machine Design formula list

Chain Drives Notations: P: pitch of chain (m) D: pitch circle diameter (m) D1: Pitch circle of smallest sprocket D2: Pitch circle of larger sprocket D0: Sprocket outside diameter D1:diameter of chain roller K: Number of chain links Ks: service factor Ft: tangential driving force Fc: Centrifugal tension in the chain Fs: Tension in the chain due to sagging L: Length of chain m:mass of chain in kg per metre n: factor of safety N1: speed of rotation of smaller sprocket (rpm ) N2:speed of rotation of larger sprocket P: Power transmitted by chain T: Number of teeth on the sprocket Wb : Breaking strength of chain



: angle subtended by one pitch length at the centre of  sprocket v : Average velocity of chain (m/s) x : Centre distance between sprockets(m) : Allowable bearing stress in MPa of N/mm² A : Projected bearing area (mm²) re : Tooth flank radius : Roller seating radius  : Roller seating angle ha: Tooth height above the pitch polygon : Top diameter : Root Diameter : tooth width rx: Tooth side radius ba: Tooth side relief  :width over teeth T1:Number of teeth on smaller sprocket T2:Number of teeth on larger sprocket W: Total load on the driving side of chain

    

Formulas for chain drives

                                                                          

1.

2.  3.

4.   5. 



6.  7. 



8. 

For velocity transmission ratio of 3, 

(For best results , min

distance centre distance distance should be 50 times the pitch.

Rim Profile of sprocket

Factor of safety 9. n =



                                                                     

10.











11. 12. 13.

Newtons







0

40

0

40

Tooth Profile Of sprocket

Power transmitted by chains

    15. P=  14. P=





                     

Where





= 1.25, for variable load with mild shock  = 1.5, for heavy shock loads

        

= 1, for drop lubrication = 1.5 for periodic lubrication = Rating factor 

Number of teeth on smaller or driving sprocket

 (m/s) Where  is the pitch circle diameter of smaller sprocket    =   (m/s)

16.

V max =

17.

V min

Principle Dimensions of tooth profile

18. re= 0.008d1(T2+180) = 0.12 d1(T+2) 19. r1 = 0.505 d1+0.069(d1)1/3 = 0.505 d1

[max] [min] [max] [min]

20.

[max]

21.



  

                                             [min]

[max]



= 0.5 (p-d1)

22. 23.

  



 



24. 25.

 

26. rx = p 27. b a= 0.1p to 0.15p 28. bf2 and bf3 = (Number of strands  1)pt + bf1 29. Design Power = Rated Power X Service factor 30. Load (W) =





y

Factor of safety (n) for bush roller and silent chain: Table 14.38 Pg.287

y

Characteristics of roller chains according according IS :2403  1991 : Pg 287 B ,table 14.40 a Power Rating (in kW) of simple roller chain

Speed of smaller sprocket or pinion (rpm)

100 200 300 500 700 1000 1400 1800 2000

06 B

08B

Power ( kW) 10B

0.25 0.47 0.61 1.09 1.48 2.03 2.73 3.44 3.80

0.64 1.18 1.70 2.72 3.66 5.09 6.81 8.10 8.67

1.18 2.19 3.15 5.01 6.71 8.97 11.67 13.03 13.49

12B

16B

2.01 3.75 5.43 8.53 11.63 15.65 18.15 19.85 20.57

4.83 8.94 13.06 20.57 27.73 34.89 38.47 ---

Permissible speed of smaller sprocket or pinion in r. p.m Type of  chain Bush Roller chain

Silent Chain

Number of teeth on sprocket pinion 15 19 23 27 30 17-35

Pitch of chain (p) in mm 15 20 25 1900 1350 1150 2000 1450 1200 2100 1500 1250 2150 1550 1300 2200 1550 1300 2650 2200 1650

12 2300 2400 2500 2550 2600 3300

30 1000 1050 1100 1100 1100 1300

Number of teeth on the smaller sprocket T ype ype of chain

Roller Silent

Number of teeth at velocity ratio

1 31 40

2 27 35

3 25 31

4 23 27

5 21 23

6 17 19

Maximum allowable speed for chains in r.p.m. Type of  chain

Number of teeth on the smaller  sprocket ( T  T1  )

12

15

20

25

30

Roller Chain

15 19 23 27 30 17-35

2300 2300 2400 2550 2600 3300

1900 2000 2100 2150 2200 2650

1350 1450 1500 1550 1550 2200

1150 1200 1250 1300 1300 1650

1100 1050 1100 1100 1100 1300

Silent Chain

Thick

Chain pitch (p) in mm

Cylinders  Principal Stresses

Variation of principal stresses (cylinders with internal pressure)

              ;

At the inner surface of the cylinder :

     =-

;

   ,

the stresses are

At the outer surface of the cylinder :

    =0;

   ,

the stresses are

Variation of stresses (Cylinders with external Pressure)

              ;

         

 

        

   



                                  

             Spur Gear

   

; P is the Power ( kW) , v is the pitch line velocity ( m/s) , Ft  is the tangential force (kN)

Ft  = FaCos , Where  is the pressure angle, and F n is the

normal force. Beam Strength: F beam= bm

  = ; F 

beam beam F max  max 



Values

of Y

 

; where 9.5  b  12.5m

    

    Y=      Y=     

o

For a 20 involute full depth tooth

Y=

o

For a 20 stub tooth o

For a 14.5 tooth

Values of Service factor (

Cs) : refer data book page 187 ,table 12.20

Values of Velocity Factor (

Cv): refer data book page 164

Dynamic Load: refer data book page 166 and 167 

        ;

Where



is the endurance limit ( = 17.5 BHN)

Gear Construction: 1. 2. 3.

If the pitch diameter d  14.8m + 60.0 mm , the pinion / gear should be of solid disc type. If the pitch diameter d23.5m + 85.0 mm ,the gear to be constructed should be of  The thickness of the rim , h= (2 to 4) m . The rim should be tapered 1 : 5 towards the centre

4. The thickness of the stiffening rib, q= (1.0+1.25)h

6. Hub length, l h = 2ds or at least equal to face width b. 7. Number of arms (j)

5. Hub diameter , dh= (1.6 to 2.0 ) d s

     

j=4 j=6 j=8

The section modulus of the arm section: Z =

If d  500 mm If 500 mm  d 1500 mm If d  1500mm

 

Stress Concentration

The static stress concentration factor : Fatigue stress concentration factor, K f  : F beam beam =





 

