Papers by Keyword: Form Error

Abstract: To address the calculation of elliptic sphere form error, a differential geometry algorithm is proposed and the presented model is answered by fminsearch function in Matlab. An example shows the effectiveness of the proposed algorithm.

Abstract: The key factors affecting the transmission error of gear mechanism are analyzed and the calculation formula of transmission error based on parts’ form and position errors is derived in this paper. Since the errors have different kinds of probability distributions, this paper calculate the expectation and variance of transmission error by statistical method, gives final transmission error value, and verify it by an example.

Abstract: The backlash of gear mechanism is generally calculated by detecting each index after finishing processing and assembling. But it cannot be used to guide the design of parts in this way. This article will analysis the backlash through a spur gear drive model based on form and position errors, draw up the backlash formulae by form and position errors conversion, extreme method and probabilistic method, and verify it by an example.

Abstract: Airspace industry components frequently need high added value part including some featuredifficult to manufacture. One of the best example is the thin walls of parts (airplanes frames orthe turbine blades) that have a very low stiffness. The finishing operations for high height to thicknessratio parts lead to chatter vibrations, unacceptable dimensional errors or poor surface finish. The optimalmachining strategy determination is often based on trial and error and may not be cost effective(acceptable conditions can be far from the optimum). Simulation of the milling process is a powerfulmean to accelerate the search for better cutting parameters. Cutting forces, vibrations, geometricerrors or roughness can be predicted before the production of the first parts. The classical mechanisticapproach is even though limited while machining flexible parts because the dynamic response ofthe workpiece changes with the position of the cutter. The objective of this paper is to demonstratethe adaptation of numerical simulation of milling operation for the machining of thin-walled plates.Three complementary approaches are developed: location-dependent stability lobes, quasi static approachand full dynamic simulation. Location dependent stability lobes extend the classical theoryto take into account the variation of dynamic response along the workpiece. Quasi static approach isintended to deal with form error during chatter-free machining operations. Full dynamic simulation isa more complex approach intended to simulate the behavior of the complete tool/machine/workpiecesystem. The numerical approach is compared to experimental tests performed on thin plate of titaniumalloys.

Abstract: A modeling method of parts surface form error distribution by precision turning for assembly is proposed in this paper. Selecting cylindrical surface by turning as the research objective, the study of modeling method of form error distribution law is carried out. According to the data from the precision surface which is measured by coordinate measuring machine (CMM), we model form error using the mathematical and numerical simulation software, followed by studying the form error distribution law of the cylindrical surface by precision turning. Finally, the form error numerical model for assembly is established based on the least square method. All the research above can provide guidance for the precision microminiature parts assembly and the improvement of assembly accuracy of precision parts.

Abstract: A model machine of multifunctional form and position measurement instrument controlled by a personal computer has been successfully developed. The instrument is designed in rotary table type with a high precision air bearing and the radial rotation error of the rotary table is 0.08 μm. A high precision vertical sliding carriage supported by an air bearing is used to the instrument, the straight motion error of the carriage is 0.3 μm/200 mm and the parallelism error of the motion of the carriage relative to the rotation axis of the rotary table is 0.4 μm/200 mm. The mathematical models have been established for assessing planar and spatial straightness, flatness, roundness, cylindricity, and coaxality errors. By radial deviation measurement, the instrument can accurately measure form and position errors of such workpieces as shafts, round plates and sleeves of medium or small dimensions with the tolerance grades mostly used in industry.

Abstract: An unconstrained optimization model is established for assessing roundness errors by the minimum circumscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the minimun circumscribed circle assessment. One example is given to verify the theoretical results presented.

Abstract: An unconstrained optimization model is established for assessing roundness errors by the maximum inscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the maximum inscribed circle assessment. One example is given to verify the theoretical results presented.

Abstract: An unconstrained optimization model is established for assessing cylindricity errors by the minimum zone method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on a subset of the four-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be applied to solve the objective function in order to get the wanted cylindricity errors by the minimun zone assessment. An example is given to verify the theoretical results presented.

Abstract: An unconstrained optimization model applicable to radial deviation measurement is established for assessing cylindricity errors by the maximum inscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on a subset of the four-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the maximum inscribed cylinder assessment. An example is given to verify the theoretical results presented.