A Cam-shaft is driven by a 2:1 reducing chain drive from a drive shaft, which is driven by a motor and worm gear-box.

Find the overall rigidity of the input-transmission referred to the cam, from the output of the worm gear-box.

Note:

We want to find out how effectively the transmission is given to the cam by the worm gear-box.

The shafts are made of medium carbon steel, and the chain and solid sprockets are steel. G = 82.5 x 109 N/m2

The coupling is sufficiently rigid in torsion, and the shaft mountings are stiff enough to be ignored in the calculation.

The transmission chain is 0.5 inch pitch with a stiffness of 6 x 106N/m, for a 1m length.

Find the rigidity of each section of the transmission separately.

Refer the Rigidities to Cam-Shaft and Cam.

1: Rigidity of the Drive Shaft: Torsion

The drive shaft transmitting torque is Ø38, and 454mm long. Therefore its rigidity is:

The drive-shaft is connected to the cam-shaft by a 2:1 reduction drive.

referred to the Cam-Shaft

2: Rigidity of the Drive Shaft: Bending

Calculate the Stiffness of the Drive-Shaft - Force to deflect it by a meter.

The Pitch Circle Radius of the Sprocket is 61mm.

Therefore, the equivalent torsional rigidity of the drive-shaft at the drive-shaft (using Equation 3)

Finally, refer that Rigidity of the Drive Shaft to the Cam-Shaft via the 2:1 reduction:

3: Rigidity of the Drive Chain

From the drawing above:

Length of chain that stretches under load = 496mm.

Stiffness, for 1m length  = 6 x106 N/m

The Pitch Circle Radius of the Chain-wheel is 122mm.

Therefore, the rigidity of the chain referred to the cam-shaft is:

4: Rigidity of the Cam Shaft Bending

The Pitch Circle Radius of the Sprocket is 122mm.

Therefore, the equivalent torsional rigidity is: (using Equation 3)

5: Rigidity of the Cam Shaft Torsion

Overall Torsional Rigidity of the Input Transmission

Comment:

The most significant element with elasticity is the bending of the primary shaft. It has the lowest Rigidity, R2. This points to the possibility of a considerable improvement if:

•The chain-drive could be moved closer to the right-hand bearings.

and / or

•the sprocket could be increased in diameter.