Program 60-145—Involute Gear Tooth Thickness Introduction · PDF fileProgram...
32
Program 60-145—Involute Gear Tooth Thickness Introduction The measured and “effective” tooth thickness of involute gears and splines are usually different. Depending on the method used for the tooth thickness measurement the difference between the measured value and the apparent, or effective, thickness “seen” by the mating gear or spline may be enough to prevent satisfactory use of the part. Further problems arise when the supplier of the gear and the inspector use different methods to measure what appears to be the same thing, the tooth thickness. The effective tooth thickness is the maximum material envelope condition on the active surfaces of a gear or spline. This envelope is the “effective” gear tooth “seen” by the mating gear or spline and controls the backlash or spline fit. The inevitable departures from the theoretical tooth form of the manufactured part decreases the theoretical backlash in gear pairs and the theoretical clearance in splines. (In the case of interference fit splines the interference is increased.) Once the desired tooth thickness is established based on the backlash of a gear pair or the fit of a spline the method of measurement must be taken into account when the measured tooth thickness is specified on the manufacturing documents. The method of measurement should be specified along with the tooth thickness – not the tooth thickness alone. In addition, the same method of measurement should be used by the manufacturer and the inspector. If two different methods are used a disagreement is nearly assured. If different methods of measurement must be used, many (but not all) disagreements may be avoided if allowance is made for the effect of the probable errors in the parts. A measurement over two pins, for example, does not take into account the lead error, the tooth spacing error, the profile error or the runout. However, measurement with a parallel axis master gear measures the effect of all errors and, therefore, measures the effective tooth thickness directly. It is obvious that a different tooth thickness would be measured by the two methods. This model will make the required adjustments between the effective and measured tooth thickness for the following measuring methods: Parallel axis master gear A precision master gear is meshed with the part and the center distance provides the effective tooth thickness. This method measures all errors. However, minimum center distance is adjusted to account for the total composite error.
Transcript of Program 60-145—Involute Gear Tooth Thickness Introduction · PDF fileProgram...
Program 60-145—Involute Gear Tooth Thickness Introduction The measured and “effective” tooth thickness of involute gears and splines are usually different. Depending on the method used for the tooth thickness measurement the difference between the measured value and the apparent, or effective, thickness “seen” by the mating gear or spline may be enough to prevent satisfactory use of the part. Further problems arise when the supplier of the gear and the inspector use different methods to measure what appears to be the same thing, the tooth thickness. The effective tooth thickness is the maximum material envelope condition on the active surfaces of a gear or spline. This envelope is the “effective” gear tooth “seen” by the mating gear or spline and controls the backlash or spline fit. The inevitable departures from the theoretical tooth form of the manufactured part decreases the theoretical backlash in gear pairs and the theoretical clearance in splines. (In the case of interference fit splines the interference is increased.) Once the desired tooth thickness is established based on the backlash of a gear pair or the fit of a spline the method of measurement must be taken into account when the measured tooth thickness is specified on the manufacturing documents. The method of measurement should be specified along with the tooth thickness – not the tooth thickness alone. In addition, the same method of measurement should be used by the manufacturer and the inspector. If two different methods are used a disagreement is nearly assured. If different methods of measurement must be used, many (but not all) disagreements may be avoided if allowance is made for the effect of the probable errors in the parts. A measurement over two pins, for example, does not take into account the lead error, the tooth spacing error, the profile error or the runout. However, measurement with a parallel axis master gear measures the effect of all errors and, therefore, measures the effective tooth thickness directly. It is obvious that a different tooth thickness would be measured by the two methods. This model will make the required adjustments between the effective and measured tooth thickness for the following measuring methods: Parallel axis master gear
A precision master gear is meshed with the part and the center distance provides the effective tooth thickness. This method measures all errors. However, minimum center distance is adjusted to account for the total composite error.
UTS Integrated Gear Software
2
Span measurement
A measurement is taken over a block or span of teeth with a conventional vernier caliper or a disc micrometer. This method does not measure lead, profile or runout. Measurement over 2 or 3 pins
Two or three pins are placed in the tooth spaces and the distance over the pins is measured. This method does not measure lead, tooth spacing, profile or runout. Tooth calipers
A special caliper is set to measure the chordal tooth thickness at a set distance from the tip of the tooth. This method does not measure lead, tooth spacing, profile or runout. Crossed axis master gear
A precision master gear of different helix angle than the part is meshed with the part at the correct shaft crossed axis angle and the center distance provides the measured tooth thickness. This method does not measure lead error. However, minimum center distance is adjusted to account for the total composite error. The adjustments are based on the effect of errors allowed by the AGMA Quality Class specified. (Individual errors can be entered in the model, if desired, overriding the errors allowed by the quality class.) The difference between the effective and measured tooth thickness is the sum of the contribution of each error not measured by each method. A normal distribution of the errors is assumed and the root mean square sum is used giving a 95% assurance that the difference will not be underestimated. If the gear to be measured is to be used in a crossed axis gear set the lead is of no consequence since these gears have point instead of line contact. If this is the case enter 'c for “Crossed or parallel axis?” and the lead error will not be adjusted for. The model will adjust the test loads for the face width and modulus of elasticity of the test gear. A short table of modulus of elasticity for some common gear materials is included in the model.
60-145—Involute Gear Tooth Thickness
3
Examples If you have not used model 60-145 before you may wish to run through these examples. See the Integrated Gear Software Introduction for more information about the interface.
Example 1 This is a steel 10 tooth, 12 normal diametral pitch, 20 degree normal pressure angle, 18 degree left hand helical pinion for use in a parallel axis gear set. The required normal effective tooth thickness is 0.1420 inch/0.1390 inch. The gear is to be made to AGMA Class Q8 accuracy. We have on hand a Class 1A 55 tooth master gear with an 18 degree right hand helix for a parallel axis center distance measurement. We also have a Class 1A 77 tooth master with the same normal pitch but a 10 degree right hand helix. (When using master gears it is essential that the outside diameter, true involute form diameter and tooth thickness be checked to insure that the master is contacting from the form diameter to the outside diameter of the gear to be measured.) First, enter the data for the parallel axis master. Figure 1-1A is the completed data input form. Report 1-1 is the solved model.
UTS Integrated Gear Software
4
Fig. 1-1A
60-145—Involute Gear Tooth Thickness
5
Report 1-1
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Message PARALLEL
m2 AXIS
m3 GEAR
m4 _
Crossed or parallel axis? 'c or 'p=Def p
Number of teeth 10
Normal diametral pitch 12.000000 1/in `
Normal module 2.116667 mm `
Normal pressure angle 20.000000 deg
Helix angle 18.000000 deg
Hand:'L,'R,'Spur L
Face width 1.100 in
Modulus of Elasticity 30000000.0 psi
Transverse pitch 11.4127 1/in
Transverse module 2.2256 mm `
Transverse pressure angle 20.9419 deg
Reference pitch diameter 0.87622 in
Lead 8.47201 in
EFFECTIVE TOOTH THICKNESS
Max normal tooth thickness 0.14200 in
UTS Integrated Gear Software
6
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Min normal tooth thickness 0.13900 in
Max transverse tooth thickness 0.14931 in
Min transverse tooth thickness 0.14615 in
Base helix angle 16.8808 deg
Base diameter 0.81834 in
AGMA Quality Number 8
Message-Quality Number OK
Runout variation (TIR) 0.00170 in
Pitch (spacing) variation 0.00059 in
Profile variation 0.00072 in
Lead variation 0.00053 in
Tooth to Tooth Composite 0.00170 in
Total Composite 0.00350 in
PARALLEL AXIS MASTER GEAR (STEEL)
Master Gear Class & Code C1A
Max measuring load 350.0 ozf
Min measuring load 290.0 ozf
MASTER, number of teeth 55
Face width 1.0000 in
Reference Pitch Diameter 4.81920 in
Normal tooth thickness 0.13000 in
Transverse tooth thickness 0.13669 in
Lead 46.5960 in
Max master gear test center distance 2.86150 in
60-145—Involute Gear Tooth Thickness
7
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Min master gear test center distance 2.85399 in
Master gear test radius 2.40841 in
Deviation from "standard" radius -0.00120 in
Max gear test radius 0.45309 in
Min gear test radius 0.44558 in
Test radius range 0.00751 in
Work arbor diameter 0.43750 in
Master gear arbor diameter 0.50000 in
Gage block stack height: At max TT 2.39275 in
Max measured normal tooth thickness 0.14200 in
Min measured normal tooth thickness 0.13900 in
Eff-Measured normal tooth thickness 0.00000 in
Max measured trans tooth thickness 0.14931 in
Min measured trans tooth thickness 0.14615 in
Eff-Measured trans tooth thickness 0.00000 in
SPAN SIZE
Max measured normal tooth thickness 0.14062 in
Min measured normal tooth thickness 0.13762 in
Max measured trans tooth thickness 0.14786 in
Eff-Measured normal tooth thickness 0.00138 in
Min measured trans tooth thickness 0.14471 in
Eff-Measured trans tooth thickness 0.00145 in
UTS Integrated Gear Software
8
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
2 OR 3 PINS
Max measured normal tooth thickness 0.14051 in
Min measured normal tooth thickness 0.13751 in
Eff-Measured normal tooth thickness 0.00149 in
Max measured trans tooth thickness 0.14775 in
Min measured trans tooth thickness 0.14459 in
Eff-Measured trans tooth thickness 0.00156 in
TOOTH CALIPER
Max measured normal tooth thickness 0.14051 in
Min measured normal tooth thickness 0.13751 in
Eff-Measured normal tooth thickness 0.00149 in
Max measured trans tooth thickness 0.14775 in
Min measured trans tooth thickness 0.14459 in
Eff-Measured trans tooth thickness 0.00156 in
CROSSED AXIS MASTER GEAR (STEEL)
Max measured normal tooth thickness 0.14164 in
Min measured normal tooth thickness 0.13864 in
Eff-Measured normal tooth thickness 0.00036 in
Max measured trans tooth thickness 0.14893 in
Min measured trans tooth thickness 0.14578 in
Eff-Measured trans tooth thickness 0.00037 in The effective tooth is larger than the measured tooth by 0.00145 inch for the span measurement, 0.00156 inch for the over pins and tooth caliper measurements.
60-145—Involute Gear Tooth Thickness
9
There is no difference for the parallel axis master gear as this method measures the effective tooth thickness directly. Note that we have all the data required to make our measurement with the master gear. Next we will enter data for the crossed axis master. Save the parallel axis master analysis, reset the data entry form, enter the data as shown in Figure 1-1B, and save the analysis.
UTS Integrated Gear Software
10
Fig. 1-1B
We will now run a report comparing the parallel axis and crossed axis analyses. In the Open Analysis dialog, select the two analyses that you have just run and click the “Compare” button. The application will generate a comparative report such as shown in Report 1-2.
60-145—Involute Gear Tooth Thickness
11
Report 1-2
Model: Program 60-145 Unit System: US
Description Ex 1-1A Ex 1-1B Unit
Message PARALLEL PARALLEL m2 AXIS AXIS m3 GEAR GEAR m4 _ _ Crossed or parallel axis? 'c or 'p=Def p p Number of teeth 10 10 Normal diametral pitch 12.000000 12.000000 1/in ` Normal module 2.116667 2.116667 mm ` Normal pressure angle 20.000000 20.000000 deg Helix angle 18.000000 18.000000 deg Hand:'L,'R,'Spur L L Face width 1.100 1.100 in Modulus of Elasticity 30000000.0 30000000.0 psi Transverse pitch 11.4127 11.4127 1/in Transverse module 2.2256 2.2256 mm ` Transverse pressure angle 20.9419 20.9419 deg Reference pitch diameter 0.87622 0.87622 in Lead 8.47201 8.47201 in
EFFECTIVE TOOTH THICKNESS Max normal tooth thickness 0.14200 0.14200 in Min normal tooth thickness 0.13900 0.13900 in Max transverse tooth thickness 0.14931 0.14931 in Min transverse tooth thickness 0.14615 0.14615 in
UTS Integrated Gear Software
12
Model: Program 60-145 Unit System: US
Description Ex 1-1A Ex 1-1B Unit Base helix angle 16.8808 16.8808 deg Base diameter 0.81834 0.81834 in
AGMA Quality Number 8 8 Message-Quality Number OK OK Runout variation (TIR) 0.00170 0.00170 in Pitch (spacing) variation 0.00059 0.00059 in Profile variation 0.00072 0.00072 in Lead variation 0.00053 0.00053 in Tooth to Tooth Composite 0.00170 0.00170 in Total Composite 0.00350 0.00350 in
PARALLEL AXIS MASTER GEAR (STEEL) Master Gear Class & Code C1A Max measuring load 350.0 ozf Min measuring load 290.0 ozf MASTER, number of teeth 55 Face width 1.0000 in Reference Pitch Diameter 4.81920 in Normal tooth thickness 0.13000 in Transverse tooth thickness 0.13669 in Lead 46.5960 in Max master gear test center distance 2.86150 in Min master gear test center distance 2.85399 in Master gear test radius 2.40841 in Deviation from "standard" radius -0.00120 in Max gear test radius 0.45309 in Min gear test radius 0.44558 in Test radius range 0.00751 in
60-145—Involute Gear Tooth Thickness
13
Model: Program 60-145 Unit System: US
Description Ex 1-1A Ex 1-1B Unit Work arbor diameter 0.43750 in Master gear arbor diameter 0.50000 in Gage block stack height: At max TT 2.39275 in Max measured normal tooth thickness 0.14200 0.14200 in Min measured normal tooth thickness 0.13900 0.13900 in Eff-Measured normal tooth thickness 0.00000 0.00000 in Max measured trans tooth thickness 0.14931 0.14931 in Min measured trans tooth thickness 0.14615 0.14615 in Eff-Measured trans tooth thickness 0.00000 0.00000 in
SPAN SIZE
Max measured normal tooth thickness 0.14062 0.14062 in Min measured normal tooth thickness 0.13762 0.13762 in Max measured trans tooth thickness 0.14786 0.14786 in
Eff-Measured normal tooth thickness 0.00138 0.00138 in Min measured trans tooth thickness 0.14471 0.14471 in Eff-Measured trans tooth thickness 0.00145 0.00145 in
2 OR 3 PINS
Max measured normal tooth thickness 0.14051 0.14051 in Min measured normal tooth thickness 0.13751 0.13751 in Eff-Measured normal tooth thickness 0.00149 0.00149 in Max measured trans tooth thickness 0.14775 0.14775 in Min measured trans tooth thickness 0.14459 0.14459 in Eff-Measured trans tooth thickness 0.00156 0.00156 in
TOOTH CALIPER
Max measured normal tooth thickness 0.14051 0.14051 in Min measured normal tooth thickness 0.13751 0.13751 in
UTS Integrated Gear Software
14
Model: Program 60-145 Unit System: US
Description Ex 1-1A Ex 1-1B Unit Eff-Measured normal tooth thickness 0.00149 0.00149 in Max measured trans tooth thickness 0.14775 0.14775 in Min measured trans tooth thickness 0.14459 0.14459 in Eff-Measured trans tooth thickness 0.00156 0.00156 in
CROSSED AXIS MASTER GEAR (STEEL) Master Gear Class & Code C1A Max measuring load 7.0 ozf Min measuring load 5.8 ozf MASTER, number of teeth 77 Transverse pitch 11.8177 Transverse pressure angle 20.2836 deg Helix angle 10.0000 deg Hand:'L,'R,'Spur R Reference pitch diameter 6.51565 in Normal tooth thickness 0.13000 in Transverse tooth thickness 0.13201 in Lead 116.0885 in Base helix angle 9.3913 deg Base diameter 6.11161 in Average test cross-axis angle 8.0251 deg Cross-axis angle at max TT 8.0296 deg Cross-axis angle at min TT 8.0206 deg Max master gear test center distance 3.70929 in Min master gear test center distance 3.70175 in Master gear test radius 3.25662 in Deivation from "standard" radius -0.00120 in Max gear test radius 0.45266 in
60-145—Involute Gear Tooth Thickness
15
Model: Program 60-145 Unit System: US
Description Ex 1-1A Ex 1-1B Unit Min gear test radius 0.44513 in Test radius range 0.00753 in Work arbor diameter 0.43750 in Master gear arbor diameter 0.50000 in Gage block stack height - max TT 3.24054 in Max measured normal tooth thickness 0.14164 0.14164 in Min measured normal tooth thickness 0.13864 0.13864 in Eff-Measured normal tooth thickness 0.00036 0.00036 in Max measured trans tooth thickness 0.14893 0.14893 in Min measured trans tooth thickness 0.14578 0.14578 in Eff-Measured trans tooth thickness 0.00037 0.00037 in
UTS Integrated Gear Software
16
Example 2
The second example is a 15 tooth, 12/24 pitch, 30 degree pressure angle straight spline made to AGMA Class Q10 tolerances. We will assume that the internal spline will be mounted and supported by the external spline so that the runout will not be a factor in the fit. The production run is not large so the tooth thickness will be measured over two pins instead of with go and no-go gages.
We will work in the Power User form. Figures 2-1A and 2-1B show the data entries; Report 2-1 is the solved model for this measurement, but with the runout included.
Fig. 2-1A
Fig. 2-1B
60-145—Involute Gear Tooth Thickness
17
Report 2-1
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Message PARALLEL
m2 AXIS
m3 GEAR
m4
Crossed or parallel axis? 'c or 'p=Def p
Number of teeth 15
Normal diametral pitch 12.000000 1/in `
Normal module 2.116667 mm `
Normal pressure angle 30.000000 deg
Helix angle 0.000000 deg
Hand:'L,'R,'Spur Spur
Face width 1.500 in
Modulus of Elasticity 30000000.0 psi
Transverse pitch 12.0000 1/in
Transverse module 2.1167 mm `
Transverse pressure angle 30.0000 deg
Reference pitch diameter 1.25000 in
Lead in
UTS Integrated Gear Software
18
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
EFFECTIVE TOOTH THICKNESS
Max normal tooth thickness 0.12990 in
Min normal tooth thickness in
Max transverse tooth thickness 0.12990 in
Min transverse tooth thickness in
Base helix angle 0.0000 deg
Base diameter 1.08253 in
AGMA Quality Number 10
Message-Quality Number OK
Runout variation (TIR) 0.00094 in
Pitch (spacing) variation 0.00031 in
Profile variation 0.00039 in
Lead variation 0.00044 in
Tooth to Tooth Composite 0.00080 in
Total Composite 0.00180 in Now enter zero for the runout and solve again. The data input is shown in Figure 2-2, the solved model in Report 2-2.
60-145—Involute Gear Tooth Thickness
19
Fig. 2-2
Report 2-2
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Message PARALLEL
m2 AXIS
m3 GEAR
m4
Crossed or parallel axis? 'c or 'p=Def p
Number of teeth 15
UTS Integrated Gear Software
20
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Normal diametral pitch 12.000000 1/in `
Normal module 2.116667 mm `
Normal pressure angle 30.000000 deg
Helix angle 0.000000 deg
Hand:'L,'R,'Spur Spur
Face width 1.500 in
Modulus of Elasticity 30000000.0 psi
Transverse pitch 12.0000 1/in
Transverse module 2.1167 mm `
Transverse pressure angle 30.0000 deg
Reference pitch diameter 1.25000 in
Lead in
EFFECTIVE TOOTH THICKNESS
Max normal tooth thickness 0.12990 in
Min normal tooth thickness in
Max transverse tooth thickness 0.12990 in
Min transverse tooth thickness in
Base helix angle 0.0000 deg
Base diameter 1.08253 in
AGMA Quality Number 10
Message-Quality Number OK
Runout variation (TIR) 0.00000 in
Pitch (spacing) variation 0.00031 in
60-145—Involute Gear Tooth Thickness
21
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Profile variation 0.00039 in
Lead variation 0.00044 in
Tooth to Tooth Composite 0.00080 in
Total Composite 0.00180 in
PARALLEL AXIS MASTER GEAR (STEEL)
Master Gear Class & Code
Max measuring load ozf
Min measuring load ozf
MASTER, number of teeth
Face width in
Reference Pitch Diameter in
Normal tooth thickness in
Transverse tooth thickness in
Lead in
Max master gear test center distance in
Min master gear test center distance in
Master gear test radius in
Deviation from "standard" radius in
Max gear test radius in
Min gear test radius in
Test radius range in
Work arbor diameter in
Master gear arbor diameter in
UTS Integrated Gear Software
22
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Gage block stack height: At max TT in
Max measured normal tooth thickness 0.12990 in
Min measured normal tooth thickness in
Eff-Measured normal tooth thickness 0.00000 in
Max measured trans tooth thickness 0.12990 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00000 in
SPAN SIZE
Max measured normal tooth thickness 0.12948 in
Min measured normal tooth thickness in
Max measured trans tooth thickness 0.12948 in
Eff-Measured normal tooth thickness 0.00042 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00042 in
2 OR 3 PINS
Max measured normal tooth thickness 0.12938 in
Min measured normal tooth thickness in
Eff-Measured normal tooth thickness 0.00052 in
Max measured trans tooth thickness 0.12938 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00052 in
TOOTH CALIPER
Max measured normal tooth thickness 0.12938 in
60-145—Involute Gear Tooth Thickness
23
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Min measured normal tooth thickness in
Eff-Measured normal tooth thickness 0.00052 in
Max measured trans tooth thickness 0.12938 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00052 in The measured tooth thickness using pins should be 0.12938 inch for an effective tooth thickness of 0.1299 inch. Other UTS TK Solver models are available for use in measurement calculations for all the methods used in this model.
UTS Integrated Gear Software
24
Example 3 In this example, we have a 27 tooth, 5 normal DP, 25 degree pressure angle steel spur gear with an unknown tooth thickness and we wish to use a 30 tooth master gear with a helix angle of 15 degrees to find the tooth thickness. Again, we will work directly in the TK Solver Variable Sheet. Sheet 3 is this sheet with the known data entered. In order to solve “backward” to obtain the tooth thickness from the center distance, it is necessary to make a guess for the tooth thickness, because the equations cannot be solved in the required order directly. (See the TK Solver documentation for information about guess values.) Sheet 3
60-145 (Ver 6.0)EFFECTIVE AND MEASURED INVOLUTE GEARTOOTH THICKNESS
USE 'TOOLS', 'RUN' TO START WIZARDm1 Messagem2m3m4
'p axis Crossed or parallel axis? 'c or 'p=Def27 n Number of teeth10 pn 1/in Normal diametral pitch
n_mod mm ` Normal module25 npa deg Normal pressure angle0 ha deg Helix angle
hand Hand:'L,'R,'Spur (Crossed-axis master)1.2 face in Face width
E psi Modulus of Elasticity (Def=Steel)pt 1/in Transverse pitcht_mod mm ` Transverse moduletpa deg Transverse pressure anglepd in Reference pitch diameterlead in Lead
Effective Tooth Thickness:G .15710 nttx in Max normal tooth thickness
ntti in Min normal tooth thicknesstttx in Max transverse tooth thicknessttti in Min transverse tooth thicknessbha deg Base helix angledb in Base diameter
9 Q AGMA Quality Numberm Message-Quality Number
(Input data may override ANSI/AGMA)Runout in Runout variation (TIR)Pitch in Pitch (spacing) variationProfile in Profile variationLead in Lead variation
(Composite data is std ANSI/AGMA)
60-145—Involute Gear Tooth Thickness
25
TtoTC in Tooth to Tooth CompositeTotC in Total Composite
TOOTH THICKNESS MEASUREMENT:
PARALLEL AXIS MASTER GEAR (Steel)MC Master Gear Class & Codemlx ozf Max measuring loadmli ozf Min measuring loadn_pm MASTER, number of teethface_pm in Face widthpd_pm in Reference Pitch Diameterntt_pm in Normal tooth thicknessttt_pm in Transverse tooth thicknesslead_pm in Leadcd_pmx in Max master gear test center distancecd_pmi in Min master gear test center distanceRrm_pm in Master gear test radiusdRrm_pm in Deviation from “standard” radiusRrw_pmx in Max gear test radiusRrw_pmi in Min gear test radiusRrw_pmr in Test radius rangeDraw_pm in Work arbor diameterDram_pm in Master gear arbor diameterLg_pm in Gage block stack height: At max TTnmeffpx in Max measured normal tooth thicknessnmeffpi in Min measured normal tooth thicknessdnp in Eff-Measured normal tooth thicknesstmeffpx in Max measured trans tooth thicknesstmeffpi in Min measured trans tooth thicknessdtp in Eff-Measured trans tooth thickness
SPAN SIZEnactsx in Max measured normal tooth thicknessnactsi in Min measured normal tooth thicknesstactsx in Max measured trans tooth thicknessdns in Eff-Measured normal tooth thicknesstactsi in Min measured trans tooth thicknessdts in Eff-Measured trans tooth thickness
2 OR 3 PINSnact2x in Max measured normal tooth thicknessnact2i in Min measured normal tooth thicknessdn2 in Eff-Measured normal tooth thicknesstact2x in Max measured trans tooth thicknesstact2i in Min measured trans tooth thicknessdt2 in Eff-Measured trans tooth thickness
TOOTH CALIPERnactcx in Max measured normal tooth thicknessnactci in Min measured normal tooth thicknessdnc in Eff-Measured normal tooth thicknesstactcx in Max measured trans tooth thicknesstactci in Min measured trans tooth thicknessdtc in Eff-Measured trans tooth thickness
CROSSED AXIS MASTER GEAR (Steel)MCx Master Gear Class & Codemlx_x ozf Max measuring loadmli_x ozf Min measuring load
30 n_xm MASTER, number of teethpt_xm Transverse pitchtpa_xm deg Transverse pressure angle
15 ha_xm deg Helix angle
UTS Integrated Gear Software
26
'L hand_xm Hand:'L,'R,'Spurpd_xm in Reference pitch diameterntt_xm in Normal tooth thicknessttt_xm in Transverse tooth thicknesslead_xm in Leadbha_xm deg Base helix angledb_xm in Base diameterxaxis deg Average test cross-axis anglexaxisx deg Cross-axis angle at max TTxaxisi deg Cross-axis angle at min TT
2.90650 cd_xmx in Max master gear test center distancecd_xmi in Min master gear test center distance
1.55290 Rrm_xm in Master gear test radiusdRrm_xm in Deivation from “standard” radiusRrw_xmx in Max gear test radiusRrw_xmi in Min gear test radiusRrw_xmr in Test radius rangeDraw_xm in Work arbor diameterDram_xm in Master gear arbor diameterLg_xm in Gage block stack height - max TTnactxx in Max measured normal tooth thicknessnactxi in Min measured normal tooth thicknessdnx in Eff-Measured normal tooth thicknesstactxx in Max measured trans tooth thicknesstactxi in Min measured trans tooth thicknessdtx in Eff-Measured trans tooth thickness
Report 3 shows the solved model.
60-145—Involute Gear Tooth Thickness
27
Report 3
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Message PARALLEL
m2 AXIS
m3 GEAR
m4
Crossed or parallel axis? 'c or 'p=Def p
Number of teeth 27
Normal diametral pitch 10.000000 1/in `
Normal module 2.540000 mm `
Normal pressure angle 25.000000 deg
Helix angle 0.000000 deg
Hand:'L,'R,'Spur Spur
Face width 1.200 in
Modulus of Elasticity 30000000.0 psi
Transverse pitch 10.0000 1/in
Transverse module 2.5400 mm `
Transverse pressure angle 25.0000 deg
Reference pitch diameter 2.70000 in
Lead in
EFFECTIVE TOOTH THICKNESS
Max normal tooth thickness 0.16077 in
UTS Integrated Gear Software
28
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Min normal tooth thickness in
Max transverse tooth thickness 0.16077 in
Min transverse tooth thickness in
Base helix angle 0.0000 deg
Base diameter 2.44703 in
AGMA Quality Number 9
Message-Quality Number OK
Runout variation (TIR) 0.00170 in
Pitch (spacing) variation 0.00053 in
Profile variation 0.00066 in
Lead variation 0.00046 in
Tooth to Tooth Composite 0.00110 in
Total Composite 0.00280 in
PARALLEL AXIS MASTER GEAR (STEEL)
Master Gear Class & Code
Max measuring load ozf
Min measuring load ozf
MASTER, number of teeth
Face width in
Reference Pitch Diameter in
Normal tooth thickness in
Transverse tooth thickness in
Lead in
60-145—Involute Gear Tooth Thickness
29
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
Max master gear test center distance in
Min master gear test center distance in
Master gear test radius in
Deviation from "standard" radius in
Max gear test radius in
Min gear test radius in
Test radius range in
Work arbor diameter in
Master gear arbor diameter in
Gage block stack height: At max TT in
Max measured normal tooth thickness 0.16077 in
Min measured normal tooth thickness in
Eff-Measured normal tooth thickness 0.00000 in
Max measured trans tooth thickness 0.16077 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00000 in
SPAN SIZE
Max measured normal tooth thickness 0.15909 in
Min measured normal tooth thickness in
Max measured trans tooth thickness 0.15909 in
Eff-Measured normal tooth thickness 0.00168 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00168 in
UTS Integrated Gear Software
30
Model Title : Program 60-145 Unit System: US Description Value Unit Comment
2 OR 3 PINS
Max measured normal tooth thickness 0.15901 in
Min measured normal tooth thickness in
Eff-Measured normal tooth thickness 0.00177 in
Max measured trans tooth thickness 0.15901 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00177 in
TOOTH CALIPER
Max measured normal tooth thickness 0.15901 in
Min measured normal tooth thickness in
Eff-Measured normal tooth thickness 0.00177 in
Max measured trans tooth thickness 0.15901 in
Min measured trans tooth thickness in
Eff-Measured trans tooth thickness 0.00177 in
CROSSED AXIS MASTER GEAR (STEEL)
Master Gear Class & Code
Max measuring load 7.0 ozf
Min measuring load 5.8 ozf
MASTER, number of teeth 30
Transverse pitch 9.6593
Transverse pressure angle 25.7693 deg
Helix angle 15.0000 deg Hand:'L,'R,'Spur L
60-145—Involute Gear Tooth Thickness
31
Model Title : Program 60-145 Unit System: US Description Value Unit Comment Reference pitch diameter 3.10583 in Normal tooth thickness 0.15707 in Transverse tooth thickness 0.16261 in Lead 36.4145 in Base helix angle 13.5663 deg Base diameter 2.79696 in Average test cross-axis angle deg Cross-axis angle at max TT 15.0183 deg Cross-axis angle at min TT deg Max master gear test center distance 2.90650 in Min master gear test center distance in Master gear test radius 1.55290 in Deivation from "standard" radius -0.00001 in Max gear test radius 1.35360 in Min gear test radius in Test radius range in Work arbor diameter in Master gear arbor diameter in Gage block stack height - max TT in Max measured normal tooth thickness 0.16045 in Min measured normal tooth thickness in Eff-Measured normal tooth thickness 0.00033 in Max measured trans tooth thickness 0.16045 in Min measured trans tooth thickness in Eff-Measured trans tooth thickness 0.00033 in
UTS Integrated Gear Software
32
The effective tooth thickness at this center distance with the master gear is 0.16077 inch. The measured tooth thickness is 0.16045 inch. The difference is 0.00033 inch from the lack of a crossed axis master to measure the lead error. References:
1. Data Extracted from ANSI/AGMA 2000-A88 Gear Classification and Inspection Handbook, with the permission of the publisher, American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, VA 22314
2. Data Extracted from ANSI/AGMA 2002-B88 Tooth Thickness Specification and
Measurement, with the permission of the publisher, American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, VA 22314
3. “The Interrelationship of Tooth Thickness Measurements as Evaluated by
Various Measuring Techniques” by Paul M. Dean, Jr., Consultant, Schenectady, NY in Gear Technology Magazine, Randall Publishing Co., Inc. Vol. 4, No. 5, Sep/Oct 1987
