TUGAS MATA KULIAH ELEMEN MESIN

Disusun Oleh,

Nama : Triono

NIM: 5201404032

Prodi : Pendidikan Teknik Mesin, SI

FAKULTAS TEKNIK

UNIVERSITAS NEGERI SEMARANG

2009

GEARS

Circuler pitch, Pe =Where

D = diameter of the pitch circle, and

T = No. of teeth on the wheelDiameter pitch, Pd = = Where

T = No. of teeth, and

D = Pitch circle diameter

Module, m = Condition for constant velocity ratio of gears law of gearing

V1 = V2 or(W1 x O1Q) = (W2 x O2Q)(W1 x O1Q) = (W2 x O2Q)

or W1. O1M = W2.O2N

=

.(i)Also From similar triangles O1 MP and O2 NP =

.(ii)Combining equations (i) and (ii) we have

= =

.(iii)Invalute TeethFrom similar triangle O2NP and O1MP

= = ..(i)Which determines the rasio of the radii of two bas circles. The radii of the base circles is given by

And

O1N = O1 P cos

O2M = O2 P cos Also the centre distance between the base circle= O1 +O2P

= Beam strength of gear teeth lewis eqution

fwWhere M = Maximum bending moment at the critical section Bc,

= WT X h

H = Length of the tooth

Y = half the thikness of the tooth at the critical section BC= I = moment of inertia about the centre line of the tooth

= b = Width of gear face

Substituting the valuesfor M, y and I in the abaout expression , we get

fw =

or = fw x b x Let t = X x Pe, and

H = k x pe

Where x and k are constant

Wr = fw x b x Subsituting Wr = fw.b.Pe.y

= fw.b.

(Pe = )Permissible working stress for gear teeth in the lewis equtionfw = fo x CvWhere

fo = Allowable static strees, andCv = Velocity factor

The values of Cv are given as follow :

Cv = , for ordinary cut gears operating at velocities up to 12.5 m/sec.

= , for carefully cut gears operating at velocities up to 12.5 m/sec.

= , for very accurately cut and graund metallic gears operating at velocities up to 20 m/sec.

= , for precision gears cut with high accuracy and operating at velocities up to 20 m/sec.

= , for non-metallic gears.Dynamic tooth load

Where WD = WT + W 1WD = Total dynamic load

WT = steady load due to transmitted torque , and

WI = Increment load due to dynamic action

The increment load (W1)depends upon the pitch line velocity, the face width, material of the gears, the accuracy of cut and the tangential load. For average conditions, the dynamic load is determined by using the following Buckingham eqution, i.e.

WD = WT + WI = WR + Where WD = Total dynamic load

WT = Steady transmitted load in Kg,

V = Pitch line velocity I metres/min.

B = face width of gears in cm, and

C = A deformation of dynamic factor in cm units.A deformation factor c depends upon the error in action between teeth, the class of cut of the gears, the rooth form and the material of he gears.The value of C may be determined by using the following relation:

C = Where, K = A factor depending upon the form of the teeth.

= 0.107, for 140 full depth involute system.

=0.111, for 200 full depth involute system.

= 0.115, for 200 stub system

Ep = Youngs modulus for the material of the pinion

EG = Youngs modulus for the material of the gears.

E = Tooth error action in cm.Static tooth loadThe static tooth load (also called beam strength or endurance strength of the tooth)is obtained by lewis formula by substituting flexural endurance limit or elastic limit stress (fe).

So, static tooth load or beam strength or endurance strength of the tooth,Ws = fe.b.Pe.y

= fe.b. . yNote, for safety againsttooth breakage , the static tooth load (WS) should be greater than dynamic load (WD). Buckingham suggests the following relationship between WS and WD.For steady loads, Ws 1.25 WD

For pulsating loads, Ws 1.35 WDFor shock loads, Ws 1.5 WDWear tooth loadWw = Dv.b.Q.KWhere Ww= Maximum or limiting load for wear in kg,

Dv = pitch circle diameter of the pinion in cm

b = Face width of the pinion in cm,

Q = Ratio factor

= , for external gears

= , for internal gears.V . R = Velocity ratio

= K = Load strees factorThe load strees factor is given by the following relation

K = Fes = surface endurance limit in kg/cm2

= Pressure angle

Ep = Youngs modulus for the material of the pinion in kg/cm2, and

EG = Youngs modulus for the material of the gear in kg/cm2Design procedur for spur gears

Where WT = X CsWT = permissible tangential tooth load

P = horse power transmisted

V = Pitch line velocity in m/min

= m/min.We know that, circular pitch

Pe = D =mTSo, the pitch line velocity may also be obtained by using the following relation, I.e.

V = = =

m = Modulus in cm, and

T = No, of teeth.

D = pitch circle diameter in cm

N = Speed in r.p.m, and

Cs = service factor

Apply the lewis equation as follow:

WT = . b.Pe.y = .b.With usual notations

= (Co)b..y (=Co)

Calculate the dynamic load (WD), on the tooth by using Buckingham eqution,i.e.

WD = WR + W1= WR +

With usual notations.

Note; In calculating the dynamic load (WD), the value of langential load (Wr) is given by.

Wr =

(Neglecting service factor, Cs)

Find the static tooth load (i.e bean strength or the endurance strength of the tooth) By using the following relation.Ws = fe . b. Pe. y

= fe .b.. yFor safery against breakage, Ws should be greater then WDFinally, find the wear tooth load by using the following relation.

Ww = Dv.b.Q.k

The wear load (Ww) should not be less than dynamic load (WD)

Spur gear consructiontR = mtR = Thikness of the rim,T = Number of teeth, and

N = Number of arm.

Design of shaft for spur gears.

In order to find the shaft diameter, for spur gears, the following procedure may be followed.1. First of all, find the normal load WN acting between the tooth surface. It is given by.

WN = WN = Normal load,

WT = Tangential load, and

= Pressure angle2. The weigh of the gear is given by

WG = 0.118 TG x b x m2 kg

Where, TG = Number of teeth on the gear

B = Face width in cm, and

m = module in cm.

3. Now the resultant load acting on the gear.

WR = 4. If the gear is overhung on the shaft, then the bending moment on the shaft due to the resultant load.

M = WR X x

x = Overhang i.ethe distance between the centre of pinioan and the centre of the bearing.

5. Since the shaft is under the combined effect of torsion and bending, therefore we shall determine the equivalent torque.We know that equivalent torque.

Te = Where, T = Twisting moment

= WT x 6. Now the diameter of the gear shaft (d) is determited by using following relation, i.e.

Te = fs . d3Where, fs = Shear stress for the material of the gear shaft.

Design Of ArmsThe stalling load may be taken as the design tangential load divided by the velocity factor.

Ws = Stalling load ,

= = DG = Pitch circle diameter of the gear,

n = Number of arms, and

fb = allowable bending stress for the material of the arms.

Now, maximum bending moment on each arm,

M = = And the section modulus of arms for elliptical eross-section,

Z = a1 = Major axis, and

b1 = Minor axis

The major axis is usually taken as twice the minor axis. Now, using the relation.

fb = We can calculate the dimensions a1 and b1 for the gear arm at the hub end.

Note; The arm are usually tapered forwards the rim about cm per cm length of the arm. Therefore

Major axis of the section at the rim end

= a1 Taper

= a1 - x Length of the arm

= a1 - x = a1 -