Research On The Theory & Technology Of Measurement For Characterized Curves Of Complex Helicoidal Surfaces

The universality of application of helicoidal surfaces in the engineering, the importance of their performance in the certain field and the non-replaceability of their functions in the specified mechanical systems have resulted in that the technology of measurement for helicoidal surfaces has been a critical research project in the field of dimensional measurements. With the rapid development of the modem science and technology, complex helicoidal surfaces are employed more and more widely, but their tolerances become narrower and narrower. Consequently, there is a rapidly increasing need of the technology for measuring helicoidal surfaces with higher efficiency, higher precision, non-linearity and so on. On the basis of retrospecting the evolution of measuring helicoidal surfaces in the past century, the author抯 research results of the theory & technology for measuring characterized curves of complex helicoidal surfaces are overall discussed in this dissertation. The main contents, results and creative ideas are as follows:I. The research on the principles for measuring deviations of characterized curves of helicoidal surfaces is systematically made, the models of deviations of the characterized curves are derived and the corresponding assessment methods are presented. Meanwhile, the forms of the deviation curves are categorized into three elemental modes for the first time, and the mathematical models of these modes are proposed.2.The general relation formula between the composite positioning error of a measuring machine and the measurement error is established, and based on it, the relation formula between the form tolerance of the surface and the accuracyIvof the measuring machine is derived. These formulae can be applied in the fields of precision machine design, error analysis, complex surface measurement and so on.3.The novel methods, the generalized polar-coordinate method for measuring involute profile and the generalized cylindrical-coordinate method for measuring deviation of contact line of involute helicoid, are proposed and studied. Their mathematical models, realizing manners and data-processing formulae are given, and error budgets are also conducted.4.The key techniques in the dynamic measurement of discontinuous helicoidal surfaces are deeply studied. A new technique, 揅urvature Method? recognizing edges of gear cutters is introduced, the tracking principle for scanning edge profile of gear cutter is developed and a robust method is proposed to automatically distinguish boundary points of assessing region. By means of these new techniques, the measurement for characterized curves of discontinuous helicoidal surfaces can be conducted at fast speed.5.Combined with the measurement for characterized curves of discontinuous helicoidal surfaces, a method using grey theory to detect unwanted asperities in the dynamic measurement of cuffing edges is studied. All the equations and the distinguishing criterion are given. Furthermore, they are verified by measurement data. Meanwhile, the calculating method of the dynamic measuring repeatability based on the mean translation is developed. It is indicated, by the theoretic analysis and the computation of practical measuring data, that mean translating method can objectively reflect the repeatability of dynamic measurement in general.6.Based on a novel method of data processing ---- accumulative sum method, a parameter estimating method of the basic form modes of the deviations of the characterized curves of the helicoidal surfaces is initiated. The formulae to solve the parameters are given and are proved by examples. The results are compared with those of least-square method.7.A CNC horizontal cylindrical-coordinate measuring machine is developed at the first time in China. The new theories and new methods above are all applied on this machine. After a brief introduction of relevant key techniques, emphatically discussed are both a parallel springs probing head with a grating sensor and the method of real-ti...