Research On The Sphericity Evaluation Method Of Microsphere

Due to their special geometric shapes,the parts with circular and spherical profile have a wide range of applications in scientific research and industrial production related fields.The form errors of these two shapes,namely the roundness error and the sphericity error,which are accurately evaluated is becoming more and more important,and it plays a very important role in guaranteeing the processing and quality control of parts.For example,the rolling bearings are widely used in modern instruments,automobile loading,aerospace and other equipment,the roundness error of the inner and outer rings directly affect the dynamic performance of the bearing.Such as high-speed centrifuges,precision machine tools,and air float gyros in the defense industry,the front bearings of their supporting spindles to ensure the accuracy of rotation mainly use the air bearings.The machining accuracy of these bearings is required to be very high,and they also have strict requirements on the sphericity of their inner and outer spherical surfaces.Another example is the spherical probe of a Nano-coordinate measuring machine(CMM).The roundness error of the cross section of the probe and the overall sphericity have a direct impact on the final measured result.At present,there is no specific method for roundness and sphericity evaluation,regardless of international standards or national standards,which is inconsistent with our actual application.Therefore,the study of the roundness and sphericity error evaluation technology is urgent.Based on the international definition of roundness error and the interpretation of sphericity error recognized by scholars,this paper proposes evaluation methods for circular and spherical profile based on the principle of minimum zone area to solve practical engineering problems and achieve accurate,rapid and effective evaluation of the two form errors.In order to avoid the difficulty of directly solving the mathematical model of topographic error,an asymptotic search model is established based on the search method of asymptotic search,search algorithms are proposed in this paper.The algorithm is called asymptotic search algorithm,and the core idea is that the control points that determine the minimum zone circle and the minimum zone sphere are gradually obtained.Then the center of the minimum zone circle and the minimum zone sphere are determined.The roundness error and sphericity error can be calculated as a result and finally the job of the roundness and sphericity error evaluation are completed.The main research work and research achievements of the thesis are summarized as follows:1)This paper proposes the asymptotic search model based on the search method of asymptotic search(gradually search along the target direction),which is used to gradually search for approximation and finally determines the target centre,and then the roundness error and sphericity error can be obtained,avoiding the problem of providing direct solution of objective function.The search process can be simply described as: The point close to the target centre is obtained by establishing a search model,and then this point is employed to search for the target centre using the search algorithm to complete the form error evaluation.2)A simple roundness evaluation method based on the minimum zone circle is proposed.By establishing a search circle model,the search direction is determined,and by means of introducing a quasi-MZC center,global convergence and local convergence are achieved.The unique solution that conforms to the minimum zone circle is searched,the true value of the roundness error is obtained and the job of the roundness error evaluation is completed as a result.The experimental verification of the roundness error evaluation algorithm was carried out.The roundness error evaluation algorithm is proven quickly,accurately and effectively through verifying the operation efficiency and accuracy of the algorithm with simulation and comparative experiments.3)A simple sphericity evaluation algorithm based on the minimum zone sphere is proposed.By establishing a search sphere model and using the feature points on the search sphere to determine the search direction.The global convergence is achieved.Introducing the concept of quasi-MZS center,the search obtains a unique solution that conforms to the minimum zone sphere and the truly value of sphericity error is determined,which improves the efficiency of the search and reduces the number of iterations of the algorithm.Through the verification of simulation experiments and comparative experiments,the results show that,in any case,the algorithm can find the sphericity error based on the principle of minimum zone area.It is proven the algorithm is also applicable to the sphericiy error evaluation of nonholonomic profile,such as the sphericity error evaluation of a spherical crown.The evaluation of sphericity error was completed quickly,accurately and efficiently.Finally,it is proven that the spericity erro evaluation algorithm can complete the error evaluation quickly,accurately and efficiently.4)Aiming at the evaluation of the sphericity error evaluation study of small-sized measured microsphere with diameters between tens and hundreds of micrometers,the design scheme and working principle of the microsphere sphericity error measurement system are briefly introduced.The microsphere topography data is employed for sphericity error evaluation using the sphericity error evaluation algorithm proposed in this paper.Through the comparison between different evaluation methods,it can be concluded that the asymptotic search algorithm has fewer iteration steps,fast convergence speed,low algorithm redundancy,and good compatibility with the number and distribution of measurement points of microsphere.It is proven the algorithm is stable,reliable and accurate for the sphericity error evaluation of microsphere and can improve the computation efficiency.Based on the above research,the roundness evaluation method based on the circle of the minimum containment area and the sphericity evaluation method based on the sphere of the minimum containment area proposed and implemented in this paper can be used to evaluate the roundness error of circular profile,sphericity error of spherical profile and sphericity error of nonholonomic profile.The results obtained by the two evaluation algorithms are accurately and reliably and also have a good ability of time efficiency and lower redundancy.This paper provides a new method and technology for the research of spherical surface form error evaluation,which has certain theoretical value and practical significance for the development of roundness and sphericity evaluation and application.