# GEOM

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```					                                                                           geometry

geom - READ THE HELP SHEET FIRST - do not overwrite any black figures, they contain formulae
1 refers to pinion, 2 to wheel    All dims in mm                    3.141592654
Feature                             Cell name         input / calc comments                  issue feb2002
calculated
angles in this
INPUT REQUIRED IN RED                                col in radians

pinion teeth z1                                    pin             25                      ratio u
wheel teeth z2                                    whl              93                      3.720
normal module                                     mn               5
normal pressure angle (deg)                      npa               20
helix angle (deg)                                  ha              15    0 for spur gears
normal pressure angle (rad)                      npar         0.34906585                involute pa=  0.014904384
helix angle (rad)                                 har        0.261799388                 noml ctrs =  305.4064732
from the info given, the centre distance should be approx.        305    check - see note on help sheet
design centre distance                              a             308                              Y= 0.518705356
Facewidth b ( least of pin or wheel)                b             100    see note on "design tips" sheet
inspection pin/ball dia                          pind              6
trans pressure angle                              pat        0.360356324  20.64689649 deg
involute pat                                      ipat        0.01645339
pinion ref dia (pcd1)                             rd1           129.410
wheel ref dia (pcd2)                              rd2           481.403
pinion working dia                               pwd            130.508
whl working dia                                  wwd            485.492
base circle dia.1                                bcd1           121.098
base circle dia.2                                bcd2           450.483

trans working pressure angle                    patw         0.382078854   21.89150578 deg
involute patw                                  ipatw         0.019746369
normal circular pitch                            pn             15.708
trans circ pitch                                  pt            16.262
trans base pitch                                 pbt            15.218
sum of add mod coefficients (sum x)            sumx              0.534

Page 1
geometry

equality of
coefficient for pinion                          general   strength factors increasers
0.3568         0.4787               0.1131
see note on "design tips" sheet
addendum mod coefficient (x1)                   admod1          0.35       input from one of three above (or own figure)
topping 1 (per side)                              top1         0.0735      amount removed from outside diameter 1
topping 2 (per side)                              top2         0.075       amount removed from outside diameter 2
nominal cutter tooth depth ratio( 2.25 Mn )         td          2.25       input as ratio of module, e.g. 2.25, 2.4 etc.
actual cutter tip radius (0.25-0.39Mn)              tr           1.5
cutter depth from ref circle1 to start of rad      sr1         3.513       pinion
cutter depth from ref circle2 to start of rad      sr2         4.344       wheel
Backlash min                                     0.200         0.220       change from no. in cell B44 if required
Backlash max                                     0.300         0.300       change from no. in cell B45 if required
ctrs 1 to working pitch line                       wp      65.25423729       4.062506227 10.110132          61.19173106
ctrs 2 to working pitch line                      wp2      242.7457627       6.388102395 15.897714          236.3576603
Lowest point of involute 1 due to cutter
tip rad                                                    124.0426173 ensure this is lower than the Lowest Point of Contact 1
Lowest point of involute 2 due to cutter
tip rad                                                    473.7834142 ensure this is lower than the Lowest Point of Contact 2
Lowest point of contact 1                        lpc1      124.5607099
Lowest point of contact 2                        lpc2      476.1012607
MANUFACTURING DETAILS

tip dia 1                                         td1         142.763  nominal o/d - topping
tip dia 2                                         td2         493.091
root dia 1                                        rt1         120.410  based on cutter depth ratio input in line 40
root dia 2                                        rt2         470.741  based on cutter depth ratio input in line 40
thk n @ rd 1                                      sn1          9.128
thk n @ rd 2                                      sn2          8.523
base helix angle                                 bha       0.245674211  14.07609542 deg

Page 2
geometry

Axial pitch                                    px           60.691

Overlap ratio                                                 1.648   see note on "design tips" sheet
Length of line base to base                    g            114.838
base circle to tip 1                           g1            37.804
base circle to tip 2                           g2           100.254
Length of line of action - trans plane         ga            23.220
Length of line of approach               pinion driving       9.747
Length of line of recession              pinion driving      13.474
Trans contact ratio                                           1.526   see note on "design tips" sheet
bcd1 to tip2                                                 14.584
bcd2 to tip1                                              77.03415707
bcd1 to hpstc1                                               29.801
bcd2 to hpstc2                                            92.25174405
HPSTC1                                                    134.9706527
HPSTC2                                                    486.8027343

tip PA 1                                     tpa1         0.558132176   31.97861807          inv   0.066218398
tip PA 2                                     tpa2         0.418768875   23.99368915          inv   0.026327837
approx tip thickness 1-normal                             3.207233488
approx tip thickness 2 - normal                           4.026773595

Sliding
uap                                           uap           0.55813
uaw                                          uaw            0.41877
up                                             up           0.45222
uw                                            uw            0.45887
Specific sliding at pinion tip contact       Vs/Vr          0.82555
Specific sliding at wheel tip contact        Vs/Vr          0.84798

INSPECTION DETAILS

Page 3
geometry

calcs for n1                       nt,nb     0.025241465    1.065487033 7.9577472
calcs for n2                     nt2,nb2     0.025241465    1.065487033 29.602819
no of teeth spanned 1                4             4       change no. if required
no of teeth spanned 2               13             12      change no. if required
calcs for bts 1                   btt,btt1   11.40690904        0.2394141
calcs for bts 2                  btt2,btt3   37.65848078     0.125723675
base tan span 1 nominal                          54.792    take off half the backlash =     54.682      to   54.642
base tan span 2 nominal                         177.566    take off half the backlash =     177.456     to   177.416

value of target cell       by changing
calc for pin dim 1                           0.014893236 0.035325355        0.4594966 use "solver" to
calc for pin dim 2                            0.01473306 0.020225853        0.3850233 find these
FOR EVEN TEETH
pin dim 1, nomina l- max - min   141.112       140.800        140.687
pin dim 2, nomina l- max - min   492.069       491.757        491.643      note! Delete these two
sets before "solving"
FOR ODD TEETH                                                              I.e. leave blank before
pin dim 1, nomina l- max - min   140.845       140.534        140.420      calculating
pin dim 2, nomina l- max - min   491.999       491.687        491.574

Multiply these
Tangential tooth load factor        ft       15.45481322 factors by the
PINION
torque (nm) to
Seperating force factor             sp       5.823523748 obtain tooth
Thrust (Axial) force factor        axl       4.141104722 newtons

Page 4
help

http://uk.geocities.com/mikebull2001/index.html
1     1 refers to pinion, 2 to wheel

2      before calculating, ensure you remove previous results from cells E111 & E112

3      the required input are those cells highlighted in red

********** DO NOT OVERWRITE ANY OF THE FIGURES IN BLACK AS THE CELLS MAY CONTAIN FORMULAE                                    ********

4      after inputting teeth, mod & HA, check that the calculated centres are within 1 module of your required
centre distance, otherwise change HA or tooth combination

5      the nominal tooth depth is based on the cutter. Input this figure as a % of the module. E.g. 2.25 for as cut teeth,
2.4 for ground teeth ( leaving 0.15Mn grinding wheel clearance), etc.

6      backlash is calculated, it may be changed to suit - check blue figures before continuing

7      the number of teeth spanned for the base tangent span measurement can be changed to suit
- check blue figures before continuing

8      for spur gears, pins or balls may be used to measure tooth size. Use the excel solver tool to calculate these
click on Tools - Solver - then set target cell to D111, equal to the value of the number in cell C111
"by changing cell" E111. For the wheel use cells D112, C112 & E112 respectively

Page 5
THESE ARE GENERAL TIPS ONLY - ALL RULES CAN BE BROKEN IF THE DESIGN IS THOROUGHLY THOUGHT OUT

min tooth numbers - depending on the pressure angle, 13 for helicals 15 for spurs to avoid weak teeth & cutter undercut.
Positive add mod can help increase strength - check for contact ratio and cutter interference

helix angle - select an angle to give axial overlap, but too much means an increase in axial load (8-15 deg is common)

Addendum modification coefficient x - positive x will increase the strength of a tooth. It is usual to have
+x on pinions and -x on wheels ( opposite for speed increasers ) The max on a tooth
should be around 0.4

facewidth - the pinion face should not be greater than 1.3 x PCD or you may have to take
the twist into account - make the wheel face a few mm smaller than the pinion

topping - this is the amount removed each side because of any space limitation or too thin a tooth tip etc.
Topping will decrease the contact ratio, so check the result

contact ratios -transverse CR should be over 1.2, greater will mean better load sharing and quieter operation

The axial CR (overlap ratio) should also be over 1.1 for helicals, spur gears will of course be zero

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 views: 11 posted: 12/11/2010 language: English pages: 6