Modeling and Experimental Work on Robotic Grinding ...

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Keywords: Robotic Grinding, Grinding Wheel Profiling, Material Removal Model, Wheel Wear. Model, Oscillation Model, Instrumentation. Abstract.
Materials Science and Technology (MS&T) 2013 October 27-31, 2013, Montreal, Quebec, Canada Copyright © 2013 MS&T'13® Advances in Hydroelectric Turbine Manufacturing and Repair

Modeling and experimental work on robotic grinding tool profiling through tool orientation control for repair of high curvature surfaces Stéphane Agnard a, Zhaoheng Liu a, Bruce Hazel b a

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École de technologie supérieure, Montreal, Quebec, Canada Institut de recherche d’Hydro-Québec, Varennes, Quebec, Canada

Keywords: Robotic Grinding, Grinding Wheel Profiling, Material Removal Model, Wheel Wear Model, Oscillation Model, Instrumentation Abstract For maintenance and repair of hydroelectric equipment, a modified plug wheel can be used to conduct robotic grinding work on high curvature surfaces or hard-to-access areas such as turbine blade junctions. During this robotic process, it is important to keep the tool profile as spherical as its initial shape in order to ensure uniform ground surfaces. In this paper, we present the material removal and tool wear models developed to control the tool profile evolution caused by wear. The objective is to control the contact area between the tool and the workpiece such that flat surface formation on the tool head is avoided. The solution proposed is an oscillation function of tool normal angle controlled by the robot arm holder. Intensive experimental work has been done to validate the models and tool angle oscillation functions using grinding, laser measurement and profilometer. Various results are presented in the paper. Introduction Several processes such as welding, grinding and polishing have been robotized for repair of hydroelectric equipment (Hazel et al., 2010; Sabourin et al., 2010). However, some surfaces with high curvature cannot be repaired using robots and the work must be conducted by hand. Grinding of such surfaces requires the use of plug grinding wheels. Due to their small size, this type of tool has the disadvantage to wear very quickly and it is difficult to control the evolution of the wheel profile. When grinding fillets by hand, the dexterity and the skill of the workers are important in shaping the surface of the workpiece while controlling the wheel profile. To achieve a uniform material removal, the operator performs intuitively tool oscillating movement. This oscillation of the wheel on the workpiece ensures that the abrasive wheel optimizes the material removal and avoids the glazing of the wheel. The grinding tool profiling therefore exists implicitly in most of the manual grinding processes. Without oscillating the tool orientation on the workpiece, the grinding wheel wears gradually and quickly such that its shape becomes conical. Generally, the higher the conformity workpiece/wheel increases, the G-ratio decreases and the risk of wheel glazing increases thereby. The objective of this work is to automate this grinding process with plug wheels using a portable robot as a tool holder. For a robotic grinding process, the grinding wheel profiling allows to control and identify the wheel geometry during the process. This information is essential for the robot to accurately estimate the position of the contact point on the work surface, thereby controlling the orientation and position of the robot. In addition, the wheel which wears while remaining abrasive makes it easier to control the material removal during the process. In fact, the grinding of the workpiece is of primary concern in this work. The profiling of the wheel constitutes a necessary step to achieve a controlled material removal on the workpiece. To do so, we use robotic grinding with a controlled metal removal strategy (CMRR), coupled with an accurate measurement system and an iterative approach.

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Grinding Wheel Profiling In order to achieve an efficient and stable grinding wheel profiling, several characteristics of this process and various technicalities have been identified. Tool Geometry Based on a series of preliminary tests, it becomes necessary to drill a hole in the center of the wheel-type 18R tip (Figure 1). This modification served to prevent the systematic formation of a conical tip at the end of the wheel and thus transformed a plug wheel into miniature cup wheel (type 6). Without drilling the hole, the presence of the conical tip destabilizes the robotic process when grinding near the wheel nose and produces excessive vibrations which may compromise the surface finish and the integrity of the robot.

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Figure 1. Plug wheel type 18R (a) Before drilling (b) After drilling Moreover, the spherical profile proved to be the ideal profile to maintain throughout the life of the wheel for various reasons. Unlike any other geometric shape, the circular profile ensures a consistent footprint at any frontal grinding angle or feed grinding angle. For a constant depth of cut and a constant feed rate, the contact surface on the wheel or uncut chip (one per revolution of the wheel) is identical regardless of the position and orientation of the wheel. Besides the ease in obtaining a uniform material removal rate, the circular profile can also ensure a constant groove width during the oscillation of the grinding wheel on the workpiece. The shape and position of the contact surface on the wheel depends on the frontal grinding angle, the feed angle and the feed direction. In this study, the feed angle is not considered and the grinding tool profiling is performed by oscillating the grinding frontal angle. In order to maintain a spherical profile, it is imperative to ensure that only the spherical part of the wheel is used to remove the material from the workpiece. The uncut chip is therefore placed at the limits of the wheel spherical surface to define the limit angles of oscillation (Figure 2).

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Figure 2. Contact surface oritentations (a) Forward (b) Backword (c) At limit positions In order to optimize the grinding servo power in the hybrid force/position robot control loop (Gagne et al., 2010), the effective grinding wheel radius variation and the robot compliance must be taken into consideration during the grinding tool profiling. The variation in these two parameters is respectively caused by the contact point displacement on the profile of the grinding wheel and the change of robot configuration during the oscillation of the grinding wheel on the workpiece. Grinding Through Vibro-Impacts Because of the flexibility of the robot and the cutting forces developed at the contact area, the presence of vibration of the grinding wheel is inevitable. The robotic grinding is thus characterized by a type of vibro-impact cutting in a steady state, where the vibration amplitude is greater than the depth of cut. During this intermittent grinding process, the wheel bounces on the workpiece surface and makes on average one impact for a complete turn. Experiments using high-speed camera and accelerometers have confirmed the presence of this vibro-impact grinding behavior (Hazel Rafieian and Liu, 2011). In such a regime, the wheel wears out through faceting and the impact point varies on the wheel during the process (Rafieian et al., 2013). As a result, the wheel wears out evenly on the circumference of the grinding wheel after a period of time. Therefore, in order to model the process of profiling, the uncut chip due to this vibro-impact cutting must be considered. Material Removal Model The material removal models used in this study were inspired by the empirical formulation proposed by Tönshoff et al.(1992). Considering the robotic grinding process under study in which the cutting speed is perpendicular to the feed speed, the model is adapted as follows: 𝑍𝑤 = 𝐶𝑣𝑠 𝑒1 𝑣𝑓 𝑒2 𝑃𝑒3 𝑅𝑒𝑞 𝑒4 𝑍𝑤 = 𝐶𝑣𝑠 𝑒1 𝑣𝑓 𝑒2 𝐹𝑛 𝑒3 𝑃𝑒4 𝑅𝑒𝑞 𝑒5

(1) (2)

where Z w is the material removal rate, C is a constant parameter, v s is the wheel tangential speed, v f is the travel speed, P is the power, R eq is the equivalent radius of the wheel, F n is the normal

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force, and e 1 to e 5 are the exponential parameters determined by experiments through a regression algorithm. The experimental results demonstrated that the consideration of normal forces to the empirical power model (equation (1)) allows to significantly improving the correlation of the model with an increase of over 70%. Therefore, measuring the grinding power and the normal force are essential to obtain a robust model that can adapt to the change of grinding regime and the variation of friction coefficient. Grinding Wheel Wear Model To maintain a desirable tool shape, the oscillation model proposed in this study requires a tool wear model in which the material removal rate is proportional to the wheel wear rate. Experimental tests, carried out at different normal angles, have demonstrated that the tangential speed at the contact point 𝑣𝑠 is a significant variable to be considered in the prediction of wheel wear rate: 𝑍𝑠 = 𝐶𝑍𝑤 𝑣𝑠 𝑒1

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where Z s is the grinding wheel wear rate, C is a constant parameter, Z w is the material removal rate, v s is the wheel tangential speed and e 1 is an exponential parameter determined by experiments. In this last equation, a negative coefficient e 1 can be interpreted as faster wear of the grinding tool on the wheel nose during grinding since it corresponds to lower tangential speed at this position. For a constant rotational speed of the grinding wheel, the tangential velocity at the contact point varies substantially as a function of the grinding frontal angle during the tool oscillation. From this model, a negative value of the coefficient 𝑒1 indicates therefore that the wheel wear is faster when grinding on the wheel nose.

Tool Oscillation Model The wheel oscillation model is a key element for the grinding tool profiling. This model is used to define the type of oscillation that the robot must perform to maintain the wheel profile. This model links the material removal rate and the wheel wear rate by the analysis of the cutting kinematics and grinding wheel wear. To develop the oscillation function, a discrete volume approach is used. As shown in Figure 3, the spherical part of a circular grinding wheel profile is represented by the sum of differential disks with thickness ∆𝑥𝑥. To ease the reading, "disk" is used to define "differential disk". This model introduces two concepts: the cut volume and the wear volume. The notion of cut volume is about the interaction between the wheel and the uncut chip for quantifying the contribution of each "disk" of the circular profile to remove the material on the piece for a given normal angle. On the other hand, the concept of wear volume is related to the amount of grinding that each disk should wear out along the circular profile to maintain a constant profile during the tool profiling. The interaction between the cut volume and the wear volume is then used to determine the time spent at each normal angle so that the total cut volume of a disk is proportional the wear volume of the corresponding disk during a half-oscillation of the wheel. Note that equation (2) is applied by considering the average tangential velocity in the contact surface for the corresponding normal angle.

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Figure 3. (a) Sherical part of a circular grinding wheel profile composed of differential disks (b) Zoom-in

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Figure 4. Experimental set-ups (a) Wheel truing bench (b) Laser profile measuring bench (c) Robotic grinding with plug wheel Experimental Set-Up and Measuring System For this work on grinding tool profiling, various tools and measuring instruments have been developed as shown in Figure 4. After drilling of the grinding wheel using a diamond hole saw, the grinding wheel is trued to a desired profile with radius R p before starting the grinding task. It is noted that the desired profile radius is bigger than the wheel radius to avoid corner singularities and to limit the normal angle oscillation range. This modification, made on a specially developed truing test bench allows imposing a spherical profile to the wheel. This spherical profile shape is to be maintained throughout the life of the grinding wheel by oscillating the wheel axis orientation on the workpiece. Thereafter, a measuring set-up allows scanning the profile over the entire periphery of the wheel in order to study the profile evolution during the process. Throughout the grinding operation, the normal force and grinding power are measured. The depth of cut is then obtained by means of an optical scanning profilometer. Special algorithms have been developed to model the deformation of the workpiece and optimize measurement accuracy.

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Experimental Results For the experimental tests, two types of oscillation patterns have been tested; a linear oscillation between the two limit angles and an oscillation function resulting from the oscillation model developed in this work. For comparison, an additional test was also performed without oscillation with a fixed frontal angle. The grinding was performed with overlapping and alternating back and forth grinding grooves on the steel plates. To measure the changes in the wheel profile, the material removal rate and the wheel wear rate during the process, the grinding task has been divided into 12 sub-tests.

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Figure 5. Wheel profile evolution for the various tests (a) Linear oscillation (b) Modeled oscillation (c) Fixed normal angle Figure 5 allows us to appreciate the wheel profile evolution for each of the tests. For the trial with a fixed normal angle (Figure 5c), it is possible to see that the conformity workpiece/wheel spreads to the entire circular profile such that a cone at the end of the wheel is formed. For the tests with oscillations (Figure 5a et Figure 5b), the profile evolves during the wheel conditioning period (sub-tests 1-3) and then remains constant until the end of the trial in both cases (in-tests 4-12). The steady state of the grinding wheel profile was observed by superimposing the profiles measured after the conditioning period by performing a translation along the axis of rotation. A polynomial regression was used to model the steady-state profiles for both types of oscillations in order to compare the two oscillations (Figure 6). Figure 6 shows that the oscillation modeled by the oscillation function helps to keep better the wheel spherical shape than what obtained from the linear oscillation. With the linear oscillation, a mean variation of 0.28 mm is measured on the profile radius obtained after truing. For the modeled oscillation, this variation is less than 0.21 mm, representing an improvement of more than 25%.

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Figure 6. Measured grinding wheel profile along radial and angular axes (a) Linear oscillation (b) Modeled oscillation Analysis of experimental results showed that the modeled wheel oscillation on the workpiece can increase the material removal rate and minimize the specific energy compared to the tests without oscillation. The specific energy of the tests without oscillation varies about 5 times more than those tests with modeled oscillation throughout the sub-tests and is on average 27% higher. These findings therefore demonstrate that the grinding tool profiling helps to stabilize and optimize the material removal rate during the process. The optimization of the grinding tool profiling can be achieved through a better compensation of flexible robot along all the six degrees of freedom and a better regulation of the grinding power. Conclusion The main objective of the work reported in this paper is to propose a method for controlling the wear of the grinding wheel profile and thus improve the workpiece material removal control during robotic grinding. Analysis of the grinding tool profiling in this work has identified some important characteristics of this new process such as the use of drilled plug wheel, maintaining a circular profile, the limit oscillation angles and the effective radius of grinding. Based on the cutting kinematics and the wheel wear assumption, an oscillation model was developed. This oscillation model can reduce more than 25% of the profile error compared to a linear oscillation between the limit angles. We conclude that the optimization of the grinding tool profiling lies in the grinding power control and the compensation of robot flexibilities. It is noted that grinding is a very complex process due to the multiple parameters involved and the interaction of these parameters. The robotization of this process complicates even more the task because of robot flexibilities. Moreover, grinding tool profiling adds its own set of challenges. The grinding wheel profiling in a robotic grinding process requires therefore an excellent control of all grinding parameters and the robot. References 1. Gagne, Jean-Louis, Laurie Bedard-T, Luc Lavoie, Bruce Hazel, Jean Côté, Yvan Laroche and Patrick Mongenot. 2010. "Robotic refurbishment of gate wheel tracks". In 2010 1st International 718

Conference on Applied Robotics for the Power Industry, CARPI 2010 (5-7 Octobre 2010). p. 1-6. Montréal, Québec, Canada: IEEE. 2. Hazel, Bruce, Jean Côté, Yvan Laroche and Patrick Mongenot. 2010. "In-situ Robotic Interventions in Hydraulic Turbines ". In 2010 1st International Conference on Applied Robotics for the Power Industry, CARPI 2010 (5-7 Octobre 2010). p. 1-6. Montréal, Québec, Canada: IEEE. 3. Sabourin, Michel, François Paquet, Bruce Hazel, Jean Côté and Patrick Mongenot. 2010. "Robotic Approach to Improve Turbine Surface Finish". In 2010 1st International Conference on Applied Robotics for the Power Industry, CARPI 2010 (5-7 Octobre 2010). p. 1-6. Montréal, Québec, Canada: IEEE. 4. Tönshoff, H. K., J. Peters, I. Inasaki and T. Paul. 1992. "Modelling and simulation of grinding processes". CIRP Annals - Manufacturing Technology, vol. 41, no 2, p. 677-688. 5. Hazel, Bruce, Farzad Rafieian et Zhaoheng Liu. 2011. "Impact-Cutting and Regenerative Chatter in Robotic Grinding", In 2011 International Mechanical Engineering Congress & Exposition, IMECE 2011 (11-17 Novembre 2011). p. 1-11. Denver, Colorado, États-Unis: ASME. 6. Rafieian, Farzad, François Girardin, Zhaoheng Liu, Marc Thomas et Bruce Hazel. 2013. "Angular analysis of the cyclic impacting oscillations in a robotic grinding process". Mechanical Systems and Signal Processing, Special issue on Instantaneous Angular Speed (IAS) processing and angular applications (accepted).

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