Program Internal Gear Set Profile Shift Coefficients With Zero Backlash Introduction

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Clare Strickland
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1 Program Internal Gear Set Profile Shift Coefficients With Zero Backlash Introduction The purpose of this model is to provide data for a gear set when the tooth thickness and/or the center distance is not standard. The model follows the European convention of gears in mesh without backlash to establish the sum of the profile shift coefficients. (The profile shift coefficient is usually designated as the X factor on European gear drawings.) To provide backlash in the gear set the tooth thickness of one or both gears must be reduced from the values given by the model (or the center distance must be reduced). The AGMA load sharing ratio and the AGMA I-factor are calculated for use in contact stress analysis using AGMA Standard Data for AGMA Load Sharing Ratio and I Factor Extracted from AGMA Standard 2001-B88, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth with the permission of the publisher, American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, VA The model will check for the following conditions and provide a warning if the geometry is outside the limits: 1. The roll angle at the pinion start of active profile is less than 5 degrees. 2. The roll angle at the gear inside diameter is less than 5 degrees. 3. The width of the tooth top land is less than 0.25/NDP (.25*Normal Module) and the normal diametral pitch is less than 20 (Normal Module is greater than 1.27). 4. The width of the tooth top land is less than 0.275/NDP (.275*Normal Module) and the normal diametral pitch is 20 or greater (Normal Module is 1.27 or less). 5. The teeth are pointed. 6. The normal operating pressure angle is less than 10 degrees or greater than 30 degrees. 7. The total contact ratio is less than one. NOTE: The model does not check for undercut on the pinion and the profile contact ratio is based on contact down to the pinion start of active profile. Undercut must be checked by other means. (See UTS Model ) 8. The specific sliding ratio is greater than three. NOTE: If the specific sliding ratio is greater than three the geometry of the gear set should be checked. However, for gear sets running at higher speeds a specific sliding ratio of three may be too high and noisy operation and scoring may result. 1

UTS Integrated Gear Software 9. The gear inside diameter is less than the base diameter. 10. Trochoidal interference between the gear inside diameter and the pinion tooth tips.

2 UTS Integrated Gear Software 9. The gear inside diameter is less than the base diameter. 10. Trochoidal interference between the gear inside diameter and the pinion tooth tips. Examples Example 1 Example 1 is a spur gear set with a 14 tooth pinion driving a 50 tooth gear. The normal diametral pitch is 10 and the nominal pressure angle is 20 degrees. If this set is made to standard proportions we would use the input data shown in Figures 1-1A and 1-1B, and would have the output data in Report 1-1. Note that the profile shift coefficient for both gears is zero. Fig. 1-1A Fig. 1-1B 2

3 Internal Gear Set Profile Shift Coefficients With Zero Backlash Report 1-1 Unit System: US PINION, number of teeth 14 GEAR, number of teeth 50 Gear ratio NORMAL PLANE Normal pitch ( US/British System) Normal module ( SI System) Normal pressure angle Normal base pitch TRANSVERSE PLANE Transverse pitch Transverse pressure angle Transverse module Transverse base pitch COMMON Helix angle Base helix angle Axial pitch Operating center distance Standard center distance /in mm ` deg in /in deg mm ` in deg deg in in in 3

4 UTS Integrated Gear Software Unit System: US Change in Opr CD from "Std" CD in CD modification coefficient Difference of shift coefficients OD, ID coef to maintain clearance Face width TOOTH THICKNESS (Zero Backlash) Pinion in Profile shift coefficient TOOTH THICKNESS (Zero Backlash) Pinion At Ref PD TOOTH THICKNESS (Zero Backlash) Pinion At OD TOOTH THICKNESS (Zero Backlash) Gear in in Profile shift coefficient TOOTH THICKNESS (Zero Backlash) Gear At Ref PD Normal space width Transverse space width TOOTH THICKNESS (Zero Backlash) Gear At ID in 4

5 Internal Gear Set Profile Shift Coefficients With Zero Backlash Unit System: US DIAMETERS Pinion in Outside diameter (Optional Input) Roll angle at OD Increased OD to maintain clearance Reference pitch diameter Pointed tooth diameter Base diameter DIAMETERS Gear Inside diameter (Optional Input) Roll angle at ID Decreased ID to maintain clearance Minimum ID (Involute Interference) Reference pitch diameter Pointed tooth diameter Base diameter OPERATING DATA Working depth Normal pressure angle Transverse pressure angle Helix angle Circular pitch Roll angle at pitch point in deg in in in in in deg in in in Below BD in in in deg deg deg in deg 5

6 UTS Integrated Gear Software Unit System: US OPERATING DATA Pinion Pitch diameter Transverse Tooth Thickness Start of active profile Roll angle at SAP at SAP at SAP OPERATING DATA Gear Pitch diameter Transverse Space Width End of active profile Roll angle at EAP at EAP at EAP Trochoidal clearance: Pin OD/Gear ID Contact Length in in deg in in in in deg in in in Length of contact, transverse plane in Approach action (Pinion Driving) % Recess action (Pinion Driving) % Contact Ratios Profile Helical Total

7 Internal Gear Set Profile Shift Coefficients With Zero Backlash Unit System: US Lines of Contact Across Teeth Max total length in Min total length in Ratio: (Max length) / (Min length) Specific Sliding Ratios Pinion start of active profile Pinion outside diameter Gear start of active profile Gear inside diameter AGMA Load sharing ratio, mn AGMA I-factor for durability Iteration trigger variable for solving CD 1.0 from tooth thickness In solving the model, you receive these warnings: 1. The gear inside diameter has been set (increased) to avoid involute interference 2. The roll angle at pinion the SAP is less than 5 degrees. 3. The specific sliding ratio at the pinion SAP is greater than 3. With 14 teeth in the pinion and standard tooth thickness the pinion will be undercut. The profile contact ratio will not be but will be considerably less. Figure 1-2 is the plot of the teeth in mesh, using UTS Gear Program The undercut in the driver is obvious. The plot was made using a generating rack with an addendum equal to 1.25, a tooth thickness equal to and a tip radius of 0.38 for 1 normal diametral pitch or 1 normal module. Using this rack gives us an actual profile contact ratio of because of the undercut on the pinion. The AGMA I- factor is

8 UTS Integrated Gear Software Fig. 1-2 If it is not necessary to maintain a standard center distance we may wish to cut the pinion on a 15 tooth blank to eliminate the undercut and decrease the center distance. Figures 1-3A and 1-3B show the additional data inputs; Report 1-2 is the solution for these conditions. Fig. 1-3A 8

9 Internal Gear Set Profile Shift Coefficients With Zero Backlash Fig. 1-3B Report 1-2 Unit System: US PINION, number of teeth 14 GEAR, number of teeth 50 Gear ratio NORMAL PLANE Normal pitch ( US/British System) Normal module ( SI System) Normal pressure angle Normal base pitch TRANSVERSE PLANE Transverse pitch Transverse pressure angle Transverse module Transverse base pitch /in mm ` deg in /in deg mm ` in 9

10 UTS Integrated Gear Software Unit System: US COMMON Helix angle Base helix angle Axial pitch Operating center distance Standard center distance Change in Opr CD from "Std" CD deg deg in in in in CD modification coefficient Difference of shift coefficients OD, ID coef to maintain clearance Face width TOOTH THICKNESS (Zero Backlash) Pinion in Profile shift coefficient TOOTH THICKNESS (Zero Backlash) Pinion At Ref PD TOOTH THICKNESS (Zero Backlash) Pinion At OD TOOTH THICKNESS (Zero Backlash) Gear in in in in Profile shift coefficient

11 Internal Gear Set Profile Shift Coefficients With Zero Backlash Unit System: US TOOTH THICKNESS (Zero Backlash) Gear At Ref PD Normal space width Transverse space width TOOTH THICKNESS (Zero Backlash) Gear At ID DIAMETERS Pinion Outside diameter (Optional Input) Roll angle at OD Increased OD to maintain clearance Reference pitch diameter Pointed tooth diameter Base diameter DIAMETERS Gear Inside diameter (Optional Input) Roll angle at ID Decreased ID to maintain clearance Minimum ID (Involute Interference) Reference pitch diameter Pointed tooth diameter Base diameter in in in deg in in in in in deg in in in Below BD in in 11

12 UTS Integrated Gear Software Unit System: US OPERATING DATA Working depth Normal pressure angle Transverse pressure angle Helix angle Circular pitch Roll angle at pitch point OPERATING DATA Pinion Pitch diameter Transverse Tooth Thickness Start of active profile Roll angle at SAP at SAP at SAP OPERATING DATA Gear Pitch diameter Transverse Space Width End of active profile Roll angle at EAP at EAP at EAP Trochoidal clearance: Pin OD/Gear ID in deg deg deg in deg in in in deg in in in in in deg in in in 12

13 Internal Gear Set Profile Shift Coefficients With Zero Backlash Unit System: US Contact Length Length of contact, transverse plane in Approach action (Pinion Driving) % Recess action (Pinion Driving) % Contact Ratios Profile Helical Total Lines of Contact Across Teeth Max total length in Min total length in Ratio: (Max length) / (Min length) Specific Sliding Ratios Pinion start of active profile Pinion outside diameter Gear start of active profile Gear inside diameter AGMA Load sharing ratio, mn AGMA I-factor for durability Note that the CD modification coefficient is NOT equal to the Difference of shift coefficients. The operating center distance is mm. 13

14 UTS Integrated Gear Software Since the OD coefficient to maintain clearance is no longer zero it would be necessary to increase the pinion outside diameter (and, under certain conditions, to decrease the gear inside diameter) to keep the same root clearance. This is seldom done with internal gear sets since the clearance is a little larger than standard and we will stay with the standard outside diameter. Note the increase in AGMA I-factor and the reduction in the specific sliding ratio at the pinion SAP. Figure 1-4 shows these gears in mesh. The plot was generated in UTS Gear Program Fig

15 Internal Gear Set Profile Shift Coefficients With Zero Backlash Example 2 Example 2 is a helical gear set with a 20 tooth pinion driving a 85 tooth internal gear. The normal module is 4 mm, the nominal pressure angle is 20 degrees, the nominal helix angle is 25 degrees and the face is 30 mm. We are required to run on a 140 mm center distance, which is less than the standard center distance. Figures 2-1A and 2-1B are the data inputs and Report 2-1 is the solution for the given data. (We need to solve this part of the model to obtain the Difference of profile shift coefficients.) Fig. 2-1A Fig. 2-1A 15

16 UTS Integrated Gear Software Report 2-1 Unit System: Metric PINION, number of teeth 20 GEAR, number of teeth 85 Gear ratio NORMAL PLANE Normal pitch ( US/British System) Normal module ( SI System) Normal pressure angle Normal base pitch TRANSVERSE PLANE Transverse pitch Transverse pressure angle Transverse module Transverse base pitch COMMON Helix angle Base helix angle Axial pitch Operating center distance Standard center distance /in mm ` deg mm /in deg mm ` mm deg deg mm mm mm 16

17 Internal Gear Set Profile Shift Coefficients With Zero Backlash Unit System: Metric Change in Opr CD from "Std" CD mm CD modification coefficient Difference of shift coefficients OD, ID coef to maintain clearance Face width mm The required operating center distance of 140 mm is mm less than standard. Therefore the Difference of shift coefficients is We will apply all of the difference to the pinion as positive profile shift and leave the gear standard. Figure 2-2 shows the additional data input and Report 2-2 is the solution for the model with this condition. Fig

18 UTS Integrated Gear Software Report 2-2 Unit System: Metric PINION, number of teeth 20 GEAR, number of teeth 85 Gear ratio NORMAL PLANE Normal pitch ( US/British System) Normal module ( SI System) Normal pressure angle Normal base pitch TRANSVERSE PLANE Transverse pitch Transverse pressure angle Transverse module Transverse base pitch COMMON Helix angle Base helix angle Axial pitch Operating center distance Standard center distance /in mm ` deg mm /in deg mm ` mm deg deg mm mm mm 18

19 Internal Gear Set Profile Shift Coefficients With Zero Backlash Unit System: Metric Change in Opr CD from "Std" CD mm CD modification coefficient Difference of shift coefficients OD, ID coef to maintain clearance Face width TOOTH THICKNESS (Zero Backlash) Pinion mm Profile shift coefficient TOOTH THICKNESS (Zero Backlash) Pinion At Ref PD TOOTH THICKNESS (Zero Backlash) Pinion At OD TOOTH THICKNESS (Zero Backlash) Gear mm mm mm mm Profile shift coefficient TOOTH THICKNESS (Zero Backlash) Gear At Ref PD Normal space width Transverse space width TOOTH THICKNESS (Zero Backlash) Gear At ID mm mm mm mm mm 19

20 UTS Integrated Gear Software Unit System: Metric DIAMETERS Pinion mm Outside diameter (Optional Input) Roll angle at OD Increased OD to maintain clearance Reference pitch diameter Pointed tooth diameter Base diameter DIAMETERS Gear Inside diameter (Optional Input) Roll angle at ID Decreased ID to maintain clearance Minimum ID (Involute Interference) Reference pitch diameter Pointed tooth diameter Base diameter OPERATING DATA Working depth Normal pressure angle Transverse pressure angle Helix angle Circular pitch Roll angle at pitch point mm deg mm mm mm mm mm deg mm mm mm mm mm mm deg deg deg mm deg 20

21 Internal Gear Set Profile Shift Coefficients With Zero Backlash Unit System: Metric OPERATING DATA Pinion Pitch diameter Transverse Tooth Thickness Start of active profile Roll angle at SAP at SAP at SAP OPERATING DATA Gear Pitch diameter Transverse Space Width End of active profile Roll angle at EAP at EAP at EAP Trochoidal clearance: Pin OD/Gear ID Contact Length mm mm mm deg mm mm mm mm mm deg mm mm mm Length of contact, transverse plane mm Approach action (Pinion Driving) 0.00 % Recess action (Pinion Driving) % Contact Ratios Profile Helical Total

22 UTS Integrated Gear Software Unit System: Metric Lines of Contact Across Teeth Max total length mm Min total length mm Ratio: (Max length) / (Min length) Specific Sliding Ratios Pinion start of active profile Pinion outside diameter Gear start of active profile Gear inside diameter AGMA Load sharing ratio, mn AGMA I-factor for durability Note that this gear set is full recess action with the pinion driving and all contact takes place after the pitch point on the line of centers. (This contact geometry would probably not be satisfactory with the gear driving.) Figure 2-3 shows the shape of the teeth in mesh in the normal plane for these gears generated with the same rack used in Example 1. The plot was generated in UTS Gear Program

23 Internal Gear Set Profile Shift Coefficients With Zero Backlash Fig

Gear Tooth Geometry - This is determined primarily by pitch, depth and pressure angle

Gear Tooth Geometry - This is determined primarily by pitch, depth and pressure angle Addendum: The radial distance between the top land and the pitch circle. Addendum Circle: The circle defining the outer