Research On A Method For On-machine Measuring Motion Errors Of A Linear Guideway Based On Grating Sensing

Precision / ultra-precision products play an increasingly important role in many fields,such as daily life,national defense,military and aerospace.The accuracy requirements of products in these areas are also becoming more stringent.For precision / ultra-precision products,the machining accuracy of a machine tool as the processing platform directly their accuracy,and the measurement accuracy of a coordinate measuring machine(CMM)as the universal measuring tool determines their quality.Therefore,how to improve the accuracy of a machine tool / CMM has always been a major concern in the industry.The linear guideway is the essential part of a machine tool /CMM.Its motion errors not only affect the accuracy of the machine tool /CMM,but also are the key parameters of the error compensation model.In addition,motion errors can reflect dynamically the operating status of a machine tool / CMM.Hence,on-machine measuring motion errors of a linear guideway has important engineering value and scientific significance.Although there are some measurement methods,they still cannot meet the industrial needs,especially for the case that a linear guideway works under the complicated condition.In this paper,a new method to on-machine measure these motion errors is proposed.It utilizes the proposed multi-probe error separation algorithm,applies the developed probe based on linear grating sensing and flexible transmission,and adopts the multi-step scanning measurement way to measure the motion errors of the linear guide.The basic theory and key technology of the proposed method are studied deeply and analyzed systematically.To separate motion errors of the linear guideway from the probe outputs,two error separation algorithms,the improved three-point algorithm in frequency domain and the new four-point algorithm in space domain,are developed.The three-point algorithm works as follows.A periodic coefficient is introduced for the zeroadjustment error to have the same configuration as the term associated with the reference profile.Then,two groups of differences derived from the probe outputs are periodically extended by the natural extension algorithm,and the corresponding spectral values are obtained by discrete Fourier series.Based on the spectral values,a weighting function is introduced to construct a periodic sequence that contains the complete spectrum of the reference profile and the relative zero-adjustment error solved.Then,the reference profile is calculated,and the straightness error separated from the probe outputs.The separation principle of the four-point algorithm is as follows.A system of linear equations is constructed based on the four probe outputs.To ensure that the linear system has a unique solution,two constraints are added: the first and last points of the reference profile are determined according to definition of the measuring coordinate system;the relative zero-adjustment error is estimated from the outputs of the first three probes through the generalized three-point algorithm.To restrain the ill-conditioned characteristics of the linear system,the Tikhonov regularization algorithm is used to solve the linear system.Finally,the straightness error and the tilt error of the linear guideway are separated from the probe outputs based on the regularization solution.The presented error separation algorithms are verified by simulation platforms,and the influences of error factors on the algorithms are quantitatively analyzed.In summary,the three-point algorithm and the four-point algorithm provide theoretical basis for the proposed method.To analyze the influences of the position and posture deviations between the readhead and the scale grating on moiré patterns and the output signals,the optical model of the linear encoder used as the sensor of the probe is established,and four algorithms are developed to identify characteristic parameters of the patterns.The optical model is established using Zemax to obtain the distribution of moiré patterns.A judgement criterion is proposed to obtain the frequency of the patterns,and then the related phase,mean and amplitude are calculated,so that the patterns are mathematically described.Then,the identification algorithms are validated using Matlab.In the optical model,the position and posture deviations of the readhead relative to the scale grating are introduced by modifying the coordinate parameters of the scale grating,and then the influences of these deviations on the characteristic parameters are analyzed.After that,the mathematical models of the output signals are established based on the characteristic parameters,and then the responses of the output signals to the position and posture deviations are analyzed.To further prove the simulation results,the experimental tests are carried out on a five-axis machining center.The above simulation analyses provide guidelines for the installation of the linear encoder and the design of the probe.Based on the linear encoders and the designed flexible mechanisms,two linear high-precision probes are constructed and their dynamic and static characteristics are analyzed.Firstly,according to the requirements of the error separation algorithms,the design principles of the flexible amplifying mechanism and the flexible loading mechanism are proposed,and then their configuration are designed.Secondly,the flexibility matrix of the notched flexure hinge is established according to the elastic mechanics theory,and then the flexibility model of the serial / parallel flexible mechanism derived using the matrix method.Thirdly,the flexibility models of the the functional modules in the flexible mechanism are established,and then the influences of dimension parameters on their kinematics and mechanical properties are analyzed.Finally,the static and modal analyses of the probes are performed using the finite element analysis.The probes consisting of the flexible mechanisms and the linear encoders lay the hardware foundation for the proposed method.To verify the feasibility and effectiveness of the proposed method,on-machine measuring the motion errors of a linear guideway is carried out.Firstly,the horizontal and vertical multi-step measurement systems are constructed using the developed probes and the micro-displacement platforms.For the multi-step measurement systems,the uncertainties of the motion errors are derived theoretically from the probe measurements.Secondly,to ensure the accuracy of the measurement data,the probes are calibrated to obtain the exact performance parameters,such as the gain coefficient and the input stiffness.Finally,with the help of the measurement systems,the two straightness errors are detected using the three-point algorithm;the two straightness errors,the yaw error,the pitch errors,the roll error and the related uncertainties are measured using the four-point algorithm.These motion errors are also measured directly using a laser interferometer.The consistencies between the experimental results of the proposed method and the measurement reulsts of the laser interferometer indicate that the proposed method is feasible and effective.