program 60-750—involute spline machining and assembly ... · program 60-750—involute spline...
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Program 60-750—Involute Spline Machining and Assembly
Introduction This model will allow you to check the suitability of spline cutting or molding tools to produce an internal/external spline set or to design new tools. A plot of the splined parts in assembly is provided for a visual check of the geometry in addition to numerical data. Examples Example 1 In this example we will design a new set of tools (a hob and a shaper cutter) to produce a spline set conforming to spline standard ANSI B92.1-1970. The required data for the spline set is on Report 1-1. (This is from UTS Model 60-710.) Report 1-1
Model Title : Program 60-710 Unit System: US Description Value Unit Comment
COMMON
Number of Teeth 26
Diametral Pitch 10.000000 1/in `
Stub Pitch 20.0000 1/in `
Spline Pitch 10/20
Standard Pressure Angle 30.0000 deg
Type of Fit ('maj or 'side Def='side) side
Pitch Diameter 2.6000000 in
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Model Title : Program 60-710 Unit System: US Description Value Unit Comment
Base Dia 2.2516660 in
Max_Effective Clearance 0.0028 in
Min_Effective Clearance 0.0000 in COMMON: Theoretical from Measured Teeth
Max_Actual Clearance 0.0064 in
Min_Actual Clearance 0.0036 in
Radial Form Clearance (Standard) 0.0026 in INTERNAL SPLINE
Internal Spline ANSI B92.1-1970 Std? Yes
Fillet or Flat Root ('fil/'flt) fil
Major Diameter - Min, rounded in
Major Diameter - Max, rounded 2.8010 in
Form Diameter, rounded 2.7050 in
Roll Angle at Form Diameter 38.144 deg
Minor Diameter - Min, rounded 2.5000 in
Minor Diameter - Max, rounded 2.5050 in
Tolerance Class 5
Machining Tolerance 0.0014 in
Variation Allowance 0.0018 in
Min_Effective_Space Width 0.1571 in
Max_Effective_Space Width 0.1585 in
Min_Actual_Space Width 0.1589 in
Max_Actual_Space Width 0.1603 in
60-750—Involute Spline Machining And Assembly
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Model Title : Program 60-710 Unit System: US Description Value Unit Comment INTERNAL SPLINE: Size Between Pins
Pin Diameter 0.14400 in
Min_Between 2 Pins 2.4431 in
Max_Between 2 Pins 2.4456 in
Min_Diameter Under 3 Pins 2.4431 in
Max_Diameter Under 3 Pins 2.4456 in
Min_Pin Contact Diameter 2.6610 in
Max_Pin Contact Diameter 2.6637 in EXTERNAL SPLINE
External Spline ANSI B92.1-1970 Std? Yes
Fillet or Flat Root ('fil/'flt) fil
Major Diameter - Max 2.7000 in
Major Diameter - Min 2.6950 in
Major_Diameter Chamfer - Max in
Major_Diameter Chamfer - Min in
Form Diameter 2.4950 in
Roll Angle at Form Diameter 27.347 deg
Minor Diameter - Min 2.3990 in
Tolerance Class 5
Machining Tolerance 0.0014 in
Variation Allowance 0.0018 in
Max_Eff_Tooth Thickness 0.1571 in
Min_Eff_Tooth Thickness 0.1557 in
Max_Actual_Tooth Thickness 0.1553 in
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Model Title : Program 60-710 Unit System: US Description Value Unit Comment
Min_Actual_Tooth Thickness 0.1539 in EXTERNAL SPLINE: Size Over Pins
Pin Diameter 0.19200 in
Max_Over 2 Pins 2.8951 in
Min_Over 2 Pins 2.8930 in
Max_Pin Contact Diameter 2.6018 in
Min_Pin Contact Diameter 2.5998 in PLOTS DATA
Mark mod/inv/fil intersections? y
Number of teeth on plot 1
GAGES
Dimensioning Method (Def='std, 'A, 'B) std This is a 26 tooth, 10/20 diametral pitch, side fit, fillet root spline. A Class 5 tolerance is desired on both the internal and external splines. Use the wizard data entry form to enter the data shown in Figure 1-1. The solved model is shown in Report 1-2 This first set of data is for maximum clearance in the spline. (If you do not know which data this requires, compare the data on Report 1-1 with that of Report 1-2.)
60-750—Involute Spline Machining And Assembly
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Fig. 1-1
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Report 1-2
Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Number of Teeth 26
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed hob ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) shp
NORMAL PLANE
Diametral Pitch 10.000000 1/in `
Nominal pressure angle 30.000000 deg
Module 2.540000 mm `
Base pitch 0.2721 in NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 0.1539 in
Total circular finish stock on tooth 0.0000 in thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 0.1539 in
Finished_space width at Ref PD 0.1603 in
Total circular finish stock on tooth 0.0000 in thickness
60-750—Involute Spline Machining And Assembly
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 10.0000 1/in `
Nominal_pressure angle 30.0000 deg
Module 2.5400 mm `
Base_pitch 0.2721 in
External_tooth thickness at Ref PD 0.1539 in
Internal_tooth thickness at Ref PD 0.1539 in
Internal_space width at Ref PD 0.1603 in COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00000 in
Actual_Trans Clearance 0.00640 in
Actual_Normal Trans Clearance 0.00554 in
Total_engagement depth - Max 0.0950 in
Total_engagement depth - Min 0.0950 in
Active contact depth - Max 0.0950 in
Active contact depth - Min 0.0950 in
Root_clearance - external 0.0559 in
Root_clearance - internal 0.0453 in
Axial pitch in
Net face width 1.5000 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 2.6950 in
Normal_top land width 0.0998 in
Start_Tip Modification in
Roll_at_Start of Tip Modification deg
Normal_OD tip relief in
Normal_circular OD tip relief in
Transverse_circular_OD tip relief in
Effective_outside diameter 2.6950 in
Normal_effective OD tip relief in
Normal_tooth_thickness_at_Eff OD 0.0998 in
Pointed tooth diameter (No tip mod) 2.8386 in
Reference PD 2.6000 in
Inv/fillet intersection dia (TIF) 2.4465 in
Roll_at_inv/fill intersection dia 24.348 deg
Normal_TT_at_inv/fill intersection d 0.2198 in
Minimum_fillet radius 0.0387 in
Root diameter 2.3931 in
Whole depth of tooth (from Eff OD) 0.1509 in
Base_diameter 2.2517 in
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.03 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 2.5050 in
Normal_top land width 0.0985 in
Start_Tip_Modification in
Roll_at_Start of Tip Modification deg
Normal_ID tip relief in
Normal_circular_ID tip relief in
Transverse_circular_ID tip relief in
Effective_inside diameter 2.5050 in
Normal_effective_ID tip relief in
Normal_Tooth Thickness at eff ID 0.0985 in
Pointed_tooth diameter (No tip mod) Below_BD in
Reference PD 2.6000 in
Inv/fillet intersection dia (TIF) 2.7458 in
Roll_at_inv/fill intersection dia 39.985 deg
Normal_TT_at_inv/fill intersection d 0.2581 in
Minimum_fillet radius 0.0429 in
Major diameter 2.7855 in
Whole depth of tooth (from Eff ID) 0.1403 in
Base_diameter 2.2517 in
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.03 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 1
EXTERNAL SPLINE HOB
Hob type n
Flank angle 30.0000 deg
Tip to Reference Line 0.1007 in
Tooth thickness at Reference Line 0.1571 in
Tip_radius 0.0353 in
Protuberance 0.0000 in
Protuberance_angle from flank deg
Protuberance_pressure angle deg
Tip_to_flank/prot intersection in INTERNAL SPLINE SHAPER
Number_of Teeth 14
Outside_Diameter 1.5800 in
Normal_Tooth_Thickness 0.1571 in
Tip_Radius - Normal Plane 0.0416 in
Protuberance - Normal Plane 0.0000 in
Center distance with shaper cutter 0.6028 in
Start_of_active_profile_diameter 1.3065 in
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A comparison of Sheet 1-1 with Sheet 1-2 indicates that the default tools meet all the requirements of the standard except for the root diameter of the external spline. The minimum diameter allowed is 2.399 inches and the hob is producing a root diameter of 2.3931 inches. To correct the root diameter we need to change the tip to reference line on the hob from 0.1007 inch to 0.0977 inch. This will increase the root diameter 0.006 inch. Report 1-3 is the solved model after changing the hob addendum. Report 1-3
Model Title : Program 60-750 Unit System: US Description Value Unit Comment
No Group
Number of Teeth 26
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed hob ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) shp
NORMAL PLANE
Diametral Pitch 10.000000 1/in `
Nominal pressure angle 30.000000 deg
Module 2.540000 mm `
Base pitch 0.2721 in NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 0.1539 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Total circular finish stock on tooth 0.0000 in thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 0.1539 in
Finished_space width at Ref PD 0.1603 in
Total circular finish stock on tooth 0.0000 in thickness TRANSVERSE PLANE
Diametral_Pitch 10.0000 1/in `
Nominal_pressure angle 30.0000 deg
Module 2.5400 mm `
Base_pitch 0.2721 in
External_tooth thickness at Ref PD 0.1539 in
Internal_tooth thickness at Ref PD 0.1539 in
Internal_space width at Ref PD 0.1603 in COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00000 in
Actual_Trans Clearance 0.00640 in
Actual_Normal Trans Clearance 0.00554 in
Total_engagement depth - Max 0.0950 in
Total_engagement depth - Min 0.0950 in
Active contact depth - Max 0.0950 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Active contact depth - Min 0.0950 in
Root_clearance - external 0.0529 in
Root_clearance - internal 0.0453 in
Axial pitch in
Net face width 1.5000 in
EXTERNAL SPLINE
Outside Diameter 2.6950 in
Normal_top land width 0.0998 in
Start_Tip Modification in
Roll_at_Start of Tip Modification deg
Normal_OD tip relief in
Normal_circular OD tip relief in
Transverse_circular_OD tip relief in
Effective_outside diameter 2.6950 in
Normal_effective OD tip relief in
Normal_tooth_thickness_at_Eff OD 0.0998 in
Pointed tooth diameter (No tip mod) 2.8386 in
Reference PD 2.6000 in
Inv/fillet intersection dia (TIF) 2.4513 in
Roll_at_inv/fill intersection dia 24.653 deg
Normal_TT_at_inv/fill intersection d 0.2182 in
Minimum_fillet radius 0.0384 in
Root diameter 2.3991 in
Whole depth of tooth (from Eff OD) 0.1479 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Base_diameter 2.2517 in
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.03 in^2 INTERNAL SPLINE
Inside (minor) Diameter 2.5050 in
Normal_top land width 0.0985 in
Start_Tip_Modification in
Roll_at_Start of Tip Modification deg
Normal_ID tip relief in
Normal_circular_ID tip relief in
Transverse_circular_ID tip relief in
Effective_inside diameter 2.5050 in
Normal_effective_ID tip relief in
Normal_Tooth Thickness at eff ID 0.0985 in
Pointed_tooth diameter (No tip mod) Below_BD in
Reference PD 2.6000 in
Inv/fillet intersection dia (TIF) 2.7458 in
Roll_at_inv/fill intersection dia 39.985 deg
Normal_TT_at_inv/fill intersection d 0.2581 in
Minimum_fillet radius 0.0429 in
Major diameter 2.7855 in
Whole depth of tooth (from Eff ID) 0.1403 in
Base_diameter 2.2517 in
60-750—Involute Spline Machining And Assembly
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.03 in^2 PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 1
EXTERNAL SPLINE HOB
Hob type n
Flank angle 30.0000 deg
Tip to Reference Line 0.0977 in
Tooth thickness at Reference Line 0.1571 in
Tip_radius 0.0353 in
Protuberance 0.0000 in
Protuberance_angle from flank deg
Protuberance_pressure angle deg
Tip_to_flank/prot intersection in INTERNAL SPLINE SHAPER
Number_of Teeth 14
Outside_Diameter 1.5800 in
Normal_Tooth_Thickness 0.1571 in
Tip_Radius - Normal Plane 0.0416 in
Protuberance - Normal Plane 0.0000 in
Center distance with shaper cutter 0.6028 in
Start_of_active_profile_diameter 1.3065 in
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A plot of the teeth in assembly is available on the Plot Sheet, or from the drop-down plots list in the Toolbar (See Figure 1-2). Individual plots of the internal and external splines are also available. Fig. 1-2
Now the tools must be checked to insure that at minimum clearance conditions we are still within the required dimensions. Figure 1-3 shows the completed data input form and Report 1-4 the data for the spline set at minimum clearance conditions.
60-750—Involute Spline Machining And Assembly
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Fig. 1-3
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Report 1-4
Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Number of Teeth 26
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed hob ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) shp
NORMAL PLANE
Diametral Pitch 10.000000 1/in `
Nominal pressure angle 30.000000 deg
Module 2.540000 mm `
Base pitch 0.2721 in NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 0.1553 in
Total circular finish stock on tooth 0.0000 in thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 0.1553 in
Finished_space width at Ref PD 0.1589 in
Total circular finish stock on tooth 0.0000 in thickness
60-750—Involute Spline Machining And Assembly
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 10.0000 1/in `
Nominal_pressure angle 30.0000 deg
Module 2.5400 mm `
Base_pitch 0.2721 in
External_tooth thickness at Ref PD 0.1553 in
Internal_tooth thickness at Ref PD 0.1553 in
Internal_space width at Ref PD 0.1589 in COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00000 in
Actual_Trans Clearance 0.00360 in
Actual_Normal Trans Clearance 0.00312 in
Total_engagement depth - Max 0.1000 in
Total_engagement depth - Min 0.1000 in
Active contact depth - Max 0.1000 in
Active contact depth - Min 0.1000 in
Root_clearance - external 0.0492 in
Root_clearance - internal 0.0416 in
Axial pitch in
Net face width 1.5000 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 2.7000 in
Normal_top land width 0.0981 in
Start_Tip Modification in
Roll_at_Start of Tip Modification deg
Normal_OD tip relief in
Normal_circular OD tip relief in
Transverse_circular_OD tip relief in
Effective_outside diameter 2.7000 in
Normal_effective OD tip relief in
Normal_tooth_thickness_at_Eff OD 0.0981 in
Pointed tooth diameter (No tip mod) 2.8406 in
Reference PD 2.6000 in
Inv/fillet intersection dia (TIF) 2.4532 in
Roll_at_inv/fill intersection dia 24.777 deg
Normal_TT_at_inv/fill intersection d 0.2188 in
Minimum_fillet radius 0.0383 in
Root diameter 2.4016 in
Whole depth of tooth (from Eff OD) 0.1492 in
Base_diameter 2.2517 in
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.03 in^2
60-750—Involute Spline Machining And Assembly
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 2.5000 in
Normal_top land width 0.0973 in
Start_Tip_Modification in
Roll_at_Start of Tip Modification deg
Normal_ID tip relief in
Normal_circular_ID tip relief in
Transverse_circular_ID tip relief in
Effective_inside diameter 2.5000 in
Normal_effective_ID tip relief in
Normal_Tooth Thickness at eff ID 0.0973 in
Pointed_tooth diameter (No tip mod) Below_BD in
Reference PD 2.6000 in
Inv/fillet intersection dia (TIF) 2.7437 in
Roll_at_inv/fill intersection dia 39.892 deg
Normal_TT_at_inv/fill intersection d 0.2579 in
Minimum_fillet radius 0.0430 in
Major diameter 2.7831 in
Whole depth of tooth (from Eff ID) 0.1416 in
Base_diameter 2.2517 in
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.03 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 1
EXTERNAL SPLINE HOB
Hob type n
Flank angle 30.0000 deg
Tip to Reference Line 0.0977 in
Tooth thickness at Reference Line 0.1571 in
Tip_radius 0.0353 in
Protuberance 0.0000 in
Protuberance_angle from flank deg
Protuberance_pressure angle deg
Tip_to_flank/prot intersection in INTERNAL SPLINE SHAPER
Number_of Teeth 14
Outside_Diameter 1.5800 in
Normal_Tooth_Thickness 0.1571 in
Tip_Radius - Normal Plane 0.0416 in
Protuberance - Normal Plane 0.0000 in
Center distance with shaper cutter 0.6016 in
Start_of_active_profile_diameter 1.3040 in
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A comparison of Report 1-1 and Report 1-4 shows that we still meet the requirements and the tools are OK. (You may wish to check the internal spline with the shaper cutter at new geometry and at life geometry, to make sure that the internal spline will stay within specifications throughout the life of the shaper cutter. This is not necessary with the hob, because the cutting edge geometry is constant.) Figure 1-4 is the plot of the spline set at minimum clearance conditions. Fig. 1-4
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Example 2 In this example we will design a spline set with a specified minimum radial play. The external spline is rolled on the shaft and the internal spline is molded. (Both are “formed” splines.) The spline has 8 teeth, a pressure angle of 45 degrees and fillet roots. It is known that the difference between the actual and effective clearance is 0.0048 inch (Tolerance Class 7 for inch series spline). An effective radial play of 0.002 inch is required so the actual radial play must be at least 0.0068 inch. The radial play is equal to the tooth/space clearance multiplied by the Cosine of the pressure angle. Since the required actual radial play is 0.0068 inch, the actual clearance must be about 0.007 inch / cos(45) or 0.0099 inch. Using the wizard data input form, enter the data shown in Figure 2-1. Note that the entered space width is the default tooth thickness of 0.0532+0.0099 or 0.0631 inch. Set the offset to the maximum of .0035 inch (half the normal clearance of 0.007 inch). Report 2-1 shows the solved model.
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Fig. 2-1
UTS Integrated Gear Software
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Report 2-1
Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Number of Teeth 8
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed frm ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) frm
NORMAL PLANE
Diametral Pitch 32.000000 1/in `
Nominal pressure angle 45.000000 deg
Module 0.793750 mm `
Base pitch 0.0694 in NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 0.0532 in
Total circular finish stock on tooth 0.0000 in thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 0.0351 in
Finished_space width at Ref PD 0.0631 in
Total circular finish stock on tooth 0.0000 in thickness
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 32.0000 1/in `
Nominal_pressure angle 45.0000 deg
Module 0.7938 mm `
Base_pitch 0.0694 in
External_tooth thickness at Ref PD 0.0532 in
Internal_tooth thickness at Ref PD 0.0351 in
Internal_space width at Ref PD 0.0631 in COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00350 in
Actual_Trans Clearance 0.00990 in
Actual_Normal Trans Clearance 0.00700 in
Total_engagement depth - Max 0.0285 in
Total_engagement depth - Min 0.0215 in
Active contact depth - Max 0.0218 in
Active contact depth - Min 0.0148 in
Root_clearance - external 0.0050 in
Root_clearance - internal 0.0037 in
Axial pitch in
Net face width 0.2000 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 0.2812 in
Normal_top land width 0.0129 in
Start_Tip Modification in
Roll_at_Start of Tip Modification deg
Normal_OD tip relief in
Normal_circular OD tip relief in
Transverse_circular_OD tip relief in
Effective_outside diameter 0.2712 in
Normal_effective OD tip relief in
Normal_tooth_thickness_at_Eff OD 0.0338 in
Pointed tooth diameter (No tip mod) 0.2993 in
Reference PD 0.2500 in
Inv/fillet intersection dia (TIF) 0.2228 in
Roll_at_inv/fill intersection dia 43.951 deg
Normal_TT_at_inv/fill intersection d 0.0701 in
Minimum_fillet radius 0.0115 in
Root diameter 0.2143 in
Whole depth of tooth (from Eff OD) 0.0334 in
Base_diameter 0.1768 in
Lead in
Area of space (Normal section) 0.00 in^2
Area of tooth (Normal section) 0.00 in^2
60-750—Involute Spline Machining And Assembly
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 0.2313 in
Normal_top land width 0.0115 in
Start_Tip_Modification in
Roll_at_Start of Tip Modification deg
Normal_ID tip relief in
Normal_circular_ID tip relief in
Transverse_circular_ID tip relief in
Effective_inside diameter 0.2345 in
Normal_effective_ID tip relief in
Normal_Tooth Thickness at eff ID 0.0189 in
Pointed_tooth diameter (No tip mod) 0.2111 in
Reference PD 0.2500 in
Inv/fillet intersection dia (TIF) 0.2852 in
Roll_at_inv/fill intersection dia 72.539 deg
Normal_TT_at_inv/fill intersection d 0.0826 in
Minimum_fillet radius 0.0209 in
Major diameter 0.2955 in
Whole depth of tooth (from Eff ID) 0.0321 in
Base_diameter 0.1768 in
Lead in
Area of space (Normal section) 0.00 in^2
Area of tooth (Normal section) 0.00 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 8
FORMED EXTERNAL SPLINE BASIC RACK FORM
Flank angle 45.0000 deg
Tip to Reference Line 0.0199 in
Tooth thickness at Reference Line 0.0491 in
Tip_radius 0.0112 in
Radial_tip chamfer (w/o mod) 0.0050 in
Normal_tip radius 0.0000 in
Normal_tip_relief exponent
FORMED INTERNAL SPLINE
Normal_fillet radius 0.0209 in
Radial_tip chamfer (w/o mod) 0.0000 in
Normal_tip radius 0.0050 in
Normal_tip_relief exponent The model indicated that the clearance is low both at the root of the external spline and at the root of the internal spline (external OD). Figure 2-2 is a plot of the teeth with the maximum offset applied.
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Fig. 2-2
The model has warned us about low root clearance and low clearance at the outside diameter for the external spline. We will change the external basic rack to get a smaller root diameter and, therefore, more root clearance. Add 0.0015 inch to the tip to reference line for the external basic rack (0.0214 inch). This will increase the root clearance directly the same amount. Add 0.008 inch to the Inv/fillet intersection dia for the internal (0.2932 inch). The clearance at the major diameter (external OD) will increase less than half this amount, since we will need a smaller fillet radius at the major diameter.
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The application immediately warns you that the basic rack tip radius is too large—greater than the maximum of .0076 inch (.193 mm). When you change the tip radius to 0.0076 inch and solve again, you get an error message that the internal normal fillet radius is too large—by .015 inch (.383 mm). Change the normal fillet radius to 0.015 inch and solve again. The completed data input file is shown in Figure 2-3, the solved model in Report 2-2. Fig. 2-3
60-750—Involute Spline Machining And Assembly
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Report 2-2
Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Number of Teeth 8
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed frm ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) frm
NORMAL PLANE
Diametral Pitch 32.000000 1/in `
Nominal pressure angle 45.000000 deg
Module 0.793750 mm `
Base pitch 0.0694 in NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 0.0532 in
Total circular finish stock on tooth 0.0000 in thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 0.0351 in
Finished_space width at Ref PD 0.0631 in
Total circular finish stock on tooth 0.0000 in thickness
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 32.0000 1/in `
Nominal_pressure angle 45.0000 deg
Module 0.7938 mm `
Base_pitch 0.0694 in
External_tooth thickness at Ref PD 0.0532 in
Internal_tooth thickness at Ref PD 0.0351 in
Internal_space width at Ref PD 0.0631 in COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00350 in
Actual_Trans Clearance 0.00990 in
Actual_Normal Trans Clearance 0.00700 in
Total_engagement depth - Max 0.0285 in
Total_engagement depth - Min 0.0215 in
Active contact depth - Max 0.0218 in
Active contact depth - Min 0.0148 in
Root_clearance - external 0.0065 in
Root_clearance - internal 0.0058 in
Axial pitch in
Net face width 0.2000 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 0.2812 in
Normal_top land width 0.0129 in
Start_Tip Modification in
Roll_at_Start of Tip Modification deg
Normal_OD tip relief in
Normal_circular OD tip relief in
Transverse_circular_OD tip relief in
Effective_outside diameter 0.2712 in
Normal_effective OD tip relief in
Normal_tooth_thickness_at_Eff OD 0.0338 in
Pointed tooth diameter (No tip mod) 0.2993 in
Reference PD 0.2500 in
Inv/fillet intersection dia (TIF) 0.2185 in
Roll_at_inv/fill intersection dia 41.609 deg
Normal_TT_at_inv/fill intersection d 0.0719 in
Minimum_fillet radius 0.0086 in
Root diameter 0.2113 in
Whole depth of tooth (from Eff OD) 0.0349 in
Base_diameter 0.1768 in
Lead in
Area of space (Normal section) 0.00 in^2
Area of tooth (Normal section) 0.00 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 0.2313 in
Normal_top land width 0.0115 in
Start_Tip_Modification in
Roll_at_Start of Tip Modification deg
Normal_ID tip relief in
Normal_circular_ID tip relief in
Transverse_circular_ID tip relief in
Effective_inside diameter 0.2345 in
Normal_effective_ID tip relief in
Normal_Tooth Thickness at eff ID 0.0189 in
Pointed_tooth diameter (No tip mod) 0.2111 in
Reference PD 0.2500 in
Inv/fillet intersection dia (TIF) 0.2932 in
Roll_at_inv/fill intersection dia 75.815 deg
Normal_TT_at_inv/fill intersection d 0.0954 in
Minimum_fillet radius 0.0150 in
Major diameter 0.2999 in
Whole depth of tooth (from Eff ID) 0.0343 in
Base_diameter 0.1768 in
Lead in
Area of space (Normal section) 0.00 in^2
Area of tooth (Normal section) 0.00 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 8
FORMED EXTERNAL SPLINE BASIC RACK FORM
Flank angle 45.0000 deg
Tip to Reference Line 0.0214 in
Tooth thickness at Reference Line 0.0491 in
Tip_radius 0.0076 in
Radial_tip chamfer (w/o mod) 0.0050 in
Normal_tip radius 0.0000 in
Normal_tip_relief exponent
FORMED INTERNAL SPLINE
Normal_fillet radius 0.0150 in
Radial_tip chamfer (w/o mod) 0.0000 in
Normal_tip radius 0.0050 in
Normal_tip_relief exponent We now have a root clearance of about 0.006 inch and no longer get the warning messages. Figure 2-4 is the plot with the new dimensions.
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Fig. 2-4
The machining tolerance is 0.0023 inch, the OD tolerance is 0.003 inch and the ID and (internal) TIF tolerance is 0.004 inch. Change the data in the model to reflect the tolerances and solve. Set the offset to half the actual normal trans clearance (0.01025/2 = .00512) and solve for the last time. (Figure 2-5 and Report 2-3)
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Fig. 2-5
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Report 2-3
Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Number of Teeth 8
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed frm ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) frm
NORMAL PLANE
Diametral Pitch 32.000000 1/in `
Nominal pressure angle 45.000000 deg
Module 0.793750 mm `
Base pitch 0.0694 in NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 0.0509 in
Total circular finish stock on tooth 0.0000 in thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 0.0328 in
Finished_space width at Ref PD 0.0654 in
Total circular finish stock on tooth 0.0000 in thickness
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 32.0000 1/in `
Nominal_pressure angle 45.0000 deg
Module 0.7938 mm `
Base_pitch 0.0694 in
External_tooth thickness at Ref PD 0.0509 in
Internal_tooth thickness at Ref PD 0.0328 in
Internal_space width at Ref PD 0.0654 in COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00512 in
Actual_Trans Clearance 0.01450 in
Actual_Normal Trans Clearance 0.01025 in
Total_engagement depth - Max 0.0266 in
Total_engagement depth - Min 0.0163 in
Active contact depth - Max 0.0200 in
Active contact depth - Min 0.0098 in
Root_clearance - external 0.0080 in
Root_clearance - internal 0.0073 in
Axial pitch in
Net face width 0.2000 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 0.2782 in
Normal_top land width 0.0137 in
Start_Tip Modification in
Roll_at_Start of Tip Modification deg
Normal_OD tip relief in
Normal_circular OD tip relief in
Transverse_circular_OD tip relief in
Effective_outside diameter 0.2682 in
Normal_effective OD tip relief in
Normal_tooth_thickness_at_Eff OD 0.0344 in
Pointed tooth diameter (No tip mod) 0.2973 in
Reference PD 0.2500 in
Inv/fillet intersection dia (TIF) 0.2166 in
Roll_at_inv/fill intersection dia 40.555 deg
Normal_TT_at_inv/fill intersection d 0.0707 in
Minimum_fillet radius 0.0088 in
Root diameter 0.2090 in
Whole depth of tooth (from Eff OD) 0.0346 in
Base_diameter 0.1768 in
Lead in
Area of space (Normal section) 0.00 in^2
Area of tooth (Normal section) 0.00 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 0.2353 in
Normal_top land width 0.0132 in
Start_Tip_Modification in
Roll_at_Start of Tip Modification deg
Normal_ID tip relief in
Normal_circular_ID tip relief in
Transverse_circular_ID tip relief in
Effective_inside diameter 0.2384 in
Normal_effective_ID tip relief in
Normal_Tooth Thickness at eff ID 0.0205 in
Pointed_tooth diameter (No tip mod) 0.2140 in
Reference PD 0.2500 in
Inv/fillet intersection dia (TIF) 0.2972 in
Roll_at_inv/fill intersection dia 77.434 deg
Normal_TT_at_inv/fill intersection d 0.0993 in
Minimum_fillet radius 0.0136 in
Major diameter 0.3030 in
Whole depth of tooth (from Eff ID) 0.0339 in
Base_diameter 0.1768 in
Lead in
Area of space (Normal section) 0.00 in^2
Area of tooth (Normal section) 0.00 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 8
FORMED EXTERNAL SPLINE BASIC RACK FORM
Flank angle 45.0000 deg
Tip to Reference Line 0.0214 in
Tooth thickness at Reference Line 0.0491 in
Tip_radius 0.0076 in
Radial_tip chamfer (w/o mod) 0.0050 in
Normal_tip radius 0.0000 in
Normal_tip_relief exponent
FORMED INTERNAL SPLINE
Normal_fillet radius 0.0136 in
Radial_tip chamfer (w/o mod) 0.0000 in
Normal_tip radius 0.0050 in
Normal_tip_relief exponent Figure 2-6 is a plot of the spline with the new dimensions.
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Fig. 2-6
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Example 3 This is a 12 tooth, 2 mm module, 37.5 degree pressure angle, side fit, fillet root spline. We wish to check an existing shaper cutter and topping hob to determine if they will produce the spline parts. The required dimensions are shown in Report 3-1. (This is from UTS Model 60-720.) Report 3-1
Model Title : Program 60-720 Unit System: Metric Description Value Unit Comment
COMMON
Number of Teeth 12
Module 2.000000 mm `
Diametral Pitch 12.700000 1/in `
Standard Pressure Angle 37.5 deg
Length of Engagement 20.0000 mm
Pitch Diameter 24.00000 mm
Base Dia 19.04050 mm
Max_Effective Clearance 0.2810 mm
Min_Effective Clearance 0.0650 mm
Max_Actual Clearance 0.3830 mm
Min_Actual Clearance 0.1660 mm
Radial Form Clearance (Standard) 0.2000 mm
Ref Line to Root TIF on Basic Rack 1.1000 mm
Inch('i) / Metric('m) Measuring Pins m
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Model Title : Program 60-720 Unit System: Metric Description Value Unit Comment INTERNAL SPLINE
Internal Spline ANSI B92.2M-1980? Yes
Fillet or Flat Root ('fil/'flt) fil
Major Diameter - Max 27.010 mm
Form Diameter 26.200 mm
Roll Angle at Form Diameter 54.156 deg
Fillet_Radius 0.6000 mm
Minor Diameter - Min 22.390 mm
Minor Diameter - Max 22.700 mm
Tolerance and Fit Class: "7H"
Tooth Thickness Reduction 0.00000 mm
Machining Tolerance 0.1080 mm
Effective Variation 0.0510 mm
Total Tolerance 0.1590 mm
Min_Effective_Space Width 3.1420 mm
Max_Effective_Space Width 3.2500 mm
Min_Actual_Space Width 3.1920 mm
Max_Actual_Space Width 3.3000 mm INTERNAL SPLINE Size Between Pins
Pin Diameter, mm 3.7500 mm `
Pin Diameter, inch 0.14764 in `
Min_Between 2 Pins 18.0480 mm
Max_Between 2 Pins 18.2220 mm
Min_Diameter Under 3 Pins 18.0480 mm
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Model Title : Program 60-720 Unit System: Metric Description Value Unit Comment
Max_Diameter Under 3 Pins 18.2220 mm
Min_Pin Contact Diameter 23.8500 mm
Max_Pin Contact Diameter 24.0640 mm INTERNAL SPLINE Analytical Inspection
Total_Index Variation 0.0620 mm
Total_Profile Variation 0.0540 mm
Lead Variation 0.0190 mm EXTERNAL SPLINE
External Spline ANSI B92.2M-1980? Yes
Fillet or Flat Root ('fil/'flt) fil
Major Diameter - Max 25.720 mm
Major Diameter - Min 25.400 mm
Form Diameter 21.920 mm
Roll Angle at Form Diameter 32.671 deg
Fillet_Radius 0.6000 mm
Minor Diameter - Min 20.910 mm
Tolerance and Fit Class "7d"
Tooth Thickness Reduction 0.06500 mm
Machining Tolerance 0.1080 mm
Effective Variation 0.0510 mm
Total Tolerance 0.1590 mm
Max_Eff_Tooth Thickness 3.0770 mm
Min_Eff_Tooth Thickness 2.9680 mm
Max_Actual_Tooth Thickness 3.0260 mm
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Model Title : Program 60-720 Unit System: Metric Description Value Unit Comment
Min_Actual_Tooth Thickness 2.9180 mm EXTERNAL SPLINE Size Over Pins
Pin Diameter, mm 5.0000 mm `
Pin Diameter, inch 0.19685 in `
Max_Over 2 Pins 32.5950 mm
Min_Over 2 Pins 32.4770 mm
Max Pin Contact Diameter 24.2230 mm
Min Pin Contact Diameter 24.1220 mm Plot Data
Mark mod/inv/fil intersections? n
Number of teeth on plot 1
GAGES
Dimensioning Method (Def='std, 'A, 'B) std First we will check the spline at minimum clearance conditions: Internal Minimum Minor Diameter Internal Minimum Actual Space Width External Maximum Major Diameter External Maximum Actual Tooth Thickness Make certain that metric units are selected. Use the wizard data entry form to enter the data as shown in Figure 3-1. The solved model is shown in Report 3-2.
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Fig. 3-1
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Report 3-2
Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment
Number of Teeth 12
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed hob ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) shp
NORMAL PLANE
Diametral Pitch 12.700000 1/in `
Nominal pressure angle 37.500000 deg
Module 2.000000 mm `
Base pitch 4.9848 mm NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 3.0260 mm
Total circular finish stock on tooth 0.0000 mm thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 3.0912 mm
Finished_space width at Ref PD 3.1920 mm
Total circular finish stock on tooth 0.0000 mm thickness
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 12.7000 1/in `
Nominal_pressure angle 37.5000 deg
Module 2.0000 mm `
Base_pitch 4.9848 mm
External_tooth thickness at Ref PD 3.0260 mm
Internal_tooth thickness at Ref PD 3.0912 mm
Internal_space width at Ref PD 3.1920 mm COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00000 mm
Actual_Trans Clearance 0.16600 mm
Actual_Normal Trans Clearance 0.13170 mm
Total_engagement depth - Max 1.5299 mm
Total_engagement depth - Min 1.5299 mm
Active contact depth - Max 1.5132 mm
Active contact depth - Min 1.5132 mm
Root_clearance - external 0.6701 mm
Root_clearance - internal 0.7075 mm
Axial pitch mm
Net face width 12.0000 mm
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 25.4499 mm
Normal_top land width 1.9036 mm
Start_Tip Modification mm
Roll_at_Start of Tip Modification deg
Normal_OD tip relief mm
Normal_circular OD tip relief mm
Transverse_circular_OD tip relief mm
Effective_outside diameter 25.4164 mm
Normal_effective OD tip relief mm
Normal_tooth_thickness_at_Eff OD 2.0007 mm
Pointed tooth diameter (No tip mod) 27.5744 mm
Reference PD 24.0000 mm
Inv/fillet intersection dia (TIF) 21.7608 mm
Roll_at_inv/fill intersection dia 31.703 deg
Normal_TT_at_inv/fill intersection d 4.1559 mm
Minimum_fillet radius 0.6595 mm
Root diameter 21.0499 mm
Whole depth of tooth (from Eff OD) 2.2000 mm
Base_diameter 19.0405 mm
Lead mm
Area of space (Normal section) 5.91 mm^2
Area of tooth (Normal section) 7.48 mm^2
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 22.3900 mm
Normal_top land width 1.8049 mm
Start_Tip_Modification mm
Roll_at_Start of Tip Modification deg
Normal_ID tip relief mm
Normal_circular_ID tip relief mm
Transverse_circular_ID tip relief mm
Effective_inside diameter 22.3900 mm
Normal_effective_ID tip relief mm
Normal_Tooth Thickness at eff ID 1.8049 mm
Pointed_tooth diameter (No tip mod) Below_BD mm
Reference PD 24.0000 mm
Inv/fillet intersection dia (TIF) 26.4441 mm
Roll_at_inv/fill intersection dia 55.221 deg
Normal_TT_at_inv/fill intersection d 5.6272 mm
Minimum_fillet radius 0.6322 mm
Major diameter 26.8648 mm
Whole depth of tooth (from Eff ID) 2.2374 mm
Base_diameter 19.0405 mm
Lead mm
Area of space (Normal section) 5.96 mm^2
Area of tooth (Normal section) 8.46 mm^2
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 1
EXTERNAL SPLINE HOB Hob type t Flank angle 37.5000 deg
Tip to Reference Line 1.4000 mm Tooth thickness at Reference Line 3.1420 mm
Tip_radius 0.6000 mm Protuberance 0.0000 mm
Protuberance_angle from flank deg Protuberance_pressure angle deg Tip_to_flank/prot intersection mm EXTERNAL SPLINE HOB TOPPING Reference_Line_To Hob Tooth Root 0.8000 mm Radius in Hob Tooth Root 0.1200 mm
Ref_Line to Hob SAP 0.7679 mm Normal_Space Width at Hob SAP 1.9627 mm INTERNAL SPLINE SHAPER Number_of Teeth 7 Outside_Diameter 16.8000 mm
Normal_Tooth_Thickness 3.1420 mm Tip_Radius - Normal Plane 0.6000 mm
Protuberance - Normal Plane 0.0000 mm Center distance with shaper cutter 5.0324 mm Start_of_active_profile_diameter 12.4328 mm
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Figure 3-2 is the plot of the teeth in assembly.
Fig. 3-2
A comparison of Report 3-1 and Report 3-2 shows that all requirements have been met at minimum clearance conditions.
Now we need to check at maximum clearance conditions:
Internal Max Minor Dia Internal Max Actual Space Width External Min Major Dia External Min Actual Tooth Thickness
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Using the cursor change the dimensions according to the max clearance data on Report 3-1. Figure 3-3 and Report 3-3 show the inputs and the solved model after these changes have been made. Fig. 3-3
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Report 3-3
Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment
Number of Teeth 12
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed hob ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) shp
NORMAL PLANE
Diametral Pitch 12.700000 1/in `
Nominal pressure angle 37.500000 deg
Module 2.000000 mm `
Base pitch 4.9848 mm NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 2.9180 mm
Total circular finish stock on tooth 0.0000 mm thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 2.9832 mm
Finished_space width at Ref PD 3.3000 mm
Total circular finish stock on tooth 0.0000 mm thickness
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 12.7000 1/in `
Nominal_pressure angle 37.5000 deg
Module 2.0000 mm `
Base_pitch 4.9848 mm
External_tooth thickness at Ref PD 2.9180 mm
Internal_tooth thickness at Ref PD 2.9832 mm
Internal_space width at Ref PD 3.3000 mm COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00000 mm
Actual_Trans Clearance 0.38200 mm
Actual_Normal Trans Clearance 0.30306 mm
Total_engagement depth - Max 1.3046 mm
Total_engagement depth - Min 1.3046 mm
Active contact depth - Max 1.2825 mm
Active contact depth - Min 1.2825 mm
Root_clearance - external 0.8954 mm
Root_clearance - internal 0.8467 mm
Axial pitch mm
Net face width 12.0000 mm
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 25.3091 mm
Normal_top land width 1.8930 mm
Start_Tip Modification mm
Roll_at_Start of Tip Modification deg
Normal_OD tip relief mm
Normal_circular OD tip relief mm
Transverse_circular_OD tip relief mm
Effective_outside diameter 25.2650 mm
Normal_effective OD tip relief mm
Normal_tooth_thickness_at_Eff OD 2.0076 mm
Pointed tooth diameter (No tip mod) 27.4557 mm
Reference PD 24.0000 mm
Inv/fillet intersection dia (TIF) 21.6499 mm
Roll_at_inv/fill intersection dia 31.007 deg
Normal_TT_at_inv/fill intersection d 4.0979 mm
Minimum_fillet radius 0.6690 mm
Root diameter 20.9091 mm
Whole depth of tooth (from Eff OD) 2.2000 mm
Base_diameter 19.0405 mm
Lead mm
Area of space (Normal section) 5.89 mm^2
Area of tooth (Normal section) 7.42 mm^2
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 22.7000 mm
Normal_top land width 1.9256 mm
Start_Tip_Modification mm
Roll_at_Start of Tip Modification deg
Normal_ID tip relief mm
Normal_circular_ID tip relief mm
Transverse_circular_ID tip relief mm
Effective_inside diameter 22.7000 mm
Normal_effective_ID tip relief mm
Normal_Tooth Thickness at eff ID 1.9256 mm
Pointed_tooth diameter (No tip mod) Below_BD mm
Reference PD 24.0000 mm
Inv/fillet intersection dia (TIF) 26.5950 mm
Roll_at_inv/fill intersection dia 55.873 deg
Normal_TT_at_inv/fill intersection d 5.6863 mm
Minimum_fillet radius 0.6243 mm
Major diameter 27.0025 mm
Whole depth of tooth (from Eff ID) 2.1513 mm
Base_diameter 19.0405 mm
Lead mm
Area of space (Normal section) 5.64 mm^2
Area of tooth (Normal section) 8.35 mm^2
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment PLOT CONFIGURATION
Mark inv/fil intersections? y
Mark mod/inv intersections? y
Number of teeth on plot 1
EXTERNAL SPLINE HOB
Hob type t
Flank angle 37.5000 deg
Tip to Reference Line 1.4000 mm
Tooth thickness at Reference Line 3.1420 mm
Tip_radius 0.6000 mm
Protuberance 0.0000 mm
Protuberance_angle from flank deg
Protuberance_pressure angle deg
Tip_to_flank/prot intersection mm EXTERNAL SPLINE HOB TOPPING
Reference_Line_To Hob Tooth Root 0.8000 mm
Radius in Hob Tooth Root 0.1200 mm
Ref_Line to Hob SAP 0.7735 mm
Normal_Space Width at Hob SAP 1.9541 mm INTERNAL SPLINE SHAPER
Number_of Teeth 7
Outside_Diameter 16.8000 mm
Normal_Tooth_Thickness 3.1420 mm
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Model Title : Program 60-750 Unit System: Metric Description Value Unit Comment
Tip_Radius - Normal Plane 0.6000 mm
Protuberance - Normal Plane 0.0000 mm
Center distance with shaper cutter 5.1013 mm
Start_of_active_profile_diameter 12.5976 mm The external spline does not meet the dimensional requirements at maximum clearance conditions. The outside diameter of the external is about 0.1 mm under the low limit in Report 3-1. The shaper cutter will produce the required internal spline but the hob sill not produce the required external spline. Figure 3-4 is a plot of the teeth at maximum clearance.
Sheet 3-5
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Example 4 This is a 15 tooth, 10 diametral pitch, 30 degree pressure angle, flat root major diameter fit spline. Select a semi-topping hob for the external and shaping for the internal. Select “Flat Root Maj Dia Fit” for both internal and external. Note also that we are back in US units. During solving, the model produces a note that the number of teeth is odd. The major and minor diameters cannot be measured directly with an odd number of teeth. This is an inconvenience during manufacturing and inspection, and an even number of teeth should be used if possible. But this is only a reminder, and if an odd number of teeth is necessary it may be ignored. Note that during the solution the model produces a warning that the clearance is low at the external OD. This is because the internal spline pilots on the external spline OD and not on the sides of the teeth. For major diameter fit splines this warning message is, of course, ignored. Figure 4-1 shows the wizard data input form with data entered. Report 4-1 gives the data for the solved model.
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Fig. 4-1
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Report 4-1
Model Title : Program 60-750 Unit System: US Description Value Unit Comment
Number of Teeth 15
EXTERNAL MANUFACTURING METHOD
Hobbed ('hob), Shaped ('shp), Formed hob ('frm) INTERNAL MANUFACTURING METHOD
Shaped ('shp) or Formed ('frm) shp
NORMAL PLANE
Diametral Pitch 10.000000 1/in `
Nominal pressure angle 30.000000 deg
Module 2.540000 mm `
Base pitch 0.2721 in NORMAL PLANE EXTERNAL
Finished tooth thickness at Ref PD 0.1548 in
Total circular finish stock on tooth 0.0000 in thickness NORMAL PLANE INTERNAL
Finished tooth thickness at Ref PD 0.1571 in
Finished_space width at Ref PD 0.1571 in
Total circular finish stock on tooth 0.0000 in thickness
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment TRANSVERSE PLANE
Diametral_Pitch 10.0000 1/in `
Nominal_pressure angle 30.0000 deg
Module 2.5400 mm `
Base_pitch 0.2721 in
External_tooth thickness at Ref PD 0.1548 in
Internal_tooth thickness at Ref PD 0.1571 in
Internal_space width at Ref PD 0.1571 in COMMON
Helix angle 0.000000 deg
Base_helix angle 0.0000 deg
Offset of Ext/Int Axes 0.00000 in
Actual_Trans Clearance 0.00230 in
Actual_Normal Trans Clearance 0.00199 in
Total_engagement depth - Max 0.1000 in
Total_engagement depth - Min 0.1000 in
Active contact depth - Max 0.0888 in
Active contact depth - Min 0.0888 in
Root_clearance - external 0.0266 in
Root_clearance - internal 0.0000 in
Axial pitch in
Net face width 2.0000 in
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment EXTERNAL SPLINE
Outside Diameter 1.6000 in
Normal_top land width 0.0665 in
Start_Tip Modification 1.5777 in
Roll_at_Start of Tip Modification 39.488 deg
Normal_OD tip relief 0.00672 in
Normal_circular OD tip relief 0.01578 in
Transverse_circular_OD tip relief 0.01578 in
Effective_outside diameter 1.5777 in
Normal_effective OD tip relief in
Normal_tooth_thickness_at_Eff OD 0.1123 in
Pointed tooth diameter (No tip mod) 1.7277 in
Reference PD 1.5000 in
Inv/fillet intersection dia (TIF) 1.3862 in
Roll_at_inv/fill intersection dia 21.337 deg
Normal_TT_at_inv/fill intersection d 0.1955 in
Minimum_fillet radius 0.0240 in
Root diameter 1.3469 in
Whole depth of tooth (from Eff OD) 0.1266 in
Base_diameter 1.2990 in
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.02 in^2
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Model Title : Program 60-750 Unit System: US Description Value Unit Comment INTERNAL SPLINE
Inside (minor) Diameter 1.4000 in
Normal_top land width 0.0990 in
Start_Tip_Modification in
Roll_at_Start of Tip Modification deg
Normal_ID tip relief in
Normal_circular_ID tip relief in
Transverse_circular_ID tip relief in
Effective_inside diameter 1.4000 in
Normal_effective_ID tip relief in
Normal_Tooth Thickness at eff ID 0.0990 in
Pointed_tooth diameter (No tip mod) Below_BD in
Reference PD 1.5000 in
Inv/fillet intersection dia (TIF) 1.5926 in
Roll_at_inv/fill intersection dia 40.634 deg
Normal_TT_at_inv/fill intersection d 0.2282 in
Minimum_fillet radius 0.0063 in
Major diameter 1.6000 in
Whole depth of tooth (from Eff ID) 0.1000 in
Base_diameter 1.2990 in
Lead in
Area of space (Normal section) 0.02 in^2
Area of tooth (Normal section) 0.02 in^2
UTS Integrated Gear Software
70
Model Title : Program 60-750 Unit System: US Description Value Unit Comment PLOT CONFIGURATION Mark inv/fil intersections? y Mark mod/inv intersections? y Number of teeth on plot 1
EXTERNAL SPLINE HOB Hob type s
Flank angle 30.0000 deg Tip to Reference Line 0.0746 in
Tooth thickness at Reference Line 0.1571 in Tip_radius 0.0200 in
Protuberance 0.0000 in Protuberance_angle from flank deg Protuberance_pressure angle deg Tip_to_flank/prot intersection in EXTERNAL SPLINE HOB SEMI-TOPPING AND TIP RELIEF Reference_Line_to Start Mod Ramp 0.0400 in
Pressure Angle of Mod Ramp 63.0000 deg
INTERNAL SPLINE SHAPER Number_of Teeth 10 Outside_Diameter 1.1000 in
Normal_Tooth_Thickness 0.1571 in Tip_Radius - Normal Plane 0.0050 in
Protuberance - Normal Plane 0.0000 in Center distance with shaper cutter 0.2500 in Start_of_active_profile_diameter 0.9077 in Figure 4-2 is a plot of the teeth for this configuration.
60-750—Involute Spline Machining And Assembly
71
Fig. 4-2
UTS Models 60-710 and 60-720 will furnish data on spline geometry, manufacturing data and gages for, respectively, ANSI standard inch series and metric series splines. To analyze external and internal splines individually, use UTS Models 60-410 and 60-460.