Method and device for determining a spray characteristic of a coating material sprayed onto a substrate

Abstract

The invention is directed to a method and apparatus (150) for determining a spray characteristic of a test coating material sprayed onto a test substrate using a spraying device operated in accordance to a predetermined set of spray parameters (124), that comprises receiving thickness data (126) associated with thickness distribution obtained by spraying the coating material on a test substrate using the predetermined set of spray parameters, and determining and providing, using the received thickness data, film build kernel function data (127) indicative of a film build kernel function associated to a circularly-symmetric spray pattern and representing the spray pattern associated to the predetermined set of spray parameters. The use film build kernel function data enables a cost efficient process for troubleshooting and / or optimizing the spraying process of a coating material on a substrate.

Description

[0001] Method and device for determining a spray characteristic of a coating material sprayed onto a substrate

[0002] FIELD OF THE INVENTION

[0003] The present invention is directed to a method and an apparatus for determining at least one spray characteristic of a test coating material sprayed onto a test substrate using a spraying device that is operated in accordance with a predetermined set of spray parameters. Further, the present invention is directed to a method for determining sample spray pattern data associated with a spray pattern of a coating material sprayed onto a substrate in accordance with a set a sample spray parameters, indicative of an estimated or expected spray pattern, to a method for determining thickness distribution data associated with a thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters and to a method for generating trajectory data associated with a trajectory followed by a spraying device upon spraying a sample coating material onto a sample substrate with the spraying device using a set of sample spray parameters. In addition, the present invention is directed a system for spraying a coating material and to a computer program.

[0004] BACKGROUND OF THE INVENTION

[0005] The spray application process of coating materials on substrates, such as, for instance, car body surfaces, typically involves spray application of primer, basecoat, and clearcoat materials. Spray application of the coating materials may require applying the coating material in a defined pattern, such as an overlapping line pattern, to cover the entire substrate. Spray application of the coating materials may be performed using spraying equipment comprising a spray nozzle. The coating material exiting the spray nozzle may be controlled via one or more components configured to control the spray pattern, such as flowrate, shaping air, high voltage, and bell speed to achieve the desired surface coverage and film build. Upon use of a new coating material in the spray application process, the traditional trial-and-error approach necessitates several days and multiple substrates to adjust and confirm the distribution of the film build to remedy deviations in color and / or appearance of the resulting coating. This trial and error approach is associated with a negative environmental impact due to the consumption of resources and the generation of waste substrates. Hence, there is a need to optimize the spray application of coating materials without having to prepare physical samples to reduce the environmental impact of the coating process.

[0006] SUMMARY OF THE INVENTION

[0007] According to a first aspect of this disclosure, a method for determining at least one spray characteristic of a test coating material sprayed onto a test substrate using a spraying device operated in accordance to a predetermined set of spray parameters is disclosed. The method comprises receiving thickness data associated with a thickness distribution of the test coating material on the test substrate obtained by spraying the test coating material on the test substrate using the predetermined set of spray parameters.

[0008] The method also comprises determining, using the received thickness data, film build kernel function data indicative of a film build kernel function that is associated with a circularly-symmetric spray pattern from a center point along a radial direction, the film build kernel function data representing a spray pattern associated with the predetermined set of spray parameters. The radial direction refers to a direction on the plane associated with the test substrate from projection of the center of the spraying device onto said plane. The method further comprises providing the film build kernel function data for generating a statistical spray model indicative of relationships or correlations between the test spray parameters and the film build kernel function data for determining the spray characteristics of the test coating material.

[0009] The spray pattern of a spraying device, e.g., of an atomizer, may referto the instantaneous paint deposition rate onto a flat surface, as a function of location on the surface, when the spraying device is approximately normal to the surface and the distance, spray parameters, and material properties take fixed values. It is a two-dimensional pattern, that can be described as a function of two variables, using either Cartesian (x, y) or polar (r, 0) coordinates. Either way, the origin of the coordinate system is the point on the painted surface directly under the atomizer bell’s center point. The spray pattern may be circularly symmetric e.g., the contours of the spray pattern function are circles.

[0010] The film build kernel data is indicative of a function, namely the film build kernel function, which gives the value of the circularly-symmetric spray pattern from the origin, moving out along any radius on a plane associated with the substrate, substantially perpendicular to spraying direction of the spraying device. Due to the symmetry assumption explained above, knowledge of the film build kernel gives complete information about the spray pattern.

[0011] In a general case the spay pattern may not be directly inferable from the received thickness data. This mainly depends on how the test coating material is sprayed onto the test substrate. By deriving the film build kernel function, more precise information about the spraying process can be derived. The knowledge of the spray pattern associated to received thickness data that is indicative of the distribution of the thickness of the coating material, e.g., a mapping of the thickness values on a section of the test substrate as a function of the position on the test substrate, obtained using a predetermined set of spray parameters provides more information about the spraying process than the mere thickness data. This knowledge, in the form of the film build kernel function, given by the film build kernel data, can be used to optimize the spraying process or to troubleshoot existing spraying processes, as it will be explained in the following.

[0012] In the following, embodiments of the method of the first aspect will be disclosed.

[0013] In the frame of this disclosure, test coating material refers to the coating material sprayed onto a test substrate for determining the thickness data that will be provided as input to the method of the first aspect. Preferably, the test substrate is a flat substrate.

[0014] In an embodiment the spray characteristics include the spray pattern of the test coating material, a thickness distribution of the sprayed test coating material on the test substrate and / or a trajectory for spraying the coating material on the test substrate.

[0015] In an embodiment, the thickness data associated with the thickness distribution of the test coating material, from which the film build kernel function can be derived, is coating material thickness distribution data obtained from a test substrate to which test coating material has been applied by moving the spraying device over the test substrate one or more times in a straight line in a motion direction at fixed speed. The coating thickness distribution data in determined in a direction transverse to the motion direction. Such coating material thickness distribution data may also be denoted as SB50 curve data. The SB50 curve data is the standard way to describe the coating by a given set of spray parameters. A pre-specified trajectory is used to move the spraying device over the test substrate one or more times in a straight line in a motion direction at fixed speed. Additionally, or alternatively, the thickness data can be received in the form of stationary spray data. The stationary spray data is associated with the thickness distribution of the test coating material obtained when, during spraying, the spraying device is arranged normal to the surface of the test substrate. Also, the distance between the spraying device and the test substrate, and the test spraying conditions, are kept constant. Hence, pre-specified trajectory of the spraying device is used to determine the stationary spray data. In this case, the pre-specified trajectory is indicative of no relative movement between the spraying device and the test substrate.

[0016] Apart from the SB50 curve data and the stationary spray data, other data denoting the thickness distribution of the test coating material on the test substrate may be used.

[0017] For instance, in an embodiment wherein the thickness data is received in the form of measurement values obtained along a SB50 curve, the method comprising receiving the thickness data obtained or generated after carrying out a test spraying process in accordance with the associated set of spraying parameters, e.g., according to a given experimental plan, and then collecting the thickness data needed for determining the spray pattern. Here test substrates, e.g., so-called SB50 panels, are sprayed and the thickness of the coating material at a plurality of points along the SB50 curve is determined. Optionally, a smoothing step is performed on the measured thickness data. In many cases, the full spray pattern may be wider than the test substrate, and, consequently, the SB50 curve will not go all the way to zero at the two ends of the substrate. In this case, a tail estimation step is advised, to approximate the entire SB50 curve, including the parts that go beyond the substrate extent. Further, the area under each of the smoothed, tail-extended SB50 curves is computed or otherwise determined, and using this area, the transfer efficiency for this spraying process can be determined. In principle, this can be done by a mass balance between the amount of paint sprayed and the amount finally remaining on the panel. This calculation requires the material density for both the wet paint and the dry film. The SB50 curve, characterized by the SB50 curve data can be converted to a probability density function, by dividing the curve by its area. The point of these calculations is to separate the amplitude of the curve (captured by the transfer efficiency) from the shape of the curve. Preferably, in an embodiment, the thickness data, in particular the SB50 curve data, is smoothed and / or tail-extended SB50 curve data indicative of the smoothed and / or tail-extended SB50 curve.

[0018] Preferably, the thickness data is indicative of a thickness distribution of a dried and / or cured coating material, determined or measured after the test coating material sprayed onto the test substrate has dried and / or was cured. Drying of the coating material may include partial removal of the solvents included in the coating material. Dried coating material may still be sticky and not fully solid, e.g. may not give a coating in a state ready for use. A cured coating results in a coating in a ready-to-use state, i.e. to a state in which the substrate provided with the respective coating can be transported, stored and used as intended. More particularly, a cured coating is no longer soft or tacky, but has been conditioned as a solid coating which does not undergo any further significant change in its properties, such as hardness or adhesion on the substrate, even under further exposure to curing conditions.

[0019] The thickness data may be obtained preparing test substrates using a spraying device with predetermined spray parameters and predetermined trajectory. The resulting film thickness of the prepared coating may be measured on the coated substrate (test substrate), at a plurality of precisely defined locations and the results may be provided as thickness data for carrying out the method.

[0020] In an embodiment, determining the film build kernel function data includes modelling the film build kernel function as a smooth spline function over a spraying range of the spraying device. The smooth spline function is represented by a corresponding set of spline coefficients. The smooth spline function may be determined by applying shape-constraining with predetermined shape restrictions to the thickness data.

[0021] The film build kernel function may be assumed to be a smooth spline function that is nonzero over a given range (e.g., [0, R]). Representing the film build kernel function as a spline function allows it to be expressed as a set of spline coefficients. Additional shape constraints may be added to the smooth spline function to ensure that it has realistic properties. For example, the following shape constraints could be included:

[0022] It has the value zero at R.

[0023] Its derivative has value zero at both 0 and R.

[0024] Its derivative has a predetermined number “n” of inflections points (that is, its nthderivative has “n” zero crossings), at “n” specified locations. Preferably, the derivative has three inflections points at three specified locations.

[0025] Given the spraying device’s (e.g., atomizer’s) trajectory (e.g. back and forth over a test substrate in a straight line one or more times at constant speed) and the locations where test coating material thickness is measured (e.g., to obtain the thickness distribution of the test coating material on the test substrate, in the form of SB50 curve data), the estimated thickness can be calculated by carrying out the appropriate numerical integration. In order to find the optimal spline coefficients, the squared error between the estimated and the measured thicknesses at the measurement locations may be minimized, subject to the constraints.

[0026] The above optimization problem is for fixed inflection point locations. The optimization may be wrapped inside an outer search algorithm to find the overall best solution, which gives the final film build kernel function, and the corresponding film build kernel function data that is provided for generating a statistical spray model indicative of correlations between the test spray parameters and the film build kernel function data for determining the spray characteristics of the test coating material.

[0027] By using shape-constrained estimation, the solution is numerically stable, and it is ensured that the estimated film build kernel function is smooth, unimodal, and decays smoothly to zero as the radius gets large.

[0028] Once the smooth film build kernel function has been determined, a “forward” integral calculation may be done to approximate the original SB50 curve. The result is a smooth and symmetric SB50 curve approximation that has tails going all the way to zero. In other words, this film build kernel function estimation procedure also provides a convenient way to simultaneously do smoothing and tail estimation from SB50 curve data. This allows the full spray pattern to be derived, even in the case of test panels that are not large enough to receive the spray pattern. Further, this improves the estimation of the transfer efficiency of material, as it will be disclosed in the following.

[0029] The thickness data may be obtained using any set of measurement locations (though the uncertainty of the estimate will be affected by the design of the spraying and measurement). By comparing the film build kernel function data obtained using different thickness data, test substrate spraying procedures (e.g., spraying device trajectory and measurement positions) that result in more, or the most, accurate estimation of the film build kernel function may be discovered.

[0030] In the case of using stationary spray data as thickness data associated with the thickness distribution of the test coating material on the test substrate (e.g., spraying onto the test panel or test substrate without moving the spraying devices), the stationary spray data is directly correlated to a 2D film build function. In practice, it is challenging to accurately estimate the spray pattern from such stationary spray data, because the resulting thickness data may be asymmetric and non-smooth, and the spray pattern may extend beyond the edges of the test substrate or test panel. The estimation procedure described above can overcome these challenges and generate a film build kernel function from the stationary spray data. Thus, even in this case, the estimation procedure described above provides a convenient way to estimate the film build kernel function, because in practice, substrates that have been subject to spot-spraying (stationary spraying) result in thickness measurements that still exhibit measurement noise and some degree of asymmetry.

[0031] The use of the film build kernel function thus allows fora general representation of a spraying process independently on the form of the thickness data received.

[0032] In another embodiment, the method of the first aspect also comprises the steps of providing density values for the coating material in liquid form (e.g. in wet form) before spraying and for the coating material in dry form (e.g. upon drying and / or curing) after spraying and dry-ing / curing. The method also comprises determining, using the provided density values, the set of spray parameters and the determined film build kernel data, a transfer efficiency value indicative of a portion of the sprayed coating material that adheres to the substrate after spraying. The transfer efficiency is preferably determined by applying a mass balance between the amount of coating material sprayed (wet) and the amount of coating material adhering the substrate (dried / cured). This determination requires data pertaining to the density of the coating material in the wet state (before and / or during spraying) and the dried coating material on the test substrate.

[0033] A second aspect of the present disclosure is directed to a method for determining sample spray pattern data associated with a spray pattern of coating material sprayed onto a substrate in accordance with a set of sample spray parameters. The method of the second aspect comprises generating film build kernel function data for a plurality of predetermined sets of spray parameters according to the method of the first aspect of the present disclosure. The method also comprises generating, using the plurality of predetermined sets of spray parameters and associated film build kernel function data, a statistical spray model that is indicative of correlations or relationships between the predetermined spray parameters and the film build kernel function data obtained using the predetermined test parameters. The method of the second aspect also comprises providing the set of sample spray parameters and generating, using the statistical spray model, the sample spray pattern data, and providing the determined sample spray pattern data. The method of the second aspect thus shares the advantages of the method of the first aspect or of any of its embodiments.

[0034] In the frame of this disclosure, a set of sample spray parameters corresponds to a set of spray parameters understudy, e.g., not yet used for spraying a substrate and therefore not associated with a respective thickness data. Sample spray pattern data corresponds to the spray pattern data provided as an output by the statistical spray model when the set of sample spray parameters is provided as input, and corresponds to an estimated spray pattern that can be expected if the set of sample spray parameters are used to spray a sample substrate.

[0035] Thus, firstly, the method of the first aspect is performed for generating a plurality of pairwise associations between spray data indicative of respective different spray parameters and a respective film build kernel function data associated to the corresponding coating material thickness distribution obtained by spraying the coating material in accordance with the spray parameters on the corresponding test substrate,

[0036] The method also comprises generating, using the pairwise associations generating applying the method of the first aspect to a plurality of test spraying procedures, a statistical spray model indicative of correlations or other relationships between the respective sets of spray parameters and the film build kernel function data obtained using the set of spray parameters.

[0037] Once the statistical model has been generated, the model can be used to estimate or generate expected spray pattern data using input data in the form of a set of spray parameters that are referred to as sample spray parameters. Thus, the method of the second aspect also comprises, for sample spray data associated with or otherwise indicative of a set of sample spray parameters, generating and providing, using the generated statistical spray model, film build kernel function data as the sample spray pattern data indicative of an estimated or expected spray pattern of a coating material sprayed onto a substrate in accordance with the trial spray parameters.

[0038] The sample spray pattern corresponds to a virtual or fictional spray pattern that is expected to be obtained when a set of sample spray parameters is used. The statistical spray model is generated starting from a plurality of relationships between predefined spray parameters and film build kernel data generated for each set of predefined spray parameters as explained with reference to the method of the first aspect. An accurate model may be obtained using different coating materials comprising different compositions and / or properties. The properties may be selected such that they cover the range of properties that are relevant. For example, a coating composition comprising a pigment may be divided into batches and each batch may be modified by additives to achieve different properties, such as solid content, viscosity and / or electrical conductivity.

[0039] Preferably, the spray model is a data-driven model allowing an estimation of the film build kernel function for arbitrary sample spray parameters. A data driven model may represent a mapping from given inputs “X” onto outputs “Y”, which is learned from a collection of training data pairs {(X1 , Y1), (X2, Y2), ..., (Xn, Yn)}. In the present disclosure, the inputs “X” may include the set of spray parameters (which include material properties as well as spray process settings), and the output “Y” may include the corresponding film build kernel functions, provided in the form of film build kernel function data. The fact that a whole function, and not a single value, is estimated implies the use of a functional data analysis model. The film build kernel function is not directly measured, however. Rather, it is estimated by solving an “inverse problem” using thickness data indicative of a coating material thickness distribution a corresponding test substrate that has been sprayed according to a known test protocol (e.g. SB50 or stationary spray). Here it is worth noting that “operating conditions” means the set of the variables that influence the instantaneous spray pattern, and not the movement trajectory of the spraying device. “Test protocol”, on the other hand, refers to a combination of fixed operating conditions and pre-specified movement trajectory. Thus, in a preferred embodiment, for implementing the method of the second aspect, a collection of different combinations of operating conditions X1 , ..., Xn of the spraying device is chosen. Then, a spraying protocol (e.g. to obtain a sample from which a SB50 curve can be extracted) is chosen and one or more test substrates are sprayed using each operating condition. The thickness is measured at a plurality of locations on each substrate’s surface. For each test, the inverse problem is solved to estimate the film build kernel function Y1 , ..., Yn corresponding to its operating conditions X1 , ..., Xn. The pairwise association of inputs and outputs (X1 , Y1), (X2, Y2), ..., (Xn, Yn) are then used to train a model that can then be used to generate trial spray pattern data for unseen trial operating conditions or trial spray data of interest.

[0040] Thus, in terms of information flow, the spray parameters (including operating conditions and optionally, e.g., for SB50 curve data, the trajectory) and the resulting thickness data are used to generate the film build kernel function data associated to said spraying parameters. Based on different predetermined spray parameters and the resulting film build kernel function data the spray model may be generated. The spray model may be used to generate generating sample spray pattern data indicative of a spray pattern of a sample coating material, when the model is applied to data set of sample spray parameters. Here, sample coating material refers to a coating material that is expected to be sprayed when the sample spray parameters are used for a spraying process.

[0041] In an embodiment the spray model can be further refined by comparing the sample spray pattern data obtained by the method of the second aspect with the film build kernel function data obtained or determined by applying the method of the first aspect on thickness data obtained by spraying the sample coating material in accordance with the sample spray parameters to determine the corresponding spray pattern, and adapting the model in case a significant deviation is found between the output of the model (expected sample spray pattern) and the spray pattern determined by applying the method of the first aspect of the present disclosure. Thus, the determined relationship between the thickness data obtained by operating the spraying device in accordance with the set of sample spray parameters and the film build kernel function data generated X(n+1), Y(n+1) can be further provided to refine the spray model.

[0042] According to a third aspect of the present disclosure, a method for determining thickness distribution data associated with a thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters is described. The method comprises generating, in accordance with the method of the second aspect of the present disclosure as described above, sample spray pattern data associated with the sample coating material sprayed onto the sample substrate using the set of sample spray parameters.

[0043] The method of the third aspect also comprises receiving trajectory data including of a set of distance values and angle values, wherein the distance values and the angle values refer to a distance and an angle between the spraying device and the sample substrate, and are provided for a plurality of points in time that form a spraying process. The method also comprises determining, based on the sample spray pattern data and the trajectory data, the thickness distribution data associated with the coating material thickness distribution.

[0044] The method of the third aspect thus shares the advantages of the methods of the first and / or the second aspect or of any of its embodiments.

[0045] The thickness distribution data associated with a thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters provided by the method of the third aspect can be advantageously used to assess a coating process on a sample substrate before actually performing the spraying process on the real substrate. This allows for a reduction of the environmental impact associated with the spraying process, since it provides an estimation of the coated material before the spraying process. A spraying process using a set of sample spray parameters resulting undesirable thickness distribution can be ignored and not carried out, thus reducing the use of coating material, and therefore the environmental impact associated therewith. The sample substrate may be a flat substrate.

[0046] The sample film build function data obtained for the set of sample spray parameters may be used in combination with trajectory data to generate the thickness distribution e. If the obtained thickness distribution is within an expected range, the set of sample application parameters can be, for instance used to control a spraying device to spray, following the given trajectory as given by the trajectory data, the sample substrate using the sample coating material.

[0047] In an embodiment that can be used to generate the thickness distribution data associated with a thickness distribution of a sample coating material sprayed onto on a curved sample substrate, the method also includes receiving substrate geometry data indicative of the geometry of the sample substrate, and, using the trial film build kernel function data, the trajectory data and the substrate geometry data, determining and providing the thickness distribution data.

[0048] The spray model may be used it to determine the dry film thickness on a sample substrate, like a car body. In order to do this, knowledge of the spraying parameters or spraying conditions as well as the spraying device’s movement trajectory is required. For a fixed trajectory, different spray parameters may be considered and their influence on the final thickness distribution of the sample coating may be determined.

[0049] The thickness distribution data is preferably indicative of thickness distribution of the coating material in a dry state. Preferably, thickness measurements on the dry (e.g. dried and / or cured) coating material are used, and the spray pattern and film build kernel function data is defined in terms of dry film deposition rates. However, the same methods can be used for wet-film thickness.

[0050] In addition, a fourth aspect of the present disclosure is directed to a method for generating trajectory data associated with a trajectory followed by a spraying device for spraying a sample coating material onto a sample substrate with the spraying device using a set of sample spray parameters. The method comprises generating in accordance with the method of the third aspect as described above, sample spray pattern data associated with the sample coating material sprayed onto the sample substrate using the set of sample spray parameters. The method further comprises receiving substrate geometry data associated to the geometry of the sample substrate. The method also includes determining, based on the sample spray pattern data and the substrate geometry data, and, using the trial film build kernel function data and the substrate geometry data, determining and providing the trajectory data, for a plurality of points in time, such that the expected thickness of the sprayed coating material on the sample substrate lies within a predetermined target thickness range.

[0051] Thus, using the method of the thirds aspect, trajectory data can be generated for coating a given substrate with a given thickness using the trial spray parameters indicated by the trial spray data.

[0052] The target thickness range can be a pre-stored range or can be provided for performing the method of the third aspect. The trajectory data is indicative of a trajectory or route to be followed by the spraying device in order to obtain a thickness of the coating material onto the sample substrate that lies within the predetermined target thickness range. In can also include time data indicative of a velocity of movement of the spraying device along the trajectory, which can be a variable velocity for different points or sections along the trajectory.

[0053] For any of the methods of the first, the second, the third and / or the fourth aspect the predetermined set of spray parameters and / or the set of sample spray parameters can include data indicative of one or more of:

[0054] - a coating material flow rate of the coating material sprayed;

[0055] - a bell rotation speed of a rotary bell atomizer included in the spraying device;

[0056] - one or more of shaping airflow rates of shaping air provided during the spraying process;

[0057] - electrostatic settings associated with the spraying device, in particular in the form of voltage values and / or current values, preferably associated with a rotary bell atomizer; - an orientation of the spraying device during the spraying process;

[0058] - a distance and / or an angle between the spraying device and the substrate during the spraying process; and

[0059] - material properties of the coating material, in particular, viscosity, solid content, and electrical conductivity, of the coating material.

[0060] The use of the concept of film build kernel function instead of the generally used SB50 curves provides some advantages. The thickness buildup for any trajectory, and not just for straight lines can be simulated with increased accuracy. Further it enables the realization of a predictive model for the SB50 curve, or directly for the kernel. The latter option could provide better physical understanding of how the process and material factors influence the spray pattern. This could potentially make it easier to build a single model that covers multiple materials or spraying devices (e.g., atomizers.). Also, it enables the generation of good, smooth estimates of the SB50 curve, including its tails, which should allow better estimation ofthe transfer efficiency. Material properties can also be included in model building, to improve prediction accuracy. Preferably, a range of coating materials with different properties are used and the determined dry film thickness is used to build the model. This allows more accurate modelling (for both thickness and transfer efficiency), relative to methods that use wet-film measurements and / or spray on foil. The use of an approach based on design on experiment (DoE) data, plus smoothing, plus functional analysis is not strictly necessary, however it is advantageous compared to other alternatives. Further, direct SB50 predictions based on the spray patterns generated by the method will naturally be smooth and symmetric, therefore more believable to the user.

[0061] A fifth aspect of the present disclosure is formed by an apparatus for determining at least one spray characteristic of a test coating material sprayed onto a test substrate using a spraying device operated in accordance with a predetermined set of spray parameters. The apparatus can be referred to as a spray characteristic determination device, and comprises a data input unit that is configured to receive thickness data associated with a coating material thickness distribution of the test coating material on the test substrate obtained by spraying the test coating material on the test substrate using the predetermined set of spray parameters.

[0062] The apparatus also comprises a processing unit that is configured to determine, based on, or otherwise using, the received thickness data, film build kernel function data indicative of a film build kernel function that is associated with a circularly-symmetric spray pattern from a center point along a radial direction, the film build kernel function data representing a spray pattern associated with the predetermined set of spray parameters.

[0063] The apparatus also comprises a data providing unit that is configured to provide the film build kernel function data for generating a statistical spray model indicative of correlations between the test spray parameters and the film build kernel function data for determining the spray characteristics of the coating material.

[0064] The spray characteristic determination device of the fifth aspect thus shares the advantages of the method of the first aspect.

[0065] In one embodiment of the spray pattern determination device, the processing unit is further configured to generate film build kernel function data for a plurality of predetermined sets of spray parameters. For instance, the processing unit can be configured to receive or generate or determine or otherwise ascertain, pairwise associations of spray data indicative of respective spray parameters and a respective film build kernel function data associated to the corresponding coating material thickness distribution obtained by spraying the coating material in accordance with the spray parameters on the corresponding test substrate.

[0066] The processing unit is also configured to generate, using or based on the plurality of predetermined sets of spray parameters and associated film build kernel function data (e.g., the pairwise associations), a statistical spray model indicative of correlations between the predetermined spray parameters and the film build kernel function data obtained using the predetermined spray parameters.

[0067] The processing unit is also configured to generate, based on a set of provided sample spray parameters, and the statistical spray model, the sample spray pattern data, and to provide the generated sample spray pattern data. For instance, the sample spray pattern data can be sample film build kernel function data associated with an estimated spray pattern of a sample coating material sprayed onto a sample substrate in accordance with the sample spray parameters.

[0068] In another embodiment, the thickness data associated with the thickness distribution of the test coating material is coating material thickness distribution data (e.g., SB50 curve data) obtained by applying the test coating material to the test substrate by moving the spraying device over the test substrate one or more times in a straight line in a motion direction at fixed speed, and determining the coating thickness distribution data in a direction transverse to the motion direction.

[0069] Additionally, or alternatively, the thickness data associated with the thickness distribution of the test coating material is stationary spray pattern data associated with the thickness distribution obtained when the spraying device is normal to the surface of the test substrate and the distance between the spraying device and the test substrate, and the test spraying conditions, are kept constant. In yet another embodiment, the data input unit is further configured to receive trajectory data including a set of distance values and angle values between the spraying device and the sample substrate for a plurality of points in time. The trajectory data can indicative of a set of distance values and angle values, both the distance values and the angle values being between the spraying device and the trial substrate, for a plurality of points in time during a spraying process. The data input unit can be optionally configured to receive substrate geometry data indicative of the geometry of a sample substrate to be coated. The processing unit can be configured to determine, using the sample spray pattern data (e.g., the sample film build kernel function data) and the trajectory data (and optionally the substrate geometry data), thickness distribution data associated with a thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters. The data providing unit is further configured to provide the determined thickness distribution data.

[0070] In another embodiment, the data input unit is additionally or alternatively configured to receive substrate geometry data indicative of the geometry of a sample substrate to be coated; and the processing unit is further configured, based on the sample spray pattern data (e.g., the film build kernel function data) and the substrate geometry data, to determine and provide trajectory data for a plurality of points in time, such that the thickness of the sprayed coating material on the sample substrate lies within a predetermined target thickness range.

[0071] A sixth aspect of the present disclosure is formed by a system for spraying a coating material onto a substrate, the system comprising an apparatus according to the fifth aspect. The apparatus is configured to provide sample spray parameters as operation spray data for controlling operation of a spraying device, the operation spray data being associated with a set of operation spray parameters. The provided sample spray parameters are associated with or indicative of allowable or significant spray pattern data, The system also comprises a spraying device (e.g. a rotary bell atomizer) for spraying the coating material onto the substrate, wherein the spraying device is signally connected to the apparatus and wherein the spraying device is configured to operate in accordance with the operation spray parameters indicated by the operation spray data provided by the apparatus-. For instance the operation spray data is indicative of a set of sample spray parameters that, according to the statistical model, results in a thickness distribution that complies with a predetermined thickness criteria, and is thus allowable or significant in view of the expected results of the spraying process.

[0072] A seventh aspect of the disclosure is formed by a computer program comprising instructions which, when executed by an apparatus in accordance with the fifth aspect, cause said apparatus to perform the method of the first aspect.

[0073] It shall be understood that the method described above, the device described above, the arrangement described above and the computer program product described above have similar and / or identical preferred embodiments, in particular, as defined in the dependent claims.

[0074] It shall be understood that a preferred embodiment of the present invention can also be any combination of the dependent claim or above embodiments with a respective independent claim.

[0075] These and other aspects of the present invention will be apparent from and elucidated with reference to the embodiments described hereafter.

[0076] BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In the following drawings:

[0078] Fig. 1 a schematic block diagram of an exemplary spray pattern determination device in accordance with an embodiment of the invention;

[0079] Fig. 2 two examples of thickness data 126 for provision to a spray pattern determination device in accordance with an embodiment of the invention, the thickness data being in the form of SB50 curves;

[0080] Fig. 3 a schematic diagram of spray application for generating an SB50 curve;

[0081] Fig. 4 a schematic block diagram of another exemplary spray pattern determination device in accordance with an embodiment of the invention; Fig. 5 a schematic block diagram of an exemplary spraying assembly including a spray pattern determination device and a spraying device, in accordance with an embodiment of the invention;

[0082] Fig. 6 an exemplary flow diagram of an embodiment of a method for determining a spray pattern of a coating material sprayed onto a substrate using a spraying device operated in accordance with a predetermined set of spray parameters;

[0083] Fig. 7 a flow diagram of an exemplary method for generating trial spray pattern data indicative of an estimated spray pattern in accordance with an embodiment of the invention;

[0084] Fig. 8 a flow diagram of an exemplary method for generating trial material thickness distribution data indicative of an estimated coating material thickness distribution on a trial substrate.

[0085] Fig. 9 a flow diagram of an exemplary method for generating trajectory data indicative of a trajectory for spraying a coating material on a trial substrate.

[0086] DETAILED DESCRIPTION OF THE EMBODIMENTS

[0087] Figure 1 shows a schematic block diagram of an apparatus 150 for determining at least one spray characteristic 160 of a test coating material 162 sprayed onto a test substrate 164 using a spraying device 180 operated in accordance with a predetermined set of spray parameters 124. Such apparatus 150 may be used to determine the film build kernel function data (see Fig. 3) for generating a statistical spray model indicative of correlations between the set of predetermined spray parameters and the film build kernel function data, for determining the spray characteristics of the test coating material.

[0088] For a test that includes spraying a test coating material 164 on a test substrate, a spraying device is operated in accordance with the predetermined set of spray parameters 124. The test coating material has then a thickness distribution that is determined and provided to the apparatus as thickness data 126. The apparatus 150 comprises a data input unit 152 that is configured to receive said thickness data 126 that is associated with a thickness distribution (see, e.g., SB50.1 , SB50.2 in Fig. 2) of the test coating material 162 on the test substrate 164 and that is obtained by spraying the coating material 162 on the test substrate 164 using the predetermined set of spray parameters 124. Thus, when the spraying device is operated in accordance with the predetermined set of spraying parameters 124, a layer of coating material 162 is deposited on the test substrate 164 and the thickness of said layer of coating material is determined at a plurality of locations and provided to the device 150 as thickness data 126 via the data input unit 152.

[0089] The apparatus 150 also comprises a processing unit 154 that is configured to determine, based on the received thickness data 126, film build kernel function data 127 indicative of a film build kernel function s(r) associated to a circularly-symmetric spray pattern 160 from a center point (-R, see FIG. 3) along a radial direction. The film build kernel function data 127 represents the spray pattern 160 associated to the predetermined set of spray parameters 124.

[0090] The apparatus further comprises a data providing unit 154 that is configured to provide the film build kernel function data 127 for generating a statistical spray model indicative of correlations between the test spray parameters 124 and the film build kernel function data 127 for determining the spray characteristics of the coating material, as it will be explained with more detail below, with reference to Fig. 4.

[0091] Fig. 2 shows two examples of thickness data 126 for provision to the spray pattern determination device 150. In this particular example, the thickness data 126 may in the form of coating material thickness distribution data SB50.1 , SB50.2 obtained by applying the test coating material to the test substrate by moving the spraying device over the test substrate one or more times in a straight line in a motion direction at fixed speed, and determining the coating thickness distribution data in a direction transverse to the motion direction. The coating material thickness distribution data SB50.1 , SB50.2 SB50 curve data SB50.1 , SB50.2. The respective SB50 curve SB50.1 , SB50.2 is indicative of a corresponding thickness distribution obtained when moving the spraying device over a test substrate one or more times in a straight line in a motion direction at fixed speed, and obtained in a direction transverse to the motion direction. This is shown with more detail in Fig. 3

[0092] Fig. 3 shows a schematic diagram of spray application for generating an SB50 curve (e.g., SB50.1 , SB50.2 in Fig. 2). The rectangle represents a test substrate 164 to be coated. It is shown positioned with its center at the origin of the x-y plane. The spraying device, e.g., an atomizer (not shown), starts at position (-R, 0) at time zero, and moves at constant speed along the path of the thick black arrow, to position (R, 0) at time T. The volcano-shaped 2D function is the spray pattern 160 associated to the spray parameters 124. It is shown at the initial and final positions. The curve highlighted in the spray pattern shown at the initial position and centered at -R is the film build kernel function s(r), which defines the deposition rate at any point a distance r from the atomizer center. As the atomizer moves over the substrate 164, the point u will experience deposition rates shown by the dashed slice 161 of the spray pattern 160. The integral of these rates over time give the final thickness at point u. The SB50 curve (e.g., SB50.1 , SB50.2) is observed by measuring thickness at many points like u along the y axis.

[0093] Preferably, for obtaining the film build kernel function data, the film build kernel function is modeled as a smooth spline function over a spraying range, the smooth spline function being represented by a corresponding set of spline coefficients. In particular, the smooth spline function is preferably determined by applying shape-constraining with predetermined shape restrictions to the smooth spline function.

[0094] Additionally, or alternatively, the thickness data 126 can be provided in the form of stationary spray data 126.2 associated with the thickness distribution obtained when the spraying device is normal to the surface of the test substrate and the distance between the spraying device and the test substrate, and the test spraying conditions, are kept constant. This is also shown in Fig. 3. Assuming that the spraying device is positioned centered over the point x=R and a short spraying process in accordance with a predetermined set of spray parameters is carried out, the deposited coating material will show a thickness profile similar to the volcano shaped 2D function shown in Fig. 3. Thicknesses distributions obtained for longer spraying times will differ, but may be still associated univocally to the spray parameters (including the spraying time).

[0095] The above-described procedure is not necessarily restricted to SB50 panels (e.g., test substrates that are sprayed in order to obtain thickness data in the form of SB50 curve data) or stationary spraying. It can, in principle, be applied to panels or substrates sprayed in any manner, with any set of measurement locations (though the uncertainty of the estimate will be affected by the design of the spraying and measurement). Thus, this procedure can be advantageously used to find new test substrate spraying procedures (e.g., spraying device trajectory and measurement positions) that result in more, or the most, accurate estimation of the film build kernel function.

[0096] Fig. 4 shows a schematic block diagram of another apparatus 150 150 in accordance with an embodiment of the invention. Here, the same reference numbers will be used to referto features of the device shown in Fig. 4 that have a similar or an identical function to those of the device of Fig. 1. The processing unit 154 of the apparatus 150 of Fig. 4 is further to receive or generate or determine or otherwise ascertain pairwise associations 120 of respective sets of spray parameters 124.1 124. m, and respective film build kernel function data 127.1 , ..., 127.m associated to the corresponding coating material thickness distribution obtained by spraying the coating material in accordance with the set of spray parameters 124.1 , ..., 124. m on the corresponding test substrate 164. Preferably, the processing unit generates the pairwise associations, as described with reference to Fig. 1 using thickness data 126.1 , 126.2, ..., 126.m, each obtained using different sets of spray parameters 124.1 , ..., 124. m.

[0097] The processing unit 154 is further configured to generate, using the pairwise associations 120, a statistical spray model M indicative of correlations between the sets of spray parameters 124.1 ,... 124.m and the generated film build kernel function data 127.1 , ..., 127. m associated with the corresponding set of spray parameters 124.1 ,..., 124. m.

[0098] The model M can be fed with sample spray data 130 associated to of a set of sample spray parameters 132, in order to generate and provide, using the generated statistical spray model M, sample spray pattern data 134, for instance sample film build kernel function data 136 indicative of an estimated spray pattern of a coating material sprayed onto a sample substrate in accordance with the sample spray parameters 132. The sample spray data is received by the data input unit 152 and provided to the processing unit 154, which enters the sample spray data 130 as an input to the model M in order to generate an estimation of the spray pattern that would result should the sample spray parameters be used for a spraying process.

[0099] Fig. 5 shows a schematic block diagram of an exemplary system 200 for spraying a coating material 162 onto a substrate 164. The system 200 comprises an apparatus 150 as described above with reference to FIG. 1 and FIG. 4 signally connected to an spraying device 180 that also forms part of the system 200. The spraying device 180 is exemplarily a rotary bell atomizer for spraying the coating material 162. The spraying device is signally connected to the apparatus 150 and configured to operate in accordance with a predetermined set of operation spray parameters that characterize the spraying process. The operation spray parameters may be provided manually by a user or may be provided by the apparatus 150 as operation spray data 131. The apparatus 150 of Fig. 5 is configured to provide as the operation spray data 131 associated with operation spray parameters, sample spray parameters 132. The sample spray parameters 132 are associated with sample spray pattern data 134 that is allowable or significant for the current spraying process, according to the results provided by the statistical model M. For instance the operation spray data is indicative of a set of spray parameters that, according to the model M, results in a thickness distribution that complies with a predetermined thickness criteria.

[0100] In this exemplary apparatus 150, which can also be used independently of the spraying device 180, the data input unit 152 may be further configured to receive trajectory data 157 including a set of distance values and angle values between the spraying device and the sample substrate for a plurality of points in time. The trajectory data may be indicative of a set of distance values and angle values, both the distance values and the angle values being between the spraying device 180 and a sample substrate (e.g. 164), for a plurality of points in time during a spraying process. The processing unit 154 is further configured, using the sample spray pattern data 134 (e.g., the sample film build kernel function data 136), generated by the model M and the trajectory data 157, to determine and provide thickness distribution data 158 associated with, or otherwise indicative of, an estimated thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters.. The provided estimated thickness distribution data 158 can be used to assess the suitability of the sample spray parameters and the trajectory to obtain a coating of sufficient quality (e.g., thickness, uniformity, etc.). The data providing unit 153 is further configured to provide the determined thickness distribution data 158, for instance for displaying it to a user.

[0101] Additionally, the input unit 152 can be further configured to receive substrate geometry data 155 indicative of the geometry of a sample substrate to be coated. This is especially beneficial in the case of sample substrates having a curved geometry. The processing unit 154 can further use the geometry data to determine the thickness distribution data 158 indicative of an estimated thickness distribution of the coating material sprayed onto a curved sample substrate.

[0102] The processing unit 154 can also be configured, using the sample spray pattern data 134 (e.g., the sample film build kernel function data 136) as provided by the model M, and the received substrate geometry data 157, to determine and provide trajectory data 156 for a plurality of points in time, such that the thickness of the sprayed coating material on the sample substrate lies within a predetermined target thickness range.

[0103] For any of the different examples of spray pattern determination devices 150 explained with reference to Figs. 1 , 4 and 5, 9, the predetermined set of spray parameters and / or the set of sample spray parameters may include data indicative of one or more of a coating material flow rate of the coating material sprayed, a bell rotation speed of a rotary bell atomizer included in the spraying device 180, one or more shaping air flow rates of shaping air provided during the spraying process, one or more electrostatic settings associated with the spraying device, a distance and / or an angle between the spraying device and the substrate during the spraying process, and material properties of the coating material, in particular, viscosity, solid content, and electrical conductivity, of the coating material.

[0104] Fig. 6 shows an exemplary flow diagram of an embodiment of a method 100 for determining at least one spray characteristic of a test coating material sprayed onto a test substrate using a spraying device operated in accordance to a predetermined set of spray parameters. The method can be carried out by an apparatus 150 (e.g., a spray characteristic determination device), as described with reference to Figs. 1 , 4 and 5. The method comprises, in a step 101 , receiving, determining or otherwise ascertaining thickness data 126 associated with a thickness distribution (e.g., SB50.1 , SB50.2) of the test coating material on the test substrate and obtained by spraying the test coating material 162 on the test substrate 164 using the predetermined set of spray parameters 124. The method also comprises, in a step 102, determining based on the received thickness data 126, film build kernel function data 127 indicative of a film build kernel function associated with a circularly-symmetric spray pattern 160 from a center point along a radial direction, the film build kernel function data 127 representing a spray pattern associated with the predetermined set of spray parameters 124. The method also comprises, in a step 103 providing the film build kernel function data 127 for generating a statistical spray model M indicative of correlations between the set of predefined spray parameters 124 and the film build kernel function data 127 for determining the spray characteristics of the test coating material.

[0105] Optionally, as indicated by the dashed lines in Fig. 6, the method 100 may include, in a step 104, providing or otherwise ascertaining (e.g., receiving, measuring or otherwise determining) density values for the coating material in liquid form before spraying and for the coating material in dry from after spraying, and, in a step 105, determining or generating, based on the density values, the set of spray parameters and the determined film build kernel data - a transfer efficiency value indicative of a portion of the sprayed coating material that adheres to the substrate after spraying.

[0106] Fig. 7 shows a flow diagram of an exemplary method 100b for determining sample spray pattern data associated with a spray pattern of a coating material sprayed onto a substrate in accordance with a set of sample spray parameters in accordance with an embodiment of the invention. The method 100b comprises, in a step 106, generating film build kernel function data for a plurality of predetermined sets of spray parameters according to the method 100 of Fig. 6. For instance, step 106 may comprise repeatedly performing the method 100 for generating a plurality of pairwise associations of spray data indicative of a respective set of spray parameters and a respective film build kernel function data associated to the corresponding thickness distribution of the coating material obtained by spraying the coating material in accordance with the predetermined set of spray parameters on the corresponding test substrate. The method 100b also comprises, in a step 107, generating, using the plurality of predetermined sets of spray parameters and associated film build kernel function data, a statistical spray model M indicative of correlations or relationships between the predetermined spray parameters 124 and the film build kernel function data 127 obtained using the predetermined spray parameters.. For sample spray data indicative of a set of sample spray parameters, provided in step 108, the method comprises, in a step 109, generating, using the generated statistical spray model M, the sample spray pattern data 134, e.g. sample film build kernel function data, indicative of an estimated spray pattern of a coating material sprayed onto a substrate in accordance with the sample spray parameters. The method also comprises, in a step 110, providing the determined sample spray pattern data 134.

[0107] Fig. 8 shows a flow diagram of an exemplary method 100c for generating thickness distribution data associated with a thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters. The method 100c comprises, in a step 111 generating sample spray pattern data associated with the sample coating material sprayed onto the sample substrate using the set of sample spray parameters according to the method 100b of Fig. 7. The method 100c further comprises, in a step 112, receiving trajectory data 157 including a set of distance values and angle values between the spraying device and the sample substrate for a plurality of points in time. The trajectory data may be indicative of a set of distance values and angle values, both the distance values and the angle values being between the spraying device and the trial substrate, for a plurality of points in time during a spraying process. The step 112 may optionally include receiving substrate geometry data indicative of the geometry of the trial substrate. The method further comprises, in a step 113, determining, based on the sample spray pattern data and the trajectory data 157 the thickness distribution data 158: The received geometry data can also be used for the case where the sample substrate is not a flat substrate but a curved sample substrate., The thickness distribution data 158 is indicative of an estimated or expected thickness distribution of a sample coating material sprayed onto a sample substrate in accordance with the sample spray data associated to the set of sample spray parameters. The method 100c also comprises, in a step 114, providing the determined thickness distribution data. Fig. 9 shows a flow diagram of an exemplary method 100d for generating trajectory data associated with a trajectory followed by a spraying device upon spraying a sample coating material onto a sample substrate with the spraying device using a set of sample spray parameters. The method comprises, in a step 115, generating sample spray pattern data associated with the sample coating material sprayed onto the sample substrate using the set of sample spray parameters, for instance by performing the method 100b (see Fig. 7). The method 100c further comprises, in a step 116, receiving, or otherwise ascertaining, substrate geometry data indicative of the geometry of the sample substrate, and, in a step 116, determining, based on the sample spray pattern data and the substrate geometry data, the trajectory data 156 for a plurality of points in time, such that the thickness of the sprayed coating material on the sample substrate lies within a predetermined target thickness range.

[0108] In summary, the invention is directed to a method and apparatus for determining a spray characteristic of a test coating material sprayed onto a test substrate using a spraying device operated in accordance to a predetermined set of spray parameters, that comprises receiving thickness data associated with thickness distribution obtained by spraying the coating material on a test substrate using the predetermined set of spray parameters, and determining and providing, using the received thickness data, film build kernel function data indicative of a film build kernel function associated to a circularly-symmetric spray pattern and representing the spray pattern associated to the predetermined set of spray parameters. The use film build kernel function data enables a cost efficient process for troubleshooting and / or optimizing the spraying process of a coating material on a substrate.

[0109] In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality.

[0110] A single unit or device may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0111] Procedure steps performed by one or several units or devices can be performed by any other number of units or devices. These procedures can be implemented as program code means of a computer program and / or as dedicated hardware.

[0112] A computer program product may be stored / distributed on a suitable medium, such as an optical storage medium or a solid-state medium, supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

[0113] Any units described herein may be processing units that are part of a classical computing system. Processing units may include a general-purpose processor and may also include a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or any other specialized circuit. Any memory may be a physical system memory, which may be volatile, non-volatile, or some combination of the two. The term “memory” may include any computer-readable storage media such as a non-volatile mass storage. If the computing system is distributed, the processing and / or memory capability may be distributed as well. The computing system may include multiple structures as “executable components”. The term “executable component” is a structure well understood in the field of computing as being a structure that can be software, hardware, or a combination thereof.

[0114] For instance, when implemented in software, one of ordinary skill in the art would understand that the structure of an executable component may include software objects, routines, methods, and so forth, that may be executed on the computing system. This may include both an executable component in the heap of a computing system, or on computer-readable storage media. The structure of the executable component may exist on a computer-readable medium such that, when interpreted by one or more processors of a computing system, e.g., by a processor thread, the computing system is caused to perform a function. Such structure may be computer readable directly by the processors, for instance, as is the case if the executable component were binary, or it may be structured to be interpretable and / or compiled, for instance, whether in a single stage or in multiple stages, so as to generate such binary that is directly interpretable by the processors.

[0115] In other instances, structures may be hard coded or hard wired logic gates, that are implemented exclusively or near-exclusively in hardware, such as within a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or any other specialized circuit. Accordingly, the term “executable component” is a term for a structure that is well understood by those of ordinary skill in the art of computing, whether implemented in software, hardware, or a combination. Any embodiments herein are described with reference to acts that are performed by one or more processing units of the computing system. If such acts are implemented in software, one or more processors direct the operation of the computing system in response to having executed computer-executable instructions that constitute an executable component. Computing system may also contain communication channels that allow the computing system to communicate with other computing systems over, for example, network. A “network” is defined as one or more data links that enable the transport of electronic data between computing systems and / or modules and / or other electronic devices. When information is transferred or provided over a network or another communications connection, for example, either hardwired, wireless, or a combination of hardwired or wireless, to a computing system, the computing system properly views the connection as a transmission medium. Transmission media can include a network and / or data links which can be used to carry desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general-purpose or special-purpose computing system or combinations. While not all computing systems require a user interface, in some embodiments, the computing system includes a user interface system for use in interfacing with a user. User interfaces act as input or output mechanism to users for instance via displays.

[0116] Those skilled in the art will appreciate that at least parts of the invention may be practiced in network computing environments with many types of computing system configurations, including, personal computers, desktop computers, laptop computers, message processors, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, mobile telephones, PDAs, pagers, routers, switches, datacenters, wearables, such as glasses, and the like. The invention may also be practiced in distributed system environments where local and remote computing system, which are linked, for example, either by hardwired data links, wireless data links, or by a combination of hardwired and wireless data links, through a network, both perform tasks. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

[0117] Those skilled in the art will also appreciate that at least parts of the invention may be practiced in a cloud computing environment. Cloud computing environments may be distributed, although this is not required. When distributed, cloud computing environments may be distributed internationally within an organization and / or have components possessed across multiple organizations. In this description and the following claims, “cloud computing” is defined as a model for enabling on-demand network access to a shared pool of configurable computing resources, e.g., networks, servers, storage, applications, and services. The definition of “cloud computing” is not limited to any of the other numerous advantages that can be obtained from such a model when deployed. The computing systems of the figures include various components or functional blocks that may implement the various embodiments disclosed herein as explained. The various components or functional blocks may be implemented on a local computing system or may be implemented on a distributed computing system that includes elements resident in the cloud or that implement aspects of cloud computing. The various components or functional blocks may be implemented as software, hardware, or a combination of software and hardware. The computing systems shown in the figures may include more or less than the components illustrated in the figures and some of the components may be combined as circumstances warrant.

[0118] Any reference signs in the claims should not be construed as limiting the scope.

Claims

CLAIMS1. Method (100) for determining at least one spray characteristic (160) of a test coating material (162) sprayed onto a test substrate (164) using a spraying device (180) operated in accordance with a predetermined set of spray parameters (124), the method comprising:- receiving (101) thickness data (126) associated with a thickness distribution (SB50.1 , SB50.2) of the test coating material on the test substrate obtained by spraying the test coating material (162) on the test substrate (164) using the predetermined set of spray parameters (124);- determining (102), based on the received thickness data (126), film build kernel function data (127) indicative of a film build kernel function (s(r)) associated with a circularly-sym-metric spray pattern (160), the film build kernel function data representing a spray pattern associated with the predetermined set of spray parameters;- providing (103) the film build kernel function data (127) for generating a statistical spray model (M) indicative of correlations between the set of predefined spray parameters (124) and the film build kernel function data (127) for determining the spray characteristics of the test coating material.

2. The method of claim 1 , wherein the spray characteristics include the spray pattern of the test coating material, a thickness distribution of the sprayed test coating material on the test substrate and / or a trajectory for spraying the test coating material on the test substrate.

3. The method of claim 1 or 2, wherein the thickness data (126) associated with the thickness distribution of the test coating material includes:- coating material thickness distribution data (SB50.1 , SB50.2) obtained by applying the test coating material to the test substrate by moving the spraying device over the test substrate one or more times in a straight line in a motion direction at fixed speed, and determining the coating thickness distribution data in a direction transverse to the motion direction; and / or- stationary spray data (126.2) associated with the thickness distribution obtained when the spraying device is normal to the surface of the test substrate and the distance between the spraying device and the test substrate, and the test spraying conditions, are kept constant.

4. The method of any of the preceding claims, wherein determining (104) the film build kernel function data includes modeling the film build kernel function as a smooth spline function over a spraying range of the spraying device, the smooth spline function being represented by a corresponding set of spline coefficients.

5. The method (100) of claim 3, wherein the smooth spline function is determined by applying shape-constraining with predetermined shape restrictions to the smooth spline function.

6. The method (100) of any of the preceding claims, further comprising:- providing (104) density values for the coating material in liquid form before spraying and for the coating material in dry from after spraying;- determining (105), based on the density values, the set of spray parameters and the determined film build kernel data, a transfer efficiency value indicative of a portion of the sprayed coating material that adheres to the substrate after spraying.

7. Method (100b) for determining sample spray pattern data associated with a spray pattern of a coating material sprayed onto a substrate in accordance with a set of sample spray parameters (132), the method comprising:- generating (106) film build kernel function data (127) for a plurality of predetermined sets of spray parameters according to the method of any one of claims 1 to 5,- generating (107), using the plurality of predetermined sets of spray parameters (124.1 , 124. m) and associated film build kernel function data (127.1 , 127. m), a statistical spray model (M) indicative of correlations between the predetermined spray parameters (124) and the film build kernel function data (127) obtained using the predetermined spray parameters;- providing (108) the set of sample spray parameters (132) and generating (109), using the generated statistical spray model (M) and the set of sample spray parameters (132), the sample spray pattern data (134); and- providing (110) the determined sample spray pattern data (134).

8. Method (100c) for determining thickness distribution data (158) associated with a thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters, the method comprising:- generating (111) sample spray pattern data associated with the sample coating material sprayed onto the sample substrate using the set of sample spray parameters according to the method (100b) of claim 7,- receiving (112) trajectory data (157) including a set of distance values and angle values between the spraying device and the sample substrate for a plurality of points in time; and- determining (113), based on the sample spray pattern data and the trajectory data (157) the thickness distribution data (158)- providing (114) the determined thickness distribution data.

9. Method (1 OOd) for generating trajectory data associated with a trajectory followed by a spraying device upon spraying a sample coating material onto a sample substrate with the spraying device using a set of sample spray parameters, the method comprising;- generating (115) sample spray pattern data associated with the sample coating material sprayed onto the sample substrate using the set of sample spray parameters according to the method (100b) of claim 7;- receiving (116) substrate geometry data (155) indicative of the geometry of the sample substrate; and- determining (116), based on the sample spray pattern data and the substrate geometry data, the trajectory data (156) for a plurality of points in time, such that the thickness of the sprayed coating material on the sample substrate lies within a predetermined target thickness range.

10. The method (100, 100b, 100c, 100d) of any of the preceding claims, wherein the predetermined set of spray parameters and / or the set of sample spray parameters include data associated with one or more of:- a coating material flow rate of the coating material sprayed;- a bell rotation speed of a rotary bell atomizer included in the spraying device;- one or more shaping airflow rates of shaping air provided during the spraying process;- one or more electrostatic settings associated with the spraying device;- an orientation of the spraying device during the spraying process;- a distance and / or an angle between the spraying device and the substrate during the spraying process; and- material properties of the coating material, in particular, viscosity, solid content, and electrical conductivity of the coating material.

11. An apparatus (150) for determining at least one spray characteristic (160) of a test coating material (162) sprayed onto a test substrate (164) using a spraying device (180) operated in accordance with a predetermined set of spray parameters (124), the apparatus (150) comprising:- a data input unit (152) configured to receive thickness data (126) associated with a thickness distribution (SB50.1 , SB50.2) of the test coating material (162) on the test substrate (164) obtained by spraying the test coating material (162) on the test substrate (164) using the predetermined set of spray parameters; and- a processing unit (154) configured to determine, based on the received thickness data (126), film build kernel function data (127) indicative of a film build kernel function (s(r)) associated with a circularly-symmetric spray pattern (160) from a center point (R) along a radial direction, the film build kernel function data representing a spray pattern associated with the predetermined set of spray parameters (124),- data providing unit (155) configured to provide the film build kernel function data (127) for generating a statistical spray model indicative of correlations between the test spray parameters and the film build kernel function data for determining the spray characteristics of the coating material.

12. The apparatus of claim 11 , wherein the processing unit is further configured- to generate film build kernel function data (127.1 , 127.m) for a plurality of predetermined sets of spray parameters (124.1 , 124. m);- to generate, using the plurality of predetermined sets of spray parameters and associated film build kernel function data, a statistical spray model (M) indicative of correlations between the predetermined spray parameters (124) and the film build kernel function data (127) obtained using the predetermined spray parameters; and- to generate, based on a set of provided sample spray parameters (132) and the generated statistical spray model (M), the sample spray pattern data (134).

13. The apparatus (150) of claims 11 or 12, wherein- the data input unit (152) is further configured to receive trajectory data (157) including a set of distance values and angle values between the spraying device and the sample substrate for a plurality of points in time;- the processing unit is further configured, using the sample spray pattern data (134) and the trajectory data (157), to determine (119) thickness distribution data (158) associated with a thickness distribution of a sample coating material sprayed onto a sample substrate with a spraying device using a set of sample spray parameters; and- the data providing unit is further configured to provide the determined thickness distribution data;and / or, wherein- the data input unit (152) is further configured to receive substrate geometry data (155) indicative of the geometry of a sample substrate to be coated; and- the processing unit (154) is further configured, based on the sample spray pattern data (134) and the substrate geometry data, to determine (116) trajectory data (156), for a plurality of points in time, such that the thickness of the sprayed coating material on the sample substrate lies within a predetermined target thickness range.

14. A system (200) for spraying a coating material onto a substrate, the system comprising an apparatus (150) according to any of the preceding claims 11 to 13, wherein the apparatus is configured to provide, as operation spray data (131) associated with operation spray parameters, sample spray parameters associated with allowable sample spray pattern data; the system further comprising- a spraying device (180) for spraying the coating material onto the substrate, wherein the spraying device is signally connected to the apparatus and wherein the spraying device is configured to operate in accordance with the operation spray parameters indicated by operation spray data (131) provided by the apparatus (150) .

15. Computer program comprising instructions which, when executed by an apparatus in accordance with any of the claims 11 to 13, cause said apparatus to perform the method of any of the claims 1 to 10.

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