Mechanisms: Converting Piston (Linear) Motion to Crank Rotation (and Rotary Motion to Linear Motion)

1. Introduction
When the first steam engines where built, in the early 19th century, they were massively constructed and operated at slow speeds, beam engines typically only performing a few cycles per minute. Consequently dynamic loads were small and gravity loads dominated. Developments in engines have resulted in small, lightweight construction designed to operate at high speeds, gravity loads and stresses are minute compared to the dynamic loads and the stresses that these generate.

Before the days of digital computers, mechanism velocities, accelerations and then forces and moments, were determined by graphical techniques, drawing first a layout then scale velocity and acceleration diagrams for every position that needed investigation. This was very time consuming! Nowadays most mechanism analysis is normally done with motion analysis packages.

One of the most common mechanisms currently in use is the slider crank used in internal combustion engines to convert the reciprocating motion of the piston (with the gas pressures acting on it) into the rotary motion of the crankshaft that ultimately provides the torque to drive drive the vehicle. The applet associated with this section (next link in this section of the contents column) or click here - which is the latest version - analyses the slider crank mechanism, determining piston velocities and accelerations, the gas pressures and temperatures generated during combustion and the torque generated at the crankshaft taking into account the reciprocating mass.

The following link is to an example of analysing a slider crank mechanism with velocity and aceleration diagrams then calculations to show the torque at the instant shown. This was the approach needed before mechanism analysis software and computers were available.

To obtain the results from the diagram approach, the following values can be used in the applet (some of these values are rather 'contrived'!):

Reciprocating mass; 0.3kg; Crank throw: 25mm; Connecting rod length: 100mm; RPM 3992 (=418 rad/s); P1: 101000N/m2; T1: 300oK;

Compression ratio: 5; Bore: 68mm; Enery input(flag): 0; Inlet valve lift: 1.966mm; Inlet valve diameter: 30mm;

Air:fuel ratio: 14.7; Fuel energy: 46000000J/kg; Ignition (degrees after bdc): 160; Combustion duration (degrees): 40;

Flag for early exhaust opening: 0; Polytropic index: 1.4.

The comparative results are tabulated below from the applet listings for 210 degrees after bdc (= 30 degrees after tdc).

 Applet result Graphical result Pressure 2.901 - 0.101MPa (abs. press. - P1) 2.8MPa Piston velocity -6.37m/s -6.36m/s ('down' is -ve) Piston acceleration -4347.18m/s2 -4344m/s2('down' is -ve) Indicated torque 154.88Nm 154Nm Torque * 2, allows for acceleration of piston mass 135.02Nm 138.4Nm

Note: The plots of P - V diagrams in the applet above and below a compression ratio of about 8:1 have a 'glitch', although the pressure and volume listings seem ok. I will try and sort this out!

David J Grieve. Revised: 24th April 2013, original: 27th February 2010.