Selection of Machining Datum and Allocation of Tolerance through Tolerance Charting Technique

Tolerance charting is an effective tool to determine the optimal allocation of working dimensions and working tolerances such that the blueprint dimensions and tolerances can be achieved to accomplish the cost objectives.The selection of machining datum and allocation of tolerances are critical in any machining process planning as they directly affect any setup methods/machine tools selection and machining time.This paper mainly focuses on the selection of optimum machining datums and machining tolerances simultaneously in process planning.A dynamic tolerance charting constraint scheme is developed and implemented in the optimization procedure.An optimization model is formulated for selecting machining datum and tolerances and implemented with an algorithm namely Elitist Non-Dominated Sorting Genetic Algorithm（NSGA-II）.The computational results indicate that the proposed methodology is capable and robust in finding the optimal machining datum set and tolerances.

Accuracy Analysis and Design of A3 Parallel Spindle Head

As functional components of machine tools, parallel mechanisms are widely used in high efficiency machining of aviation components, and accuracy is one of the critical technical indexes. Lots of researchers have focused on the accuracy problem of parallel mechanisms, but in terms of controlling the errors and improving the accuracy in the stage of design and manufacturing, further efforts are required. Aiming at the accuracy design of a 3-DOF parallel spindle head（A3 head）, its error model, sensitivity analysis and tolerance allocation are investigated. Based on the inverse kinematic analysis, the error model of A3 head is established by using the first-order perturbation theory and vector chain method. According to the mapping property of motion and constraint Jacobian matrix, the compensatable and uncompensatable error sources which affect the accuracy in the end-effector are separated. Furthermore, sensitivity analysis is performed on the uncompensatable error sources. The sensitivity probabilistic model is established and the global sensitivity index is proposed to analyze the influence of the uncompensatable error sources on the accuracy in the end-effector of the mechanism. The results show that orientation error sources have bigger effect on the accuracy in the end-effector. Based upon the sensitivity analysis results, the tolerance design is converted into the issue of nonlinearly constrained optimization with the manufacturing cost minimum being the optimization objective. By utilizing the genetic algorithm, the allocation of the tolerances on each component is finally determined. According to the tolerance allocation results, the tolerance ranges of ten kinds of geometric error sources are obtained. These research achievements can provide fundamental guidelines for component manufacturing and assembly of this kind of parallel mechanisms.

A comparison of sensitivity indices for tolerance design of a transmission mechanism

Sensitivity analysis is used to quantify the contribution of the uncertainty of input variables to the uncertainty of systematic output responses.For tolerance design in manufacturing and assembly,sensitivity analysis is applied to help designers allocate tolerances optimally.However,different sensitivity indices derived from different sensitivity analysis methods will always lead to conflicting results.It is necessary to find a sensitivity index suitable for tolerance allocation to transmission mechanisms so that the sensitivity results can truly reflect the effects of tolerances on kinematic and dynamic performances.In this paper,a variety of sensitivity indices are investigated and compared based on hybrid simulation.Firstly,the hybrid simulation model of the crank-slider mechanism is established.Secondly,samples of the kinematic and dynamic responses of the mechanism with joint clearances and link length errors are obtained,and the surrogate model established using polynomial chaos expansion(PCE).Then,different sensitivity indices are calculated based on the PCE model and are further used to evaluate the effect of joint clearances and link length errors on the output response.Combined with the tolerance-cost function,the corresponding tolerance allocation schemes are obtained based on different sensitivity analysis results.Finally,the kinematic and dynamic responses of the mechanism adopting different tolerance allocation schemes are simulated,and the sensitivity index corresponding to the optimal response is determined as the most appropriate index.