Efficient computational techniques for statistical analysis and optimization of slider-crank mechanisms in internal combustion engines

Dimensional tolerances refer to differences from nominal values in joint clearances and link lengths which arise during manufacturing. Inappropriate dimensional tolerances can cause engine outputs to fall below the expected value resulting in a diminished performance. This thesis develops tolerance analysis and allocation methods for dynamic mechanical systems with discontinuous forcing functions. Four example cases are considered for demonstration: rigid single cylinder and four cylinder engines, and single cylinder and four cylinder engines with elastic connecting rods.;In this thesis, tolerances on link lengths and radial clearances and uncertainties in pin location are treated as random variables. Based on truncated Taylor expansion, an efficient analytical approach is presented to evaluate statistics by computing the mean values and variances of speed, torque, and deflection for a stochastically defined internal combustion engine. Modeling the effective lengths of the links of the systems permits probabilistic analysis to use the nominal equations of motion, while the alternating frequency/time domain method (AFT technique) is applied to accurately and efficiently determine the steady state responses (mean values of crank speed, driving torque, and transverse vibration and Fourier coefficients of temporal variations in desired outputs) of reciprocating internal combustion engines. These dynamic mechanical systems are governed by a system of nonlinear differential equations with discontinuous forcing function due to the nature of the pressure-volume (P-V) diagram. In the light of statistical analysis, nonlinear optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables.;Tolerance allocation standards do not exist for mechanical systems whose response are time varying and are subjected to discontinuous forcing functions. Therefore developed analytical techniques are well suited as a design and analysis tool for the tolerance allocation for dynamic mechanical systems with discontinuous forcing functions and flexible links.