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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.

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.

A system for measuring the rail profiles of a long hydrostatic guideway is proposed and applied to a precision roll lathe. The rail profiles, consisting of rail form errors and a parallelism error, are measured with four capacitive probes placed on the two rail surfaces, and a laser interferometer with angular optics. The form error of each rail is measured using a mixed sequential two-probe method, while the parallelism error between the rails is measured with two opposing capacitive probes. To eliminate the necessity for additional guidance mechanisms, theprobe table is guided by air bearings and the rails being measured. To verify the measurement results, two self-verification techniques are suggested and tested. Firstly, the linear motion errors of the probe table on the two rails are compared, yielding a difference of 0.79 μm in 2σ. Secondly, the sum of the rail form errors is compared with the slope-removed sum of the two capacitive probes used for the parallelism measurement, yielding a difference of 0.81 μm in 2σ. According to the self-verification results, the accuracy of the proposed measurement method is about 1 μm for a rail length of 2,825 mm.

In the machine manufacture industry, the on-line test technique applies very extensively, the particularly automatic test technique is more outstanding. This article with the form error margin for example, designed a set of simple on-line test system to raise the accuracy of the machine product examination, assurance product quality, decline low cost depletion.

Dynamic precision measurement of transmission error involves many subjects such as optical, mechanical and electrical and computer at the forefront of technology has very important significance in the production. In order to achieve the accurate testing of motion error automobile gear, convenient and quick to obtain the gear tooth form error parameters, this paper research and design of the automobile gear error motion detection based on virtual instrument technology system, can accurately test automation, including visual inspection process, real-time detection information, read the data measured parameters, the analysis of characteristic curve, and other functions.

Assembly stress exists in mechanical equipment and instrumentation widely. Especially for precision mechanical systems, assembly stress may influence the system accuracy and performance. In this paper, taking form error and assembly force into account, the assembly stress and deformation were studied. By employing numerical simulation technology, the contact state of the part combining surface and additional deformational error were obtained, and an experiment was performed to verify the simulation calculation.

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.

An extracting method of normal residual error from a ground profile was proposed in this paper. Original measurement data was re-processed for obtaining an actual ground profile in an on-machine contact measurement system. The robust Gaussian regression filtering and NURBS fitting methods were employed to filter and fit these discrete data for getting the accurate realistic ground profile. By utilizing iterative partitioning algorithm, the normal residual error could be accurately obtained between the actual ground profile and the ideal one. Measurement data achieved from grinding experiment of aspheric mould were dealt with. After form error compensation grinding, the difference between normal residual error and original reached 40 nm in stead of initially 140 nm.

Assessment of spatial straightness error is one of the most difficult tasks in form error evaluation, especially when the minimum zone three-dimensional (3D) straightness is decided by four datapoints. This paper develops a solution that can transform the non-linear system into a linear system. To solve the linear indeterminate system of equations, a method of factor fixed is proposed. Given adequate initial conditions, this solution will be the exact solution. The effectiveness and efficiency of the novel approach are illustrated by two examples.

Design and manufacturing of spiral bevel and hypoid gears is highly complicated and has to be based on the employment of computerized tools. This paper comprehensively describes the latest developments in computerized modeling of tooth surface generation, flank form error correction, ease-off calculation, and tooth contact analysis for spiral bevel and hypoid gears. Accordingly, advanced software programs for computerized design and manufacturing of hypoid gears are developed.

Due to performance improvement and the trend of miniaturized sizes in optical devices, the need for micro lenses is increasingly presented. In this paper, characteristic study of a micro aspheric mold having a diameter of only 0.3 mm was performed. According to the experimental results of rough cuttings using a diamond tool, the machined surfaces were with a mean peak-to-valley (PV) form error of 1.47 µm. The Taguchi Method was employed to determine the optimal cutting parameters by selecting the cutting depth, work spindle speed, and compensation ratio as the control factors. Experimental trials were conducted according to the L9(34) orthogonal array (OA), and a mean PV form error of 0.79 µm was obtained due to compensation cuttings. Based on signal-to-noise (S/N) ratios, the optimal levels of control factors were determined. By performing the confirmation test, the PV form error was reduced from rough cutting of 1.49 µm to 0.60 μm. The effectiveness of using the Taguchi Method was demonstrated. The systematic approach performed in this paper can be applied to micro-fabrications for precision components in molds and dies industry.

Gear form grinding is an efficient finish machining method for the gears with hard face. There are many factors which have an influence on tooth error in grinding process. In addition to the form error of form grinding wheel, the radial feed depth of grinding wheel has large impact on the tooth error. Based on the principle of gear form grinding, the influence of wheel feed depth on tooth error is analyzed theoretically. The magnitude of error is also analyzed quantitatively according to the simulation result obtained by means of tooth error analysis module, which is developed based on VC + +6.0 software analysis. The research result has a certain reference value for preparing CNC form grinding process and setting machine tool properly.

According to needs of aspheric lens grinding and measurement with X/Y/Z 3-axis grinding machines, a CAM system is designed and implemented. The system, based on the parallel grinding geometry model, has realized the function of grinding locus planning, form error compensation, NC program auto-generation, on-machine measurement, grinding wheel on-machine measurement, simulation and technical database. To verify the stability of this CAM system, experiments were performed with three independent machining experiments. The experimental results indicate that the system realized the whole process of aspheric grinding, and it improved the machining efficiency and automation. Especially, this system adopted on-machine form error compensation technology and improved the machining accuracy. By implementing the error compensation integrated in the CAM system, the surface form error of a 430mm×430mm aspheric lens is decreased from PV8.2µm to PV4.1µm. The grinding accuracy was improved 100%.

This paper reported an experimental study on ultra-precision grinding for micro aspherical lens mould. One-point grinding mode and inclined axis grinding mode are employed and investigated in grinding process. Grinding test of a micro-lens mould using form error compensation technique is conducted. The experimental results show that ground micro aspheric mould surfaces with form (PV) around 0.122 µm and a roughness (Ra) less than 2 nm is achieved successfully.

In this study, an approach by the feed rate control was applied for the improvement of form accuracy in the micro end milling process. In this approach called adaptive control constraint, the feed rate is controlled so that the cutting load is constantly kept and the deflection of tool does not occur. However, this method is not always effective in the micro cutting process that the influence of size effect cannot ignore. Therefore, the relationship between the cutting conditions and the form error in the micro end milling is experimentally investigated. The experiments on the machining of metal mold steel with the micro end mill are carried out and the formulation as function of the cutting conditions and the form error is identified by means of regression analysis. The performance of the feed rate control was validated based on experimental results. As the result, it was confirmed that the form accuracy was improved.

A non-contact on-machine measurement system has been developed since various precise machines are getting lighter and smaller; therefore, processing with nano-precision is demanded recently. This system makes possible to measure with high precision without any damages and it is unnecessary for workpieces to attach or detach from a machine tool. Moreover, this system achieves on-machine form error compensation with high precision. On the other hand, the details of the system performances are still unknown. This study focuses on evaluating the performances by the comparison of the results that measured by this system and an existing measurement instrument under various conditions. As a result, this system shows an equivalent capability of measurement with high precision as the existing measurement instrument.

Aspherical parts are installed in various optical instruments. At present, a higher form accuracy is required for aspherical parts to improve the resolution of the optical instruments. To meet this demand, an arc envelope grinding method has been developed. In the arc envelope grinding process, a spherical shaped grinding wheel is used and the form error of the cross-sectional profile of the grinding wheel is transcribed to the workpiece profile. Therefore, the grinding wheel should be trued previously. However, the form error of the grinding wheel cannot be removed perfectly. To reduce the affect of the form error of the grinding wheel, compensation grinding must be carried out. In this work, the wheel path of a new compensation grinding method is proposed for a high NA value of the workpiece. Tests using the new compensation grinding method demonstrate the reduction in the form error of aspherical parts.