Precision forward design for 3D printing using kinematic sensitivity via Jacobian matrix considering uncertainty
- PDF / 5,805,014 Bytes
- 15 Pages / 595.276 x 790.866 pts Page_size
- 65 Downloads / 174 Views
ORIGINAL ARTICLE
Precision forward design for 3D printing using kinematic sensitivity via Jacobian matrix considering uncertainty Xu Jinghua 1,2,3
&
Feng Xueqing 3 & Cen Jun 3 & Zhang Shuyou 1,2,3
Received: 31 December 2019 / Accepted: 11 August 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract This paper presents a precision forward design method for 3D printing (3DP) using kinematic sensitivity via Jacobian matrix (KSJM) considering uncertainty. The advanced manufacturing such as 3DP profoundly affects us everywhere. However, in many cases, practical uncertain factors such as mechanical and thermal effects affect the precision unquantifiably. Aiming at realizing forward design from requirements to performance, the various kinematic chains are summarized to propose the concept of kinematic sensitivity. The Jacobian matrix which reflects the relationship between input error and output error is decomposed through singular value decomposition (SVD). The KSJM is hereby proposed by furtherly defining four sensitivity parameters: compositive amplification factor of error, reliability of error, absolute amplification factor of error, and comprehensive index of error. The influence of uncertainty such as thermal deformation on the accuracy of end-effector in Cartesian space is investigated by heat fluid-solid coupling simulation and piecewise fitting of thermal deformation. Taking delta 3DP robot as example, the kinematic chains and error sensitivity of the multi-body system are addressed. The physical experiment is implemented via attitude sensors with accelerometers, gyroscopes, and magnetometer. The results proved that trajectory accuracy and reliability can be improved especially under complex random uncertainty. Keywords Precision forward design . 3D printing (3DP) robot . Kinematic sensitivity via Jacobian matrix (KSJM) . Singular value decomposition (SVD) . Trajectory accuracy
1 Introduction The equipment precision plays an important role in advanced manufacturing such as 3D printing (3DP). Precision error is the difference between the actual and the anticipated (ideal) response of the machine to a command issued according to the machine’s accepted protocol. Several factors that are responsible for errors are geometric-kinematic errors, thermally induced errors, static and dynamic loading errors, clamping and
* Xu Jinghua [email protected] 1
State Key Laboratory of Fluid Power and Mechatronic Systems, Hangzhou 310027, China
2
Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Hangzhou 310027, China
3
College of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
spindle errors, etc. Accuracy retention is not only reflected in the short-term accuracy but also the ability to keep the original positioning accuracy and repeated positioning accuracy in long-term work [1]. In the mechanical system, the friction between the moving pairs increases the temperature of the mechanical structure, which leads to the thermal deformation of the structure [2]
Data Loading...
