Off-line compensation of the tool path deviations on robotic machining: Application to incremental sheet forming

doi:10.1016/j.rcim.2012.10.008

Robotics and Computer-Integrated Manufacturing

Volume 29, Issue 4, August 2013, Pages 58-69

https://doi.org/10.1016/j.rcim.2012.10.008 Get rights and content

Abstract

In this paper, a coupling methodology is involved and improved to correct the tool path deviations induced by the compliance of industrial robots during an incremental sheet forming task. For that purpose, a robust and systematic method is first proposed to derive the elastic model of their structure and an efficient FE simulation of the process is then used to predict accurately the forming forces. Their values are then defined as the inputs of the proposed elastic model to calculate the robot TCP pose errors induced by the elastic deformations. This avoids thus a first step of measurement of the forces required to form a test part with a stiff machine. An intensive experimental investigation is performed by forming a classical frustum cone and a non-symmetrical twisted pyramid. It validates the robustness of both the FE analysis and the proposed elastic modeling allowing the final geometry of the formed parts to converge towards their nominal specifications in a context of prototyping applications.

Highlights

► A method is proposed to correct the tool path deviations of robots used for incremental sheet forming. ► It involves a systematic elastic calibration of robots and FE simulations of the process. ► Experiments validate the robustness of the proposed method.

Introduction

In order to reduce manufacturing costs and to improve production flexibility, the industrial robot manipulators are nowadays involved for processes such as machining, assembly or forming [1], [2]. Robots can be used for incremental sheet forming (ISF) which is an interesting process for small series production and prototyping [3]. In ISF the sheet is deformed locally by successive paths of a simple tool. It means that lower forming forces than stamping are needed to form a part. These forming forces are fundamental data to predict the tool pose deviations of the robot [1]. These deviations are mainly due to the elastic deformations of the robot structure which lack of stiffness in comparison to dedicated machines [4], [5]. The resulting tool center point (TCP) pose errors degrade the process results in terms of geometry, surface, etc. In past decades, much of the work in the area of robot calibration including studies on the modeling of their structure, the measurement data collection and the model error identification has been done [6], [7], [8]. For that purpose two main approaches are available in the literature.

The first approach is to perform the dynamic elastic modeling of the robot structure in order to compensate by a linear or nonlinear feedback control the elastic deformations of the structure that degrade the TCP pose accuracy [9], [10], [11]. Outputs of such control consist in modifying the actuator torques. Therefore its implementation is difficult in actual industrial robots where only the TCP pose is controlled [12]. Moreover, the dynamic parameters (inertia, center of gravity, gear ratio) must be identified by dedicated methodologies [8], [13].

The second approach is based on realistic parametric models of the robots to predict the elastic deformations. The methodologies proposed in the literature are based either on Lumped-parameter [14], [15], [16] or more realistic Finite Element models [17], [18], [19]. Since outputs of these models are TCP pose errors, the term elastic model is used. As a result, a correction of the tool path deviations in the programming language of the controller (real-time or off-line programming) is possible. This method has already been applied on a Two Point Incremental Forming (TPIF) process (a supporting tool is used to hold the sheet on the backside) [20], [1]. In these works, the tool path deviations are computed with a Multi-Body System (MBS) modeling of the robot structure coupled to a Finite Element analysis (FE). In the MBS model, the links are assumed rigid and the elastic behavior of the robot structure is described considering the joint stiffness only. The ISF FE simulation computes the estimated forming forces required to form the part assuming an ideal stiff robot. These values are then used to estimate the MBS model with the TCP pose errors that are due to the robot elastic deformations.

The main objective of our paper is to bring consistent contributions to these last works. For that purpose, our work focussed on the following points:

1.
The TCP pose errors induced by the elastic deformations are calculated with a parametrical modeling method based on a new notation instead of a MBS modeling. The main advantage of this approach is that a realistic and complete 3D elastic model can be derived automatically for any industrial robot manipulators including open- and closed-loop structures. Thereby the robot structure can be described considering the joint and the link stiffness.
2.
Thanks to an efficient FE simulation of the process, the predicted forming forces are calculated and then used as inputs of the proposed elastic model. The advantage of this approach is to avoid the measuring of the forming forces during a first run without any compensations as in [20]. Actually in the case of really compliant robots, the measuring forces might be really lower as those exerted by an assuming stiff structure and this can lead to inaccurate corrections of the tool path.
3.
In order to validate the coupling approach an intensive experimental investigation is performed by considering on one hand a classical frustum cone as in [20] and on the other hand a twisted pyramid. The non-symmetrical geometry of this last one allows to validate the robustness of both the FE analysis and the elastic-modeling.

The paper is organized as follows. First the ISF process requirements are given and the TCP pose accuracy abilities of a FANUC S420iF are verified according to ISO-9283 standard. Next sections describe respectively the new proposed systematic elastic modeling and its application to the FANUC S420iF. The resulting elastic model of its structure is next identified and then involved to compensate both the geometrical errors and elastic deformations during the ISF of a frustum cone and a twisted pyramid on an aluminum sheet. For each shape, experimental results are deeply analyzed and discussed.

Section snippets

Incremental forming process requirements

To be as efficient as dedicated machines the serial robots have to verify the process requirements. For example, to form a frustum cone of 40 mm depth and 50° wall angle with a 1.2 mm thick aluminum sheet, a maximum force of 600 N is needed. Feed rates usually programmed are included between 1 m/min and 2 m/min so the process can be considered as quasi-static [21]. The forces required to form thin aluminum parts are compatible with the FANUC robot S420iF. It is a typical robot used for mechanical

Elastic modeling

Denavit–Hartenberg or Khalil–Kleinfinger notations are usually used for the geometrical modeling of industrial robots [6], [8]. Finite Element theory [24] is involved to derive the elastic model by discretizing the robot structure into a set of nodes and beams. Nodes can represent the start or the end of a link, an intermediate frame or a characteristic point on the real structure. However, the definition of the frames used for the geometrical modeling is not really appropriated for the elastic

Modeling

The FANUC S420iF has a number L=9 revolute joints $(q_{j} = θ_{j})$ and $n + 1 = 9$ links where link C₀ is the fixed base and $B = L - n = 1$ closed loop. There are N=6 active joints. A complete segmentation of the structure can be done with 17 nodes (Fig. 4). The vector q is defined by $q_{a} = [q_{1} q_{2} q_{4} q_{5} q_{6} q_{7}]^{T},$ $q_{p} = [q_{3} q_{8}]^{T}, q_{c} = q_{9} .$

Closed-loop constraint gives: $q_{3} = q_{9} = - q_{8} = q_{2} + q_{7}$

Experimental validation: application to ISF process

A post-processor including the FE analysis of the process and the elastic model of the FANUC S420iF is developed (Fig. 8) as proposed in [20].

The process FE simulation performed with the ABAQUS^© software computes the estimated forces required to form the part assuming an ideal stiff robot structure. The advantage of this approach is to avoid the measuring of the forming forces during a first run without any compensation as in [20]. Actually in the case of really compliant robots, the measuring

Conclusion

This paper brings a contribution to the works of Meier et al. [20], [1]. First, instead of a MSB modeling, a robust and systematic notation is proposed for the elastic modeling of industrial open- and closed-loop robot manipulators. Second, due to an efficient FE analysis of the forming task, the predicted forming forces are computed and then used as the inputs of the proposed elastic model. This avoids to measure the forming forces during a first run without any compensation as in [20]. The

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^☆: The present work is supported in part by the European Union (EU). EU is committed in Brittany via FEDER founds.

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Off-line compensation of the tool path deviations on robotic machining: Application to incremental sheet forming☆