program 60-050—external gear set introduction · this model will design a 20-degree normal...

Program 60-050—External Gear Set

Introduction The primary purpose of this model is to provide a preliminary set of data and an estimate of the load capacity for an external gear set. If the gear set is not for critical service, the load capacity check using K factor and Unit Load may be all that is required. The model contains a table of approximate allowable K factors and Unit Loads for steel gears that may be adjusted for service factor, required life cycles and ratio. In addition, the size over pins or balls may be calculated for manufacturing inspection. The shape of the root fillet is that produced by a straight-sided rack. The dimensions of the rack may be entered to provide the actual tooth shape produced by a hob or rack type shaper cutter. A plot of the teeth of the gears in mesh at first point of contact, pitch point or last point of contact of the driver is available. A plot of the tooth/ball contact section between the gear and measuring ball is provided if desired. Gear Set “Standard” 20 deg PA This model will design a 20-degree normal pressure angle “standard” gear set after the user enters the number of teeth, normal pitch, helix angle, etc. The normal diametral pitch may be from 0.1 to 120. (254 mm to 0.21 mm metric module). The virtual number of teeth in a gear is equal to the actual number of teeth divided by the cube of the cosine of the helix angle. The virtual numbers of teeth are restricted to: Coarse Pitch Fine Pitch Minimum virtual total teeth in the set 28 29 Minimum virtual teeth in either gear 10 12 The “standard” basic rack dimensions are: Coarse Pitch Fine Pitch Addendum 1.25/NDP 1.20/NDP + 0.002 inch 1.25*Mod 1.20*Mod + 0.05 mm Tooth thick 0.5*pi/NDP 0.5*pi/NDP 0.5*pi*Mod 0.5*pi*Mod

UTS Integrated Gear Software

2

Tip radius 0.3/NDP 0.38/NDP 20 –100 NDP 0.0031 inch NDP >100 0.3*Mod 0.38*Mod 1.27 –.254 Mod 0.08 mm Mod < .254 (Coarse pitch is < 20, Fine pitch is >= 20) Working depth is 2/NDP or 2*Mod. If the driver or driven gear would be undercut using “standard” proportions or if the roll angle at the start of active profile (with a “standard” rack) would be less than 5 degrees, the model will add enough “high addendum” to eliminate the condition. The amount of “high addendum” added to the gears will be included in the center distance. The “Standard” normal backlash is recommended for gear sets where the gears and mounting have the same coefficient of thermal expansion and the gears do not attain a temperature excessively higher than the mounting. NOTE: The restrictions listed for a “Standard” gear set do not apply to the model in general but only to the wizard selection used for designing a “Standard” set. The model checks many conditions to be sure that the gear set will function as intended (except for gear load, which must be judged against the load table for the material and quality class to be used). The gear geometry caution conditions are listed in the following table: Summary: All geometry caution messages

The model checks a number of geometry parameters that may cause problems or may be of interest:

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 and the strength balance between the driver and driven is not compromised.

2. Approach Action Over 55% –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 is higher in approach than in recess action. More high addendum on the driver and/or low addendum on the driven will reduce approach action.

60-050—External Gear Set

3

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. Contact Below Base Circle –the tooth tip of one or both of the gears is

attempting to contact the mating tooth below the base circle. Since there is no involute below the base circle, this condition will reduce the profile contact ratio and may cause interference in some gears.

5. Contact Ratio Less Than One –the gear set is not conjugate and is not

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

6. Teeth Entered Not Integer –you have entered a non-integer for the

number of teeth in one or both of the gears. 7. 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.

8. Low Axial Contact Ratio –the face width is less than one axial pitch. The

tooth action is between a spur and helical gear set. All the disadvantages, but few of the advantages, of helical gears will be present.

9. Specific Sliding Over Three –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 greater than “standard", high addendum, higher operating pressure angle).

10. Aspect Ratio Greater Than 2 –the aspect ratio is the face width divided by

the pinion pitch diameter. If the face is too large, it will not be possible to keep the entire face in contact due to misalignment of the teeth. This condition is more critical with high stiffness materials such as steel. This design MUST be checked using methods such as the AGMA analytical method for lead mismatch.


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11. Top Land Width–(normal tooth thickness at outside diameter) 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.

12. Contact Below TIF DIA –the tooth tip of one or both of the gears is

attempting to contact the mating tooth below the finished involute. Since there is no involute below the true involute form diameter (TIF), the profile contact ratio will be reduced and, if the cutting tool did not produce enough undercut in the root area, interference will result.

The load and speed caution conditions are given below: Summary: All load and speed caution messages

The model checks a number of load and speed parameters that may cause problems or may be of interest:

1. Aspect Ratio Too High –the aspect ratio is the min face width of the gears divided by the pinion pitch diameter. If the face is too large, it may not be possible to keep the entire face in contact because of misalignment of the teeth. This condition is more critical with high stiffness materials such as steel. The loading intensity due to the imposed tangential load may be too high at one end of the tooth because of the high aspect ratio. The K factor and Unit Load table for steel gears are not valid with this aspect ratio.

2. Pitch Line Velocity Too High –the pitch line velocity is higher than

recommended based on the AGMA Quality class of the gears. The maximum recommended velocity is 20000 feet/min (100 meters/sec) for helical gears and 10000 feet/min (50 meters/sec) for spur gears regardless of quality class. If higher speeds are necessary, a complete analysis of specific sliding and hot scoring is required.

3. Axial Meshing Velocity High –the axial velocity of the contact lines (and air

flow) between the gear teeth is greater than 100000 feet/min (500 meters/sec). You need a good lubrication system and a large case clearance. Check for thermal distortions of gears and case. (The axial meshing velocity can be reduced by increasing the helix angle.)

4. Axial Meshing Velocity Too High –the axial velocity of the contact lines (and

air flow) between the gear teeth is greater than 170000 feet/min (865 meters/sec). Thermal problems are assured. It is very difficult to run gears


5

with axial meshing velocity above Mach 2 with success. DO NOT USE. (The axial meshing velocity can be reduced by increasing the helix angle.)

In the model, both groups of messages are listed as comments in the TK Solver model. If the model finds that one or more of these conditions is present, they will display during solving, the number of caution messages will be noted on the Variable Sheet and the messages will be copied to the caution message table.


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Examples

Example 1

Example 1 is a spur gear set with a 12-tooth pinion driving a 36-tooth gear. The normal diametral pitch is 10 and the normal pressure angle is 20 degrees. The housing and the gears have about the same coefficient of thermal expansion and the gears are not expected to run more than about 100 degrees F hotter than the housing; so we can use the backlash recommended by the model. The face width is 1 inch.

Since the number of teeth in the pinion and the total number of teeth in the mesh are within the limits of the “Standard” gear set, we can use the “Gear set standard” entry point in the data input form to quickly obtain a design. (The pressure angle must, of course, be 20 degrees.)

The completed data input form is shown in Figure 1A. We will overwrite the calculated default face width and will not enter load data at this point. The solved model is shown in Report 1A.

Fig. 1A


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Report 1A

Model Title : Program 60-050 Unit System: US Description Value Unit Comment

GEOMETRY

Number_of_Geometry Caution Messages 0

Check_Geometry (Table of Messages) None

m2

m3

m4

DRIVER, number of teeth 12

DRIVEN, number of teeth 36

Gear_ratio 3 NORMAL PLANE

Normal_pitch 10.000000 1/in

Normal_pressure angle 20.000000 deg

Normal_module 2.540000 mm

Normal_base pitch 0.2952 in TRANSVERSE PLANE

Transverse_pitch 10 1/in

Transverse_pressure angle 20 deg

Transverse_module 3 mm

Transverse_base pitch 0.2952 in


8

Model Title : Program 60-050 Unit System: US Description Value Unit Comment COMMON

Helix angle 0.000000 deg

Base_helix angle 0.0000 deg

Axial pitch --- in

Operating_center distance 2.4467 in

Standard_center distance 2 in

Face width 1.000 in

DIAMETERS DRIVER

Outside diameter 1.4934 in

Roll_angle_at_OD 49.750 deg

Reference pitch diameter 1.2000 in

Pointed tooth diameter 1.5282 in

Inv/fillet intersection dia (TIF) 1.1304 in

Roll_angle_at_intersection (TIF) 4.019 deg

Root diameter 1.0424 in

Minimum fillet radius 0.0337 in

Base diameter 1.1276 in

Lead in DIAMETERS DRIVEN






9







Lead in

gsd mm TOOTH THICKNESS DRIVER

Normal_tooth thickness @ Ref PD 0.1907 in

Transverse_tooth thickness @ Ref PD 0.1907 in

Normal_TT at OD (Top Land) 0.0307 in

Normal_tooth_thickness_at_TIF dia 0.1964 in

TOOTH THICKNESS DRIVEN




Normal_tooth_thickness_at_TIF dia 0.1934 in DRIVER GENERATING RACK FORM

Flank angle 20.0000 deg

Tip_to_Reference Line 0.1250 in

Thickness_at_Reference Line 0.1571 in

Tip radius 0.0300 in


10

Model Title : Program 60-050 Unit System: US Description Value Unit Comment DRIVEN GENERATING RACK FORM





OPERATING DATA COMMON

Working depth 0.2000 in

Change in Opr CD from "Std" CD 0.0467 in

Basic transverse backlash 0.0024 in

Normal_backlash 0.0040 in

Transverse_circular backlash 0.0040 in

Normal_diametral pitch 10 1/in

Transverse_diametral pitch 10 1/in

Normal_pressure_angle 22.8149 deg

Transverse_pressure_angle 22.8149 deg

Transverse_circular_pitch 0.3203 in

Helix_angle 0.0000 deg

Roll_at_operating pitch point 24.102 deg OPERATING DATA DRIVER

Effective_outside diameter 1.4934 in

Roll_angle_at_effective OD 49.750 deg

Pitch_diameter 1.2233 in

Normal_tooth_thickness 0.1852 in


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Transverse_tooth_thickness 0.1852 in

Mid-point, length of contact 1.2648 in

Roll_angle_at_mid-point 29.106 deg

Start of active profile 1.1399 in

Roll_angle_at_SAP 8.461 deg

Root_clearance 0.0255 in

Max_specific sliding ratio 2.465 OPERATING DATA DRIVEN











Max_specific sliding ratio 2.199 OPERATING DATA CONTACT LENGTH

Length of contact, transverse plane 0.4063 in

Approach action 37.88 %

Recess action 62.12 %


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Model Title : Program 60-050 Unit System: US Description Value Unit Comment OPERATING DATA CONTACT RATIOS

Profile - NO Undercut 1.3763

Helical 0.0000

Total 1.3763 OPERATING DATA LINES OF CONTACT ACROSS TEETH

Max total length 2.0000 in

Min total length 1.0000 in

Ratio: (Max length / Min length) 2.0000 LOADING

Number_of_Loading Caution Messages

Check_Load (Table of Messages)

ms2

ms3

ms4

AGMA Quality Number

Power HP

Driver_speed rpm

Driver_torque lbf-in

Driven_speed rpm

Driven_torque lbf-in

Pitch_Line Velocity in/min

Axial_Meshing Velocity --- in/min

Tangential load lbf


13


K-factor | See Table for Allowable lbf/in^2

Unit load | Values for Steel Gears lbf/in^2

Aspect ratio (Face/Pinion PD) 0.817

Operating PD, Pinion 1.2233 in

Operating PD, Gear 3.6700 in PLOT TOOTH POSITION

PLOT TOOTH POSITION: first

MEASUREMENT OVER PINS

Plot Ball/Teeth? ('n=no Def='y=yes) y MEASUREMENT OVER PINS DRIVER

Pin dia for contact at tooth=space 0.20467 in

Actual_pin (or ball) diameter in

Radius over one pin (or ball) in

Measurement over two balls in

Measurement over two pins in

Actual pin (or ball) contact dia in MEASUREMENT OVER PINS DRIVEN






Actual pin (or ball) contact dia in


14

The plot of the teeth at the first point of contact on the driver should look like Figure 1B.

Fig. 1B

If we are happy with the gear set (we are), we can now enter the load and speed data into the data input form. At the same time, we will select measuring pins for both gears and enter them. For actual pin (or ball) diameter, toggle to the TK Solver model and open the Standard Pin table (std_pin) (for US Customary units) or Standard Pin Metric (std_pin_m) (for SI units) and choose the size that is approximately equal to or greater than the space pin diameter. To allow for proper measurement, the diameter over pins should be greater than the minimum outside diameter.

Enter the additional data by changing the “Select Entry Point” to “Normal entry”. (Don’t click the Enter key; if you do it will clear the other data.) Click the mouse pointer directly in the “AGMA quality number” in the “Loading Data” section of the form, enter 8, then click Enter. Follow the sequence from there to enter the remaining load data and pin diameters. We will not plot the mesh this time.


15

Figure 1C shows the completed data input form and Report 1C the solved model. Fig. 1C


16

Report 1C


GEOMETRY



m2

m3

m4











17




Transverse_base pitch 0.2952 in COMMON



Axial pitch --- in



Face width 1.000 in

DIAMETERS DRIVER













18










Lead in














19




DRIVEN GENERATING RACK FORM





















20

























21


Recess action 62.12 % OPERATING DATA CONTACT RATIOS


Helical 0.0000





Number_of_Loading Caution Messages 0

Check_Load (Table of Messages) None

ms2

ms3

ms4

AGMA Quality Number 8

Power 10.00 HP

Driver_speed 4500.0 rpm

Driver_torque 140.1 lbf-in

Driven_speed 1500.0 rpm

Driven_torque 420.2 lbf-in

Pitch_Line Velocity 17295 in/min



22


Tangential load 229.0 lbf

K-factor | See Table for Allowable 250 lbf/in^2

Unit load | Values for Steel Gears 2290 lbf/in^2






Plot Ball/Teeth? ('n=no Def='y=yes) y

MEASUREMENT OVER PINS DRIVER


Actual_pin (or ball) diameter 0.21600 in

Radius over one pin (or ball) 0.8100 in

Measurement over two balls 1.6200 in

Measurement over two pins 1.6200 in

Actual pin (or ball) contact dia 1.2871 in MEASUREMENT OVER PINS DRIVEN






Actual pin (or ball) contact dia 3.6030 in


23

Note that the K factor is 250 psi and the Unit Load is 2290 psi for our gears. We will check the factor table for class Q8 spur gears to compare our gears with the allowable values.

To do this, go to the “Plot and Factor Table” tab of the data input form, click the radio button for “Refresh K and UL Factor Table”, then click the button labeled “Refresh Table Data”. Scroll down to the row for the appropriate AGMA Q number—in this case, 8. The table is shown in Figure 1D.

For the life and service factor listed, the allowable K factor is 270 and the allowable Unit Load is 6400 for carburized gears. (Carburized gears would be required at this load since the through hardened gears do not have the required allowable K factor.) The unit load for our gears is far under the allowable while the K factor is not. This indicates that the pitch is too coarse and we should have more teeth on the same diameter pinion.

Now we will have a look at the measuring ball (or pin) position in the tooth space. On the “Plot and Factor Table” tab, click the radio button for “Show Ball/Tooth Plot for”, then the button for “Driver”. The resulting plot is shown in Figure 1E.

Fig. 1D


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Fig. 1E

You may check the measuring ball for the driven if you like.


25

Example 2 Example 2 is a high contact ratio spur gear set with a 40 tooth pinion driving a 120 tooth gear. The normal diametral pitch is 10 and the normal pressure angle is 17.5 degrees. The face width is 1.25 inches. Open the wizard and select “Normal Data Entry Sequence.” This time, select “Normal entry” for the “Select Entry Point”. Enter the gearset data as shown in the completed data input form, shown in Figure 2A. We will skip the load data and pin/ball diameters this time, but we will plot the gear mesh. It is shown in Figure 2B. Fig. 2A


26

Report 2A


GEOMETRY



m2

m3

m4













27




Axial pitch --- in



Face width 1.250 in

DIAMETERS DRIVER

















28






Lead in





Normal_tooth_thickness_at_TIF dia 0.1853 in TOOTH THICKNESS DRIVEN





DRIVER GENERATING RACK FORM









29


























30




















Helical 0.0000

Total 2.1303


31

Model Title : Program 60-050 Unit System: US Description Value Unit Comment OPERATING DATA LINES OF CONTACT ACROSS TEETH






ms2

ms3

ms4

AGMA Quality Number

Power HP

Driver_speed rpm


Driven_speed rpm




Tangential load lbf





Operating PD, Gear 12.0000 in


32

Model Title : Program 60-050 Unit System: US Description Value Unit Comment PLOT TOOTH POSITION

PLOT TOOTH POSITION: none MEASUREMENT OVER PINS















33

Fig. 2B


34

Example 3 Example 3 is a 35-degree helical gear set with a 10-tooth pinion driving a 55-tooth gear. The normal diametral pitch is 10 and the normal pressure angle is 20 degrees. The number of teeth in the pinion and the total number of teeth in the mesh are within the limits of the “Standard” gear set, so we can use the “Gear set standard” choice in the “Select Entry Point” of the data input form to quickly obtain a design. We will use the backlash recommended by the model. We will set the face width to obtain a full helical gear set with a helical contact ratio a little over one (the wizard will give us this value). It may be necessary to change the face width later due to load but the combination of helix angle and face width should produce a helical contact ratio near an integer value. This will keep the change in contact line length nearly constant through the mesh. For now we will not enter load data. We want a plot of the gear teeth in mesh. We will plot the teeth in mesh at the first point of contact on the pinion (the driver) since that is likely to be the most critical point. (We can later plot the other mesh positions if we like.) The completed data input form is shown in Figure 3A. The solved model is shown in Report 3A. As the model is solved, we find that we have a warning message about specific sliding ratio. Close the message form for now. The mesh plot is shown in Figure 3B.


35

Fig. 3A


36

Report 3A


GEOMETRY


Check_Geometry (Table of Messages) DRIVER:

m2 SPECIFIC

m3 SLIDING

m4 OVER 3













37




Axial pitch 0.54772 in



Face width 0.548 in

DIAMETERS DRIVER










Lead 5.47720 in DIAMETERS DRIVEN







38






Lead 30.12460 in


















39


























40





















Helical 1.0005

Total 2.1595


41







ms2

ms3

ms4

AGMA Quality Number

Power HP

Driver_speed rpm


Driven_speed rpm



Axial_Meshing Velocity in/min

Tangential load lbf







42


















43

Fig. 3B

Even though the high specific sliding may cause problems unless the gears were lightly loaded and running slowly, we will ignore the problem and continue with the example. Change “Select Entry Point” to “Normal entry: and move to the bottom of the data input form to enter pin (or ball) diameters for measuring the tooth thickness. We will use the closest standard pin diameters to the pin diameters that would contact where the tooth equals the space. Again, we use the Standard Pin (std_pin) table, as explained in Example 1. The completed data input form is shown in Figure 3C. After solving, the results are shown in Report 3B.


44

Fig. 3C


45

Report 3B


GEOMETRY


Check_Geometry (Table of Messages) DRIVER:

m2 SPECIFIC

m3 SLIDING

m4 OVER 3













46







Face width 0.548 in

DIAMETERS DRIVER

















47






Lead 30.12460 in


















48


























49





















Helical 1.0005

Total 2.1595


50







ms2

ms3

ms4

AGMA Quality Number

Power HP

Driver_speed rpm


Driven_speed rpm




Tangential load lbf







51




Plot Ball/Teeth? ('n=no Def='y=yes) n













Actual pin (or ball) contact dia 6.7056 in The plots of the contact sections between the measuring balls and the teeth are shown in Figures 3C1 and 3C2.


52

Fig. 3C1


53

Fig. 3C2

Note that the section plotted is a transverse (plane of rotation) section through the contact point between the left tooth and the measuring ball. The diameter of the ball at the section plane is shown in dashed lines. The full diameter of the ball is shown in full line and is in front of the section plane. It can be seen that the ball projects above the outside diameter and is well above the root of the tooth (marked “R”). The actual contact point (between the dashed lines) is well above the true involute form diameter (marked “T”). The ball contacts a pair of adjacent teeth on a great circle of the ball which is normal to the ball helix angle. (The ball helix angle is the helix angle of the path of the ball center if allowed to roll in the tooth space.) Therefore, a pin of the same diameter may be substituted for the ball without altering the location of the ball or pin center from the center of the gear.


54

Balls or pins can be used interchangeably on spur gears with odd or even teeth and on helical gears with even teeth if the balls are constrained to a single transverse plane in all cases. In the case of odd tooth helical gears, the pins will not stay in a transverse plane and will rock along the ball helix under the pressure of the measuring instrument until a minimum distance between them is reached. The model will compensate for the movement of the pins and the tilt of the measuring device so that two pins can be used for measuring odd tooth helicals. Note the difference in over ball and over pin measurements for the driven gear which is an odd tooth helical.


55

Example 4

Example 4 is a 23 degree helical gear set with a 22 tooth pinion driving a 55 tooth gear. The normal diametral pitch is 36 and the normal pressure angle is 20 degrees.

Since the number of teeth in the pinion and the total number of teeth in the mesh are within the limits of the “Standard” gear set, we can use this selection in the Data Entry Wizard. We will use the backlash recommended by the model. We will set the face width to obtain a full helical gear set with a helical contact ratio a little over one.

After working with the gear set using “US/British” units, we will change the units to “SI” units.

Start a new analysis in 60-050 and make certain US units are selected. Select “Gear set standard” and enter other data as shown in Figure 4A. We will use the default face width and “standard” normal backlash. We will not enter load and speed data. We want a plot of the gear teeth in mesh at the pitch point. The solved model is shown in Report 4A.

Fig. 4A


56

Report 4A


GEOMETRY



m2

m3

m4













57







Face width 0.224 in

DIAMETERS DRIVER

















58






Lead 12.28378 in


















59


























60





















Helical 1.0029

Total 2.4960


61







ms2

ms3

ms4

No Group

AGMA Quality Number

Power HP

Driver_speed rpm


Driven_speed rpm




Tangential load lbf






62



PLOT TOOTH POSITION: pitch















Note that, with 22 teeth in the pinion, it was not necessary to use “high addendum” and extend the operating center distance above “standard."

Next we will find the size over pins for the tooth thickness of the gears. The closest standard pins to the equal tooth/space diameters is 0.048 inches. Enter these numbers directly into the data input form, as in Example 1. After solving, the measuring data should match Report 4B. (For this report we have selected only the input and output data that pertains to size over pins.)


63

Report 4B














Actual pin (or ball) contact dia 1.6586 in Now we will change to metric units. Click the radio button for metric units on the toolbar. The application will change from US to metric units (or back again) throughout the model. Figure 4C is the data input form, Report 4C the solved model, Figure 4C1 the tooth mesh plot, and Figures 4C2 and 4C3 the ball/tooth plots.


64

Fig. 4C


65

Report 4C

Model Title : Program 60-050 Unit System: Metric Description Value Unit Comment

GEOMETRY



m2

m3

m4







Normal_base pitch 2.0829 mm TRANSVERSE PLANE




Transverse_base pitch 2.2393 mm


66

Model Title : Program 60-050 Unit System: Metric Description Value Unit Comment COMMON



Axial pitch 5.67287 mm

Operating_center distance 29.5097 mm

Standard_center distance 30 mm

Face width 5.690 mm

DIAMETERS DRIVER

Outside diameter 18.2728 mm


Reference pitch diameter 16.8627 mm

Pointed tooth diameter 19.1403 mm

Inv/fillet intersection dia (TIF) 15.8344 mm


Root diameter 15.0230 mm

Minimum fillet radius 0.3092 mm

Base diameter 15.6814 mm


Outside diameter 43.5686 mm


Reference pitch diameter 42.1568 mm

Pointed tooth diameter 44.6819 mm


67


Inv/fillet intersection dia (TIF) 40.8052 mm


Root diameter 40.2543 mm

Minimum fillet radius 0.2874 mm

Base diameter 39.2035 mm

Lead 12.28378 in


Normal_tooth thickness @ Ref PD 1.0922 mm

Transverse_tooth thickness @ Ref PD 1.1865 mm

Normal_TT at OD (Top Land) 0.5002 mm

Normal_tooth_thickness_at_TIF dia 1.2992 mm


Normal_tooth thickness @ Ref PD 1.0693 mm

Transverse_tooth thickness @ Ref PD 1.1617 mm

Normal_TT at OD (Top Land) 0.5196 mm

Normal_tooth_thickness_at_TIF dia 1.4635 mm DRIVER GENERATING RACK FORM


Tip_to_Reference Line 0.8966 mm

Thickness_at_Reference Line 1.1074 mm

Tip radius 0.2692 mm


68

Model Title : Program 60-050 Unit System: Metric Description Value Unit Comment DRIVEN GENERATING RACK FORM


Tip_to_Reference Line 0.8966 mm

Thickness_at_Reference Line 1.1074 mm

Tip radius 0.2692 mm


Working depth 1.4110 mm

Change in Opr CD from "Std" CD 0.0000 mm

Basic transverse backlash 0.0000 mm

Normal_backlash 0.0550 mm

Transverse_circular backlash 0.0597 mm





Transverse_circular_pitch 2.4080 mm



Effective_outside diameter 18.2728 mm


Pitch_diameter 16.8627 mm

Normal_tooth_thickness 1.0922 mm


69


Transverse_tooth_thickness 1.1865 mm

Mid-point, length of contact 16.8032 mm


Start of active profile 15.9110 mm


Root_clearance 0.2139 mm


Effective_outside diameter 43.5686 mm


Pitch_diameter 42.1567 mm

Normal_tooth_thickness 1.0694 mm

Transverse_tooth_thickness 1.1617 mm

Mid-point, length of contact 42.2172 mm


Start of active profile 41.0941 mm


Root_clearance 0.2462 mm


Length of contact, transverse plane 3.3435 mm


Recess action 47.55 %


70

Model Title : Program 60-050 Unit System: Metric Description Value Unit Comment OPERATING DATA CONTACT RATIOS


Helical 1.0029


Max total length 9.1423 mm

Min total length 9.1243 mm




ms2

ms3

ms4

AGMA Quality Number

Power kW

Driver_speed rpm

Driver_torque N-m

Driven_speed rpm

Driven_torque N-m

Pitch_Line Velocity m/sec

Axial_Meshing Velocity m/sec

Tangential load N


71


K-factor | See Table for Allowable N/mm^2

Unit load | Values for Steel Gears N/mm^2


Operating PD, Pinion 16.8627 mm

Operating PD, Gear 42.1567 mm PLOT TOOTH POSITION

PLOT TOOTH POSITION: none MEASUREMENT OVER PINS

Plot Ball/Teeth? ('n=no Def='y=yes) n


Pin dia for contact at tooth=space 1.19913 mm

Actual_pin (or ball) diameter 1.21920 mm

Radius over one pin (or ball) 9.2616 mm

Measurement over two balls 18.5232 mm

Measurement over two pins 18.5232 mm

Actual pin (or ball) contact dia 16.8559 mm MEASUREMENT OVER PINS DRIVEN

Pin dia for contact at tooth=space 1.18393 mm

Actual_pin (or ball) diameter 1.21920 mm

Radius over one pin (or ball) 21.8884 mm

Measurement over two balls 43.7595 mm

Measurement over two pins 43.7556 mm

Actual pin (or ball) contact dia 42.1294 mm


72

Fig. 4C1


73

Fig. 4C2


74

Plot 4C3


75

Control And Error Messages In addition to the geometry and load/speed caution messages, there are a number of other checks performed by the model when solved. Some of these guard against impossible entry values. Others will warn you if a condition has been detected that is marginal for a good design or stop you if the gear set will not function. A list of warning and stop messages is shown below: Gear Set "Standard” 20 deg PD (Data Entry Wizard selection):

1. No Standard Gear Set for (pitch, etc. out of range) 2. Total teeth in set is less than (XX) –No “Standard” Set 3. No “Standard” Set With Less Than (XX) Teeth

Model:

1. AGMA Quality Number in Error 2. AGMA Quality Number Out of Range 3. Minimum number of teeth is 3 4. Maximum helix angle is 50 degrees 5. Face Width is Over 40 inches (1.015 m)-Data is Not Valid 6. Operating CD or Pressure Angle Too Small 7. Pointed Teeth On (XXXXX) 8. Root Interference On (XXXXX) 9. (XXXXX) Rack Tooth is Pointed 10. (XXXXX) Rack Tip Radius Greater Than Max of (XXX) 11. (XXXXX) pin center below base diameter –Use larger pin 12. (XXXXX) Measuring Pin Contacts Tooth Tip Corners 13. (XXXXX) Measuring Pin Contacts On Root 14. (XXXXX) Measuring Pin Contacts Below Finished Involute 15. Measuring Pin Below Outside Diameter on (XXXXX)

program 60-050—external gear set introduction · this model will design a 20-degree normal...

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