12.0 CALCULATION OF GEAR PERFORMANCE CRITERIA
Essential to proper application of gears is the derivation of values of performance criteria Most important are: backlash, transmission error and total position error. In evaluating a gear mesh, its performance depends not only on specific gear parameters, but also on many installation and design features such as bearings, shafting, and housing.
12.1 Backlash In a Single Mesh
All sources of backlash must be identified and combined in order to obtain the total backlash for the mesh. Sources can be grouped according to the following categories:
| I. II. III. IV. V. |
Design backlash allowance 1. Gear size allowance — any reduction of tooth thickness (or testing radius) below nominal value 2. Center distance — any increase in center distance above nominal value Major tolerances 1. Gear size tolerance (tooth thickness or testing radius) 2. Center distance tolerance Gear center shift due to secondary sources 1. Fixed bearing eccentricities a. Outer-race eccentricity of ball bearing b. Inside-diameter and outside-diameter runout of sleeve bearing 2. Racial clearances due to tolerances and allowances a. Racial play of ball bearing b. Fit between shaft and bearing bore c. Fit between outside diameter of beating and housing bore Backlash sources which are functions of gear rotation 1. Total composite error 2. Clearance between gear bore and shaft 3. Runout at point of gear mounting 4. Eccentricity of rotating race of ball beating Miscellaneous sources 1. Dimensional changes due to thermal expansion or contraction 2. Deflections: teeth, gear body, shaft, and housing |
A more complete and detailed coverage of these backlash sources is given in Reference 5. From the above listing of backlash sources, those which contribute significantly can be evaluated and summed. Thus, the total backlash for a mesh is expressed as:
Bmesh = S B (48)
When using equation 48, it should be noted that all sources of radial backlash, such as center- distance tolerance and racial shift due to eccentricities, must be converted to backlash measured along the pitch circle in accordance with equation 22a prior to addition of sources such as tooth- thickness tolerances, etc. Also, note that sources of backlash can be divided into two categories: those of constant magnitude; and those the magnitude of which varies with gear rotation. The latter sources are associated with runout. Thus, backlash can be expressed as follows:
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