An image-based algorithm for generating smooth and interference-free five-axis sweep scanning path

https://doi.org/10.1016/j.rcim.2021.102159Get rights and content

Highlights

  • The proposed method adopts image-based algorithm to efficiently calculate the interference-free area of the stylus.

  • The time-consuming heuristic algorithm is avoided in the optimization of the probe head trajectory.

  • Compared with the existing zigzag scanning path, the proposed sweep scanning path helps to reduce the kinematic loads and dynamic errors.

  • In real experiment, the length of probe head trajectory in sweep scan mode is merely 14.55% of that in zigzag mode.

  • The proposed method performs well when obstacle exists in the inspection environment.

Abstract

Five-axis continuous scanning inspection is an emerging technology in measuring free-form surfaces. Compared to the traditional three-axis scanning inspection, the five-axis continuous surface scanning tremendously boosts the inspection efficiency and suffers from less dynamic error due to adopting a special sweep scanning working mode, which lets the super-light and high-speed rotary two-axis probe head take over the majority of the inspection work. However, there has not been any efficient method to generate sweep scanning path for a free-form surface with external obstacle. The major problem is how to guarantee the non-interference condition during the scanning process. In this paper, a two-step algorithm for generating smooth and interference-free sweep scanning path is proposed. First, an image-based algorithm is proposed to incrementally calculate the admissible area of the stylus along the scanning path. Then an optimized B-spline fitting algorithm is proposed to find the optimal probe head trajectory within the admissible area, which simultaneously guarantees the smoothness and non-interference of the trajectory. In the real experiment, the average tangential velocity and acceleration of the machine's translational axes with the proposed five-axis sweep scanning path are only 16.45% and 17.19% of those with three-axis zigzag scanning path respectively. When inspecting a high-accuracy cylindrical surface with high scanning velocity, the root mean square of the surface profile error is 0.002 mm and 0.004 mm in five-axis scanning and three-axis scanning respectively. The experimental result manifests that the sweep scanning path tremendously helps to reduce the kinematic loads and the dynamic errors of the inspection machine.

Introduction

The parts with free-form surface have been widely used in industries such as aerospace and aviation. Precise and efficient inspection of these products is required in both quality control and reverse engineering, where a large quantity of high-precision points should be collected during a short period [1,2]. The coordinate measuring machine (CMM) is mainly applied for measuring those products which require micron-level accuracy, e.g. the turbine blades. However, the traditional three-axis or three + two-axis CMM inspection usually works in a point-by-point manner, as shown in Fig. 1(a). The surface is discretized as a series of sample points. The probe tip is controlled to touch each sample point independently with approaching-retraction operations [3]. Under such circumstances, the air-move between two sample points is very time-consuming. When the number of the sample points gets large, the point-by-point inspection may take several hours, which cannot meet the requirement of efficient inspection in the product line. To handle this problem, an emerging inspection technology, called five-axis sweep scanning, has been developed recently. A probe head, which is composed of two orthogonal rotary axes, is mounted at the traditional linear three-axis CMM. The stylus can quickly swing around the pivot point, i.e. the intersection of the two rotary axes, and keep in touch with the surface during the inspection, as shown in Fig. 1(b). Different from the traditional three + two-axis CMM inspection, the five axes move simultaneously whilst acquiring high-density points (e.g. up to 2000 per second) in the five-axis continuous sweep scan.

The errors in CMM inspection can roughly be classified into two types, i.e. the quasi-static error and the dynamic error [4]. The sources of quasi-static error generally contain the geometric error and thermal error, which has been comprehensively investigated. Many compensation methods of quasi-static error have been proposed [5,6] and applied to commercial measurement systems. However, the dynamic error is another story. The dynamic error in CMM inspection is considered to be velocity-related or acceleration-related. As the rising demand for shorter inspection time in industry manufacturing, the CMM is required to work at high speed. The heavy CMM gantry causes considerable inertia load and geometric distortion at high speed, because of the large inertia and low-stiffness structures [7]. To minimize the influence of dynamic error, various methods have been proposed, such as decreasing the mass of CMM parts [8] and predicting the dynamic error by mathematic models [9,10]. However, the dynamic error compensation is much more complex than quasi-static error compensation and not thoroughly solved.

Five-axis inspection does not aim to compensate the dynamic error, but to control it from the source. In five-axis inspection, the heavy CMM gantry moves smoothly and slowly to avoid large inertia loads. The extremely light stylus, which is made of carbon fiber, oscillates at high speed to accomplish the majority of scanning work. Many existing researches have revealed the advantage of five-axis measurement in reducing the dynamic errors. Sousa [7] measured a standard ring gage at increasing speeds. When the scanning speed reaches 50 mm/s, the diameter error of the ring gage is 12μm and 3.0μm in three-axis and five-axis measurement respectively. The roundness error is 12.9μm and 4.0μm in three-axis and five-axis measurement respectively. Gaska et al. [11] and Krajewski et al. [12] obtained similar results in their articles. Thus, the main principle of five-axis sweep scanning path planning is that the trajectory of the probe head (driven by the heavy CMM gantry) should be short and smooth, while the probe tip (driven by the extremely light rotary stylus) should move fast to take over a larger proportion of the whole scanning work.

In the field of three or three + two-axis CMM inspection, most current researches on the inspection path planning mainly focus on the selection strategy of sample point. There are two main categories of sampling methods, i.e. the blind sampling [13,14] and adaptive sampling. In the blind sampling strategy, the sample points are chosen with predefined principles, such as isoparametric curves [13] and mean Gaussian curvature [14]. Another kind of sampling strategy is adaptive sampling, in which the least number of sample points are expected to be selected. Yu et.al [15] proposed a method to iteratively add sample points until the form error is under the predefined threshold. Yin et al. [16] proposed an intelligent sampling strategy based on dependent Gaussian process to determine the distribution of the sample points. The distribution of sample points in adaptive sampling is changeable and is dependent on the permissible error. Nevertheless, the distribution of sample points in traditional three-axis CMM inspection is not suitable for the five-axis sweep scanning. As it only considers the geometric characteristic of the measured surface, the kinematic performance of the CMM machine is totally neglected. Thus, the path planning for five-axis sweep scanning still needs to be fully investigated.

The fundamental issues of the five-axis inspection mainly fall into 2 categories, i.e. accessibility analysis and inspection path optimization. Hu et al. [17] proposed a semiautomatic method to generate a five-axis continuous scanning path on a large and relatively flat surface. They introduce some basic algorithms of sweep path planning under some assumptions, e.g. the surface must be relatively flat. Zhou et al. [18] proposed a guiding curve based path planning method to iteratively adjust the stylus orientation in order to satisfy the requirement of the contact angle between the stylus and the surface. However, the guiding curve and the initial contact angle are specified manually by the users’ experience. Zhang et al. [19] proposed a method to generate sweep scanning path on an arbitrary surface. The surface is first partitioned and approximated by several elementary shapes, e.g. plane, cylinder and cone, and then the inspection path is planned for each patch individually. The above mentioned works [17], [18], [19] have two common drawbacks. One is that the interference problem is not considered. The inspected surface is usually assumed relatively flat so that the possibility of interference is low. Another one is that the criterion of choosing the stylus orientation at each guiding curve point is not clear. Then, Zhang et al. [20] defined an index called hybrid swept area as the criteria of determining the trajectory of the probe head. They took both the kinematics of the inspection machine and the geometric properties of the surface into consideration. However, this criterion is local optimum but not global optimum. Hu et al. [21] proposed a concept called aggregate admissible orientation domain to construct the interference-free area of the stylus and used a heuristic optimization algorithm to obtain the optimal stylus orientation. However, the construction of aggregate admissible orientation domain is quite time-consuming.

The existing research on five-axis sweep scanning path planning is rather scarce. Because the process of five-axis sweep scanning is somewhat similar to the five-axis numerical-controlled (NC) machining, the path planning algorithm of five-axis machining can be partially applied to the five-axis sweep scanning.

In five-axis machining, many access-based methods are proposed to prevent the collision between the tool and the surface. Morishige et al. [22] proposed configuration space (C-space) method to obtain the feasible orientations of the stylus. When the obstacles are projected to the two-dimensional C-space, the remaining area in C-space represents the feasible orientations. Balasubramaniam et al. [23] proposed the concept of visibility cone to convert the collision problem into the visibility problem. The candidate orientations are vertexes of the triangulation mesh of the Gaussian sphere. Wang et al. [24] proposed a method to efficiently calculate the visibility map (VMap). The visibility map is a rectangular domain of the stylus orientations, which is similar to the C-space. Bi et al. [25] proposed a GPU-based method to implement the collision checking. With the occlusion query functionality of the graphics hardware, the infeasible orientations are removed. In five-axis continuous scanning, the stylus should be interference-free in the whole process of oscillating motion, which is more difficult than the collision-free problem in five-axis machining.

As for path optimization, different methods are proposed to obtain the optimal trajectory of the machine axes within the feasible region. Ma et al. [26] proposed a smoothing method to optimize the tool axis vector by quaternion interpolation. Bi et al. [27] tried to minimize the distance between two neighboring cutter location (CL) points. This minimization problem was solved by finding a shortest path in the graph with Dijkstra algorithm. Lu et al. [28] defined the tool path smoothness as the sum of the square of the first, second and third derivatives of the tool path. A heuristic algorithm, i.e. differential evolution algorithm, is applied to solve the optimal joint motion of a six-axis industrial robot. Although there are plenty of researches about the five-axis machining path planning, these algorithms cannot be applied directly to the field of five-axis continuous scanning. It is because the rotary axes of five-axis machine tool are much heavier than that of the probe head. In other words, the rotary axes of five-axis machine tool cannot move fast as they have much larger inertia. For this reason, an important criterion in five-axis machining path planning is to avoid the drastic change of the tool orientation. In contrast, the rotary axes of the probe head for five-axis sweep scanning should move very fast due to its extremely slight structure.

Apart from the path planning, the velocity scheduling is also an important part in NC machining or robotic machining to improve the kinematic performance. The velocity scheduling takes into account several constraints, e.g. the chord error, speed limit, acceleration limit and jerk limit, to determine the feed rate along the path [29,30]. The velocity scheduling can be divided into two categories, i.e. scheduling in part space and scheduling in joint space. When scheduling in the part space, the trajectory can precisely track the given path and control the overall positioning errors [31,32]. When scheduling in the joint space, the dynamics (velocity, acceleration and jerk) can be addressed separately for each axis [33,34]. By establishing time interpolation model for one-dimensional motion, the machine trajectory can be obtained by synchronizing all the axes motions. The velocity scheduling indeed helps to constrain the maximum velocity and acceleration of the axes, which can result in better kinematic performances of the machine. However, the kinematics and servo controllers of most of current commercial five-axis CMMs have not been technically opened to engineers and researchers (e.g. the Renishaw UCCServer system employed in our job), that is the velocity scheduling is conducted automatically in a commercial black-box controller. In this paper, we mainly focus on the issue of path planning while leaving out the velocity scheduling issue.

Inspired by the existing works, this paper presents an algorithm to efficiently generate an interference-free sweep scanning path. First, the admissible orientation of the stylus over the whole surface is calculated with image processing methods. Then, an optimized spline fitting algorithm is applied to extract the optimal orientation from the candidate orientations. These optimal orientations finally form the trajectory of the probe head and the stylus tip. Compared to the existing methods, the proposed method has the following advantages:

  • 1

    Instead of checking all the candidate orientations, the proposed method takes full advantage of the discretized admissible map and checks the least number of stylus orientations. The resulting orientations meet the unique interference-free constraints of generating a probe head trajectory for effective five-axis sweep scanning.

  • 2

    A cubic B-spline fitting method is applied to find an optimal trajectory of the probe head, which avoids the time-consuming process of heuristic optimization process and ensures the smooth movement of the three CMM axes.

The paper is organized as follows. In Section 2, the procedure of generating five-axis sweeping path is briefly introduced. In Section 3, the algorithm of calculating admissible area is proposed. In Section 4, a B-spline fitting method is applied to extract the trajectory curve of the probe head. Experiments are conducted in Section 5 to verify the proposed method. The conclusions are drawn in Section 6.

Section snippets

Brief introduction of generating five-axis sweeping path

In this section, the generation method of five-axis continuous sweeping path is briefly introduced. More details of generating a sweeping path can be found in our earlier work [19,20]. A typical five-axis scanning system is shown in Fig. 2. The configuration is composed of a CMM with three linear axes X, Y and Z and a probe head with two rotary axes A and C. In five-axis inspection, the movement of CMM determines the position of the probe head. The motion of two rotary axes of the probe head

Introduction of AOD

The admissible orientation domain (AOD) of the stylus is proposed by Hu [21]. The admissible orientation domain is similar to the visibility map in the inspection planning with laser scanning [37] and accessibility map in the tool path generation of five-axis machining [24]. Before we introduce the proposed method of constructing the AOD, the definition should be first explained.

There are three constraints that need to be considered before constructing the AOD.

Constraint 1: The stylus should

Trajectory curve generation with cubic B-spline fitting

In this section, generation of the trajectory of the probe head, i.e. the trajectory curve, is investigated in detail.

Experiments

The real inspection experiment is conducted to verify the effectiveness of the proposed method. The five-axis inspection machine used in the experiment is composed of a three-axis Renishaw Agility CMM and a Renishaw Revo probe head system with two continuous rotary axes. Stylus module RSP2 and stylus RSH250 are used in the experiment. The stylus length is 250 mm and the tip radius is 3 mm. Renishaw CMM controller supports Inspection-plusplus Dimensional Measurement Equipment Interface (I++

Conclusion

This paper presents an image-based algorithm for generating smooth and interference-free sweep scanning path. Considering the similarity of admissible areas of the adjacent path points, an incremental algorithm is proposed to efficiently calculate the interference-free area of each path point. Then, an optimized B-spline fitting algorithm is proposed to smooth the trajectory curve of the probe head. Compared with previous researches, the proposed path planning method has the following

CRediT authorship contribution statement

Yijun Shen: Conceptualization, Methodology, Writing - original draft. Wenze Zhang: Formal analysis, Investigation. Limin Zhu: Supervision, Project administration. Yang Zhang: Funding acquisition, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research was supported by the National Natural Science Foundation of China (Grant No. 51905346 and No. 91948301) and the Science & Technology Commission of Shanghai Municipality (Grant No. 19511106000).

References (42)

  • P. Hu et al.

    Automatic generation of efficient and interference-free five-axis scanning path for free-form surface inspection

    Comput. Aided Des.

    (2018)
  • M. Balasubramaniam et al.

    Generating 5-axis NC roughing paths directly from a tessellated representation

    Comput. Aided Des.

    (2000)
  • N. Wang et al.

    Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath

    Comput. Aided Des.

    (2007)
  • P. Bosetti et al.

    Feed-rate and trajectory optimization for CNC machine tools

    Rob. Comput. Integr. Manuf.

    (2014)
  • S.D. Timar et al.

    Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds

    Rob. Comput. Integr. Manuf.

    (2007)
  • J. Huang et al.

    Real-time feedrate scheduling for five-axis machining by simultaneously planning linear and angular trajectories

    Int. J. Mach. Tools Manuf

    (2018)
  • D.F. ElKott et al.

    Isoparametric line sampling for the inspection planning of sculptured surfaces

    Comput. Aided Des.

    (2005)
  • D.K. Moru et al.

    A machine vision algorithm for quality control inspection of gears

    Int. J. Adv. Manuf. Tech.

    (2020)
  • Y. Li et al.

    Orientation-point relation based inspection path planning method for 5-axis OMI system

    Rob. Comput. Integr. Manuf.

    (2020)
  • Y. Echerfaoui et al.

    Experimental Investigation of Dynamic Errors in Coordinate Measuring Machines for High Speed Measurement

    Int. J. Precis. Eng. Manuf.

    (2018)
  • M. Vermeulen, P. Rosielle, P.H.J. Schellekens, C. Cirp, Design of a high-precision 3D-Coordinate Measuring Machine,...
  • Cited by (0)

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