TUTORIAL 2To Study about Helical Gears

(1) What are the advantages of helical gears over spur gears?

(2) What is formative number of teeth in helical gear? Derive the expression for formative number of teeth in helical gears.

(3) A helical gear speed reducer is to be designed, the rated power of the speed reducer is 75 kw at a pinion speed of1200 rpm. The speed ratio is 3:1 for medium shock condition and 24 hr operation. Determine module, face width, no. of teeth in each gear. Specify material & heat treatment. The teeth are 200 full depth in the normal plane.

(4) Design a gear pair of helical gear

Gear PinionMaterial 50C4 60C4

Ultimate strength MPa 660 750BHN 241 255Pressure angle in degree

200 200

Number of teeth 70 35Normal module in mm 5 5Face width in normal plane, mm

50 50

Modulus of Elasticity GPa

205 200

Assume service factor 1.5 and factor of safety 3. Check wear and dynamic strength of gear. Helix angle is 250 , speed of pinion is 720 rpm.

Material Error 0.02 Error 0.04Steel steel 20 degree involute

228 456

Velocity factor Kv = 6

(6+V ) , Fw = dp.b.Q.k/cos2φ

K = ((σes)2 sin (∅ n)/1.4)( 1Ep + 1Eg ) , σes = 2.75(BHN) – 70

Fd = Ft + ¿¿

(5) A pair of parallel helical gears consists of a 20 teeth pinion meshing with a 100 teeth gear. The pinion rotates at 720 rpm. The normal pressure angle is 200 , while the helix angle 250 . The face width is 40 mm and the normal module is 40 mm. The pinion as well as the gear are made of steel 40C8 having ultimate tensile strength of 600 N/mm2 and heat treated to a surface hardness of 300 BHN. The service factor and factor of safety are .5 and 2 respectively. Assume that the velocity factor accounts for the dynamic load and calculate the power transmitting capacity of gears.

(6) A pair of helical gears having a transmission ratio 8 : 3, with a steady load condition, used for turbine. The maximum speed is 2400 r.p.m. the pinion is to have 27 teeth and a face width of 100 mm. the circular module is 6 mm. the material used for gears is heat treated steel with 250 BHN and have static stress of 210 MPa. The gears are carefully cut. Calculate value of dynamic l0ad and wear load.

(7) Determine the power capacity of a pair of helical turning gears having a transmission ratio of 10: 1. The teeth are 200 full depth involute – 6 mm module. The pinion has 25 teeth and rotates at 5000 r.p.m. the active face width is 76 mm and material is C-40 steel untreated.

(8) Design a pair of helical gears to transmit 50 kw at a speed of 1440 rpm to a shaft required to run at 480 rpm. The helix angle is approximately 250 and 200 full depth teeth are used. Both the gear and pinion are made of steel with permissible stress 80 N/mm2 and 100 N/mm2 respectively. Take minimum number of teeth on pinion 16. Check your design for dynamic load and determine minimum hardness of teeth required.

(9) A pair of parallel helical gear consist of 24 teeth pinion rotating at 5000 rpm and supplying 12 kW power to a gear. The speed reduction is 4:1. The normal pressure angle and helix angle are 200 and 230 respectively. Both

gears are made of hardened steel {Sut = 600 N/mm2}. The service factor and factor of safety are 1.5 and 3 respectively. Calculate 1. Module and face width of gears.2. Surface hardness for the gears assuming a factor of safety of 1.5 for

wear consideration.