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

This 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

First 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 is:

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.