Jiangang Li

Bio: Jiangang Li is an academic researcher from Harbin Institute of Technology. The author has contributed to research in topics: Motion control & Machine tool. The author has an hindex of 6, co-authored 23 publications receiving 128 citations.

Numerical computing method of noncircular gear tooth profiles generated by shaper cutters

Abstract: A simple and accurate numerical method was proposed for calculating the tooth profile of a noncircular gear. This method is directly based on the real gear shaping process, rather than deducing and solving complicated meshing equations used in the traditional method. The tooth profile is gradually obtained from the boundary produced by continuously plotting the cutter profile on the gear transverse plane. The key point of the method is picking up the graph boundaries. The relative position of the cutter profile on the gear transverse plane is determined by the given pitch line of the noncircular gear, parameters of the shaper cutter, and the shaping process data. In comparison with the traditional method, it is universal and is much more efficient and accurate, especially for noncircular gears, which have nontrivial pitch lines. Special problems in gear design and manufacturing, such as tooth pointing, undercut, and fillet interference, are included in the process. As an application example of the numerical method, a square internal gear is chosen from a new type of hydraulic motor with noncircular planetary gears, and the tooth profile of that gear is computed. The gear is successfully machined by electromagnetic discharge (EMD) using the resulting data.

Bevel gear machining method

Abstract: The invention discloses a bevel gear machining method. According to the geometric parameters and the required tooth system of a gear to be machined, the method comprises the following steps that: (1) the parameters of a shaping gear wheel are determined; (2) the tooth traces of the shaping gear wheel are determined; (3) the parameters of a cutter are determined; (4) the cutter movement on the tooth surface of the shaping gear wheel is determined; (5) the basic tooth surface modification of the shaping gear wheel is determined; (6) the movement of the shaping gear wheel generating the gear is determined; (7) the movement of the gear generated by the shaping gear wheel is corrected; and (8) the generation of the gear to be machined is completed. The invention has the advantages that: (1) the cutting and the grinding of bevel gears with straight teeth, curved teeth, cycloidal teeth, quasi-involute teeth and the like can be implemented on one machine tool; (2) the dimension of the cutter is determined only by the module of the gear to be machined and has nothing to do with the diameter of the gear to be machined and the tooth width; (3) the diameter of the cutter or the grinding wheel is small, the torque of the machine tool spindle is small, the force applied to the machine tool is small, the deformation of the machine tool is small and the machining accuracy is high; (4) the position, the dimension and the shape of the contact spots on the tooth surface can be conveniently controlled and all kinds of theoretically full-conjugated bevel gear pairs can be machined; and (5) the transmission ratio function required by the gear pairs to be machined can be accurately realized.

Time-optimal and energy-efficient trajectory generation for robot manipulator with kinematic constraints

Abstract: This paper designs an algorithm to generate time-optimal and energy-efficient trajectory for manipulators along a predefined geometric path. The path is first parameterized by cubic spline, then the trajectory generation problem is transformed into a nonlinear optimization problem with single state variable. After discretization, Sequence quadratic programming(SQP) method is applied for optimal solution. Finally, applications to a 6-DoF manipulator along different paths demonstrates the feasibility of the proposed method.

An adaptive off-line NURBS interpolator for CNC machining

Abstract: As a key technique in CNC machining, nonuniform rational B-spline (NURBS) interpolator has been proposed to overcome the drawbacks caused by linear and circular interpolator, such as large data size, velocity discontinuity, shocks or variations in mechanical systems, and low machining efficiency. To improve machining quality and efficiency, an adaptive off-line interpolator was developed for NURBS curves in this paper. Both the chord accuracy and the acceleration/deceleration capability of machine tool are considered in the algorithm. There are four modules in the algorithm, adaptive feed rate adjustment, acceleration/deceleration disposal, feed rate modification, and S-type velocity generation. The acceleration/deceleration around the sharp corners is carefully calculated by those modules. A case study was provided to evaluate the feasibility of the interpolator.

Cubic spline interpolation on new condition

Abstract: Based on analysis of basic cubic spline interpolation,the traditional cubic spline interpolation is generalized.The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given.At last,these calculation methods are illustrated through the examples.

Development of a real-time look-ahead interpolation methodology with spline-fitting technique for high-speed machining

Abstract: Methodologies for converting short line segments into parametric curves were proposed in the past. However, most of the algorithms only consider the position continuity at the junctions of parametric curves. The discontinuity of the slope and curvature at the junctions of the parametric curve might cause feedrate fluctuation and velocity discontinuous. This paper proposes a look-ahead interpolation scheme for short line segments. The proposed interpolation method consists of two modules: spline-fitting and acceleration/deceleration (acc/dec) feedrate-planning modules. The spline-fitting module first looks ahead several short line segments and converts them into parametric curves. The continuities of the slope and curvature at each junctions of the spline curve are ensured. Then the acc/dec feedrate-planning module proposes a new algorithm to determine the feedrate at the junction of the fitting curve and unfitted short segments, and the corner feedrate within the fitting curve. The chord error and acceleration of the trajectory are bounded with the proposed algorithm. Simulations are performed to validate the tracking and contour accuracies of the proposed method. The computational efforts between the proposed algorithm and the non-uniform rational B-spline (NURBS)-fitting technique are compared to demonstrate the efficiency of the proposed method. Finally, experiments on a PC-based control system are conducted to demonstrate that the proposed interpolation method can achieve better accuracy and reduce machining time as compared to the approximation optimal feedrate interpolation algorithm.

Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration

Abstract: In this paper, an efficient algorithm is proposed to generate a smooth near-time-optimal feedrate function along a parametric tool path for three-axis CNC machining under a feedrate bound, an acceleration bound for each axis, and a chord error bound. The algorithm first gives a discrete and computationally efficient algorithm to find a sequence of globally optimal velocity points under the feedrate, acceleration, and chord error bounds. A linear programming strategy is proposed to smooth the velocity points sequence. Finally, the velocity points sequence is fitted into a cubic spline to obtain a near-time-optimal and smooth feedrate function. Simulation and experiment results for Non-uniform rational basis spline curves are presented to illustrate the feasibility of the algorithm.

Task Polar Coordinate Frame-Based Contouring Control of Biaxial Systems

Abstract: Contouring control is crucial in high-speed and high-precision manufacturing. In this paper, a novel task polar coordinate frame (TPCF), moving along the desired contour, is proposed to naturally calculate and control the estimated contouring error by the circular approximation, a second-order approximation. The dynamics in the world Cartesian coordinate frame is transformed into radial and angular dynamics in the local polar coordinate frame. By the feedback linearization technique and an input feedforward compensation, the closed-loop dynamics are decoupled in terms of the estimated contouring error and the angular error, respectively. Proportional-plus-derivative controllers can be assigned to stabilize the individual axis dynamics in the TPCF. By tuning the control parameters, different strengthening on estimated contouring error and angular error can be imposed explicitly and directly. Various experiments on an XY-stage biaxial system with typical contours, a circle and a figure-“8,” were conducted. Comparative studies are carried out for the TPCF- and traditional Frenet frame-based controls. The contouring errors were drastically reduced by the proposed approach, particularly in high-speed and large-curvature contouring cases.