Positioning Accuracy Determination of the Servo Axes for Grinding Wavy-Tilt-Dam Seals Using a Four-Axis Grinder

The wavy-tilt-dam (WTD) seal is considered to be one of the ideal sealing patterns used in nuclear reactor coolant pumps (RCPs). Grinding such seals with a four-axis grinder had been proposed and six grinding implementation strategies were described in our previous studies. However, another important issue is to determine the positioning accuracy of each servo axis so that the high-precision moving components can be selected properly. In the present paper, the positioning accuracy analysis is carried out to seek a balance between the manufacturing cost and the accuracy requirements. First, a geometric model is established for investigating the error sensitivity of each axis and setting reasonable accuracy allocation of the four axes. Subsequently, the combined influence of all four axes is assessed based on multi-body system (MBS) theory and homogeneous transformation matrix (HTM). According to the results calculated, positioning errors of the X-axis, Z-axis, B-axis, and C-axis within ±10 μm, ±0.1 μm, ±1 arcsec and ±60 arcsec are acceptable, respectively. Meanwhile, the form error calculated of the ground wavy face is no more than 109.74 nm. It is indicated that the accuracy level of the moving components is achievable by modern manufacturing techniques. The present paper is expected to serve as a theoretical basis for the design and development of the four-axis grinder.

Application of Advanced Simulation Methods for the Tolerance Analysis of Mechanical Assemblies

In the frame of a statistical tolerance analysis of complex assemblies, for example an aircraft wing, the capability to predict accurately and fast specified, very small quantiles of the distribution of the assembly key characteristic becomes crucial. The problem is significantly magnified, when the tolerance synthesis problem is considered in which several tolerance analyses are performed and thus, a reliability analysis problem is nested inside an optimisation one in a fully probabilistic approach. The need to reduce the computational time and accurately estimate the specified probabilities is critical. Therefore, herein, a systematic study on several state of the art simulation methods is performed whilst they are critically evaluated with respect to their efficiency to deal with tolerance analysis problems. It is demonstrated that tolerance analysis problems are characterised by high dimensionality, high non-linearity of the state functions, disconnected failure domains, implicit state functions and small probability estimations. Therefore, the successful implementation of reliability methods becomes a formidable task. Herein, advanced simulation methods are combined with in-house developed assembly models based on the Homogeneous Transformation Matrix method as well as off-the-self Computer Aided Tolerance tools. The main outcome of the work is that by using an appropriate reliability method, computational time can be reduced whilst the probability of defected products can be accurately predicted. Furthermore, the connection of advanced mathematical toolboxes with off-the-self 3D tolerance tools into a process integration framework introduces benefits to successfully deal with the tolerance allocation problem in the future using dedicated and powerful computational tools.

Coupling and Decoupling Measurement Method of Complete Geometric Errors for Multi-Axis Machine Tools

Precision and ultra-precision machining technology rely mainly on the machine tools’ accuracy. To improve it, the measurement, calculation, prediction and control of geometric errors are critical. The traditional measurement methods have lower precision because of ignoring small angle errors. To obtain complete geometric errors of multi-axis machine tools, this paper proposes a new method of coupling and decoupling measurement. Specifically, we used a laser interferometer and dial indicators to measure 36 items of complete geometric errors of multi-axis machine tools. A homogeneous transformation matrix (HTM) was applied to model the error transfer route. The transfer law of complete errors for each machining point was explored and derived. Furthermore, we selected and calculated integrated errors of 36 machining points. Finally, we proved the correctness of the method by comparing the measurement result of a ball bar test and coupling and decoupling measurement of geometric errors. We found that items of small geometric angle errors have a greater impact on machining accuracy than those of geometric displacement errors. Complete geometric errors measured via the coupling and decoupling measurement method can evaluate integrated errors more precisely and comprehensively.

Posture adjustment method for large components of aircraft based on hybrid force-position control

Purpose Flexible tooling for adjusting the posture of large components of aircraft (LCA) is composed of several numerical control locators (NCLs). Because of the manufacture and installation errors of NCL, the traditional control method of NCL may cause great interaction force between NCLs and form the internal force of LCA during the process of posture adjustment. Aiming at this problem, the purpose of this paper is to propose a control method for posture adjustment system based on hybrid force-position control (HFPC) to reduce the internal force of posture adjustment. Design/methodology/approach First of all, the causes of internal force of posture adjustment were analyzed by using homogeneous transformation matrix and inverse kinematics. Then, axles of NCLs were divided into position control axle and force control axle based on the screw theory, and the dynamic characteristics of each axle were simulated by MATLAB. Finally, a simulated posture adjustment system was built in the laboratory to carry out HFPC experiment and was compared with the other two traditional control methods for posture adjustment. Findings The experiment results show that HFPC method for redundant actuated parallel mechanism (RAPM) can significantly reduce the interaction force between NCLs. Originality/value In this paper, HFPC is applied to the control of the posture adjustment system, which reduces the internal force of LCA and improves the assembly quality of aircraft parts.

Improving the Method for Kinematic Analysis of Mechanisms That Was Based on Parametric Polynomial System With Gröbner Cover

A polynomial system that contains parameters is termed a parametric polynomial system (PPS). We had previously proposed a method of kinematic analysis of mechanisms based on PPS with Gröbner cover, where the parameters are used to express link lengths, displacements of active joints, and so on. Calculating Gröbner cover of PPS that expresses kinematic constraints, and interpreting the segments of the parameter space that are generated by Gröbner cover, it is possible to gain an insight for comprehensively understanding kinematic properties of mechanisms characterized by the parameters. In this study, certain improvements to the method were made to enhance its practical application. The validity check of the segments in the real domain using quantifier elimination provides an automatic reliable check even for a large number of segments. The evaluation of the solution spaces in the segments using primary decomposition facilitates the kinematic interpretation of the complex solution spaces. The active joint selection based on the variable order in Gröbner cover enables the analyses without explicitly specifying active joints. Moreover, the alternative algebraic formulation of kinematic problems based on a homogeneous transformation matrix provides further insight regarding the mechanisms containing zero-length links. The effectiveness of these improvements was verified by the analyses of the configurations of 3RPR mechanism and five-bar linkage.

Kinematic analysis of a PPPR spatial serial mechanism with geometric errors

The present study focuses on the kinematic analysis of a PPPR spatial serial mechanism with a large number of geometric errors. The study is implemented in three steps: (1) development of a map between the end-effector position error and geometric source errors within the serial mechanism kinematic chains using homogeneous transformation matrix; (2) selection of geometric errors which have significant effects on end-effector positioning accuracy by sensitivity analysis; (3) kinematic analysis of the serial mechanism within which the geometric errors are modelled as interval variables. The computational algorithms are presented for positioning accuracy analysis and workspace analysis in consideration of geometric errors. The analysis results show that the key factors which have significant effects on end-effector position error can be identified efficiently, and the uncertain workspace can also be calculated efficiently.

Reference trajectory tracking for a multi-DOF robot arm

This paper presents the problem of tracking the generated reference trajectory by the simulation model of a multi-DOF robot arm. The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. To obtain the solution of the forward kinematics problem, the homogeneous transformation matrix is used. A solution to the inverse kinematics is a vector of joint configuration coordinates calculated using of pseudoinverse Jacobian technique. These coordinates correspond to a set of task space coordinates. The algorithm is presented which uses iterative solution and is simplified by considering stepper motors in robot arm joints. The reference trajectory in Cartesian coordinate system is generated on-line by the signal generator previously developed in MS Excel. Dynamic Data Exchange communication protocol allows sharing data with Matlab-Simulink. These data represent the reference tracking trajectory of the end effector. Matlab-Simulink software is used to calculate the representative joint rotations. The proposed algorithm is demonstrated experimentally on the model of 7-DOF robot arm system.