Citation: Fang, Y.; Li, P.; Zhen, X.;
Shen, Z. Modeling of Adjustable
Bending Pipe to Compensate for Pipe
Assembly Production Errors.
Machines 2022, 10, 409. https://
doi.org/10.3390/machines10060409
Academic Editors: Fang Cheng,
Qian Wang, Tegoeh Tjahjowidodo
and Ziran Chen
Received: 30 March 2022
Accepted: 18 May 2022
Published: 24 May 2022
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Article
Modeling of Adjustable Bending Pipe to Compensate for Pipe
Assembly Production Errors
Yijun Fang
1
, Pin Li
2,3,
*, Xijin Zhen
3
and Zongbao Shen
2
1
School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China; fangyijun@ujs.edu.cn
2
School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China; szb@ujs.edu.cn
3
Shipbuilding Technology Research Institute, Shanghai 200032, China; zxj20laser@163.com
* Correspondence: lip@ujs.edu.cn
Abstract: The production of pipe assembly for a rocket engine has experienced challenges owing to
the higher requirements of the joining and sealing performance. An adjustable laser bending pipe is
a flexible and economical means of compensating for production errors after welding, located in the
“closing” segment. To improve the productivity and accuracy of the adjustable laser bending pipe,
inline measurement systems are integrated into production to develop an adaptive control system.
The models of adjustable laser bending pipe to compensate for pipe assembly production errors are
established using kinematics and the displacement screw system, and the proposed adaptive control
system is validated by the experiment based on the springback-free laser pipe bending process.
Using the proposed adaptive control system, the angle deviation decreases from 7.086
◦
to 0.154
◦
, and
the distance deviation decreases from 5.076 mm to 0.104 mm. The validation results satisfactorily
meet the requirement of the welding axis alignment of the pipe ends. These models demonstrate
significant potential to be applied for calculating the feedback parameters required in the adjustments
to compensate for pipe assembly production errors.
Keywords: errors compensation; pipe production; laser bending; adaptive
1. Introduction
The pipe assembly process is commonly encountered in various fields, such as the
aircraft, aerospace, and ship building industries. Pipe assembly plays an important role
in product quality, including the safety, reliability, performance, and life cycle of the
product [
1
]. In an aero-engine, approximately 50 accessories, hundreds of clamps, and
100–250 pipes exist within the narrow space between the engine casing and nacelle. These
pipes connect the engine components, accessories, and aircraft to transmit fluids and
ensure that the engine operates. Academic researchers and practitioners in engineering
disciplines generally pay considerable attention to pipe routing algorithms in the field of
pipe assembly design [
2
]. Pipe routing is a time-consuming and difficult task, even for
skilled designers, owing to the complexity of 3D space and the vast amount of engineering
rules involved, such as avoiding obstacles, closely following obstacle contours, and meeting
assembly feasibility requirements. In practice, there are equally significant difficulties in
pipe assembly production. Certain digital assembly and measurement techniques have
been realized. For example, a simulation technology for the pipe bending process has
been applied to collision detection [
3
]. A 3D measurement system for pipe assembly was
developed to improve the assembly productivity and accuracy [4]. Simulation of the pipe
assembly process has been utilized for interference checking and sequence optimization in
pipe assembly [5].
Aimed at locating and clamping different pipe types during assembly, a flexible
combine-clamp and flexible pipe assembly platform represent a good solution. Moreover,
pipe recognition and measurement systems [
6
] were used to calculate and control robot mo-
tion in an automatic pipe assembly system. However, the production of pipe assembly for
Machines 2022, 10, 409. https://doi.org/10.3390/machines10060409 https://www.mdpi.com/journal/machines
