12.21 Load distribution factor

This 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:

  1. Net face width to pinion pitch diameter ratios less than or equal to 2.0. (For double helical gears the gap is not included in the face width).
  2. The gear elements are mounted between bearings, i.e., not overhung.
  3. Face widths up to 40 inches.
  4. Tooth contact extends across the full face width of the narrowest member when loaded.

The input values used for the empirical method for the load distribution factor calculation can be found by pressing the plus button PIC beside the field:


Figure 12.9: AGMA 2001/2101 - Face load distribution factor

12.21.1 Lead correction factor (Cmc)

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.

12.21.2 Pinion proportion modifier (Cpm)

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.

12.21.3 Mesh alignment factor (Cma)

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:

12.21.4 Mesh alignment correction factor (Ce)

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.

12.21.5 Double Helical

For double-helical gears, the mesh alignment factor is calculated based on one helix (one half of the net face width).

12.21.6 Transverse load distribution factor

Since no information about the transverse load distribution factor Cmt{K} is given in AGMA 2001 the load distribution factor is equal to the face load distribution factor. Km = Cmf{KHβ}

12.21.7 Notes

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:

Design Factors
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

Manufacturing Accuracy
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 Effects
Centrifugal forces may cause misalignment for high-speed gears

External Effects
Misalignment with coupled machines
Gear tipping from external loads on shafts
External thrust from shaft couplings