Program 60-108—Internal Gear Contact and Backlash 60-108—Internal Gear Contact And...

Program 60-108—Internal Gear Contact and Backlash

1

Introduction This is a model of the contact conditions between two internal spur or helical involute gears. The contact ratios, start of active profile, specific sliding and many other geometrical conditions are calculated and checked. In addition, the tooth thickness, center distance and backlash are calculated. The tooth thickness of gears is specified at the reference pitch diameter which is the diameter obtained by dividing the number of teeth by the transverse pitch (diametral pitch in the plane of rotation). The reference pitch diameters will be the same as the operating pitch diameters only if the gears are meshed at “standard” center distance. The “standard” center distance is one half the difference in the reference pitch diameters. The transverse backlash at the “standard” center distance will be the reference transverse circular pitch less the tooth thickness of both gears and would be a circular arc measurement along the reference pitch diameter. The operating pressure angle will be equal to the “nominal” pressure angle. When the gears are meshed on any other center distance the operating pitch diameters will not be the reference pitch diameters. The operating pressure angle will not be the “nominal” pressure angle. The transverse backlash will then be the operating circular pitch less the tooth thickness at the operating pitch diameters of both gears and would be a circular arc measurement along the operating pitch diameter. The change in reference pitch diameter tooth thickness calculated in the usual manner for high or low addendum gears operating on “non-standard” centers uses the “nominal” pressure angle of the gear as an approximation. Since the operating pressure angle changes with the center distance this introduces an error in the backlash calculated for these gear sets. If the center distance change from “standard” is extensive the error can be quite large. (The operating backlash will be smaller than anticipated whether the center distance is larger or smaller than “standard”. The amount will be equal to the “Basic transverse backlash”.) The model avoids this problem by using the “operating” dimensions of the gear set for these calculations after finding the operating pitch diameters.

UTS Integrated Gear Software

2

Caution Conditions:

The model checks many conditions to be sure that the gear set will function as intended. A number of geometry parameters that may cause problems or may be of interest are checked:

1. All Recess Action–All contact between teeth occurs past the operating pitch point of the set. This is a desirable condition if the sliding velocity is not too high at the end of action. The effective coefficient of friction is much lower in the recess action zone.

2. Approach Action Over 50%–There is more contact before the pitch point

than after the pitch point. This should be avoided as the teeth are approaching each other and the effective coefficient of friction may be higher in approach than in recess action for soft gear materials. More high addendum on the driver and/or low addendum on the driven will reduce approach action.

3. Total Contact Ratio Less than 1.2–A total contact ratio this low will

usually result in a gear set that is noisy and rough running. In spur gears the highest point of single tooth load will be near the tooth tip. Very little room is available for the application of tip relief.

4. Pinion: Possible Undercut in Root–There is a possibility of undercut in

the root area of the pinion. Without the cutting tool geometry, it is not possible to be sure that undercutting will occur but for “standard” cutting tools it is likely. This condition must be checked further (see UTS Models 60-410 and 60-450).

5. Specific Sliding Over 3–The ratio of sliding to rolling velocity between the

contacting flanks is over 3. This condition can cause wear, scoring and noisy operation - high specific sliding is more detrimental at higher pitch line velocities - specific sliding can usually be reduced by moving contact away from the base circle (center distance smaller than “standard”, high addendum, higher operating pressure angle).

6. Trochoidal Interference Between Gear ID and Pinion Tip–The path of

the tip of the pinion tooth interferes with the gear tooth tip at some point (usually outside of the line of action). A major cause of this condition is too little difference between the numbers of teeth in the pinion and gear.

60-108—Internal Gear Contact And Backlash

3

7. Gear ID Below Min–Involute Interference–The profile of the gear extends below the point of tangency of the line of action and the pinion base circle.

8. Contact Ratio Less than One–The gear set is not conjugate and is not

useable. The loaded tooth pair will drop the load before the next pair is in contact. The set may jam.

9. Negative Backlash Will Not Assemble–The total thickness of the gears

when assembled at the operating center distance is greater than the operating circular pitch. This will prevent assembly of the gears at the operating center distance.

10. Trans PA Negative Will Not Mesh–The center distance is too large for the

base circle diameters of the gears. The base circles are overlapping. It is not possible for gears to be conjugate under this condition.

11. Teeth Entered Not Integer–You have entered a non-integer for the

number of teeth in one or both of the gears. 12. Top Land Width–(normal tooth thickness at the tooth tip) is less than

0.275/Normal Diametral Pitch (or 0.275*Module). The tooth tip is quite pointed. If the gear is case hardened the tooth tip may be over hardened and brittle.

Because TK Solver allows partial solutions, you may investigate contact conditions directly in the TK Solver model as you add more and more data. For example, you might start like this to obtain a gear ratio: Enter: 17 for PINION, number of teeth 5.67 for Gear ratio Solve Output: 96.39 for GEAR, number of teeth The number of teeth must be an integer so: Enter: 96 for GEAR, number of teeth Blank: Gear ratio Solve Output: 5.647 for Gear ratio


4

In this manner you can build a solution for the model as far as you wish. However, it is best to proceed until the CAUTION MESSAGE is blank, because of the number of conditions that are checked for problems. If desired, of course, a full set of data can be input and a solution obtained through the Integrated Gear Software interface.


5

Examples Example 1 Example 1 is a helical gear set running on “standard” center distance. The outside diameter of the pinion and the inside diameter of the gear are “standard” for 10 normal diametral pitch. The tooth thickness has been adjusted to give about 0.01 inch backlash. Figure 1-1 is the data input form and Report 1-1 the inputs and outputs of a complete solution for this gear set. Fig. 1-1


6

Report 1-1

Model Title : Program 60-108 Unit System: US CAUTION MESSAGE

CAUTION MESSAGE GEAR ID

BELOW MIN

INVOLUTE

INTERFER

PINION, number of teeth 17

GEAR, number of teeth 104

Driver: 'pin, 'gear pin

Pinion shaved or ground? ('s or 'g) no

Gear ratio 6.1176

NORMAL PLANE

Normal pitch 10.000000 1/in `

Normal pressure angle 14.500000 deg

Normal module 2.540000 mm `

Normal base pitch 0.3042 in

TRANSVERSE PLANE

Transverse pitch 8.1915 1/in `

Transverse pressure angle 17.5216 deg

Transverse module 3.1008 mm `

Transverse base pitch 0.3657 in


7

Model Title : Program 60-108 Unit System: US COMMON

Helix angle 35.0000 deg

Base helix angle 33.7318 deg

Axial pitch 0.5477 in

Face width 1.1000 in

Operating center distance 5.3104 in

Standard center distance 5.3104 in

TOOTH THICKNESS & SPACE WIDTH PINION AT REF PD

Normal tooth thickness 0.1520 in

Transverse tooth thickness 0.1856 in

TOOTH THICKNESS & SPACE WIDTH PINION AT OD



TOOTH THICKNESS & SPACE WIDTH GEAR AT REF PD



Normal space width 0.1622 in

Transverse space width 0.1980 in

TOOTH THICKNESS & SPACE WIDTH GEAR AT ID



CLEARANCE (FOR UNDERCUT CHECK)

Root clearance, Pinion (approx) 0.0250 in


8

Model Title : Program 60-108 Unit System: US DIAMETERS PINION

Outside diameter 2.2753 in

Roll angle at OD 32.5035 deg

Reference pitch diameter 2.0753 in

Pointed tooth diameter 2.4499 in

Base diameter 1.9790 in

DIAMETERS GEAR

Inside diameter 12.4961 in

Roll angle at ID 14.6423 deg

Minimum ID (Involute Interference) 12.5222 in


Pointed tooth diameter Below BD in


OPERATING DATA

Working depth 0.2000 in

Basic transverse backlash 0.0000 in

Change in Opr CD from "Std" CD 0.0000 in

Normal backlash 0.0101 in

Transverse backlash 0.0124 in



Circular pitch 0.3835 in

Roll angle at pitch point 18.0902 deg


9

Model Title : Program 60-108 Unit System: US OPERATING DATA PINION

Pitch diameter 2.0753 in

Transverse Tooth Thickness 0.1856 in

Start of active profile 1.9790 in

Roll angle at SAP 0.0000 deg

Normal tooth thickness at SAP 0.1635 in

Transverse tooth thickness at SAP 0.1965 in

OPERATING DATA GEAR


Transverse Space Width 0.1979 in





Trochoidal clearance: Pin OD/Gear ID 0.0458 in

OPERATING DATA CONTACT LENGTH

Length of contact, transverse plane 0.5613 in

Approach action 55.66 %

Recess action 44.34 %

OPERATING DATA CONTACT RATIOS

Profile 1.5349

Helical 2.0083

Total 3.5432


10

Model Title : Program 60-108 Unit System: US OPERATING DATA LINES OF CONTACT ACROSS TEETH

Max total length 2.0327 in

Min total length 2.0272 in

Ratio: (Max length) / (Min length) 1.0027

SPECIFIC SLIDING RATIOS

Pinion start of active profile Too High

Pinion outside diameter 0.371

Gear start of active profile 0.590

Gear inside diameter 1.205

Coefficient of friction

Approx power loss %

Approx efficiency %

AGMA Load sharing ratio, mN 0.5426

AGMA I-factor for durability 0.316

This “standard” gear set would not be successful. There is involute interference because the gear profile extends below the point of tangency between the line of action and the base circle of the pinion. In addition, the specific sliding ratio is too high at the pinion “start of active profile” (SAP). Since the gear inside diameter is below the minimum to avoid involute interference (12.5222 inches) we will increase the gear ID to 12.525 inches to eliminate the interference. Report 1-2 shows the inputs and outputs after making this change and solving.


11

Report 1-2


CAUTION MESSAGE PINION:

SPECIFIC

SLIDING

> THREE





Gear ratio 6.1176

NORMAL PLANE





TRANSVERSE PLANE






12

Model Title : Program 60-108 Unit System: US COMMON
























13

Model Title : Program 60-108 Unit System: US DIAMETERS PINION






DIAMETERS GEAR







OPERATING DATA











14

Model Title : Program 60-108 Unit System: US OPERATING DATA PINION







OPERATING DATA GEAR













Profile 1.5198

Helical 2.0083

Total 3.5282


15






Pinion start of active profile 46.616





Approx power loss %

Approx efficiency %


AGMA I-factor for durability 0.341 We still have some problems with this gear set. The specific sliding ratio is very high, 46.6, at the pinion SAP. The roll angle on the pinion at the start of action is less than 1 degree. Operation this close to the base circle is the cause of the high specific sliding ratio. In addition, it is very difficult to produce and measure an involute profile this close to the base circle as the radius of curvature is very small. The set also has more approach action than recess action. To illustrate one method of improving the gear set we will take the existing solution and modify it to obtain a full recess action gear set. (It is not necessary to modify the gear set to this extent to correct the existing problems but a full recess action set is sometimes desirable and as an example we will make this modification. Keep in mind that the pinion is driving and this solution would not be advisable if the gear were driving.)


16

To make these changes we must use the Power User form. Since the outside diameter of the pinion and the inside diameter of the gear must be changed, the first step is to change the ID of the gear. The ID of the driven gear must be equal to the operating pitch diameter to insure that all tooth action must take place past the pitch point. On the “Common Data” tab of the Power User form, enter the operating pitch diameter of the gear as the ID of the gear. Blank the value for the OD of the pinion, as this is the value we are solving for. Next, on the “Operating Data” tab of the form, enter 0.2 inch for the working depth to maintain a full tooth depth design. (The working depth for “standard” full depth is equal to 2/NDP.) And on the “Clearance” tab of the form, blank the values of the tooth thickness for both gears. We will set the tooth thickness after we have established the outside diameter. Also on this tab, enter .06 for the coefficient of friction. Report 1-3 is the model after solving. Report 1-3


CAUTION MESSAGE





Gear ratio 6.1176


17

Model Title : Program 60-108 Unit System: US NORMAL PLANE





TRANSVERSE PLANE





COMMON








Normal tooth thickness in

Transverse tooth thickness in





18

Model Title : Program 60-108 Unit System: US TOOTH THICKNESS & SPACE WIDTH GEAR AT REF PD



Normal space width in

Transverse space width in






DIAMETERS PINION




Pointed tooth diameter in


DIAMETERS GEAR





Pointed tooth diameter in



19

Model Title : Program 60-108 Unit System: US OPERATING DATA




Normal backlash in

Transverse backlash in





OPERATING DATA PINION


Transverse Tooth Thickness in



Normal tooth thickness at SAP in

Transverse tooth thickness at SAP in

OPERATING DATA GEAR


Transverse Space Width in



Normal tooth thickness at SAP in

Transverse tooth thickness at SAP in


20

Model Title : Program 60-108 Unit System: US Trochoidal clearance: Pin OD/Gear ID 0.0239 in






Profile 1.1785

Helical 2.0083

Total 3.1869

OPERATING DATA LINES OF CONTACT ACROSS TEETH









Coefficient of friction 0.0600

Approx power loss 0.72 %

Approx efficiency 99.28 %


AGMA I-factor for durability 0.507


21

This set looks pretty good. The maximum specific sliding ratio is only about 0.94 at the gear SAP (gear root). The roll angle of the pinion SAP is well away from the base circle at 18 degrees. The I-factor (contact stress factor) has increased from 0.341 to 0.507 which represents a large decrease in contact stress. Note that with a coefficient of friction of .06, the efficiency is about 99.28%. The efficiency is calculated in accordance with the methods in Chapter 12 of Dudley's Gear Handbook, 2nd Edition, by E.E. Shipley, published by McGraw-Hill. Now we need to address the tooth thickness and backlash of the new gear set. We will keep the backlash the same as in the original set. Again in the Power User form, enter 0.0101 inch for the normal backlash. We know that the top land (normal tooth thickness at the outside diameter) of the pinion will probably be less than the gear. We will set the pinion top land to 0.275/NDP. Enter 0.0275 inch for the tooth thickness at the OD of the pinion. The solved model is shown in Report 1-4. Report 1-4

Model Title : Program 60-108 Unit System: US

CAUTION MESSAGE

CAUTION MESSAGE None





22

Model Title : Program 60-108 Unit System: US Pinion shaved or ground? ('s or 'g) no

Gear ratio 6.1176

NORMAL PLANE





TRANSVERSE PLANE





COMMON











23

Model Title : Program 60-108 Unit System: US TOOTH THICKNESS & SPACE WIDTH PINION AT OD













DIAMETERS PINION






DIAMETERS GEAR




24

Model Title : Program 60-108 Unit System: US Minimum ID (Involute Interference) 12.5222 in




OPERATING DATA

















OPERATING DATA GEAR




25

Model Title : Program 60-108 Unit System: US Start of active profile 12.9817 in










Profile 1.1785

Helical 2.0083

Total 3.1869












26

Model Title : Program 60-108 Unit System: US Approx power loss 0.72 %



AGMA I-factor for durability 0.507 The Caution Message does not indicate All Recess Action, but Recess action approaches 100%. Note that the specific sliding ratio is zero at the first point of contact because the inside diameter of the driven gear is at the pitch point where the sliding is zero. Figure 1-3 is a plot of these gears in mesh at the pitch point which is, of course, the first point of contact for full recess action gears. (The plot was made with UTS Model 60-450.)


27

Fig. 1-3


28

Example 2 For this example we will find the tight mesh center distance of an internal work gear with a master gear and the proper OD for the master gear to contact at the required true involute form (TIF) on the work gear. Because we are solving for values required by the Integrated Gear Software input form, we will work directly in the TK Solver Variable Sheet. (You may also use the Power User form.) Sheet 2-1 is the model with the known data entered. The work gear has 117 teeth and the master gear has 48 teeth (standard 2-inch PD at 24 Transverse Diametral Pitch). The master gear has a tooth thickness at the reference PD of 2 inches–that is, one-half of the circular pitch. The work gear has a tooth thickness of 0.060 inch and a required TIF of 4.9700 inches. The backlash has been set to zero. Sheet 2-1

60-108 INTERNAL GEAR SET (Ver 6.0)USE 'TOOLS', 'RUN' TO START WIZARD

m1 CAUTION MESSAGEm2m3m4

48 np PINION, number of teeth117 ng GEAR, number of teeth'pin drive Driver: 'pin, 'gear (Def='pin)'no fin Pinion shaved or ground? ('s or 'g)

mg Gear ratio

NORMAL PLANE:24 pn 1/in Normal pitch20 npa deg Normal pressure angle

n_mod mm ` Normal modulepnb in Normal base pitch

TRANSVERSE PLANE:pt 1/in Transverse pitchtpa deg Transverse pressure anglet_mod mm ` Transverse moduleptb in Transverse base pitch

COMMON:0.0000 ha deg Helix angle

bha deg Base helix angleap in Axial pitch

.5000 face in Face widthcd in Operating center distancestd_cd in “Standard” center distance

TOOTH THICKNESS & SPACE WIDTH:Pinion:At Ref PD:


29

.0654 nttp in Normal tooth thicknesstttp in Transverse tooth thickness

At OD:nttodp in Normal tooth thicknesstttodp in Transverse tooth thickness

Gear:At Ref PD:

.0600 nttg in Normal tooth thicknesstttg in Transverse tooth thicknessnswg in Normal space widthtswg in Transverse space width

At ID:nttidg in Normal tooth thicknesstttidg in Transverse tooth thickness

CLEARANCE: (For undercut check)cl_p in Root clearance, Pinion (approx)

DIAMETERS:Pinion:

odp in Outside diameterE_od_p1 deg Roll angle at ODr_pdp in Reference pitch diameterpt_p in Pointed tooth diameterdbp in Base diameter

Gear:4.7900 idg in Inside diameter

E_id_g deg Roll angle at IDmin_id in Minimum ID (Involute Interference)r_pdg in Reference pitch diameterpt_g in Pointed tooth diameterdbg in Base diameter

OPERATING DATA:work in Working depthbtbl in Basic transverse backlashdelta in Change in Opr CD from “Std” CD

0.0000 nbl in Normal backlashtbl in Transverse backlashtpa` deg Transverse pressure angleha` deg Helix anglecp` in Circular pitchE_opr_p deg Roll angle at pitch point

Pinion:pdp in Pitch diameterttt_p in Transverse Tooth Thicknesssap_p in Start of active profileE_ld_p deg Roll angle at SAPnttldp in Normal tooth thickness at SAPtttldp in Transverse tooth thickness at SAP

Gear:pdg in Pitch diametertsw_g in Transverse Space Width

4.9700 sap_g in Start of active profileE_ld_g deg Roll angle at SAPnttldg in Normal tooth thickness at SAPtttldg in Transverse tooth thickness at SAP

When the model is solved we have Report 2-1. (Note that TK Solver used an iterative method to arrive at the solution for the center distance, as the equation cannot be


30

solved directly in this “direction”. We did not need to make a guess for the CD as the guess value is built into the model.) Report 2-1


CAUTION MESSAGE

CAUTION MESSAGE





Gear ratio 2.4375

NORMAL PLANE



Model Title : Program 60-108 Unit System: US Normal module 1.058333 mm `


TRANSVERSE PLANE



31




COMMON



Axial pitch in













Model Title : Program 60-108 Unit System: US Normal space width 0.0709 in





32




DIAMETERS PINION

Outside diameter in

Roll angle at OD deg




DIAMETERS GEAR







OPERATING DATA

Working depth in

Basic transverse backlash -0.0001 in

Model Title : Program 60-108 Unit System: US Change in Opr CD from "Std" CD 0.0074 in






33










OPERATING DATA GEAR







Trochoidal clearance: Pin OD/Gear ID in


Length of contact, transverse plane in

Model Title : Program 60-108 Unit System: US Approach action %

Recess action %


Profile

Helical 0.0000

Total


34


Max total length in

Min total length in

Ratio: (Max length) / (Min length)


Pinion start of active profile

Pinion outside diameter




Approx power loss %

Approx efficiency %

AGMA Load sharing ratio, mN

AGMA I-factor for durability


35

We now have the tight mesh center distance of 1.4449 inches. The last step is to find the outside diameter of the master gear that will contact the work gear at the TIF diameter of 4.9700 inches. This time we will have to make a guess for the master gear OD as the guess is not built into the model for this value. (If you do not know if a guess is required try solving directly. If you get no answer for your variable, and sufficient data has been entered to define the value of the variable, then make a guess.) We will use the pitch diameter (2 inches) of the master gear as a guess. Change the center distance to an input value as it is now known. Do this by double-clicking the Status box by this variable and selecting “Input”. TK Solver needs the exact value as calculated, so do not retype the value shown here, because it has been rounded off. Sheet 2-2 is the Variable Sheet before solving. Sheet 2-2

60-108 INTERNAL GEAR SET (Ver 6.0)USE 'TOOLS', 'RUN' TO START WIZARD

m1 CAUTION MESSAGEm2m3m4

48 np PINION, number of teeth117 ng GEAR, number of teeth'pin drive Driver: 'pin, 'gear (Def='pin)'no fin Pinion shaved or ground? ('s or 'g)

mg 2.4375 Gear ratio

NORMAL PLANE:24 pn 1/in Normal pitch20 npa deg Normal pressure angle

n_mod 1.0583333 mm ` Normal modulepnb .1230 in Normal base pitch

TRANSVERSE PLANE:pt 24 1/in Transverse pitchtpa 20 deg Transverse pressure anglet_mod 1.0583333 mm ` Transverse moduleptb .1230 in Transverse base pitch

COMMON:0.0000 ha deg Helix angle

bha 0.0000 deg Base helix angleap in Axial pitch

.5000 face in Face width->1.4449 cd in Operating center distance

std_cd 1.4375 in “Standard” center distance

TOOTH THICKNESS & SPACE WIDTH:Pinion:At Ref PD:

.0654 nttp in Normal tooth thicknesstttp .0654 in Transverse tooth thickness


36

At OD:nttodp in Normal tooth thicknesstttodp in Transverse tooth thickness

Gear:At Ref PD:

.0600 nttg in Normal tooth thicknesstttg .0600 in Transverse tooth thicknessnswg .0709 in Normal space widthtswg .0709 in Transverse space width

At ID:nttidg .0307 in Normal tooth thicknesstttidg .0307 in Transverse tooth thickness

CLEARANCE: (For undercut check)cl_p .0103 in Root clearance, Pinion (approx)

DIAMETERS:Pinion:

>G 2.0000 odp in Outside diameterE_od_p1 deg Roll angle at ODr_pdp 2.0000 in Reference pitch diameterpt_p 2.1466 in Pointed tooth diameterdbp 1.8794 in Base diameter

Gear:4.7900 idg in Inside diameter

E_id_g 17.5036 deg Roll angle at IDmin_id 4.6945 in Minimum ID (Involute Interference)r_pdg 4.8750 in Reference pitch diameterpt_g 4.6715 in Pointed tooth diameterdbg 4.5810 in Base diameter

After solving we have Report 2-2.


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Report 2-2


CAUTION MESSAGE

CAUTION MESSAGE APPROACH

ACTION

OVER 50%

No Group





Gear ratio 2.4375

NORMAL PLANE





TRANSVERSE PLANE




38

Model Title : Program 60-108 Unit System: US Transverse module 1.0583 mm `


COMMON



Axial pitch in



















39

Model Title : Program 60-108 Unit System: US CLEARANCE (FOR UNDERCUT CHECK)


DIAMETERS PINION






DIAMETERS GEAR







OPERATING DATA










40

Model Title : Program 60-108 Unit System: US Roll angle at pitch point 21.7562 deg








OPERATING DATA GEAR













Profile 2.1464

Helical 0.0000

Total 2.1464


41











Approx power loss %

Approx efficiency %


AGMA I-factor for durability 1.0000 We now have a solution for the OD of the master (2.0845 inches) required to contact the work gear at the required TIF. Figure 2-1 is a plot of the gears in mesh at the pitch point. (The plot was made with UTS Model 60-450.)


42

Fig. 2-1


43

Example 3 In this example we will examine a gear set with only three teeth difference between the pinion and gear. The gears will first be checked when made to “standard” proportions. The tooth thickness is a little less then one half the normal circular pitch (for backlash) and the outside diameter of the pinion is equal to the standard reference pitch diameter plus 2/NDP. The inside diameter of the gear is a little larger than the minimum ID to avoid involute interference. Our gears have 25 teeth in the pinion and 28 teeth in the gear. The normal diametral pitch is 10 with a 20 degree pressure angle. The tooth thickness of both is 0.155 inch. Figure 3-1 shows the completed input form and Report 3-1 the inputs and outputs for the model after entering the known data and solving. Fig. 3-1


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Report 3-1


CAUTION MESSAGE

CAUTION MESSAGE TROCHOID

INTERFER

GEAR ID

PIN TIP





Gear ratio 1.1200

NORMAL PLANE





TRANSVERSE PLANE





45

Model Title : Program 60-108 Unit System: US Transverse base pitch 0.2952 in

COMMON



Axial pitch in



















46

Model Title : Program 60-108 Unit System: US CLEARANCE (FOR UNDERCUT CHECK)


DIAMETERS PINION






DIAMETERS GEAR







OPERATING DATA









47

Model Title : Program 60-108 Unit System: US Circular pitch 0.3142 in









OPERATING DATA GEAR







Trochoidal clearance: Pin OD/Gear ID -0.0534 in






Profile 2.1863

Helical 0.0000


48

Model Title : Program 60-108 Unit System: US Total 2.1863











Approx power loss %

Approx efficiency %


AGMA I-factor for durability 1.0000 We have a serious problem with this gear set. Trochoidal interference is taking place between the inside diameter of the gear and the pinion tooth tip. (The maximum interference is 0.0534 inch.)


49

Figure 3-2A is a plot of the gears in mesh at the first point of contact on the pinion. Contact in this zone looks OK. Fig. 3-2A

Figure 3-2B is the same plot but with 9 teeth shown. It is obvious that we have a serious interference problem outside of the zone of involute tooth action.


50

Fig. 3-2B

A possible solution to the interference problem is shown on Figure 3-3 and Report 3-2. The pressure angle has been increased to 30 degrees. The outside diameter of the pinion and the inside diameter of the gear have both been set to 2.8 inches and the center distance has been increased by 0.01 inch.


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Fig. 3-3

Report 3-2


CAUTION MESSAGE

CAUTION MESSAGE CONTACT

RATIO

LESS THAN

1.2000




52

Model Title : Program 60-108 Unit System: US Driver: 'pin, 'gear pin


Gear ratio 1.1200

NORMAL PLANE





TRANSVERSE PLANE





COMMON



Axial pitch in





53


















DIAMETERS PINION







54

Model Title : Program 60-108 Unit System: US DIAMETERS GEAR







OPERATING DATA


















55

Model Title : Program 60-108 Unit System: US OPERATING DATA GEAR













Profile 1.0335

Helical 0.0000

Total 1.0335









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Model Title : Program 60-108 Unit System: US Gear start of active profile 0.013



Approx power loss 0.44 %



AGMA I-factor for durability 1.423 The trochoidal clearance is now 0.0215 inch. The profile contact ratio is quite low at 1.0335, but a slight amount of deflection would bring adjacent teeth into contact because of the very slight clearance of the teeth next to the conjugate tooth on the driving side. The approach action is much larger than the recess action but the specific sliding ratios are very low and not much sliding is taking place. The capacity of this type of drive can be quite high. Figure 3-4A shows the gears in mesh at the first point of contact on the line of action. The close conformity of the teeth can be seen. In Figure 3-4B, 9 teeth are shown. The clearance between the pinion tooth tips and the gear ID is no longer a problem.


57

Fig. 3-4A


58

Fig. 3-4B

Program 60-108—Internal Gear Contact and Backlash 60-108—Internal Gear Contact And...

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