In this article, the assembly of axi-symmetric rigid structures from imprecisely manufactured components is considered to produce a ‘straight-build’ assembly. The eccentricity of the assembly is improved by selecting the best relative orientation of each component and using four different strategies to control the assembly errors. The presentation is simplified by considering the assembly of two-dimensional structures, and the Monte Carlo simulation technique is used to quantify the propagation of random component variations on the resulting assembly. The axial and radial run-outs for each component are used to represent component variability and these quantities are represented as Gaussian random variables. The influence of component variations on the assembly is predicted using connective assembly models. Numerical results are presented for assemblies consisting of: (a) identical rectangular components; and (b) non-identical rectangular components. The results are compared with each other and those obtained using ‘direct-build’ assembly, which does not control the assembly errors. It is found that assembly variations can be reduced significantly using the proposed techniques.

A mathematical model is developed to describe the 2θ in-plane flexural response of supported ring-based Coriolis Vibrating Gyroscopes (CVGs) as the ring is driven into large amplitude vibration. Whilst the 2θ degenerate modes have same resonance frequency in the linear regime, mechanical non-linearity within the support structure induces a frequency split as the vibration amplitude increases. The origins and effects of geometrical non-linearity are investigated using the proposed analytical model.

This paper investigates the effect of electrostatic nonlinearity on the rate-sensing performance of imperfect ring-based Coriolis Vibrating Gyroscopes (CVGs) for devices having 8 and 16 evenly distributed electrodes. Mathematical models are developed for CVGs operating in (i) an open loop for a linear electrostatically trimmed device, (ii) a closed loop where a sense force balancing is applied to negate the sense quadrature response, and the effects of electrostatic nonlinearity are investigated for increasing drive amplitudes. The modeling indicates the nonlinear responses for 8- and 16-electrode arrangements are quite different, and this can be attributed to the nonlinear frequency imbalance, which depends on the drive and sense frequency softening as well as the presence of self-induced parametric excitation in the sense response. In open loop the 16-electrode arrangement exhibits much weaker levels of nonlinearity than the 8-electrode arrangement because the nonlinear frequency imbalance is less sensitive to drive amplitude. For devices operating in closed-loop with sense force balancing to ensure the drive and sense responses are in-phase/anti-phase, it is shown that ideal rate-sensing performance is achieved at large drive amplitudes for both 8- and 16-electrode arrangements. Using sense force balancing, rate sensing can be achieved using either the sense response or the required balancing voltage. For the latter, large nonlinear frequency imbalances and low damping levels enhance rate-sensing performance.