Investigations on Material Loads during Grinding by Speckle Photography

Abstract

The knowledge of the loads occurring during a manufacturing process (e.g., grinding) and of the modifications remaining in the material is used in the concept of process signatures to optimize the manufacturing process and compare it with others (e.g., laser processing). The prerequisite for creating a process signature is that the loads can be characterized during the running process. Due to the rough process conditions, until now there is no in-process technique to measure the loads in the form of displacements and strains in the machined boundary zone. For this reason, the suitability of speckle photography is demonstrated for in-process measurements of material loads in a grinding process without cooling lubricant and the measurement results are compared with finite element method (FEM) simulations. As working hypothesis for the simulation it is assumed, that dry grinding is a purely thermally driven process. Despite the approximation by a purely thermal model with a constant heat source, the measured displacements differ only by a maximum of approximately 20% from the simulations. In particular, the strain measurements in feed speed direction are in good agreement with the simulation and support the thesis, that the dry grinding conditions used here lead to a primarily thermally affecting process.

1. Introduction

Process-induced internal material loads directly cause workpiece modifications and generate the surface integrity of a workpiece (e.g., residual stress and hardness) [1]. The correlation between internal material loads and induced modifications is used in the concept of process signatures and can be used to design optimized processes and process chains specifically oriented on the functional properties of the final component [2,3]. For the prediction of residual stresses occurring in the grinding process, various theoretical approaches can be derived [4,5]. However, to gain comprehensive knowledge about the stresses acting during machining, it is necessary to characterize and analyze the loads while they are affecting the workpiece. Simulations can help to understand the effects of the elastic and plastic strains [6]. However, the simulations are usually simplified by approximations and do not always accurately reflect real conditions. Therefore, it is essential to determine the actual loads by in-process measurements and to validate the simulation results.

Although external loads such as forces affecting the workpiece during material processing can be measured and analyzed in detail (e.g., with force dynamometers), there is currently no in-process measuring method that is capable of determining the strains in the contact zone. Steel integrated thin film sensors to measure the mechanical loads in test workpieces during the manufacturing process are subject of current scientific research [7,8,9]. However, this measurement approach is invasive and currently only allows single-point measurements with a limited spatial resolution in the millimeter range.

To enable non-invasive field measurements of displacement and strain with a high spatial resolution in the micrometer range, the digital speckle photography (DSP) is a promising measurement approach [10,11]. Theoretical considerations show that the fundamental uncertainty limits of speckle photography are only limited by Heisenberg’s uncertainty relation [12]. For displacement measurements, uncertainties of less than 7 nm can be achieved with current camera and laser technology [12]. As a non-contact optical measuring method speckle photography is consequently predestined for fast and precise in-process measurements. Speckle photography was recently used for a rolling process [7] and a milling process [13], but has not yet been applied to investigate the grinding process.

For this reason, the aim is to demonstrate the usability of DSP for the in-process measurement of internal loads during grinding. The usage of cooling lubricant adds additional measurement challenges, because the movement of the cooling lubricant or the movement of containing particles, respectively, can be misinterpreted as material displacement. Therefore, the usability of the speckle measuring technology is tested in a first step in a dry grinding process without cooling lubricant. Furthermore, grinding parameters are chosen that tend to generate high thermal stresses and induce large displacements. Under these circumstances, however, strong sparks occur, which also move through the measuring field. The scientific question is, whether speckle photography measurements are possible despite the demanding in-process conditions and how to achieve robust image evaluation algorithms? Furthermore, finite element method simulations of the dry grinding process with the considered conditions are based on the assumption, that grinding is a purely thermally effected process [14,15], and the contact zone between the grinding wheel and the workpiece can be approximated as a constant heat source. However, the assumption could not be supported by real strain measurements yet, because up to now in-process measurements of displacements in the contact zone are not possible. For this reason, another research aspect of the article is whether the assumption of a constant heat source as contact zone is justified and valid for machining without cooling lubricant.

To answer the question about the usability of speckle photography and to validate the FEM simulations, the article is structured as follows: At first, the recorded material loads during grinding such as forces and powers are described in Section 2.1. Both are used as input variables for the numerical simulation, which is subsequently explained in Section 2.2. The theoretical background for the displacement and strain field measurements including the measurement principle of speckle photography then follows in Section 2.3. Section 2.4 shows the experimental setup for the speckle photography measurements during grinding. A comparison between the FEM simulations and the measurement results of the speckle photography are presented in Section 3. In the concluding Section 4, a summary of the comparison between speckle measurements and simulations and an outlook on future work is given.

2. Materials and Methods

2.1. Material Loads

Various methods allow in-process measurements of loads like forces, contact zone temperature and power during grinding [16,17,18]. These external loads cause internal loads of the workpiece-like stress, strain or internal heat distribution and their gradients which result in modification of the surface layer. For scientific purposes the forces are usually determined by piezoelectric-based force measurement systems [16]. In the present work, the tangential force F_t in direction of the cutting speed v_c are recorded with a three axis force measurement system. From the process parameters and force the specific grinding power P_c″,

$${\mathrm{P}}_{\mathrm{c}}″=\frac{{\mathrm{F}}_{\mathrm{t}}·{\mathrm{v}}_{\mathrm{c}}}{{\mathrm{a}}_{\mathrm{p}}·{\mathrm{l}}_{\mathrm{g}}},$$

(1)

as an indicator for the energy transformation is calculated where a_p describes the width of cut and l_g the contact length. This knowledge is used to calculate the heat flux $\dot{\mathrm{q}}$ into the workpiece as a fraction (0 ≤ k_w ≤ 1) of the specific grinding power P_c″ transferred to heat:

$$\dot{\mathrm{q}}={\mathrm{k}}_{\mathrm{w}}·{\mathrm{P}}_{\mathrm{c}}″,$$

(2)

which is necessary for FE simulations to be compared with the measurements.

2.2. FEM Approach and Simulative Setup

For the comparison with the experimental measurements, finite element simulations are used to simulate the impact of the grinding process on the workpiece material. The material flow is considered in the used software DEFORM-3D from the company Scientific Forming Technologies Corporation (Columbus, OH, USA) by shifting the grid nodes. Since no coolant is applied in the experiments, it can be assumed that the thermal impact of the process is much higher than others like the mechanical, which is a common assumption in the analysis of grinding processes [14,15]. Therefore, the simulation setup is derived from Kuschel et al. [19], using a moving heat source on the workpiece surface. To represent the experimental setup more realistic, the simulative setup is transferred to a 3D elasto-plastic modelling approach. The geometrical boundary conditions which include the geometric contact length l_g and the tangential feed speed v_ft, which is referred to the heat source here, are applied from the grinding experiments. The heat flux is estimated as 60% of the specific grinding power according to Kuschel [19], which is an appropriate assumption for the dry grinding process. Heat transfer between the workpiece and the environment (air) is defined by a heat transfer coefficient of 100 W/(mm²·K). Figure 1 shows a schematic view of the 3D model approach and the used boundary conditions.

2.3. Displacement and Strain Field Measurement with DSP

Digital speckle photography is a well-known technique for characterizing in-plane displacements of surface elements [20,21]. A camera captures the coherent laser light, diffusely scattered at the surface. The phase elements of the light wave, modulated by the surface, generate an image of the topography in the image plane (on the camera chip), which is superimposed with a speckle pattern (Figure 2). The size of the speckle can be varied in a wide range by the aperture of the lens. An outstanding feature of the subjective speckle is that they can be assigned to specific surface points, according to the imaging system. Therefore, shifts of individual speckle can be interpreted as displacements of local surface points in the object plane. A global displacement field of the measured surface is calculated by scanning a small evaluation window over the measurement field and calculating the cross correlation between two consecutive speckle images at each point. The size of the evaluation window can be computed automatically and should include at least three speckles on the diagonal. An optimal speckle diameter of about 3–5 pixels is adjusted [22]. By determining the shift of the correlation maxima, elastic and plastic deformations with previously unachieved spatial resolutions of about 20 nm and temporal resolutions in the microsecond range can be reconstructed [13]. After calculating the point displacement field $P\left(\mathrm{u},\mathrm{v}\right)$ (where u und v are the displacements in the x and y directions), the deformation gradient field F_2D can be determined according to Kajberg [23]:

$$F_{2\mathrm{D}}=\left(\begin{array}{cc}1+\frac{\partial \mathrm{u}}{\partial \mathrm{x}}& \frac{\partial \mathrm{u}}{\partial \mathrm{y}}\\ \frac{\partial \mathrm{v}}{\partial \mathrm{x}}& 1+\frac{\partial \mathrm{v}}{\partial \mathrm{y}}\end{array}\right)$$

(3)

The polar decomposition of the F_2D field leads to

$$F_{2\mathrm{D}}=R_{2\mathrm{D}}{U}_{2\mathrm{D}}$$

(4)

where R_2D is the orthogonal rotation tensor (R^T_2DR_2D = I) and U_2D is the positive definite and symmetric right stretch sensor (U^T_2D = U_2D). Then F^T_2DF_2D = (R_2DU_2D)^TR_2DU_2D = U^T_2DU_2D, which can be written in the form

U²_2D = F^T_2DF_2D

(5)

To solve the square root, the spectral decomposition is used:

U_2D = λ₁n₁n^T₁ + λ₂n₂n^T₂

(6)

Here λ₁ and λ₂ are the square roots of the eigenvalues of the symmetric matrix U²_2D and n₁ and n₂ are the corresponding eigenvectors. The logarithmic (Hencky) in-plane strain matrix ε_2D is finally computed as [24]

ε_2D = ln(U_2D)

(7)

The basic setup for strain measurements in the surface grinding process is indicated in Figure 2. The measuring field is located on the side face—the unmachined side of the workpiece—directly at the border to the machined surface. The lens and the charged-coupled device (CCD) camera are fixed relative to the workpiece system, so that occurring speckle movements can be directly correlated with shifts of surface points. Out-of-plane deformations of the surface in the grinding process lead to a decorrelation of the speckle pattern, whereby the desired measuring effect is destroyed. The use of a high-speed camera (Optronis: CP70, Kehl, Germany) with a fast image-to-image evaluation at a frame rate of 167 fps, reduces this decorrelation since the out-of-plane displacement in the short period of 1/167 s is so small that almost no speckle decorrelation occurs. The measured displacements in the object plane are correspondingly small in this short time. However, with a suitable two-dimensional sub-pixel interpolation displacements of a few hundredths of a pixel (here 1 pixel $\widehat{=}$ 1.94 µm) can be determined [25].

2.4. Experimental Setup

The experiments are conducted on a Blohm Profimat 412 HSG (Hamburg, Germany) profile grinding machine with the process parameters to the displayed results shown in Figure 3. The presented parameters are one combination exemplarily selected from a variation of process parameter combinations. The parameters were selected to be in a practical range for a surface grinding process with consideration of the absence of cooling lubricants. Accordingly the estimated heat generation in the workpiece was considered. Integrated force and power measurements are used to record the external material loads. The applied abrasive tool is a vitrified bonded corundum grinding wheel with the specification 9A60H16. The material used in the experiments is alloy steel AISI4140 (42CrMo4) which is widely used in industrial applications. The selected heat treatment of the alloy steel leads to a normalized state, which is characterized by a ferrite-perlite microstructure. Thus, the surface hardness of the material is measured as 213 HV1 with a standard deviation of 3.6. The workpieces are designed as cuboids with a length of 165 mm, 18 mm width and 41.5 mm in height. To setup the peripherals (camera, laser and optical components) preferably close to the contact area, adapters and connection devices are constructed. The workpiece side-plain facing the speckle measuring system is shot-blasted before the experiments in order to generate a rough surface, which leads to a sufficient phase mixing of the laser wave front and to the formation of a fully developed and homogeneous speckle pattern. The measurement is performed on a spot in the middle section of the workpiece and the measurement setup is connected to the linear movement of the workpiece in x-axis direction. Therefore the tangential feed speed v_ft in this work is referring to the relative grinding wheel feed speed against the workpiece respectively the moving heat source. The feed of the workpiece is counter-directional to the cutting speed v_c of the grinding wheel (up-grinding) and thus the grinding wheel tangential feed speed v_ft is in the same direction as v_c.

The absence of the cooling lubricant in the investigated dry grinding process avoids measurement distortions due to irregular liquid and vapor behavior, creates a direct, clear optical channel for the camera and laser and protects the measuring system from contamination. However, the absence of the cooling lubricants leads to a strong development of flying sparks (see Figure 4). Optical components can be damaged by the red-hot chips and must be covered or placed at a correspondingly large distance from the point of the tool engagement. The large working distance of about 90 mm is achieved with a high-performance enlarging lens (Rodenstock: Apo-Rodagon N, Feldkichen, Germany).

The use of various extension tubes allows a threefold magnification, thus leading to a measuring field of about 6 mm × 8 mm. To stabilize the extension tubes and to ensure a fixed position of the CCD-camera in relation to the workpiece while grinding, a mounting fixture was designed. A fixation at the front end of the lens prevents the transmission of vibrations from the machine to the camera (see Figure 3). By adapting the camera system to the magnetic clamping plate which is setup on the force measurement plate, it is possible to take blur-free images of the object even during the grinding process. Thereby, vibrations are equalized for both measurement units and workpiece.

After grinding, a burr can be observed on the machined surface. The burr formation corresponds to a different inclination of the measuring surface, by what the light from the upper part of the workpiece area is not reflected into the camera. This leads to a loss of contrast of the speckle pattern at the upper edge of the workpiece and thus to a high measurement uncertainty in this region. Therefore, the displacement field of the contact zone near the surface is only calculated from a depth of approx. 800 µm below the machined surface, where the influence of contrast loss is reduced. Taking into account the depth of cut of a_e = 200 µm, the area between y = −1000 µm and y = 0 µm below the surface is not evaluated. Therefore, the boundary area is also not indicated in the simulation results.

In the dry grinding process the emergence of sparks and particles is misinterpreted by the conventional DSP analysis methods as displacement of surface points. The particle movement can be almost completely eliminated by using optimized algorithms. For this purpose, the size of the speckles inside the evaluation window is compared to the average speckle size in the global speckle image. Usually, disruptive particles caused by sparks are significantly larger than the adjusted speckle diameter and therefore immediately recognizable. In this case, the local deformation for the measuring position is set to zero. The error that occurs while summing the displacements is negligible due to the high clock speed of the camera.

3. Results of In-Process Measurements and Simulations of Material Loads

In the following comparisons, the internal material loads in the workpiece surface during dry grinding are analyzed. For this purpose, the process is observed directly below the grinding wheel in the experiments. Respectively, the simulation results are determined while the constant heat source is right above the analysis window. To obtain an equally large, meaningful field of view for the measurement as for the simulation, the high amount of individual images of the measurement are stitched together to form a large field of 6 mm × 32 mm. Stitching is possible because the grinding wheel moves slowly through the measuring field at times t₁ to t_1+3n during the image acquisition of the speckle pattern. Assuming a homogeneous workpiece and constant grinding conditions, each time step can be assigned to a certain grinding wheel position and thus, the global displacement field can be reconstructed (see Figure 5).

The length of the contact zone (8.94 mm) is calculated from the grinding parameters (see Figure 3) and is in the dimension of a single speckle image. The partial image at time t₁ shows an example of a picture with strong particle flight in the measuring field. The influence of the moving particles can be eliminated by a high recording rate and the special evaluation described in Section 2.4.

Despite the neglect of mechanical loads in the simulation, the simulation results show a qualitative accordance to the speckle measurements in feed speed direction (−x-displacements). In the simulation, however, the mechanical component caused by the force components described above is not considered. The tangential force component shifts the entire workpiece 20 µm in the direction of the tool movement v_c. After subtraction of this offset, the values are in a good quantitative agreement. Figure 6 shows the total (elastic and plastic) displacements in feed speed direction, measured with the speckle photography (a) in comparison with the FEM simulations (b). The minimum displacement (=maximum negative displacement) lies in both cases approx. 2.5 mm after the first interaction between tool and workpiece and is 22 µm in feed speed direction. Towards the end of the effective surface the displacement decreases to approx. −15 µm. The exact evaluation of the minimum displacement below the grinding wheel results in a value of 3 mm for the measurement and 2.2 mm for the simulation after the start of tool engagement. The discrepancy of 800 µm is partly due to the fact that the beginning of the contact zone in the speckle images can only be defined optically (see subframe t_1+n in Figure 5), which is in principle subjective and can only be estimated. The relative measurement uncertainty resulting from the estimation for the position of the contact zone is approx. ±1 mm. Within this framework, the positions of the x-displacement minimum in the measurement and in the simulation are congruent.

The total displacements in normal direction are shown in Figure 7. The speckle measurements show a qualitatively similar behavior, but in the measurement the surface is shifted further down in the y-direction. In the measurement, the displacement 10 mm behind the heat source has increased to 25 µm. In the simulation the calculated value of 20 µm is 20% lower than in the measurements using speckle photography. This slight deviation may be caused by the neglect of the mechanical stress component in the simulation or by the fact that the assumed heat flow $\mathrm{q}\dot{}$ over the contact length l_g cannot be regarded as constant or is higher than assumed.

The stepped behavior in the FEM simulation results from the limited number of nodes in the mesh of the large-volume 3D model (165 mm × 18 mm × 41.5 mm), which is discretized finer only at the interface to the heat source (y$\to$−1 mm). As described in Section 2.2, the measured strain field has been calculated from the displacements determined by speckle photography. A good agreement can be seen for the resulting elongation during the grinding process in the feed speed direction (see Figure 8).

An interesting result is that the strain in front of the grinding wheel is obviously caused only by the thermal energy input and not by a mechanical effect. In the speckle measurement as in the FEM simulation, the minimum elongation lays approx. 3 mm in front of the grinding wheel and has a value of −1.2 × 10⁻³ mm/mm. The maximum x-strain in the simulation is located at the end of the heat source. The peak value of 1.3 × 10⁻³ mm/mm is 15% lower than in the measurement, where it rises to 1.5 × 10⁻³ mm/mm. In the strain analysis as in the investigation of the displacements, a slight displacement of the measured data in the x-direction can be observed. The shifting between the measurement and the simulation is probably induced by an inaccurate visual determination of the contact zone in the speckle images.

Also for the strain in normal direction (see Figure 9) the simulation shows a slightly graduated behavior, caused by the limited possibilities of discretization and representation in the simulation tool DEFORM-3D. Nevertheless, the results for the simulation and the measurement for the y-strain are basically the same. No expansions build up in front of the grinding wheel or heat source respectively. Behind the influence zone, the strain values in both cases rise up to over 2 × 10⁻³ mm/mm.

Since the maximum values of the speckle measurement and the pure thermal FEM simulation for the displacement and strain analyses all in all differ only by a maximum of 20%, the simulation approach of a primarily thermally driven process for dry grinding can be regarded as valid.

4. Conclusions and Outlook

For the first time, process-accompanying displacement field and strain field measurements are carried out during a grinding process, in this case without application of cooling lubricant. Under these conditions, it can be assumed that the grinding process is predominantly thermally driven. Hence for the FEM simulation of this dry grinding process the model of a constant heat source was assumed. Despite this idealized assumption and the rough experimental conditions with flying sparks, the comparison between speckle photography measurement and FEM simulation shows a good agreement. Measurement and simulation indicate that the energy input takes place very locally. The negative strain that builds up in front of the grinding wheel is obviously primarily thermal in nature. The results demonstrate that speckle photography is able to measure strain fields during machining and confirm the assumption that thermal aspects prevail during the applied grinding process without coolant and therefore the process can be simulated by a constant heat source. In connection with the concept of process signatures, speckle photography shows that it can measure both elastic stresses and plastic changes in the material behind the tool. Thus, speckle photography is predestinated to acquire internal material stresses and to design optimized processes and process chains that are specifically oriented to the functional properties of the final component.

Future work will investigate whether the use of metalworking fluids is possible in the process and how they influence the measurements. First experiments have shown that speckle photography is possible through closed liquid films, where the air-liquid surfaces remain constant. Therefore, a measuring setup is currently being implemented with which the gap between workpiece and measuring system is completely filled with cooling lubricant. With an adapted grinding setup, the speckle photography also can be able to determine not only a dominant thermal but also a dominant mechanical impact of the loads.