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This paper aims to improve calibration and force measurement accuracy of multi-sensors’ piezoelectric dynamometer used in thrust measurement of rocket/air vehicle engine.

This paper presents a mapping solution method of sensors’ outputs based on the Kirchhoff thin plate theory, builds force-deformation differential equations with specific boundary conditions, uses finite difference (FD) method to solve the equations and analyzes outputs in offset loading forces in four-sensor square layout in main direction. The resultant force deviations calculated by the Kirchhoff theory are optimized with sequence quadratic program (SQP) method, and a calibration method of multiple loading points (MLP) based on the Kirchhoff theory is presented. Experiments of static calibration and verification are complemented to contrast the novel and single loading point (SLP) calibration method.

Experiments of static calibration and its verification show that at a loading force of 5,000N, the average resultant force deviations with MLP is 17.87N (0.35% FS) compared with single loading point method 26.45N (0.53% FS), improving calibration and measurement precision.

A novel calibration method with MLP is presented. Force distributions of multiple sensors of main direction in piezoelectric dynamometer with offset loading force are solved with the Kirchhoff theory. The resultant force deviations calculated by Kirchhoff theory are optimized with the SQP method.

The purpose of this paper is to solve the problem that the analytic solution model of spatial three-dimensional coordinate measuring system based on dual-position sensitive detector (PSD) is complex and its precision is not high.

A new three-dimensional coordinate measurement algorithm by optimizing back propagation (BP) neural network based on genetic algorithm (GA) is proposed. The mapping relation between three-dimensional coordinates of space points in the world coordinate system and light spot coordinates formed on dual-PSD has been built and applied to the prediction of three-dimensional coordinates of space points.

The average measurement error of three-dimensional coordinates of space points at three-dimensional coordinate measuring system based on dual-PSD based on GA-BP neural network is relatively small. This method does not require considering the lens distortion and the non-linearity of PSD. It has simple structure and high precision and is suitable for three-dimensional coordinate measurement of space points.

A new three-dimensional coordinate measurement algorithm by optimizing BP neural network based on GA is proposed to predict three-dimensional coordinates of space points formed on three-dimensional coordinate measuring system based on dual-PSD.

The purpose of this paper is to solve the problem that the relationship between loading forces, which were applied at different positions on a plane, and output values of load-sharing dynamometer is non-linear.

First, the analytical model of ISPM (isodynamic surface proportional mapping method) method, which is used to calibrate dynamometer, was established. Then, a series of axial force calibration tests were performed on a load-sharing dynamometer at different loading positions. Finally, according to output values, calibration forces at different loading positions were calculated by ISPM method, and corresponding distribution histogram of calibration force error was generated.

The largest error between calculated force and standard force is 2.92 per cent, and the probability of calculated force error within 1 per cent is 91.03 per cent, which verify that the ISPM method is reliable for non-linear calibration of dynamometers.

The proposed ISPM method can achieve non-linear calibration between measured force and output signal of load-sharing dynamometer at different positions. In addition, ISPM method can also solve some complex non-linear problems, such as prediction of plane cutting force under the influence of multiple parameters, the force measurement of multi-degree-of-freedom platform and so on.

The purpose of this paper is to improve the reliability of the force measurement system by determining the reliable test range of dynamometer.

Based on the principle of leverage and moment balance, a general force distribution model is applicable in where the test point is located either inside or outside the support region of four three-component force links of dynamometer is established. After corroborating the correctness of the model through verification experiments, the boundary conditions that each three-component force link should satisfy are analyzed by considering the characteristic of the dynamometer components comprehensively. Furthermore, the reliable test range of dynamometer is determined, followed by a calibration experiment to verify its rationality.

The relationships between the reliable test range and the tested force, the bolt pre-tightening force and the bearing capacity of quartz wafers are clarified. Further, the experimental calibration results show that when the test point is within the reliable test range, the three-directional output voltage of dynamometer has excellent linearity and repeatability. The nonlinearity and repeatability in X-, Y- and Z-directions are all less than 1.1%.

A general mathematical model of force distribution of four three-component force links is constructed, which provides a theoretical basic for the mechanical analysis of multi-sensors’ dynamometer. Comprehensively considering the performance of dynamometer components, the value of measured force and the pre-tightening force, the simultaneous equations of reliable test range are deduced, which limits the boundary of allowable test position of piezoelectric dynamometer.