It is not intended to assure the performance of assembled gear drive systems. These fundamental rating formulas are applicable for f04 the pitting resistance and bending strength of internal and external spur and helical involute gear teeth operating on parallel axes. The formulas evaluate gear tooth capacity as influenced by the major factors which affect gear tooth pitting and gear tooth fracture at the fillet radius.
The knowledge and judgment required to evaluate the various rating factors come agmx years of d04 experience in designing, manufacturing, and operating gear units. Empirical factors given in this standard are general in nature. AGMA application standards may use other empirical factors that are more closely suited to the particular field of application.
This standard is intended for use by the experienced gear designer, capable of selecting reasonable values for the factors. It is not intended for use by the engineering public at large. The formulas of this standard are not applicable amga any of the following conditions exist: The effect of this undercut is to move the highest point of single tooth contact, negating the assumption of this calculation method.
However, the reduction in tooth root thickness due to protuberance below the active profile is handled correctly by this method. The YJ factor calculation uses the stress correction factors developed by Dolan and Broghamer [19]. These factors may not be valid for root forms which are not smooth curves. For root profiles which are stepped or irregular, other stress correction factors may be more appropriate.
Scuffing criteria are not included in this standard. Design considerations to prevent fractures emanating from stress risers on the tooth profile, tip chipping, and failures of the gear blank through the web or hub should be analyzed by general machine design methods. The symbols and terms contained in this document may vary from those used in other AGMA standards. Users of this standard should assure themselves that they are using these symbols and terms in the manner indicated herein.
At the time of development, the editions were valid. All publications are subject to revision, and the users of this standard are encouraged to investigate the possibility of applying the most recent editions of the publications listed. Where no applicable AGMA application standard exists, numerical values may be estimated for the factors in the general formulas, and the approximate pitting resistance and bending strength ratings calculated.
The constants and coefficients used in curve fitting often have significant digits in excess of those inferred by the reliability of the empirical data. Experimental data from actual gear unit measurements are seldom repeatable within a plus or minus 10 percent band.
Calculated gear ratings are intended to be conservative, but the scatter in actual results may exceed 20 percent. Where sufficient experience is available from similar designs, satisfactory results can be obtained by extrapolation of previous tests or field data. When suitable test results or field data are not available, values for the rating factors should be chosen conservatively. Gear tooth accuracy considerations include: Gear element support considerations include: Hardness, tensile strength, microstructure and cleanliness are some criteria for determining allowable stress numbers.
Allowable stress numbers in this standard are based on cycles, 99 percent reliability and unidirectional loading. The allowable stresses are only valid for materials and conditions listed in this standard see clause For example, materials such as aluminum or stainless steel may encounter lubrication problems that invalidate calculations of pitting resistance and bending strength. Variations in microstructure account for some variation in gear capacity.
Higher levels of cleanliness and better metallurgical control permit the use of higher allowable stress numbers. Conversely, lower metallurgical quality levels require the use of lower allowable stress numbers.
The formulas of this standard are only valid for appropriate material quality and geometric quality that conforms to the manufacturing tolerances. If properly managed, these stresses should be compressive at the surface and should enhance the bending strength performance of the gear teeth. Shot peening, case carburizing, nitriding, and induction hardening are common methods of inducing compressive pre-stress in the surface of the gear teeth.
Grinding the tooth surface after heat treatment may reduce the residual compressive stresses. The procedure is as follows: 1 Ensure that the taper gage The basic rack shown in fIgure 1 is used to Illustrate the tooth proportions covered by this standard. This standard AGMA A05 pdf free download.
This information sheet provides a method for calculating the pitting resistance and bending strength of hypoid gears using Where applicable AGMA application standards exist, they should be used in preference to this standard. The definition of acceptable initial pitting varies widely with gear application. Initial pitting 4. It tends to The wear resistance of mating gears can be a redistribute the load by progressively removing high dictating performance limitation, particularly in low contact spots.
Generally, when the load has been speed, heavily loaded gears. Gear wear is a difficult reduced or redistributed, the pitting stops. The aim of the pitting resistance formula is to Wear may occur when the oil film that separates the determine a load rating at which progressive pitting contacting surfaces of mating gear teeth is not of the teeth does not occur during their design life. The ratings for pitting resistance are based on the Wear in low speed applications may be tolerable.
The adhesive wear is a welding and standard but could be a problem. It occurs when the oil film thickness is small enough to allow the flanks of the gear teeth to contact 4. Micropitting is one type of gear tooth surface fatigue. Scuffing is not a fatigue phenomenon and it may It is characterized by very small pits on the surface of occur instantaneously.
AGMA A03 provides a the material, usually less than 0. This deterioration of the surface of operating bulk temperature of gear blanks, sliding the material is generally thought to occur because of velocity, surface roughness of teeth, gear materials excessive Hertzian stresses due to influences from and heat treatments, and surface pressure. Ko is overload factor see clause 9 ; Kv is dynamic factor see clause 8 ; The user should ensure that the gear blank construc- tion is representative of the basic theory embodied in Ks is size factor see clause 20 ; this standard.
Gear blank design is beyond the Km is load distribution factor see clause15 ; scope of this standard see 5. Cf is surface condition factor for pitting resist- ance see clause 13 ; The bending strength ratings determined by this F is net face width of narrowest member, in; standard are based on plate theory modified to consider: I is geometry factor for pitting resistance see clause 6 ; -- The compressive stress at tooth roots caused d is operating pitch diameter of pinion, in.
C is operating center distance, in; mG is gear ratio never less than 1. The pitting resistance power rating is based on the lowest value of the product sac ZN CH for each of KB is rim thickness factor see 5.
J is geometry factor for bending strength see 5. Pd is Pnd for spur gears. This data is based on external SF is safety factor for bending strength see clause It is a function of the backup ratio, mB, see annex B. CAUTION: The ratings of both pinion and gear teeth The effects of webs and stiffeners can be an must be calculated to evaluate differences in geometry improvement but are not accounted for in annex B. The effect of tapered rims has not been investigated.
The bending strength power rating is based on the low- When previous experience or detailed analysis est value of the term justifies, lower values of KB may be used. KB factor where it is applicable see These radii are used to evaluate the Hertzian contact stress in the tooth flank. Effects of In terms of this standard the allowable unit load is modified tooth proportions and load sharing are defined as: considered. Both the tangential bending and radial compressive The allowable unit load, Uat, is the lowest of the components of the tooth load are included.
It includes tables for some than at the root fillet. Published data [5] suggest the common tooth forms and the analytical method for use of a stress modifying factor, KB, in this case. These forces result from the Therefore, the transmitted tangential load will vary. Ideally, a gear set would have a at which the driven device will perform. Wt represents uniform velocity ratio between the input and output the tooth load due to the driven apparatus.
Transmission error is defined as the departure from uniform relative angular motion of the Overload factor, Ko see clause 9 , and Dynamic pair of meshing gears. It is influenced by all the factor, Kv see clause 8 , are included in the rating deviations from the ideal gear tooth form and ideal formulas see clause 5 to account for loads in spacing. The dynamic factor relates the total tooth load 7. When the transmitted load is not uniform, consider- -- Gear mesh stiffness variation as the gear ation should be given not only to the peak load and its teeth pass through the meshing cycle.
This anticipated number of cycles, but also to intermedi- source of excitation is especially pronounced in spur gears without profile modification. Spur ate loads and their numbers of cycles. This type of gears with properly designed profile modification, load is often considered a duty cycle and may be and helical gears with axial contact ratios larger represented by a load spectrum. In such cases, the than 1.
A method of calculating -- Transmitted load. Loads different from the design load will give increased transmis- sion error. It is now greater than 1.
In earlier AGMA transmission error. Gear tooth alignment is in- 8. Even if the -- Tooth friction induced excitation. The dynamic response of this system depends on The dynamic tooth forces are influenced by: the distribution of the masses, stiffness, and damp- -- Mass of the gears, shafts, and other major in- ing. In certain cases, a system may possess a ternal components.
The dynamic -- Damping. The principal source of coulomb or viscous damping is the shaft bearings. Generally factor, Kv, does not include considerations of the oil film bearings provide greater damping than dynamic tooth loads due to torsional vibration of the rolling element bearings. Other sources of damp- gear system. These loads must be included with ing include the hysteresis of the gear shafts, and other externally applied forces in the overload factor, viscous damping at sliding interfaces and shaft Ko.
For critical drives, a separate dynamic analysis couplings. The dynamic factor, Kv, does not apply to shafts are usually much higher than the operating resonance. For high speed gears, however, it is recommended that the shaft critical speeds be 8.
The dynamic factor, Kv, If a particular frequency of the transmission error does not account for the dynamic tooth loads due to excitation is close to the natural frequency of the gear spring--mass system, or some multiple of the this mode of vibration. The dynamic factor, Kv, does not account for gear pair Large cyclical variation in gear mesh stiffness and resonance, and operation in this regime is to be impact loads may lead to additional regions of avoided.
This is primarily a problem with lightly--loaded, lightly--damped spur gears 8. Gear blanks may have natural frequencies within the operating speed range. If the gear blank is excited 8. This occurs more in the absence of specific knowledge of the dynamic frequently in high speed, light weight gear blanks, loads. The curves of figure 1 and the equations but can also occur in other thin rimmed or thin given are based on empirical data, and do not webbed blanks.
The dynamic factor, Kv, does not account for resonance. A separate investigation is recommended when these condi- Due to the approximate nature of the empirical tions occur. For purposes of calculation, equation 24 To use these values, the gearing must be maintained defines the end points of the curves in figure 1.
When Av or A are not available, it is reasonable to refer to the pitch accuracy, and to some extent profile 8. Overload factors can only be established after the pinion and gear with the following formulas, considerable field experience is gained in a rounded to the next higher integer. Values of Av particular application.
Some of these are: system 26 vibrations, acceleration torques, overspeeds, varia- rounded to the next highest integer tions in system operation, split path load sharing where among multiple prime movers, and changes in process load conditions.
This standard provides a means to account P nd for: variations in load with overload factor , de is outside diameter of pinion or gear, in. With specific knowledge of the influencing factors listed in 8. Product application 8. Equations 28 and 29 are used to establish power ratings for unity service factor to which established service factors may be applied using equation When this is done, the stress cycle factor is 9 Overload factor, Ko calculated using the number of cycles equivalent to a specific number of hours at a specific speed, to The overload factor is intended to make allowance establish power rating for unity service factor.
The greater the uncertainties or consequences of these 28 considerations, the higher the safety factor should and from equation be. Therefore, the power rating for unity service factor should be based on the lowest values of the ex- Safety factors must be established from a thorough pressions for each of the mating gears. A minimum safety factor is normally established for the designer by specific agreement s at Y N J for bending strength between manufacturer and purchaser.
When specif- KB ic service experience is not available, a thorough The allowable transmitted power for the gear set, Pa, analytical investigation should be made.
The CH to, cutting, shaving, lapping, grinding, shot peen- factor varies with the surface finish of the pinion, fp, ing; and the mating gear hardness. The amount of non--uniformity of the load distribution is caused by, -- Gear ratio; and is dependent upon, the following influences: -- Surface finish of pinion; Manufacturing variation of gears -- Hardness of pinion and gear. The pinion and the gear. Assembly variations of installed gears Typical values of CH are shown in figure 2.
Deflections due to applied loads The values from figure 2 can be calculated as -- Elastic deflections of the pinion and gear follows: teeth. Its magnitude is affected by two For spur gears, where instantaneous contact lines components: are parallel to the axes, Cmf is affected primarily by Cmf is face load distribution factor; lead and parallelism see figure 4 B.
In this case, Cmt is transverse load distribution factor. Cmt is affected by the transverse contact ratio. Cmf and Cmt can be interrelated depending on the For helical gears having two or less axial overlaps, form of the instantaneous contact line in the plane of the interaction of lead and profile effects are so action as shown by figure 4.
The transverse load distribution factor accounts for It is affected primarily by the correctness of pinion the non--uniform distribution of load among the gear and gear leads. Gradual lead deviation such as teeth which share the load.
It is affected primarily by results from helix error, misalignment, or pinion the correctness of the profiles of mating teeth: i. Therefore, evaluation of Bearing clearances affect the gear contact in the the numeric value of the transverse load distribution same way as offset straddle mounted pinions. Equation 36 therefore, can same support side can compound the effect. This be modified to: effect is addressed by the pinion proportion modify- ing factor, Cpm. The face load distribution factor accounts for the When the gap in a double helical gear set is other non--uniform distribution of load across the gearing than the gap required for tooth manufacture, for face width.
The magnitude of the face load example in a nested design, each helix should be distribution factor is defined as the peak load treated as a single helical set. This standard provides an empirical method This method will give results similar to those only, but includes a theoretical discussion for analyti- obtained in previous AGMA standards.
Designs cal analysis in annex D. For double helical gears the gap is not Cpm is pinion proportion modifier; included in the face width. Cma is mesh alignment factor; -- The gear elements are mounted between Ce is mesh alignment correction factor. Cmc is 0. In this case, it may be necessary to modify the lead matching or lead corrections to compensate for lead or profile of the gears to arrive at a satisfactory re- deflection are employed, it may be desirable to use an sult.
The empirical method shall not be used when ana- analytical approach to determine the load distribution lyzing the effect of a momentary overload.
See When gear elements are overhung, consideration The pinion proportion factor, Cpf, accounts for must be given to shaft deflections and bearing deflections due to load. These deflections are clearances. The pinion proportion factor can be obtained the gear forces to the extent that resultant deflec- from figure 5.
Cpm is 1. The values for Cpf as shown in figure 5 can be determined by the following equations: where S1 is the offset of the pinion; i. S S1 2 The pinion proportion modifier, Cpm, alters Cpf, S based on the location of the pinion relative to its bearing centerline. The four curves of figure 7 provide effective mesh alignment. The following values are representative values for Cma based on the accuracy suggested for the mesh alignment correction factor: of gearing and misalignment effects which can be expected for the four classes of gearing shown.
Ce is 0. All requirements for the quality grade must be met in order to use the stress values for that grade. This can be accom- The allowable stress numbers for gear materials plished by specifically certifying each requirement vary with items such as material composition, where necessary, or by establishing practices and cleanliness, residual stress, microstructure, quality, procedures to obtain the requirements on a produc- heat treatment, and processing practices.
For tion basis. It is not the intent of this standard that all materials other than steel, a range is shown, and the requirements for quality grades be certified, but that lower values should be used for general design practices and procedures be established for their purposes.
Intermediate values are not classified since the effect of Allowable stress numbers in this standard tables 3 deviations from the quality standards cannot be through 6 are determined or estimated from labora- evaluated easily. When justified by testing or tory tests and accumulated field experiences. They experience, higher stress levels for any given grade are based on unity overload factor, 10 million stress may be used. The allowable stress numbers are cycles, unidirectional loading and 99 percent shown in tables 3 through 6, and figures 8 through reliability.
The allowable stress numbers are desig- For service life other than 10 million cycles, the allowable stress numbers are The grade cleanliness requirements apply only to adjusted by the use of stress cycle factors see those portions of the gear material where the teeth clause On Allowable stress numbers for steel gears are estab- external gears this portion of the gear blank normally lished by specific quality control requirements for will be less than 25 percent of the radius.
Since the shape of the effective S--N curve is flat, the sensitivity to shock should be investigated before proceeding with the design. The upper values may be used when: -- High quality material is used. Table 7 -- Major metallurgical factors affecting the allowable contact stress number, sac, and allowable bending stress number, sat, of through hardened steel gears1 2 3 Metallurgical factor Grade 1 Grade 2 ASTM E grain size Predominantly 5 or finer Predominantly 5 or finer Upper transformation products which Not specified Max controlling Max upper primarily include bainite and fine section, inches transformation pearlite.
Castings are permissible with primarily round Type 1 sulfide inclusions Sulfur Not specified 0. On external gears, this portion of the gear blank normally will be less than 25 percent of the radius. Sulfur content Not specified 0. On external gears, this por- tion of the gear blank normally will be less than 25 percent of the radius.
Limits: maximum of one indication per inch of face width and maximum of five in one tooth flank. Removal of defects which exceed the stated limits is acceptable provided the integrity of the gear is not compromised. Castings not applicable7 A recommended but not required. Limits 0. Criteria for grades 1, 2, and 3 apply to both stress numbers unless ac at otherwise specified in the metallurgical factor column. Test coupons shall be from the same alloy steel not necessarily same heat as the production parts.
Coupon should be sized to produce a similar cooling rate to that obtained in the gear teeth of the actual gear. Microhardness is to be measured on the test coupon at a depth not more than 0. A distance amplitude correction curve is not intended. Inspection is from the O. Other UT specifications which ensure the same quality level are permitted.
Sub--zero treatment should not be employed to transform large amounts of retained austenite e. The allowable stress numbers are established for the grade selected based on hardness. Because higher contact stresses are allowed for carburized and hardened gears, the resulting higher bending stresses must also be accommodated.
Therefore, for gearing of this type, higher core hardnesses are specified for the bending strength. The gear rating may be limited by either pitting resistance or bending strength for the selected grade and its core hardness requirement. Therefore, a minimum nd hardness of 25 HRC is acceptable in such cases. A distance amplitude correction curve is not in tended. Type B indicates only hardening of flanks extending to the form diameter.
Figure 12 -- Variations in hardening pattern obtainable on gear teeth with flame or induction hardening Through hardened gears specified above HB tion, loading, and manufacturing procedures to may vary widely in endurance strength, depending determine the desirable gradients of hardness, on the transformation characteristics of the steel, strength, and internal residual stresses throughout heat treating technique used and the size and shape the tooth.
The effective case depth for induction and flame A guide for minimum case depth for nitrided external Another guideline for determining case depth is not internal teeth based on the depth of maximum shown in figure These case depths have had a shear from contact loading is given by the formula: long history of successful use on carburized gears.
0コメント