program 60-103—external gear set profile shift ... · pdf fileprogram...

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.

UTS Integrated Gear Software

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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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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



TOOTH THICKNESS (Zero Backlash) Driven


TOOTH THICKNESS (Zero Backlash) Driven At Ref PD



TOOTH THICKNESS (Zero Backlash) Driven At OD




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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






Base dia 5.638 in

OPERATING DATA

Working depth 0.200 in




Roll angle at pitch point 20.8540 deg

Circular Pitch 0.314 in


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OPERATING DATA Driver

Pitch diameter 1.200 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









Contact Length

Length of contact, transverse plane 0.415 in

Approach action 49.46 %

Recess action 50.54 %


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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.


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Fig. 1-3

Report 1-2




Gear ratio 5.0000

NORMAL PLANE





TRANSVERSE PLANE





10



COMMON



Axial pitch in







Face width 0.750 in










Profile shift coefficient -0.50000


11








DIAMETERS Driver






Base dia 1.128 in

DIAMETERS Driven






Base dia 5.638 in

OPERATING DATA



12


























13


Contact Length




Contact Ratios

Profile 1.4481

Helical 0.0000

Total 1.4481






Driver start of active profile 2.470



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.


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Report 1-3


No Group



Gear ratio 5.0000

NORMAL PLANE





TRANSVERSE PLANE





COMMON



Axial pitch in



16







Face width 0.750 in


















17


DIAMETERS Driver






Base dia 1.128 in

DIAMETERS Driven






Base dia 5.638 in

OPERATING DATA








18




















Contact Length





19


Contact Ratios

Profile 1.4213

Helical 0.0000

Total 1.4213









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




Gear ratio 5.0000

NORMAL PLANE





TRANSVERSE PLANE





21



COMMON



Axial pitch in







Face width 0.750 in












22








DIAMETERS Driver



Reduced OD to maintain clearance in



Base dia 1.128 in

DIAMETERS Driven



Reduced OD to maintain clearance in



Base dia 5.638 in

OPERATING DATA



23


























24


Contact Length




Contact Ratios

Profile 1.3907

Helical 0.0000

Total 1.3907









Driven outside diameter 0.686 Figure 1-6, generated with UTS Gear Program 60-400, shows these gears in mesh.


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Figure 1-6


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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


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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 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



Gear ratio 2.7500

NORMAL PLANE



29





TRANSVERSE PLANE




Transverse base pitch 6.433 mm

COMMON



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




Face width 15.000 mm




Normal tooth thickness 4.161 mm


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Transverse tooth thickness 4.591 mm












DIAMETERS Driver

Outside diameter (Optional Input) 50.935 mm


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




31


Reduced OD to maintain clearance 127.065 mm



Base dia 112.629 mm

OPERATING DATA

Working depth 4.175 mm





Circular Pitch 7.121 mm


Pitch diameter 45.333 mm


Start of active profile 43.063 mm


Normal tooth thickness at SAP 4.428 mm

Transverse tooth thickness at SAP 4.865 mm

Mid-point, length of contact 46.393 mm






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Contact Length

Length of contact, transverse plane 8.489 mm



Contact Ratios

Profile 1.3195

Helical 1.0089

Total 2.3284


Max total length 21.664 mm

Min total length 21.519 mm








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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




Gear ratio 2.7500

NORMAL PLANE






34


TRANSVERSE PLANE




Transverse base pitch 6.433 mm

COMMON



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




Face width 15.000 mm







35













DIAMETERS Driver



Reduced OD to maintain clearance mm



Base dia 40.956 mm

DIAMETERS Driven



Reduced OD to maintain clearance mm


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Base dia 112.629 mm

OPERATING DATA

Working depth 3.825 mm





Circular Pitch 7.121 mm















37







Contact Length

Length of contact, transverse plane 7.816 mm



Contact Ratios

Profile 1.2149

Helical 1.0089

Total 2.2238


Max total length 19.970 mm

Min total length 19.825 mm








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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

program 60-103—external gear set profile shift ... · pdf fileprogram...

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