Gear box designing Gear

1 gear box designing

1.1 procedure stepwise solution
1.2 speed chart
1.3 gear box diagram
1.4 inspection

gear box designing

the essential information required designing gear box follows.

procedure stepwise solution

let n1, n2, n3… n z rpm values available on machine tool in geometric progression.

rn= nz/( n1)= Ø z-1

where rn= range ratio, Ø= progression ratio

Ø= rn (1/z-1)

z= log rn. Ø/ log Ø

suppose speed on 1 shaft yields 2 speed values on next shaft i.e. number of speed steps of particular transmission group p=2. transmission ratio provide 2 speed values must lie in following range:

i max= 2 & min= ¼

maximum reduction of speed limited 4 times keep radial dimensions of gear box within reasonable limits, maximum increase of speed limited 2 times due limitations of pitch line velocity.

i max/i min= 8

structural formula: z= p1(x1) p2(x2) p3(x3)

here x1= 1, x2= characteristics of x1= p1 & x3=characteristics of x1x2= p1p2

let understand e.g. n min = 16 rpm n max =770 rpm Ø= 1.41 rn= 770/( 16)= 1.4112-1 z= log (770/16). 1.41/ log 1.41 z=12 z= 2x2x3 z= 2(1) x 2(2) x 3(4)

this called structural formula.

the possible structural formula above z are: 2(1) x 2(2) x 3(4), 2(1) x 2(2) x 3(4), 2(2) x 2(1) x 3(4), 2(6) x 2(1) x 3(2), 2(6) x 2(3) x 3(1), 2(3) x 2(6) x 3(1), 3(1) x 2(3) x 2(6), 3(1) x 2(6) x 2(3), 3(2) x 2(1) x 2(6), 3(4) x 2(1) x 2(2), 3(4) x 2(2) x 2(1), 3(2) x 2(6) x 2(1) 2(1) x 3(2) x 2(6), 2(1) x 3(4) x 2(2), 2(3) x 3(1) x 2(6), 2(6) x 3(1) x 2(3), 2(6) x 3(2) x 2(1), 2(2) x 3(4) x 2(1), in z= p1(x1) p2(x2) p3(x3)

the best version ensures 1 in n min values of intermediate shafts maximum , n max values of intermediate shafts re minimum p1>p2>p3 & x1<x2<x3

of above 18 structural formula 3(1) x 2(3) x 2(6) appropriate structural diagram. let draw structural diagram generated structural formula.

u = no. of stages

here in case u=3 transmission group

speed chart

structural diagram depicts range ratio of transmission groups gives no information transmission ratios. in order determine transmission ratios of transmissions , rpm values of gearbox shafts, need draw speed chart.

the line horizontal, corresponds transmission ratio =1, i.e. no speed change.
the line inclined upward, depicts >1, i.e., speed increase.
the line inclined downward, depicts <1, i.e., speed reduction.

draw z+1 no. of vertical lines , u+1 horizontal lines intersecting vertical lines @ convenient distance. (here 13 horizontal lines , 4 vertical lines.)

draw rays depicting transmission between shaft , shaft preceding it. rays drawn lowest rpm of last shaft keeping in mind transmission ratio restriction condition max≤ 2 , min>=1/4.

here. max= 2 = ф 2 [(1.41) 2 = 1.9881

i min = 1/4 = 1/ ф 4 [(1.41) 4 = 3.9525],

mark speeds of shaft in front of each horizontal line, starting n min* ф on first line, n min* ф2 on second line, n min* ф3 on third line , on.

select best speed chart i.e. should have concave shape.

gear box diagram

number of teeth on smallest gear should such there no undercutting of gear teeth z min≥17. if gears on parallel shafts sum of number of teeth of mating gear pair should same. spacing between 2 adjacent gears should such 1 should such 1 should disengage before other mate. center distance between 2 shafts, a=m (z1+z2)/2. in machine tools large inertia of driven member, friction clutch , brake should provided on input shaft. reversing devices should provided tool can returned initial position after completion of cutting process. reversal speed = 1.3-1.5 times greater cutting speed. if spindle head traverse, electric motor should mounted on speed box , transmission motor shaft input shaft of speed box obtained through clutch or gear pair. spindle kinematic ally linked feed mechanism, spindle feed train must shown on gearing diagram. largest of gears on spindle should mounted closest front spindle bearing.

z min=2 k (1+√(1±i(2±i) sin⁡〖 ^2 α〗 ))/((2±i)sin⁡〖 ^2 α〗 )

k=tooth addendum

i= transmission ratio

α= pressure angle

z min=17

let s return our question:

n min = 16 rpm, n max =770 rpm, Ø= 1.41, n motor =1440 rpm, input shaft=630 rpm.

from gearbox diagram z7 link gear

z7/z14= 250/250

z10/z11= 63/250 z10 +z11= 86, z10=23, z11=63

z12/z13= 63/250 z12+ z13= 86, z12=17, z13=69

z15/z16= 125/63 z15=60, z18=30

z17/z18= 16/63 z17=18, z18= 72

inspection

overall gear geometry can inspected , verified using various methods such industrial ct scanning, coordinate-measuring machines, white light scanner or laser scanning. particularly useful plastic gears, industrial ct scanning can inspect internal geometry , imperfections such porosity.

important dimensional variations of gears result variations in combinations of dimensions of tools used manufacture them. important parameter meshing qualities such backlash , noise generation variation of actual contact point gear rotates, or instantaneous pitch radius. precision gears inspected method produced paper gear tape record showing variations resolution of .0001 inches gear rotated.

the american gear manufacturers association organized in 1916 formulate quality standards gear inspection reduce noise automotive timing gears; in 1993 agma assumed leadership of iso committee governing international standards gearing. ansi/agma 2000 a88 gear classification , inspection handbook specifies quality numbers q3 q15 represent accuracy of tooth geometry; higher number better tolerance. dimensions can measured millionths of inch in controlled-environment rooms.