awareness of the effects of the items discussed. The formulae in the ISO 6336 series are intended to establish a uniformly acceptable method for calculating the load capacity of cylindrical gears with straight or helical involute teeth. The ISO 6336 series includes procedures based on testing and theoretical studies as referenced by each method. The methods are validated for: — normal working pressure angle from 15° to 25°; — reference helix angle up to 30°; — transverse contact ratio from 1,0 to 2,5. If this scope is exceeded, the calculated results will need to be confirmed by experience. The formulae in the ISO 6336 series are not applicable when any of the following conditions exist: — gears with transverse contact ratios less than 1,0; — interference between tooth tips and root fillets; — teeth are pointed; — backlash is zero. The rating formulae in the ISO 6336 series are not applicable to other types of gear tooth deterioration such as plastic deformation, case crushing and wear, and are not applicable under vibratory conditions where there can be an unpredictable profile breakdown. The ISO 6336 series does not apply to teeth finished by forging or sintering. It is not applicable to gears which have a poor contact pattern. The influence factors presented in these methods form a method to predict the risk of damage that aligns with industry and experimental experience. It is possible that they are not entirely scientifically exact. Therefore, the calculation methods from one part of the ISO 6336 series is not applicable in another part of the ISO 6336 series unless specifically referenced. The procedures in the ISO 6336 series provide rating formulae for the calculation of load capacity with regard to different failure modes such as pitting, tooth root breakage, tooth flank fracture, scuffing and micropitting. At pitch line velocities below 1 m/s the gear load capacity is often limited by abrasive wear (see other literature such as References [23] and [22] for further information on such calculation).

This document specifies the fundamental formulae for use in the determination of the surface load capacity of cylindrical gears with involute external or internal teeth. It includes formulae for all influences on surface durability for which quantitative assessments can be made. It applies primarily to oil‑lubricated transmissions, but can also be used to obtain approximate values for (slow‑running) grease‑lubricated transmissions, as long as sufficient lubricant is present in the mesh at all times. The given formulae are valid for cylindrical gears with tooth profiles in accordance with the basic rack standardized in ISO 53. They can also be used for teeth conjugate to other basic racks where the actual transverse contact ratio is less than εαn = 2,5. The results are in good agreement with other methods (see References [5], [7], [10], [12]). These formulae cannot be directly applied for the assessment of types of gear tooth surface damage such as plastic yielding, scratching, scuffing and so on, other than that described in Clause 4. The load capacity determined by way of the permissible contact stress is called the "surface load capacity" or "surface durability". If this scope does not apply, refer to ISO 6336-1:2019, Clause 4.

This document specifies the fundamental formulae for use in tooth bending stress calculations for involute external or internal spur and helical gears with a rim thickness sR > 0,5 ht for external gears and sR > 1,75 mn for internal gears. In service, internal gears can experience failure modes other than tooth bending fatigue, i.e. fractures starting at the root diameter and progressing radially outward. This document does not provide adequate safety against failure modes other than tooth bending fatigue. All load influences on the tooth root stress are included in so far as they are the result of loads transmitted by the gears and in so far as they can be evaluated quantitatively. This document includes procedures based on testing and theoretical studies such as those of Hirt[11], Strasser[14] and Brossmann[10]. The results are in good agreement with other methods (References [5], [6], [7] and [12]). The given formulae are valid for spur and helical gears with tooth profiles in accordance with the basic rack standardized in ISO 53. They can also be used for teeth conjugate to other basic racks if the virtual contact ratio εαn is less than 2,5. The load capacity determined on the basis of permissible bending stress is termed "tooth bending strength". The results are in good agreement with other methods for the range, as indicated in the scope of ISO 6336‑1. If this scope does not apply, refer to ISO 6336-1:2019, Clause 4.

This document specifies the information and standardized conditions necessary for the calculation of the service life (or safety factors for a required life) of gears subject to variable loading for only pitting and tooth root bending strength. If this scope does not apply, refer ISO 6336-1:2019, Clause 4.

This document describes a procedure for the calculation of the tooth flank fracture load capacity of cylindrical spur and helical gears with external teeth. It is not intended to be used as a rating method in the design and certification process of a gearbox. The formulae specified are applicable for driving as well as for driven cylindrical gears while the tooth profiles are in accordance with the basic rack specified in ISO 53. They can also be used for teeth conjugate to other racks where the actual transverse contact ratio is less than εα = 2,5. The procedure was validated for case carburized[15] gears and the formulae of this document are only applicable to case carburized gears with specifications inside the following limits: — Hertzian stress: 500 N/mm2 ≤ pH ≤ 3 000 N/mm2; — Normal radius of relative curvature: 5 mm ≤ ρred ≤ 150 mm; — Case hardening depth at 550 HV in finished condition: 0,3 mm ≤ CHD ≤ 4,5 mm. This document is not applicable for the assessment of types of gear tooth damage other than tooth flank fracture.

The example calculations presented here are provided for guidance on the application of the technical specification ISO/TS 6336‑22 only. Any of the values or the data presented should not be used as material or lubricant allowables or as recommendations for micro-geometry in real applications when applying this procedure. The necessary parameters and allowable film thickness values, λGFP, should be determined for a given application in accordance with the procedures defined in ISO/TS 6336‑22.

This document describes a procedure for the calculation of the micropitting load capacity of cylindrical gears with external teeth. It has been developed on the basis of testing and observation of oil-lubricated gear transmissions with modules between 3 mm and 11 mm and pitch line velocities of 8 m/s to 60 m/s. However, the procedure is applicable to any gear pair where suitable reference data are available, providing the criteria specified below are satisfied. The formulae specified are applicable for driving as well as for driven cylindrical gears with tooth profiles in line with the basic rack specified in ISO 53. They are also applicable for teeth conjugate to other basic racks where the virtual contact ratio (εαn) is less than 2,5. The results are in good agreement with other methods for normal working pressure angles up to 25°, reference helix angles up to 25° and in cases where pitch line velocity is higher than 2 m/s. This document is not applicable for the assessment of types of gear tooth surface damage other than micropitting.

ISO/TS 6336-21:2017 specifies the integral temperature method for calculating the scuffing load capacity of cylindrical, bevel and hypoid gears.

ISO/TS 6336-20:2017 specifies methods and formulae for evaluating the risk of scuffing, based on Blok's contact temperature concept. The fundamental concept is applicable to all machine elements with moving contact zones. The flash temperature formulae are valid for a band-shaped or approximately band-shaped Hertzian contact zone and working conditions characterized by sufficiently high Péclet numbers.

The formulae specified in this International Standard are intended to establish a uniformly acceptable method for calculating the pitting resistance and bending strength capacity of industrial gears with spur or helical teeth. The rating formulae in this International Standard are not applicable to other types of gear tooth deterioration such as plastic yielding, micropitting, scuffing, case crushing, welding and wear, and are not applicable under vibratory conditions where there may be an unpredictable profile breakdown. The bending strength formulae are applicable to fractures at the tooth fillet, but are not applicable to fractures on the tooth working profile surfaces, failure of the gear rim, or failures of the gear blank through web and hub. This International Standard does not apply to teeth finished by forging or sintering. It is not applicable to gears which have a poor contact pattern. This International Standard provides a method by which different gear designs can be compared. It is not intended to assure the performance of assembled drive gear systems. Neither is it intended for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the effects of the items discussed. CAUTION — The user is cautioned that the calculated results of this International Standard should be confirmed by experience.

This part of ISO/TR 14179 presents a means for determining the thermal load carrying capacity of gears that includes measurement on original gear units under practical conditions. This takes the form of either measurement of the power loss, heat dissipation or both, or, in the case of splash-lubricated gear units, the determination of the quasi-stationary temperature in the oil sump. The methods of calculation for all individual components of power loss and heat dissipation described in this part of ISO/TR 14179 are to be regarded as an alternative method.

This part of ISO/TR 14179 utilizes an analytical heat balance model to provide a means of calculating the thermal transmittable power of a single- or multiple-stage gear drive lubricated with mineral oil. The calculation is based on standard conditions of 25 °C maximum ambient temperature and 95 °C maximum oil sump temperature in a large indoor space, but provides modifiers for other conditions.

The formulae specified in this International Standard are intended for the establishment of a uniformly acceptable method for calculating the pitting resistance and bending strength capacity for the endurance of the mainpropulsion and auxiliary gears of ships, offshore vessels and drilling rigs, having straight or helical teeth and subject to the rules of classification societies. The rating formulae in this International Standard are not applicable to other types of gear tooth deterioration, such as plastic yielding, micropitting, scuffing, case crushing, welding and wear, and are not applicable under vibratory conditions where there may be an unpredictable profile breakdown. The bending strength formulae are applicable to fractures at the tooth fillet, but are not applicable to fractures on the tooth working profile surfaces, failure of the gear rim, or failures of the gear blank through web and hub. This International Standard does not apply to teeth finished by forging or sintering. This standard is not applicable to gears having a poor contact pattern. This International Standard provides a method by which different gear designs can be compared. It is not intended to assure the performance of assembled drive gear systems. It is not intended for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the effects of the items discussed. WARNING — The user is cautioned that the calculated results of this International Standard should be confirmed by experience.

ISO 6336-2:2006 specifies the fundamental formulas for use in the determination of the surface load capacity of cylindrical gears with involute external or internal teeth. It includes formulas for all influences on surface durability for which quantitative assessments can be made. It applies primarily to oil-lubricated transmissions, but can also be used to obtain approximate values for (slow-running) grease-lubricated transmissions, as long as sufficient lubricant is present in the mesh at all times.

ISO 6336-1:2006 presents the basic principles of, an introduction to, and the general influence factors for, the calculation of the load capacity of spur and helical gears. Together with ISO 6336-2, ISO 6336-3, ISO 6336-5 and ISO 6336-6, it provides a method by which different gear designs can be compared. It is not intended to assure the performance of assembled drive gear systems. It is not intended for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the effects of the items discussed. The formulae in ISO 6336 are intended to establish a uniformly acceptable method for calculating the pitting resistance and bending strength capacity of cylindrical gears with straight or helical involute teeth.

ISO 6336-3:2006 specifies the fundamental formulae for use in tooth bending stress calculations for involute external or internal spur and helical gears.

ISO 6336-6:2006 specifies the information and standardized conditions necessary for the calculation of the service life (or safety factors for a required life) of gears subject to variable loading. While the method is presented in the context of ISO 6336 and calculation of the load capacity of spur and helical gears, it is equally applicable to other types of gear stress.

Gives the fundamental formulae for use in tooth bending strength calculations for involute internal and external gears with a minimum rim thickness under the root.

Gives the fundamental formulae for use in the determination of the load capacity of cylindrical gears with involute internal or external teeth.

Provides together with parts 2, 3 and 5 a method by which different gear designs can be compared. It is not intended to assure the performance of gear systems. Preferably intended for use by the experienced gear designer.