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The present work investigates the influence of uncertain tooth profile modifications on the nonlinear dynamic response of a spur gear pair induced by a backlash nonlinearity. To this end, an original approach based on bifurcation tracking is developed. The equations of motion are solved in the frequency domain with the harmonic balance method (HBM) coupled to an arc-length continuation algorithm and a bordering technique. The evolution of the bifurcation points with respect to the uncertain parameter is computed in a deterministic way. The study focuses on minimizing the amplitude-jump instabilities induced by the backlash nonlinearity around the primary resonance peak. The proposed methodology allows for a fast and reliable estimation of the tooth profile modification that minimizes the amplitude-jump instability by defining two criteria using the results of the bifurcation tracking algorithm. Probability density functions (PDF) of various indicators of the severity of vibro-impacts can be computed with Monte-Carlo (MC) simulation with minimal computational burden. Results show that the tooth profile modification that minimizes the amplitude-jump instabilities differs from the optimum obtained with static computations. [ABSTRACT FROM AUTHOR]

Weight reduction is a recurring concern in the design of modern mechanical systems. This search may lead engineers to resort to using gears with holes in order to meet their requirements. This paper presents a methodology to carry out nonlinear dynamic analyses of a gear transmission with holes in the gear blanks subjected to a multiharmonic internal excitation. This work investigates the influence of these holes on the vibration levels, occurrence of contact loss and possible bifurcations. The numerical model features two flexible shafts coupled by a spur gear pair with holes. The gear model consists in two lumped masses and inertias and includes the gear backlash as well as the internal excitation sources that are the time-varying stiffness and the static transmission error (STE). The resulting mechanical system is solved in the frequency domain by the Harmonic Balance Method (HBM) coupled with an arc-length continuation algorithm and its stability is evaluated with Hill's method. Results show that adding holes not only impacts the STE but also the mesh stiffness. The interactions of these two quantities has a substantial influence on the bifurcation structure along the main solution branch and leads to a decrease of the span of vibro-impact regions. As the applied static torque is increased, it is found that using holed gear blanks can effectively prevent contact loss and lead to a linear response. [ABSTRACT FROM AUTHOR]