© Engineering Department, De Montfort University Inertia Bending of a Connecting Rod Experiment Objective 1) To produce the peak dynamic bending moment diagram for the connecting rod of a simple engine mechanism and compare it with that obtained from theory. 2) To determine, and compare with the calculated value, the position and magnitude of the maximum peak dynamic bending moment. 3) To confirm that the maximum peak dynamic bending moment occurs when the crank and connecting rod are at right angles. Apparatus Simple engine mechanism rig with strain-gauged connected rod (Fig. 3a,b) Strain gauge bridge Tachometer (Fig. 4a) Calibration level and weights (Fig. 4b) Storage oscilloscope (Fig. 4a) Data Mass of connecting rod M=1.01kg. Length between centres L=720mm. Crank radius r=80mm Theory The connecting rod is assumed to be a uniform bar of length L and mass per unit length m= M / L. The bending is due to transverse inertia loading in the plane of the motion. It is anticipated that the maximum bending occurs when the crank and connecting rod are at right angles. In this position the transverse acceleration of the big end is r2 and that of the small end is negligible. Thus the intensity of transverse loading varies linearly from zero at the small end to mr2 at the big end. Balance of forces on connecting rod AB: Balance of torque around point B: Hence:     L A B mr L dy L mr y R R 0 2 2  2  3 3 2 0 2 2 2 mr L ydy mr L R L mr y R L A L A         2 2 3 6 2 mr 2L mr 2L mr 2L R mr L R B A         Bending moment at section x (see Fig. 1) Fig. 1 Schematic representation of distributed inertia loads along the connected rod. Fig. 2 Theoretical prediction for the bending moment Mxx in different cross sections of the connected rod. Procedure 1. Measure the position of the gauges using the centre of the big end of the connecting rod as a datum. 2 2 2 3 2   2 3 0 2 2 6 2 3 6 ( ) L x x L mr L mr x x L mr x x mr L x y dy L mr y M R x x xx  B             (see Fig. 2) 6 3 3 3 9 3 3 (0) ( ) 0; maximum 0 3 0 2 3 3 2 2 max 2 2 L L mr L L mr M L L x x dx dM M M L M xx xx xx xx xx                      2. Connect the output of one of the five strain gauges to the oscilloscope. 3. Run the mechanism and adjust the size of the oscilloscope trace. Store the image and note the shape. 4. Measure the time between maximum strains of opposite sign and the time for one complete cycle. 5. Measure the peak-to-peak height of the trace which is proportional to the peak-to-peak dynamic bending moment experienced by the connecting rod. 6. Without altering the gain of the strain gauge bridge measure the peak-to-peak voltage of the other pairs of gauges in turn. 7. To calibrate the system convert the connecting rod into a horizontal simply supported beam using the locking pin in the crank. Apply central concentrated loads using a minimum of six different weights with the lever system built into the rig. Note the voltage deflection of the trace on the oscilloscope for each load. Plot a calibration curve of mass (ordinate) vs voltage and hence determine the calibration constant for the measuring system in Nm/volt. 8. Determine the peak dynamic bending moment foe each gauge station and hence plot the peak dynamic bending moment diagram for the connecting rod. On the same diagram plot the curve produced by calculation from theory. 9. From the time measurements taken in step 4 determine the fraction of the cycle time, and hence the angular rotation of the crank, between peak strains of the opposite sign. a) b) Fig. 3 Simple engine mechanism rig with strain-gauged connecting rod. General view with the five strain gauges switch-on/off panel (left photo). Rig with open cover and rotating crank, red strips show location of five strain gauges (right photo). a) b)Fig. 4 Tachometer and two digital oscilloscopes (left photo). The crank is locked by the locking pin converting the connecting rod into a horizontal simply supported beam for calibration experiment, calibration weight is applied via the lever system built into the rig (right photo). Conclusions Comment on the agreement between the peak dynamic bending moment diagrams produced by measurement and calculation including the position and magnitude of the maximum value. Can the hypothesis that the peak dynamic bending moment occurs when the crank and connecting rod are at right angles be confirmed from the results?