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
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.
2
60-145—Involute Gear Tooth Thickness
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.
3
UTS Integrated Gear Software
Fig. 1-1A
4
60-145—Involute Gear Tooth Thickness
Report 1-1
Model Title :
Program 60-145
Unit System:
US
Description
Value
Message
Unit
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
5
Comment
UTS Integrated Gear Software
Model Title :
Program 60-145
Unit System:
US
Description
Value
Unit
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
6
Comment
60-145—Involute Gear Tooth Thickness
Model Title :
Program 60-145
Unit System:
US
Description
Value
Unit
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
7
Comment
UTS Integrated Gear Software
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.
8
60-145—Involute Gear Tooth Thickness 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.
9
UTS Integrated Gear Software
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.
10
60-145—Involute Gear Tooth Thickness
Report 1-2
Model:
Program 60-145
Unit System: US Description
Ex 1-1A
Message
Ex 1-1B
PARALLEL
PARALLEL
m2
AXIS
AXIS
m3
GEAR
GEAR
m4
_
_
Crossed or parallel axis? 'c or 'p=Def Number of teeth Normal diametral pitch Normal module
p
p
10
10
Unit
12.000000
12.000000 1/in `
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
Face width
1.100
Modulus of Elasticity
30000000.0
Transverse pitch
11.4127
Transverse module
2.2256
L 1.100 in 30000000.0 psi 11.4127 1/in 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
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
EFFECTIVE TOOTH THICKNESS
11
UTS Integrated Gear Software
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 Message-Quality Number
8
8
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
-0.00120
in
Max gear test radius
0.45309
in
Min gear test radius
0.44558
in
Test radius range
0.00751
in
Deviation from "standard" radius
12
60-145—Involute Gear Tooth Thickness
Model:
Program 60-145
Unit System: US Description
Ex 1-1A
Work arbor diameter
0.43750
Ex 1-1B
Unit 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
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
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
Max measured normal tooth thickness
0.14051
0.14051 in
Min measured normal tooth thickness
0.13751
0.13751 in
SPAN SIZE
2 OR 3 PINS
TOOTH CALIPER
13
UTS Integrated Gear Software
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
14
60-145—Involute Gear Tooth Thickness
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
15
UTS Integrated Gear Software
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
16
60-145—Involute Gear Tooth Thickness
Report 2-1
Model Title :
Program 60-145
Unit System:
US
Description
Value
Message
Unit
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
17
Comment
UTS Integrated Gear Software
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 22, the solved model in Report 2-2.
18
60-145—Involute Gear Tooth Thickness
Fig. 2-2
Report 2-2
Model Title :
Program 60-145
Unit System:
US
Description
Value
Message
Unit
PARALLEL
m2
AXIS
m3
GEAR
m4 Crossed or parallel axis? 'c or 'p=Def
p
Number of teeth
15
19
Comment
UTS Integrated Gear Software
Model Title :
Program 60-145
Unit System:
US
Description
Value
Normal diametral pitch
Unit
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
20
Comment
60-145—Involute Gear Tooth Thickness
Model Title :
Program 60-145
Unit System:
US
Description
Value
Unit
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
21
Comment
UTS Integrated Gear Software
Model Title :
Program 60-145
Unit System:
US
Description
Value
Gage block stack height: At max TT
Unit 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
22
Comment
60-145—Involute Gear Tooth Thickness
Model Title :
Program 60-145
Unit System:
US
Description
Value
Min measured normal tooth thickness
Unit
Comment
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.
23
UTS Integrated Gear Software
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 GEAR TOOTH THICKNESS USE 'TOOLS', 'RUN' TO START WIZARD Message
m1 m2 m3 m4 'p 27 10 25 0 1.2
G .15710
9
axis n pn n_mod npa ha hand face E pt t_mod tpa pd lead nttx ntti tttx ttti bha db
1/in mm ` deg deg in psi 1/in mm ` deg in in in in in in deg in
Q m Runout Pitch Profile Lead
in in in in
Crossed or parallel axis? 'c or 'p=Def Number of teeth Normal diametral pitch Normal module Normal pressure angle Helix angle Hand:'L,'R,'Spur (Crossed-axis master) Face width Modulus of Elasticity (Def=Steel) Transverse pitch Transverse module Transverse pressure angle Reference pitch diameter Lead Effective Tooth Thickness: Max normal tooth thickness Min normal tooth thickness Max transverse tooth thickness Min transverse tooth thickness Base helix angle Base diameter AGMA Quality Number Message-Quality Number (Input data may override ANSI/AGMA) Runout variation (TIR) Pitch (spacing) variation Profile variation Lead variation (Composite data is std ANSI/AGMA)
24
60-145—Involute Gear Tooth Thickness
TtoTC TotC
in in
Tooth to Tooth Composite Total Composite TOOTH THICKNESS MEASUREMENT:
in in in in in in in in in in in in in in in in in in in in in
PARALLEL AXIS MASTER GEAR (Steel) Master Gear Class & Code Max measuring load Min measuring load MASTER, number of teeth Face width Reference Pitch Diameter Normal tooth thickness Transverse tooth thickness Lead Max master gear test center distance Min master gear test center distance Master gear test radius Deviation from “standard” radius Max gear test radius Min gear test radius Test radius range Work arbor diameter Master gear arbor diameter Gage block stack height: At max TT Max measured normal tooth thickness Min measured normal tooth thickness Eff-Measured normal tooth thickness Max measured trans tooth thickness Min measured trans tooth thickness Eff-Measured trans tooth thickness
nactsx nactsi tactsx dns tactsi dts
in in in in in in
SPAN SIZE Max measured Min measured Max measured Eff-Measured Min measured Eff-Measured
normal tooth thickness normal tooth thickness trans tooth thickness normal tooth thickness trans tooth thickness trans tooth thickness
nact2x nact2i dn2 tact2x tact2i dt2
in in in in in in
2 OR 3 PINS Max measured Min measured Eff-Measured Max measured Min measured Eff-Measured
normal tooth thickness normal tooth thickness normal tooth thickness trans tooth thickness trans tooth thickness trans tooth thickness
nactcx nactci dnc tactcx tactci dtc
in in in in in in
TOOTH CALIPER Max measured Min measured Eff-Measured Max measured Min measured Eff-Measured
normal tooth thickness normal tooth thickness normal tooth thickness trans tooth thickness trans tooth thickness trans tooth thickness
MC mlx mli n_pm face_pm pd_pm ntt_pm ttt_pm lead_pm cd_pmx cd_pmi Rrm_pm dRrm_pm Rrw_pmx Rrw_pmi Rrw_pmr Draw_pm Dram_pm Lg_pm nmeffpx nmeffpi dnp tmeffpx tmeffpi dtp
30 15
MCx mlx_x mli_x n_xm pt_xm tpa_xm ha_xm
ozf ozf
ozf ozf deg deg
CROSSED AXIS MASTER GEAR (Steel) Master Gear Class & Code Max measuring load Min measuring load MASTER, number of teeth Transverse pitch Transverse pressure angle Helix angle
25
UTS Integrated Gear Software
'L
2.90650 1.55290
hand_xm pd_xm ntt_xm ttt_xm lead_xm bha_xm db_xm xaxis xaxisx xaxisi cd_xmx cd_xmi Rrm_xm dRrm_xm Rrw_xmx Rrw_xmi Rrw_xmr Draw_xm Dram_xm Lg_xm nactxx nactxi dnx tactxx tactxi dtx
Hand:'L,'R,'Spur Reference pitch diameter Normal tooth thickness Transverse tooth thickness Lead Base helix angle Base diameter Average test cross-axis angle Cross-axis angle at max TT Cross-axis angle at min TT Max master gear test center distance Min master gear test center distance Master gear test radius Deivation from “standard” radius Max gear test radius Min gear test radius Test radius range Work arbor diameter Master gear arbor diameter Gage block stack height - max TT Max measured normal tooth thickness Min measured normal tooth thickness Eff-Measured normal tooth thickness Max measured trans tooth thickness Min measured trans tooth thickness Eff-Measured trans tooth thickness
in in in in deg in deg deg deg in in in in in in in in in in in in in in in in
Report 3 shows the solved model.
26
60-145—Involute Gear Tooth Thickness
Report 3
Model Title :
Program 60-145
Unit System:
US
Description
Value
Message
Unit
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
27
Comment
UTS Integrated Gear Software
Model Title :
Program 60-145
Unit System:
US
Description
Value
Unit
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
28
Comment
60-145—Involute Gear Tooth Thickness
Model Title :
Program 60-145
Unit System:
US
Description
Value
Unit
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
29
Comment
UTS Integrated Gear Software
Model Title :
Program 60-145
Unit System:
US
Description
Value
Unit
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
30
Comment
60-145—Involute Gear Tooth Thickness
Model Title :
Program 60-145
Unit System:
US
Description
Value
Unit
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
31
Comment
UTS Integrated Gear Software 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
32
