P is the power transmitted per gear mesh. For multiple power paths load-sharing must be considered:
Branched offsets: If the pinion meshes with two or more gears (or the gear meshes with two or more pinions), use the power of the more highly-loaded branch.
Epicyclic Gearboxes: The degree of load sharing depends on the number of planets, accuracy of the gears and mountings, provisions for self-aligning, and compliance of the gears and mountings.
The pinion is defined as the smaller of a pair of gears. For planetary sun/planet gearsets, the sun is the pinion for mGo >= 4 and the planet is the pinion for mGo < 4. For star sun/planet gearsets, the sun is the pinion for mGo >= 3 and the planet is the pinion for mGo < 3. For planet/internal gearsets, the planet is always the pinion since it is smaller than the internal gear. Epicyclic gearsets are analyzed using relative speeds. The pinion and gear speeds are in proportion to the gear ratio:
mG = -nP ∕nG = pinion speed/gear speed
A gearset’s design life L is determined by the particular application. Some gears such as hand tools are considered expendable, and a short life is acceptable, while others such as marine gears must be designed for long life. Some applications have variable loads where the maximum loads occur for only a fraction of the total duty cycle. In these cases, the maximum load usually does the most fatigue damage, and the gearset can be designed for the number of hours at which the maximum load occurs.
Typical design lives:
|Application||No. Cycles||Design Life, L(hr)|
|Vehicle||107 - 108||3000|
|Aerospace||106 - 109||4000|
|Petrochemical||1010 - 1011||200000|
The number of load cycles per gear is calculated from the required life (L), the speed (n) and the number of contacts per revolution (q):
The overload factor Ko makes allowance for the externally applied loads which are in excess of the nominal tangential load, Wt. Overload factors can only be established after considerable field experience is gained in a particular application. For an overload factor of unity, this rating mehtod includes the capacity to sustain a limited number of up to 200% momentary overload cycles (typically less than four starts 8 hours, with a peak not exceeding one second duration). Higher or more frequent momentary overloads shall be considered separately. In determining the overload factor, consideration should be given to the fact that many prime movers and driven equipment, individually or in combination, develop momentarypeak torques appreciably greater than those determined by the nominal ratings of either the prime mover or the driven equipment. There are many possible sources of overload which should be considered. Some of these are: system vibrations, acceleration torques, overspeeds, varitions in system operation, split path load sharing among multiple prime movers, and changes in process load conditions.
Examples of operating characteristics of driving machines:
Examples of operating characteristics of driving machines:
Operating Characteristics of Driven Machine
|of Driving Machine||uniform||light shock||medium shock||heavy shock|
The factor allows for the variation in contact brought about by differing manufacturing processes, operating conditions and mounting error on assembly. The load distribution factor Km can either be defined directly or calculated by the empirical method of AGMA 2001/2101. This empirical method is recommended for normal, relatively stiff gear designs which meet the following requirements:
The input values used for the empirical method for the load distribution factor calculation can be found by pressing the plus button beside the field:
Lead Correction Factor)
The nominal setting ’Unmodified lead’ should be used when the machining quality is not known. An option ’Lead properly modified by crowning or lead correction’ exists to define a well defined lead modification possible using high quality grinding machines.
Lead modification (helix correction) is the tailoring of the lengthwise shape of the gear teeth to compensate for the deflection of the gear teeth due to load, thermal or other effects. Certain gear grinding machines have the capability to grind the helical lead to almost any specified curve. Many high-speed gears are through-hardened, hobbed and shaved. Usually the gear member is shaved to improve the surface finish, profiles and spacing, but the helix lead is not changed significantly. The pinion and gear are then installed in the housing and a contact pattern is obtained by rolling the gears together under a light load with marking compound applied to the gear teeth. Based on the contact pattern obtained from this test, the pinion is shaved to match the lead of the gear. The process is repeated until the desired no-load contact pattern is obtained.
Pinion proportion modifier )
This setting allows consideration of the degree of alignment change as the pinion is offset under a defelction of the bearings. The Cpm value alters the pinion proportion factor, Cpf, based on the location of the pinion relative to its bearing center line.
Mesh alignment factor )
The mesh alignment factor Cma accounts for the misalignment of the axes of rotation of the pitch cylinders of the mating gear elements from all causes other than elastic deformation. The factor is dependend on the face width and the follwing options:
Mesh alignment correction factor
This selection can be used to account for improved corrective action after manufacturing for a better contact condition.
Some gearsets are adjusted to compensate for the no-load shaft alignment error by means of adjustable bearings and/or by re-working the bearings or their housings to improve the alignment of the gear mesh. Lapping is a finishing process used by some gear manufacturers to make small corrections in the gear tooth accuracy and gear mesh alignment. Lapping is done by either running the gear in mesh with a gear-shaped lapping tool or by running the two mating gears together while an abrasive lapping compound is added to the gear mesh to promote removal of the high points of the gear tooth working surface.
For double-helical gears, the mesh alignment factor is calculated based on one helix (one half of the net face width).
It usually is not possible to obtain a perfectly uniform distribution of load across the entire face width of an industrial gearset. Misalignment between the mating gear teeth causes the load and stress distribution to be non-uniform along the tooth length. The load distribution factor is used to account for the effects of the non-uniform loading. It is defined as the ratio of the maximum load intensity along the face width to the nominal load intensity, i.e.,
Km = Cm = Maximum Load Intensity/(Wt/F)
Variations in the load distribution can be influenced by:
Ratio of face width to pinion diameter
Bearing arrangement and spacing
Internal bearing clearance
Geometry and symmetry of gear blanks
Material hardness of gear teeth
Gear housing machining errors (shaft axes not parallel)
Tooth errors (lead, profile, spacing & runout)
Gear blank and shaft errors (runout, unbalance)
Eccentricity between bearing bores and outside diameter
Elastic Deflection of:
Gear tooth (bending)
Gear tooth (hertzian)
Pinion shaft (bending and torsional)
Bearings (oil film or rolling elements)
Thermal Distortion of:
Gear teeth, gear blank, shafts, and housing
Centrifugal forces may cause misalignment for high-speed gears
Misalignment with coupled machines
Gear tipping from external loads on shafts
External thrust from shaft couplings
The dynamic factor accounts for internally generated gear tooth loads which are induced by non-uniform meshing action (transmission error) of gear teeth. If the actual dynamic tooth loads are known from a comprehensive dynamic analysis, or are determined experimentally, the dynamic factor may be calculated from:
where Wt = Nominal transmitted tangential load and
Wd = Incremental dynamic tooth load due to the dynamic response of the gear pair to the transmission error excitation, not including the transmitted tangential loads.
If the factor is calculated according AGMA, the Transmission Accuracy Grade Anu is used. Anu is calculated following formula (21) in AGMA2001, page 15. Therefore Anu is not always identical but close to the gear quality.
CAUTION: This factor has been redefined as the reciprocal of that used in
previous AGMA standards. It is now greater than 1.0. In earlier AGMA standards
it was less than 1.0.
GEARCALC needs to know whether pinion or gear is driving when determining the optimum addenda modification for maximum scoring resistance. The driving member influences load-sharing between successive pairs of teeth and load distribution along the path of contact. This in turn influences the flash temperature and scoring resistance.
Usually a pair of gears rotate in one direction without torque reversals and the gear teeth are loaded on one side only. For this case, the gear teeth are subjected to one-way bending or uni-directional loading.
Some gears are loaded on both sides of the teeth and are subjected to reverse bending. Examples are:
For a single pinion in mesh with a single gear, each member has one contact per revolution. Some gears have more than one cycle of load contact per revolution. An epicyclic gearset (planetary or star gear) is shown below:
In this example, if the pinion is the driver or is driven, it has 2 contacts/rev. If the pinion is an idler, it has 1 contact per revolution and reversed bending. The mating gears each have 1 contact/rev.