Modeling of vacuum grippers for the design of energy efficient vacuum-based handling processes

The effective holding force results from multiple interdependencies of design parameters (for gripper and object) and process parameters (Fig. 2). It defines the force with that the vacuum gripper can encounter the weight and inertial force of an attached object. For example, a good form fit at the GOI reduces the leakage flow which would reduce the pressure difference available for generation of the holding force. The form fit is mainly influenced by the specific gripper-object combination, but will potentially be affected by process-induced loads at the GOI. A straightforward approach for determining the quantitative relations between these influencing parameters is to explore the resulting parameter space experimentally.

The required hardware and automation setup is time- and cost-intensive but makes up for high modeling and computational effort and—considering non-linear material behavior of the applied materials such as silicone or rubber—potential inaccuracies in simulations based on numerical models. The most simple possible approach is to measure the pull-off force of specific grippers and therefore enable a relative reduction of the oversizing margin. In this work, we firstly propose a model approach that extends the standard model by the influence of different gripper-object combinations on the pull-off force that is applied axially to the gripper. The standard model [38] calculates the maximum force F acting on the object by one vacuum gripper as given in Eq. (1):with the pressure difference \(\Delta p\), the effective suction area A and the number of grippers z. By division by the safety margin S, the theoretical holding force is reduced. The sealing and deformation behaviors of the gripper are expressed by the deformation coefficient n and the leakage factor \(\eta\). Then, our extended standard model approach replaces the product of \(n\cdot \eta\) by considering the influence of the object geometry, the gripper material and design in a single factor \(n_{\mathrm {GOI}}\). At a relatively low modeling resp. experimental effort, this approach offers the potential to reduce the need for oversizing since more detailed knowledge about the expected maximum force is available. Equation (2) shows the extension of Equation (1) by the proposed factor \(n_{\mathrm {GOI}}\):However, an analytic surrogate model is an adequate compromise between modeling effort and the remaining need for oversizing and allows to be built-up and refined through both experimentally acquired measured data and simulation results. Thus, for a more detailed and accurate prediction of the gripper behavior, we propose an analytical spring-damper surrogate model based on a generalized Kelvin–Voigt model (parallel connection of spring and damper) as introduced in [30, 31]. In extension of the already pre-sent work, this model approach describes the gripper deformation due to axial and radial stress (in the scope of this work, we focus on the axial gripper behavior) as well as it considers the influence of the specific gripper-object combination and its influence on sealing and force transmission. The knowledge about process-induced gripper deformations and the corresponding grasp stability potentially enables to design robot trajectories and gripper systems in such a way that it can be assured that gripper-specific critical load values are never exceeded, while eliminating the need for oversizing.

A robot-based experimental setup has been built-up for acquisition of the required measurement data and is described in the following. Several grippers that are commonly used for metal sheet or package handling were selected for experimental characterization. For the objects to be grasped, there is no standardized definition of adequate geometries for such a fundamental characterization problem. Therefore, primitive test objects were designed parametrically to generate multiple geometry variants (Fig. 3).

In a robot-based setup (Fig. 4), the selected grippers (ø 60 mm) can be tested in combination with the different objects and—for further experiments in the future—at arbitrarily complex load cases. The experimental setup comprises of an industrial robot (KUKA KR60-3) with compressed air supply and a vacuum ejector with a pre-connected proportional valve to vary the ejector input pressure. For measurement of the occurring loads, a 6-D force-torque-sensor is used to which single vacuum grippers of different types can be attached. The force data are acquired at a sampling rate of 500 Hz. For vacuum generation, a compact ejector with integrated pressure measurement is used. The input pressure is varied by a proportional valve.

In this setup, the balance of forces between robot and the fixed test object provides direct information about the reaction forces inside the vacuum gripper, since the gripping area is fixed to the test object and the pulling force that is generated by the robot can be measured. Therefore, the measured force data can be directly used for model parametrization.

For the extended standard model, the maximum achievable forces just before the gripper pull-off are regarded. In this work, grippers (provided by J. Schmalz GmbH) with 1.5 foldings of different gripper materials (nitrile butadiene rubber NBR, high temperature material HT, Vulkollan VU) are considered in combination with the object geometries. As these grippers were designed for different application fields, they differ in the detailed design of support structures and inner diameters. Table 1 shows the parameters that were tested in full-factorial experiments. 30 repetitions were conducted per parameter setting to compensate for statistical variance and outliers. The test runs were packed into batches of five runs per setting and then randomized in such a way that gripper and object were changed every five test runs.

The objective is to aggregate such influences into the above introduced factor \(n_{\mathrm {GOI}}\) for a more precise prediction of the gripper-object-specific pull-off force. Therefore, pull-off tests were conducted with all selected test objects (and a plane object as reference) at a target velocity of 10 mm/s (in orientation to the test velocity for tensile testing of rubber [39]). The test objects consist of milled aluminium and have an average surface roughness \(R_\mathrm{Z}=0.43\,\pm\,0.08\) \({\upmu }\)m (six measurements in milling direction with Hommel Wave W10 skidded roughness gage). The input pressure for the ejector has been set to 4.0 bar for all tests since this is the most efficient operating point. On the basis of the force data and the gripper specifications provided by the manufacturer, the introduced factor \(n_{\mathrm {GOI}}\) was computed for all gripper-object combinations as shown in Fig. 5. The third convex dome object could not be considered since the large curvature resulted in too strong leakage.

The gripper made of NBR does not reach the theoretically calculated holding force, since \(n_{\mathrm {GOI}}\) is below 1 in all cases. The gripper made of HT2 material shows significantly lower forces than theoretically calculated, except for two concave dome objects. For the gripper made of HT1 material, \(n_{\mathrm {GOI}}\) reaches the theoretical force in most cases. The gripper made of VU, however, provides exceptionally high suction forces, especially in combination with the concave dome objects. For a concrete mathematical description of the observed phenomena, a function \(n_{\mathrm {GOI}}(r_{\mathrm {c}},f_{\mathrm {s}})\) can be built via regression, where \(r_{\mathrm {c}}\) is the curvature radius and \(f_{\mathrm {s}}\) describes the degree of object symmetry. Such object-specific knowledge about the achievable pull-off force can potentially be applied to grasp planning problems where the optimal positions of the vacuum gripper on an object are determined. However, it is further intended to elaborate a dynamic surrogate model to provide for a more detailed model-based process design.

The objective of this spring-damper model is the prediction of the gripper elongation due to process-indu-ced forces. With one selected gripper (SAB HT2), pull-off tests were conducted at 15 target velocities (0.5, 1, 5, 10, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250 mm/s) at 3.0 bar in combination with only the flat object to demonstrate the modeling workflow. Here, a lower pressure level was chosen in order to achieve a relatively large gripper deformation for the model validation. 30 repetitions per parameter set were packed into six batches of five runs per target velocity setting and then randomized. Algorithm 1 shows the schematic procedure of the pull-off tests.

As a first step, the spring characteristics were extracted from the pull-off test at 0.5 mm/s, which can be regarded as quasi-static. The regression can be conducted with the following kernel function:Figure 6 shows the regression (mean squared error, MSE, over all curves of 0.897 N\(^2\)) of the quasi-static pull-off measurement for the selected vacuum gripper.

Regression of all force measurements provides a 3D-map of the resilience inside the vacuum gripper (dashed in Fig. 7). In accordance with the equilibrium of forces that is present inside the spring-damper element during the pull-off experiments, the difference of the force curves and the quasi-static spring characteristics curve results in the damping characteristics (dotted in Fig. 7).

The elongation velocity is displayed only up to 160 mm/s because higher target velocities could not be reached by the robot due to acceleration limits. Using a fourth degree polynomial as kernel function, a regression of the damping force \(F_{\mathrm {d}}(\dot{z})\) dependent on the elongation velocity \(\dot{z}\) can be calculated (MSE=7.001 N\(^2\)). By fitting of the curve-wise polynomial coefficients, a two-dimensional regression of the damping force dependent on the actual elongation z and the elongation velocity \(\dot{z}\) provides the damping force as shown in Eq. (4).Hence, the damping force can directly be calculated for a specific combination of z and \(\dot{z}\) (green in Fig. 7). For the numerical computation of the gripper elongation due to externally applied forces, the resulting damping factor can directly be extracted.

In the first section of this paper, we raised the research hypothesis that it is possible to reduce the overall energy consumption by deliberately allowing for a certain limited gripper deformation. This would require that the gripper deformation is fully reversible below this limit. In order to evaluate this assumption, further pull-off tests are conducted at a velocity of 10 mm/s (this velocity was chosen for a relatively low time required for conducting the experiments; the velocity dependency of the deformation will be examined in the future). After full attachment at \(\mathrm{POS}_{\mathrm {a}}\) the elongation is firstly generated until the target position \(\mathrm{POS}_{\mathrm {t}}\) is reached, reset to \(\mathrm{POS}_{\mathrm {a}}\) and pulled off entirely to ensure independent data. This is repeated 30 times. The z-component of \(\mathrm{POS}_{\mathrm {t}}\) is increased stepwise by 1 mm until the maximum elongation is reached.

Figure 8 shows the resilience force that is generated in the vacuum gripper (by applying an external pull force) and then decreased (due to the release motion back to the initial position \(\mathrm{POS}_{\mathrm {a}}\)). Up to a certain limit (around 13 mm), a slight hysteresis can be identified, but the resilience force in- and decreases steadily. Above that limit, the force drops significantly as soon as the release of the external force begins. The tests at all other target positions are displayed in light gray for better visibility of the highlighted curves.

With regard to a handling process in industrial practice, this implies that a gripper deformation up to the identified limit can be described as reversible. Above that limit, the gripper is not able to retract immediately which indicates that a permanent deformation will remain.

For experimental validation of the proposed spring-damper model, the robot end effector was equipped with an ultrasonic distance sensor (Balluff BUS0026) directed to the top face of the test object (flat surface, 2.4 kg). In order to enable a significantly visible gripper elongation, the input pressure was set to 3.0 bar for a reduced suction flow. Initially, the vacuum gripper was in full contact with the test object. Subsequently, the robot was accelerated in the z axis and stopped at a target position of \(z_{\mathrm {max}}=680\) mm. Figure 9 depicts the measured and simulated gripper elongation.

The simulation of the elongation was conducted by numerical calculation of a generalized Kelvin–Voigt model where spring and dam-per are arranged in parallel. The inertial force of the attached mass was calculated by means of the acceleration that is applied due to the robot trajectory. The results of the simulation do not match the measured data. The simulated maximum elongation is however close to the measured values. The apparent prediction errors can potentially be attributed to phenomena of the gripper deformation behavior that cannot be modeled with the proposed spring-damper model. Moreover, a detailed model of the retraction behavior of the gripper may improve the simulation results. In this validation experiment, a simplified robot trajectory was used to evaluate the gripper elongation. Nevertheless, the model can be applied to determine critical deformations in the context of robot trajectory optimization, given that the prediction accuracy will be improved significantly. The proposed experiment-based modeling method is generally feasible and can also be applied to other gripper-object combinations for a prediction of the gripper deformation that is more detailed than previously available methods.