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Program 60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
1
Introduction The primary 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. 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 increased). The model will check for the following conditions and provide a warning if the geometry is outside the limits: 1. The profile shift coefficient is too small to keep the roll angle at the start of active
profile above 5 degrees. 2. The roll angle at the start of active profile 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 and the profile contact ratio is based on contact down to the start of active profile. Undercut must be checked by other means, such as UTS Gear Program 60-400.
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.
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Examples Example 1 Example 1 is a spur gear set with a 12 tooth pinion driving a 60 tooth gear. The normal diametral pitch is 10 and the nominal pressure angle is 20 degrees. If this set were made to “standard” proportions we would use the inputs shown in Figure 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
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Report 1-1
Model Title : Program 60-103 Unit System: US Description Value Unit Comment
DRIVER, number of teeth 12
DRIVEN, number of teeth 60
Gear ratio 5.0000
NORMAL PLANE
Normal pitch ( US/British System) 10.000000 1/in
Normal module ( SI System) 2.540000 mm `
Normal pressure angle 20.000000 deg
Normal base pitch 0.295 in
TRANSVERSE PLANE
Transverse pitch 10.0000 1/in
Transverse pressure angle 20.0000 deg
Transverse module 2.5400 mm `
Transverse base pitch 0.295 in
COMMON
Helix angle 0.000000 deg
Base helix angle 0.0000 deg
Axial pitch in
Operating center distance 3.600 in
Standard center distance 3.6000 in
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Change in Opr CD from "Std" CD 0.000 in
CD modification coefficient 0.00000
Sum of profile shift coefficients 0.00000
OD coefficient to maintain clearance 0.00000
Face width 0.750 in
TOOTH THICKNESS (Zero Backlash) Driver
Profile shift coefficient 0.00000
TOOTH THICKNESS (Zero Backlash) Driver At Ref PD
Normal tooth thickness 0.157 in
Transverse tooth thickness 0.157 in
TOOTH THICKNESS (Zero Backlash) Driver At OD
Normal tooth thickness 0.062 in
Transverse tooth thickness 0.062 in
TOOTH THICKNESS (Zero Backlash) Driven
Profile shift coefficient 0.00000
TOOTH THICKNESS (Zero Backlash) Driven At Ref PD
Normal tooth thickness 0.157 in
Transverse tooth thickness 0.157 in
TOOTH THICKNESS (Zero Backlash) Driven At OD
Normal tooth thickness 0.079 in
Transverse tooth thickness 0.079 in
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
DIAMETERS Driver
Outside diameter (Optional Input) 1.400 in
Roll angle at OD 42.159 deg
Reduced OD to maintain clearance 1.400 in
Reference pitch diameter 1.200 in
Pointed tooth diameter 1.481 in
Base dia 1.128 in
DIAMETERS Driven
Outside diameter (Optional Input) 6.200 in
Roll angle at OD 25.025 deg
Reduced OD to maintain clearance 6.200 in
Reference pitch diameter 6.000 in
Pointed tooth diameter 6.362 in
Base dia 5.638 in
OPERATING DATA
Working depth 0.200 in
Normal pressure angle 20.0000 deg
Transverse pressure angle 20.0000 deg
Helix angle 0.0000 deg
Roll angle at pitch point 20.8540 deg
Circular Pitch 0.314 in
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
OPERATING DATA Driver
Pitch diameter 1.200 in
Transverse tooth thickness 0.157 in
Start of active profile 1.128 in
Roll angle at SAP 0.0000 deg
Normal tooth thickness at SAP 0.164 in
Transverse tooth thickness at SAP 0.164 in
Mid-point, length of contact 1.202 in
Roll angle at mid-point 21.080 deg
OPERATING DATA Driven
Pitch diameter 6.000 in
Transverse tooth thickness 0.157 in
Start of active profile 5.870 in
Roll angle at SAP 16.5929 deg
Normal tooth thickness at SAP 0.196 in
Transverse tooth thickness at SAP 0.196 in
Mid-point, length of contact 5.999 in
Roll angle at mid-point 20.809 deg
Contact Length
Length of contact, transverse plane 0.415 in
Approach action 49.46 %
Recess action 50.54 %
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Contact Ratios
Profile 1.4053
Helical 0.0000
Total 1.4053
Lines of Contact Across Teeth
Max total length 1.500 in
Min total length 0.750 in
Ratio: (Max length / Min length) 2.0000
Specific Sliding Ratios
Driver start of active profile Too High
Driver outside diameter 0.606
Driven start of active profile 1.541
Driven outside diameter 1.000 In solving the model we have received these warnings: 1. The driver profile shift coefficient, 0, is less than recommended, +.466 2. The roll angle at the SAP is less than 5 degrees for the driver. 3. The specific sliding ratio at the driver SAP is greater than 3. With 12 teeth in the pinion and “standard” tooth thickness the pinion will be undercut. The profile contact ratio will not be 1.4053 but will be considerably less. Figure 1-2 is a plot of the teeth in mesh. 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 1.571 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 1.277 because of the undercut on the pinion. (Plots can generate with UTS Gear Programs 60-400 and 60-610.)
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Fig. 1-2
If we must stay at a “standard” center distance of 3.6 inches we might cut the 12 tooth driver on a “13 tooth” blank and the 60 tooth driven on a “59 tooth” blank. Since the center distance is still “standard” the root clearance will not change. (The “OD coefficient to maintain clearance” will still be zero.) To increase the pinion to “13 tooth” blank proportions the profile shift coefficient is +0.5. Figure 1-3 shows the input and Report 1-2 the solution data for this set of conditions.
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Fig. 1-3
Report 1-2
Model Title : Program 60-103 Unit System: US Description Value Unit Comment
DRIVER, number of teeth 12
DRIVEN, number of teeth 60
Gear ratio 5.0000
NORMAL PLANE
Normal pitch ( US/British System) 10.000000 1/in
Normal module ( SI System) 2.540000 mm `
Normal pressure angle 20.000000 deg
Normal base pitch 0.295 in
TRANSVERSE PLANE
Transverse pitch 10.0000 1/in
Transverse pressure angle 20.0000 deg
Transverse module 2.5400 mm `
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Transverse base pitch 0.295 in
COMMON
Helix angle 0.000000 deg
Base helix angle 0.0000 deg
Axial pitch in
Operating center distance 3.600 in
Standard center distance 3.6000 in
Change in Opr CD from "Std" CD 0.000 in
CD modification coefficient 0.00000
Sum of profile shift coefficients 0.00000
OD coefficient to maintain clearance 0.00000
Face width 0.750 in
TOOTH THICKNESS (Zero Backlash) Driver
Profile shift coefficient 0.50000
TOOTH THICKNESS (Zero Backlash) Driver At Ref PD
Normal tooth thickness 0.194 in
Transverse tooth thickness 0.194 in
TOOTH THICKNESS (Zero Backlash) Driver At OD
Normal tooth thickness 0.029 in
Transverse tooth thickness 0.029 in
TOOTH THICKNESS (Zero Backlash) Driven
Profile shift coefficient -0.50000
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
TOOTH THICKNESS (Zero Backlash) Driven At Ref PD
Normal tooth thickness 0.121 in
Transverse tooth thickness 0.121 in
TOOTH THICKNESS (Zero Backlash) Driven At OD
Normal tooth thickness 0.084 in
Transverse tooth thickness 0.084 in
DIAMETERS Driver
Outside diameter (Optional Input) 1.500 in
Roll angle at OD 50.260 deg
Reduced OD to maintain clearance 1.500 in
Reference pitch diameter 1.200 in
Pointed tooth diameter 1.532 in
Base dia 1.128 in
DIAMETERS Driven
Outside diameter (Optional Input) 6.100 in
Roll angle at OD 23.661 deg
Reduced OD to maintain clearance 6.100 in
Reference pitch diameter 6.000 in
Pointed tooth diameter 6.287 in
Base dia 5.638 in
OPERATING DATA
Working depth 0.200 in
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Normal pressure angle 20.0000 deg
Transverse pressure angle 20.0000 deg
Helix angle 0.0000 deg
Roll angle at pitch point 20.8540 deg
Circular Pitch 0.314 in
OPERATING DATA Driver
Pitch diameter 1.200 in
Transverse tooth thickness 0.194 in
Start of active profile 1.136 in
Roll angle at SAP 6.8187 deg
Normal tooth thickness at SAP 0.199 in
Transverse tooth thickness at SAP 0.199 in
Mid-point, length of contact 1.260 in
Roll angle at mid-point 28.539 deg
OPERATING DATA Driven
Pitch diameter 6.000 in
Transverse tooth thickness 0.121 in
Start of active profile 5.828 in
Roll angle at SAP 14.9727 deg
Normal tooth thickness at SAP 0.171 in
Transverse tooth thickness at SAP 0.171 in
Mid-point, length of contact 5.950 in
Roll angle at mid-point 19.317 deg
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Contact Length
Length of contact, transverse plane 0.428 in
Approach action 32.31 %
Recess action 67.69 %
Contact Ratios
Profile 1.4481
Helical 0.0000
Total 1.4481
Lines of Contact Across Teeth
Max total length 1.500 in
Min total length 0.750 in
Ratio: (Max length / Min length) 2.0000
Specific Sliding Ratios
Driver start of active profile 2.470
Driver outside diameter 0.702
Driven start of active profile 2.357
Driven outside diameter 0.712 The sum of the profile shift coefficients is zero so the profile shift coefficient of the driven must be -0.5. The outside of the pinion is now 1.5 inches, which is “standard” for 13 teeth, and the outside diameter of the gear is 6.1 inches, which is “standard” for 59 teeth. The 12 tooth pinion will no longer be undercut and the contact ratio is 1.4481. Figure 1-4, generated with UTS Gear Program 60-400, shows these teeth in mesh.
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Fig. 1-4
If it is not necessary to maintain a “standard” center distance we may wish to cut the pinion on a “13 tooth” blank and the 60 tooth gear on a “standard” blank and increase the center distance. Enter .5 for the driver profile shift coefficient (see Figure 1A). Report 1-3 the solution for these conditions.
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Report 1-3
Model Title : Program 60-103 Unit System: US Description Value Unit Comment
No Group
DRIVER, number of teeth 12
DRIVEN, number of teeth 60
Gear ratio 5.0000
NORMAL PLANE
Normal pitch ( US/British System) 10.000000 1/in
Normal module ( SI System) 2.540000 mm `
Normal pressure angle 20.000000 deg
Normal base pitch 0.295 in
TRANSVERSE PLANE
Transverse pitch 10.0000 1/in
Transverse pressure angle 20.0000 deg
Transverse module 2.5400 mm `
Transverse base pitch 0.295 in
COMMON
Helix angle 0.000000 deg
Base helix angle 0.0000 deg
Axial pitch in
Operating center distance 3.648 in
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Standard center distance 3.6000 in
Change in Opr CD from "Std" CD 0.048 in
CD modification coefficient 0.47716
Sum of profile shift coefficients 0.50000
OD coefficient to maintain clearance 0.02284
Face width 0.750 in
TOOTH THICKNESS (Zero Backlash) Driver
Profile shift coefficient 0.50000
TOOTH THICKNESS (Zero Backlash) Driver At Ref PD
Normal tooth thickness 0.194 in
Transverse tooth thickness 0.194 in
TOOTH THICKNESS (Zero Backlash) Driver At OD
Normal tooth thickness 0.029 in
Transverse tooth thickness 0.029 in
TOOTH THICKNESS (Zero Backlash) Driven
Profile shift coefficient 0.00000
TOOTH THICKNESS (Zero Backlash) Driven At Ref PD
Normal tooth thickness 0.157 in
Transverse tooth thickness 0.157 in
TOOTH THICKNESS (Zero Backlash) Driven At OD
Normal tooth thickness 0.079 in
Transverse tooth thickness 0.079 in
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
DIAMETERS Driver
Outside diameter (Optional Input) 1.500 in
Roll angle at OD 50.260 deg
Reduced OD to maintain clearance 1.495 in
Reference pitch diameter 1.200 in
Pointed tooth diameter 1.532 in
Base dia 1.128 in
DIAMETERS Driven
Outside diameter (Optional Input) 6.200 in
Roll angle at OD 26.208 deg
Reduced OD to maintain clearance 6.195 in
Reference pitch diameter 6.000 in
Pointed tooth diameter 6.362 in
Base dia 5.638 in
OPERATING DATA
Working depth 0.202 in
Normal pressure angle 21.9669 deg
Transverse pressure angle 21.9669 deg
Helix angle 0.0000 deg
Roll angle at pitch point 23.1105 deg
Circular Pitch 0.318 in
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
OPERATING DATA Driver
Pitch diameter 1.216 in
Transverse tooth thickness 0.190 in
Start of active profile 1.138 in
Roll angle at SAP 7.6222 deg
Normal tooth thickness at SAP 0.200 in
Transverse tooth thickness at SAP 0.200 in
Mid-point, length of contact 1.263 in
Roll angle at mid-point 28.941 deg
OPERATING DATA Driven
Pitch diameter 6.080 in
Transverse tooth thickness 0.128 in
Start of active profile 5.901 in
Roll angle at SAP 17.6805 deg
Normal tooth thickness at SAP 0.188 in
Transverse tooth thickness at SAP 0.188 in
Mid-point, length of contact 6.038 in
Roll angle at mid-point 21.944 deg
Contact Length
Length of contact, transverse plane 0.420 in
Approach action 36.32 %
Recess action 63.68 %
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Contact Ratios
Profile 1.4213
Helical 0.0000
Total 1.4213
Lines of Contact Across Teeth
Max total length 1.500 in
Min total length 0.750 in
Ratio: (Max length / Min length) 2.0000
Specific Sliding Ratios
Driver start of active profile 2.438
Driver outside diameter 0.648
Driven start of active profile 1.843
Driven outside diameter 0.709
Note that the “CD modification coefficient” is NOT equal to the “Sum of profile shift coefficients”.
Since the “OD coefficient to maintain clearance” is no longer zero it will be necessary to reduce the outside diameters below “standard” to keep the same root clearance. Enter the “Reduced OD to maintain clearance” for the “Outside diameter” for both gears, as shown in Figure 1-5. Report 1-4 is the solution with the reduced outside diameters.
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Fig. 1-5
Report 1-4
Model Title : Program 60-103 Unit System: US Description Value Unit Comment
DRIVER, number of teeth 12
DRIVEN, number of teeth 60
Gear ratio 5.0000
NORMAL PLANE
Normal pitch ( US/British System) 10.000000 1/in
Normal module ( SI System) 2.540000 mm `
Normal pressure angle 20.000000 deg
Normal base pitch 0.295 in
TRANSVERSE PLANE
Transverse pitch 10.0000 1/in
Transverse pressure angle 20.0000 deg
Transverse module 2.5400 mm `
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Transverse base pitch 0.295 in
COMMON
Helix angle 0.000000 deg
Base helix angle 0.0000 deg
Axial pitch in
Operating center distance 3.648 in
Standard center distance 3.6000 in
Change in Opr CD from "Std" CD 0.048 in
CD modification coefficient 0.47716
Sum of profile shift coefficients 0.50000
OD coefficient to maintain clearance 0.02284
Face width 0.750 in
TOOTH THICKNESS (Zero Backlash) Driver
Profile shift coefficient 0.50000
TOOTH THICKNESS (Zero Backlash) Driver At Ref PD
Normal tooth thickness 0.194 in
Transverse tooth thickness 0.194 in
TOOTH THICKNESS (Zero Backlash) Driver At OD
Normal tooth thickness 0.032 in
Transverse tooth thickness 0.032 in
TOOTH THICKNESS (Zero Backlash) Driven
Profile shift coefficient 0.00000
UTS Integrated Gear Software
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
TOOTH THICKNESS (Zero Backlash) Driven At Ref PD
Normal tooth thickness 0.157 in
Transverse tooth thickness 0.157 in
TOOTH THICKNESS (Zero Backlash) Driven At OD
Normal tooth thickness 0.081 in
Transverse tooth thickness 0.081 in
DIAMETERS Driver
Outside diameter (Optional Input) 1.495 in
Roll angle at OD 49.905 deg
Reduced OD to maintain clearance in
Reference pitch diameter 1.200 in
Pointed tooth diameter 1.532 in
Base dia 1.128 in
DIAMETERS Driven
Outside diameter (Optional Input) 6.195 in
Roll angle at OD 26.096 deg
Reduced OD to maintain clearance in
Reference pitch diameter 6.000 in
Pointed tooth diameter 6.362 in
Base dia 5.638 in
OPERATING DATA
Working depth 0.198 in
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Normal pressure angle 21.9669 deg
Transverse pressure angle 21.9669 deg
Helix angle 0.0000 deg
Roll angle at pitch point 23.1105 deg
Circular Pitch 0.318 in
OPERATING DATA Driver
Pitch diameter 1.216 in
Transverse tooth thickness 0.190 in
Start of active profile 1.139 in
Roll angle at SAP 8.1851 deg
Normal tooth thickness at SAP 0.200 in
Transverse tooth thickness at SAP 0.200 in
Mid-point, length of contact 1.264 in
Roll angle at mid-point 29.045 deg
OPERATING DATA Driven
Pitch diameter 6.080 in
Transverse tooth thickness 0.128 in
Start of active profile 5.903 in
Roll angle at SAP 17.7515 deg
Normal tooth thickness at SAP 0.187 in
Transverse tooth thickness at SAP 0.187 in
Mid-point, length of contact 6.037 in
Roll angle at mid-point 21.924 deg
UTS Integrated Gear Software
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Model Title : Program 60-103 Unit System: US Description Value Unit Comment
Contact Length
Length of contact, transverse plane 0.411 in
Approach action 35.78 %
Recess action 64.22 %
Contact Ratios
Profile 1.3907
Helical 0.0000
Total 1.3907
Lines of Contact Across Teeth
Max total length 1.500 in
Min total length 0.750 in
Ratio: (Max length / Min length) 2.0000
Specific Sliding Ratios
Driver start of active profile 2.188
Driver outside diameter 0.644
Driven start of active profile 1.811
Driven outside diameter 0.686 Figure 1-6, generated with UTS Gear Program 60-400, shows these gears in mesh.
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Figure 1-6
UTS Integrated Gear Software
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Example 2 Example 2 is a helical gear set with a 20 tooth gear driving a 55 tooth gear. The normal module is 2 mm, the nominal pressure angle is 20 degrees, the nominal helix angle is 25 degrees and the face is 15 mm. We are required to run on an 85 mm center distance. Figure 2-1 shows the part of the wizard data entry form with the entries of the given data, and Report 2-1 shows the solution. (We need to solve this part of the model to obtain the “Sum of profile shift coefficients”.) Fig. 2-1
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Sheet 2-1
Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment DRIVER, number of teeth 20 DRIVEN, number of teeth 55
Gear ratio 2.7500
NORMAL PLANE Normal pitch ( US/British System) 12.700000 1/in Normal module ( SI System) 2.000000 mm `
Normal pressure angle 20.000000 deg
Normal base pitch 5.904 mm
TRANSVERSE PLANE Transverse pitch 11.5101 1/in Transverse pressure angle 21.8802 deg Transverse module 2.2068 mm ` Transverse base pitch 6.433 mm
COMMON Helix angle 25.000000 deg
Base helix angle 23.3990 deg Axial pitch 14.867 mm Operating center distance 85.000 mm
Standard center distance 82.7533 mm Change in Opr CD from "Std" CD 2.247 mm CD modification coefficient 1.12333 Sum of profile shift coefficients 1.21091
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OD coefficient to maintain clearance 0.08758 Face width 15.000 mm The required operating center distance of 85 mm is 2.247 mm greater than “standard”. Therefore the “Sum of profile shift coefficients” is +1.21091. We will apply +0.7 of this sum to the pinion as we would like a little more “high addendum” on the driver. (The profile shift coefficients can be balanced for equal strength of the driver and driven. See UTS Program 500.) Figure 2-2 is the data input and Report 2-2 the solution with this condition. Fig. 2-2
Report 2-2
Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
DRIVER, number of teeth 20
DRIVEN, number of teeth 55
Gear ratio 2.7500
NORMAL PLANE
Normal pitch ( US/British System) 12.700000 1/in
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
Normal module ( SI System) 2.000000 mm `
Normal pressure angle 20.000000 deg
Normal base pitch 5.904 mm
TRANSVERSE PLANE
Transverse pitch 11.5101 1/in
Transverse pressure angle 21.8802 deg
Transverse module 2.2068 mm `
Transverse base pitch 6.433 mm
COMMON
Helix angle 25.000000 deg
Base helix angle 23.3990 deg
Axial pitch 14.867 mm
Operating center distance 85.000 mm
Standard center distance 82.7533 mm
Change in Opr CD from "Std" CD 2.247 mm
CD modification coefficient 1.12333
Sum of profile shift coefficients 1.21091
OD coefficient to maintain clearance 0.08758
Face width 15.000 mm
TOOTH THICKNESS (Zero Backlash) Driver
Profile shift coefficient 0.70000
TOOTH THICKNESS (Zero Backlash) Driver At Ref PD
Normal tooth thickness 4.161 mm
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Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
Transverse tooth thickness 4.591 mm
TOOTH THICKNESS (Zero Backlash) Driver At OD
Normal tooth thickness 0.943 mm
Transverse tooth thickness 1.071 mm
TOOTH THICKNESS (Zero Backlash) Driven
Profile shift coefficient 0.51091
TOOTH THICKNESS (Zero Backlash) Driven At Ref PD
Normal tooth thickness 3.885 mm
Transverse tooth thickness 4.287 mm
TOOTH THICKNESS (Zero Backlash) Driven At OD
Normal tooth thickness 1.444 mm
Transverse tooth thickness 1.608 mm
DIAMETERS Driver
Outside diameter (Optional Input) 50.935 mm
Roll angle at OD 42.364 deg
Reduced OD to maintain clearance 50.585 mm
Reference pitch diameter 44.135 mm
Pointed tooth diameter 52.349 mm
Base dia 40.956 mm
DIAMETERS Driven
Outside diameter (Optional Input) 127.415 mm
Roll angle at OD 30.308 deg
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
Reduced OD to maintain clearance 127.065 mm
Reference pitch diameter 121.372 mm
Pointed tooth diameter 130.341 mm
Base dia 112.629 mm
OPERATING DATA
Working depth 4.175 mm
Normal pressure angle 23.1701 deg
Transverse pressure angle 25.3863 deg
Helix angle 25.5929 deg
Roll angle at pitch point 27.1893 deg
Circular Pitch 7.121 mm
OPERATING DATA Driver
Pitch diameter 45.333 mm
Transverse tooth thickness 4.183 mm
Start of active profile 43.063 mm
Roll angle at SAP 18.6134 deg
Normal tooth thickness at SAP 4.428 mm
Transverse tooth thickness at SAP 4.865 mm
Mid-point, length of contact 46.393 mm
Roll angle at mid-point 30.489 deg
OPERATING DATA Driven
Pitch diameter 124.667 mm
Transverse tooth thickness 2.938 mm
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Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
Start of active profile 120.416 mm
Roll angle at SAP 21.6714 deg
Normal tooth thickness at SAP 4.197 mm
Transverse tooth thickness at SAP 4.625 mm
Mid-point, length of contact 123.674 mm
Roll angle at mid-point 25.990 deg
Contact Length
Length of contact, transverse plane 8.489 mm
Approach action 36.11 %
Recess action 63.89 %
Contact Ratios
Profile 1.3195
Helical 1.0089
Total 2.3284
Lines of Contact Across Teeth
Max total length 21.664 mm
Min total length 21.519 mm
Ratio: (Max length / Min length) 1.0067
Specific Sliding Ratios
Driver start of active profile 0.628
Driver outside diameter 0.488
Driven start of active profile 0.955
Driven outside diameter 0.386
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
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Since the center distance is not “standard” we need to reduce the outside diameters to maintain root clearance. Figure 2-3 shows the data input and Report 2-3 is the solution with the outside diameters reduced. Fig. 2-3
Report 2-3
Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
DRIVER, number of teeth 20
DRIVEN, number of teeth 55
Gear ratio 2.7500
NORMAL PLANE
Normal pitch ( US/British System) 12.700000 1/in
Normal module ( SI System) 2.000000 mm `
Normal pressure angle 20.000000 deg
Normal base pitch 5.904 mm
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Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
TRANSVERSE PLANE
Transverse pitch 11.5101 1/in
Transverse pressure angle 21.8802 deg
Transverse module 2.2068 mm `
Transverse base pitch 6.433 mm
COMMON
Helix angle 25.000000 deg
Base helix angle 23.3990 deg
Axial pitch 14.867 mm
Operating center distance 85.000 mm
Standard center distance 82.7533 mm
Change in Opr CD from "Std" CD 2.247 mm
CD modification coefficient 1.12333
Sum of profile shift coefficients 1.21091
OD coefficient to maintain clearance 0.08758
Face width 15.000 mm
TOOTH THICKNESS (Zero Backlash) Driver
Profile shift coefficient 0.70000
TOOTH THICKNESS (Zero Backlash) Driver At Ref PD
Normal tooth thickness 4.161 mm
Transverse tooth thickness 4.591 mm
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Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
TOOTH THICKNESS (Zero Backlash) Driver At OD
Normal tooth thickness 1.163 mm
Transverse tooth thickness 1.319 mm
TOOTH THICKNESS (Zero Backlash) Driven
Profile shift coefficient 0.51091
TOOTH THICKNESS (Zero Backlash) Driven At Ref PD
Normal tooth thickness 3.885 mm
Transverse tooth thickness 4.287 mm
TOOTH THICKNESS (Zero Backlash) Driven At OD
Normal tooth thickness 1.606 mm
Transverse tooth thickness 1.788 mm
DIAMETERS Driver
Outside diameter (Optional Input) 50.585 mm
Roll angle at OD 41.534 deg
Reduced OD to maintain clearance mm
Reference pitch diameter 44.135 mm
Pointed tooth diameter 52.349 mm
Base dia 40.956 mm
DIAMETERS Driven
Outside diameter (Optional Input) 127.065 mm
Roll angle at OD 29.925 deg
Reduced OD to maintain clearance mm
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Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
Reference pitch diameter 121.372 mm
Pointed tooth diameter 130.341 mm
Base dia 112.629 mm
OPERATING DATA
Working depth 3.825 mm
Normal pressure angle 23.1701 deg
Transverse pressure angle 25.3863 deg
Helix angle 25.5929 deg
Roll angle at pitch point 27.1893 deg
Circular Pitch 7.121 mm
OPERATING DATA Driver
Pitch diameter 45.333 mm
Transverse tooth thickness 4.183 mm
Start of active profile 43.301 mm
Roll angle at SAP 19.6664 deg
Normal tooth thickness at SAP 4.376 mm
Transverse tooth thickness at SAP 4.812 mm
Mid-point, length of contact 46.431 mm
Roll angle at mid-point 30.600 deg
OPERATING DATA Driven
Pitch diameter 124.667 mm
Transverse tooth thickness 2.938 mm
Start of active profile 120.627 mm
60-103—External Gear Set Profile Shift Coefficients With Zero Backlash
37
Model Title : Program 60-103 Unit System: Metric Description Value Unit Comment
Roll angle at SAP 21.9729 deg
Normal tooth thickness at SAP 4.130 mm
Transverse tooth thickness at SAP 4.552 mm
Mid-point, length of contact 123.641 mm
Roll angle at mid-point 25.949 deg
Contact Length
Length of contact, transverse plane 7.816 mm
Approach action 34.40 %
Recess action 65.60 %
Contact Ratios
Profile 1.2149
Helical 1.0089
Total 2.2238
Lines of Contact Across Teeth
Max total length 19.970 mm
Min total length 19.825 mm
Ratio: (Max length / Min length) 1.0073
Specific Sliding Ratios
Driver start of active profile 0.522
Driver outside diameter 0.471
Driven start of active profile 0.890
Driven outside diameter 0.343
UTS Integrated Gear Software
38
Figure 2-4, generated with UTS Gear Program 60-400, shows the shape of the teeth in mesh in the normal plane for these gears generated with the same rack used in Example 1. Fig. 2-4