Ray Diagram Kinematic Layout

4.5 Ray Diagram (Or) Speed Diagram

This is the graphical representation of drive arrangement & this provides the following information: •  No. of stages •  No. of speeds in each stage • Values of transmission ratio. 4.6 Principles to be followed to obtain Optimum Design To avoid excessively large diagram of beam & to limit the pitch line velocity of gear. 1. No. of gears gears on the the last last shaft shaft must must be be minim minimum. um. 2. No. of gears gears on any shaf shaftt should should not not be more more than than . . !t is pref prefer erabl ablee to to have have n ma x≥ n mi n in every stage except first stage. i n pu t≥ n ". The The tran transm smis issi sion on rat ratio io #. The ratio

n ma x n mi n

n ma x n i np ut

≤ 2&

n mi n

n i np ut

. 2 5 ≥0

≤8

$. Neve Neverr %ee %eep p the the rati ratio o

n ma x n i n p u t

>

n i n p u t n mi n

ymbolically this condition is represented by

!igure

'or example in ( speed gear box. tep )i* → +raw  vertical lines indicating  shafts )2 stages* tep )ii*→ )ii*→ +raw ( hori,ontal lines e-ually spaced across these vertical lines represented the speeds. tep )iii*→ )iii*→ roceed the ray diagram from last shaft to 1 st.

!igure " speed

(/

3 ( 1 )3 ( 3 ) . I I I

 No. inside the brac%et represents the no. of steps to be considered in each stage & no. outside the brac%et represents the no. of speeds. 0hy do we re-uire multiple speeds. ultiple speeds are re-uired to • • !*

Various load handling Varying production rate elect the spindle speeds for following data

12 speeds between # rpm & $ rpm Nmax Nmi n

⇒

= φ n 1 −

6 0 0 n1 = φ  5 0 −

⇒ φ  = 1 . 2 5 3 3asic series of preferred numbers φ corresponds to 41 series #5 $5 65 15 12#5 1$5 25 2#5 1#5 "5 #5 $ The given maximum speed is $ rpm ∴

∴ to chec% deviation )within # 7 limit* is calculated5 7 deviation /

6 3 0− 6 0 0 =5 % 6 0 0

∴The permissible deviation is calculated by

0 ( ) % ±1 φ  − 1 0 ( 1. 25− 1 ) ⇒ ±1 . 5 % ⇒ ±2 3ut since the 7 deviation is greater then permissible deviation5 ta%e $ leaving $. ∴ eries is #5 $5 65 15 12#5 1$5 25 2#5 1#5 "5 #5 and $. SP##DS $% &#'R O 'R# $% &#O*#+R$, PRO&R#SS$O% (&.P)

8 series have the speed range with constant step ratio a5 a25 a5 999an The advantages of this progression are    

peed loss is minimum  No. of gears used is minimum ayout is compact rovides more even range of speeds in single step.

4.4 -inematic ayout Of ' &ear o/

This layout represents the arrangement of gears in a gear box. The no. of gears in each shaft is found by the no. available outside the brac%et in the structural formula. ;x: ( speed gear box ∴

3 ( 1 )3 ( 3 ) I I I

( possible speeds

!igure

1 → 1 < 2 = >< 6 2 → 1 <2 = ( <1  → 1 < 2< 11 = 12 " →  = " = > = 6 # →  = " = ( = 1 $ →  = " = 11 = 12 > → # = $ = > = 6 6 → # = $ = ( <1 ( → # < $ = 11 = 12 The %inematic layout provides following information: •  No. of speeds available in each shaft. •  No. of stages •  No. of simple gear trains & their arrangements. 4.5 Ray Diagram (Or) Speed Diagram

This is the graphical representation of drive arrangement & this provides the following information: •  No. of stages •  No. of speeds in each stage • Values of transmission ratio.