Simulation of workpiece surface roughness after flat

This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg)Nanyang Technological University, Singapore.

Simulation of workpiece surface roughness afterflat grinding by electroplated wheel

Mohammad Rabiey; Lee, Joseph Zhi Wei

2018

Mohammad Rabiey., & Lee, J. Z. W. (2018). Simulation of workpiece surface roughness afterflat grinding by electroplated wheel. Procedia CIRP, 77, 303‑306. doi:10.1016/j.procir.2018.09.021

https://hdl.handle.net/10356/90194

https://doi.org/10.1016/j.procir.2018.09.021

© 2018 The Author(s). Published by Elsevier Ltd. This is an open access article under the CCBY‑NC‑ND license (http://creativecommons.org/licenses/by‑nc‑nd/4.0/).

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2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.

28th CIRP Design Conference, May 2018, Nantes, France

A new methodology to analyze the functional and physical architecture of existing products for an assembly oriented product family identification

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France

* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Abstract

In today’s business environment, the trend towards more product variety and customization is unbroken. Due to this development, the need of agile and reconfigurable production systems emerged to cope with various products and product families. To design and optimize productionsystems as well as to choose the optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the productionsystem. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to clusterthese products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrativeexample of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.

Keywords: Assembly; Design method; Family identification

1. Introduction

Due to the fast development in the domain of communication and an ongoing trend of digitization anddigitalization, manufacturing enterprises are facing importantchallenges in today’s market environments: a continuingtendency towards reduction of product development times andshortened product lifecycles. In addition, there is an increasingdemand of customization, being at the same time in a global competition with competitors all over the world. This trend, which is inducing the development from macro to micro markets, results in diminished lot sizes due to augmentingproduct varieties (high-volume to low-volume production) [1]. To cope with this augmenting variety as well as to be able toidentify possible optimization potentials in the existingproduction system, it is important to have a precise knowledge

of the product range and characteristics manufactured and/or assembled in this system. In this context, the main challenge inmodelling and analysis is now not only to cope with single products, a limited product range or existing product families,but also to be able to analyze and to compare products to definenew product families. It can be observed that classical existingproduct families are regrouped in function of clients or features.However, assembly oriented product families are hardly to find.

On the product family level, products differ mainly in twomain characteristics: (i) the number of components and (ii) thetype of components (e.g. mechanical, electrical, electronical).

Classical methodologies considering mainly single products or solitary, already existing product families analyze theproduct structure on a physical level (components level) which causes difficulties regarding an efficient definition andcomparison of different product families. Addressing this

Procedia CIRP 77 (2018) 303–306

2212-8271 © 2018 The Authors. Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)Selection and peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018).10.1016/j.procir.2018.09.021

© 2018 The Authors. Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)Selection and peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018).

Available online at www.sciencedirect.com

ScienceDirect Procedia CIRP 00 (2018) 000–000


2212-8271 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018)..

8th CIRP Conference on High Performance Cutting (HPC 2018)

Simulation of workpiece surface roughness after flat grinding by electroplated wheel

Mohammad Rabieya* , Joseph Lee Zhi Weib aUniversity of Applied Science Rapperswil, Oberseestrasse 10, 8640 Rapperswil, Switzerland

bNanyang Technological University, 50 Nanyang Ave, 639798 Singapur

* Corresponding author. Tel.: +41-55-222-4058; fax: +41-55-222-4769. E-mail address: [email protected]

Abstract

The stochastic nature of grinding wheel topography together with grinding process parameters and kinematics have great influence on the surface roughness of workpiece. This paper aims to achieve a method of kinematics simulation of flat grinding process using MATLAB to predict the surface roughness of workpiece based on the topography of the electroplated Cubic Boron Nitride (CBN) wheel. Grain distribution, protrusion height and size are varied for each simulation. Based on trajectory of spherical grain forms in flat grinding kinematics, a 3D simulation of surface roughness is resulted. Suggestions are made for the improvement in accuracy of predicting workpiece profile.

Keywords: Grinding; Surface roughness; Simulation; Cubic boron nitride (CBN)

1. Introduction and state of the art

Grinding is one of the most important machining processes particularly if higher accuracy and fine surface finish are needed. The demand for higher quality, higher precision and longer lasting product drives the advancements in manufacturing processes among which the process simulation is in front side and crucial not only for the prediction but also for understanding of the processes. This allows for cost reductions, process stability and more productivity.

1.1. Generating the grinding wheel topography

A numerical model is applied by Nguyen and Butler [1] which generates a non-Gaussian grinding wheel topography having height distribution and autocorrelation functions similar to a wheel topography used for test verification.

A simplified model approximated the grains to be spheres with random grain size adopted a computationally efficient 3D wheel model with 2D cutting edge profiles for vitrified grinding wheels to investigate the workpiece surface roughness using three different grain shapes (sphere, truncated cone, and

cone [2, 3, 4]. Liu et al [5] applied a ‘shaking’ technique to distribute the grains such that they do not overlap and also a dressing model developed by Chen and Rowe [2]. McDonald et al [6] obtained wheel topography measurements of a vitrified aluminum oxide grinding wheel using the optical grinding wheel scanner system after dressing with a single-point diamond tool. They developed a new method of removing erroneous spikes from the measured data and a method based on process kinematics to identify cutting edges.

1.2. Prediction of the workpiece surface

Two types of grinding simulation methods have been developed for prediction of workpiece surface finish. Some of the researcher [1, 2, 3], adopted the kinematics simulation method where the trajectories of the cutting edges were determined then merged and trimmed in the appropriate manner to create a surface. The alternate method of subtraction adopted by other researcher [4] involves subtracting the interaction of abrasive cutting points along their respective trajectories with the workpiece in a stepwise manner.










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304 Mohammad Rabiey et al. / Procedia CIRP 77 (2018) 303–3062 Author name / Procedia CIRP 00 (2018) 000–000

2. Grinding wheel topography model

In this paper, the model of grain distribution for calculation of theoretical grain spacing used by Rabiey [7; 8] for electroplated CBN grinding wheel is adopted. A new grain distribution model is developed that ensures uniform cutting edge density throughout the entire wheel while randomizing grain size, grain protrusion height and grain spacing. A kinematics approach is developed that predicts the workpiece surface based on the spherical shape of the grain.

2.1. Initial values for protrusion height, grain size and grain distance

The average grain distance 𝑠𝑠 in 𝑚𝑚𝑚𝑚 is given as:

2/1cLK (1)

grainK dLs (2)

where c is the cutting edge density per unit area of wheel surface measured as 50.5 𝑐𝑐𝑚𝑚−2 for electroplated CBN wheel with grain size of B126 [7], the average distance between grain edges defined by s and 𝑑𝑑𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 is the average diameter of a single CBN grain. The approximate number of grains will be:

sdrn

grain

wheel

(3)

Where 𝑟𝑟𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 is the radius of the grinding wheel. To have a faster simulation process time the number of columns of grains along the grinding wheel’s height surface (z-direction) is considered 10. Table 1 shows the initial paraments considered for the simulation.

Table 1. Grinding Wheel Topography Parameters.

Parameter Value

Diameter of Grinding Wheel 400 mm Average grain diameter 0.126 mm Cutting Edge density 50.5 cm-2 Number of columns of grains 10 Average Protrusion height 0.0378 mm

Average Grain Separation 0.2705 mm Number of grains in a column 3169 Geometry of grains spherical Grain type CBN

2.2. Stochastic protrusion height, grain size and grain distance

Protrusion heights of grains are randomized following a normal distribution between the minimum protrusion height of 20% and the maximum protrusion height given by 40% of grain diameter based on the experimental measurement for electroplated wheel. Grain size is randomized with variance of

±0.025 𝑚𝑚𝑚𝑚 and the grain distance is randomized with variance between +50% and -50% of the average distance between grain edges. Figure 1 illustrate the schematic of the grain size and distance based on randomized distribution.

Fig. 1. Schematic of the grain size and grain distance based on stochastic distribution

Grain size and grain distance are randomized based on the condition that the sum of n random grain sizes and grain distances must be equal to the sum of n average grain size and average grain distances i.e.:

)...( 1 randnrandsum sss (4)

)...( 1 randnrandsum ddd (5)

2.3. Position of grains with random distance and random grain size

The coordination of each grain follows the iterative equation shown in table 2, where r is the radius of the grain and S is the random distance between the present grain and the next grain.

Table 2. Iteration in x and z direction to position the grain coordination.

Grain Position Iteration

1 x1,z1 rgn+S1+rg1

2 x2,z2 rgn+S1+rg1

+rg1+S2+rg2

3 xn,zn rgn+S1+rg1

+rg1+S2+rg2

+…+rg(n-1)+Sn+rgn

The final distribution is shown in Fig. 2 with random grain

size, grain separation and protrusion height, where all above mentioned randomized parameter applied on the surface topography of the wheel.

Fig. 2. Random grain size and distance distribution

Author name / Procedia CIRP 00 (2018) 000–000 3

Due to the condition set for each column of grains, the last grain for each column would meet at the same position. Thus, an additional random distance between –s and +s is added to each column to shift each column forward and back; rotating the entire column on the grinding wheel. This ensures a random distribution for the last row of grains and for the total length of column cannot exceed wheel circumference. The angular location of each grain can be determined by the division of the x coordinates of the grain which represents the arc length on the grinding wheel by the radius r of the grinding wheel. Fig.3 shows the three-dimensional grinding wheel topography with the final grain distribution

Fig. 3. Grinding wheel topography based on angular location

3. Simulation of grinding process kinematic

To simulate the kinematics of the grinding process the parameters mentioned in table 3 are considered.

Table 3. Grinding parameters:

Parameter Value

Depth of cut, ae 0.025 mm

Feed rate, vf 3000 mm/min

Grinding speed; vs 80 m/s

Strategy Up grinding

In order to find the cycloidal trajectory of each grain on the

workpiece surface the following equations can be used [10]:

tvtrvrx f

s

si

sin (6)

t

rvry

s

si cos (7)

Where the parameters are defined in table 4:


Parameter Dimension

Radial distance from center of wheel, ri m Grinding speed, vs m/s Feed rate; vf mm/min Angular position θ radian

Applying the equation 6 and 7 based on one single column of the stochastic wheel topography defined the section 2, the results of the kinematics simulation by MATLAB is shown by the separate two-dimensional plot in Fig. 4.

Fig. 4. 2D Simulation (upper figure is the trajectory of each grain and the bottom figure is the topography on workpiece surface)

To reduce simulation time, a cut off line is implemented which only allows trajectories with maximum depth lower than the line to be simulated. The cut off line is based on the sum of the radius of the grinding wheel and 125% of the average protrusion height. This method of simulation is only accurate in producing two-dimensional workpiece surfaces and assuming all the trajectories lie in the same x-height plane. When the simulation is applied to predict a three-dimensional workpiece surface, a workpiece topography with sharp edges is produced as shown in Fig.5. Compared to a realistic workpiece surface finish produced by CBN grinding, the simulated workpiece surface indicates inaccuracy. A realistic workpiece surface finish depicts a smoother surface with curved edges instead of sharp and straight edges.

For an accurate kinematic simulation of the full stochastic wheel topography, a novel approach is used to produce a three-dimensional surface profile illustrated in Fig.6.

Mohammad Rabiey et al. / Procedia CIRP 77 (2018) 303–306 3052 Author name / Procedia CIRP 00 (2018) 000–000

2. Grinding wheel topography model

In this paper, the model of grain distribution for calculation of theoretical grain spacing used by Rabiey [7; 8] for electroplated CBN grinding wheel is adopted. A new grain distribution model is developed that ensures uniform cutting edge density throughout the entire wheel while randomizing grain size, grain protrusion height and grain spacing. A kinematics approach is developed that predicts the workpiece surface based on the spherical shape of the grain.

2.1. Initial values for protrusion height, grain size and grain distance

The average grain distance 𝑠𝑠 in 𝑚𝑚𝑚𝑚 is given as:

2/1cLK (1)

grainK dLs (2)

where c is the cutting edge density per unit area of wheel surface measured as 50.5 𝑐𝑐𝑚𝑚−2 for electroplated CBN wheel with grain size of B126 [7], the average distance between grain edges defined by s and 𝑑𝑑𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 is the average diameter of a single CBN grain. The approximate number of grains will be:

sdrn

grain

wheel

(3)

Where 𝑟𝑟𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 is the radius of the grinding wheel. To have a faster simulation process time the number of columns of grains along the grinding wheel’s height surface (z-direction) is considered 10. Table 1 shows the initial paraments considered for the simulation.

Table 1. Grinding Wheel Topography Parameters.

Parameter Value

Diameter of Grinding Wheel 400 mm Average grain diameter 0.126 mm Cutting Edge density 50.5 cm-2 Number of columns of grains 10 Average Protrusion height 0.0378 mm

Average Grain Separation 0.2705 mm Number of grains in a column 3169 Geometry of grains spherical Grain type CBN

2.2. Stochastic protrusion height, grain size and grain distance

Protrusion heights of grains are randomized following a normal distribution between the minimum protrusion height of 20% and the maximum protrusion height given by 40% of grain diameter based on the experimental measurement for electroplated wheel. Grain size is randomized with variance of

±0.025 𝑚𝑚𝑚𝑚 and the grain distance is randomized with variance between +50% and -50% of the average distance between grain edges. Figure 1 illustrate the schematic of the grain size and distance based on randomized distribution.

Fig. 1. Schematic of the grain size and grain distance based on stochastic distribution

Grain size and grain distance are randomized based on the condition that the sum of n random grain sizes and grain distances must be equal to the sum of n average grain size and average grain distances i.e.:

)...( 1 randnrandsum sss (4)

)...( 1 randnrandsum ddd (5)

2.3. Position of grains with random distance and random grain size

The coordination of each grain follows the iterative equation shown in table 2, where r is the radius of the grain and S is the random distance between the present grain and the next grain.

Table 2. Iteration in x and z direction to position the grain coordination.

Grain Position Iteration

1 x1,z1 rgn+S1+rg1

2 x2,z2 rgn+S1+rg1

+rg1+S2+rg2

3 xn,zn rgn+S1+rg1

+rg1+S2+rg2

+…+rg(n-1)+Sn+rgn

The final distribution is shown in Fig. 2 with random grain

size, grain separation and protrusion height, where all above mentioned randomized parameter applied on the surface topography of the wheel.

Fig. 2. Random grain size and distance distribution

Author name / Procedia CIRP 00 (2018) 000–000 3

Due to the condition set for each column of grains, the last grain for each column would meet at the same position. Thus, an additional random distance between –s and +s is added to each column to shift each column forward and back; rotating the entire column on the grinding wheel. This ensures a random distribution for the last row of grains and for the total length of column cannot exceed wheel circumference. The angular location of each grain can be determined by the division of the x coordinates of the grain which represents the arc length on the grinding wheel by the radius r of the grinding wheel. Fig.3 shows the three-dimensional grinding wheel topography with the final grain distribution

Fig. 3. Grinding wheel topography based on angular location

3. Simulation of grinding process kinematic

To simulate the kinematics of the grinding process the parameters mentioned in table 3 are considered.


Parameter Value

Depth of cut, ae 0.025 mm

Feed rate, vf 3000 mm/min

Grinding speed; vs 80 m/s

Strategy Up grinding

In order to find the cycloidal trajectory of each grain on the

workpiece surface the following equations can be used [10]:

tvtrvrx f

s

si

sin (6)

t

rvry

s

si cos (7)

Where the parameters are defined in table 4:


Parameter Dimension

Radial distance from center of wheel, ri m Grinding speed, vs m/s Feed rate; vf mm/min Angular position θ radian

Applying the equation 6 and 7 based on one single column of the stochastic wheel topography defined the section 2, the results of the kinematics simulation by MATLAB is shown by the separate two-dimensional plot in Fig. 4.

Fig. 4. 2D Simulation (upper figure is the trajectory of each grain and the bottom figure is the topography on workpiece surface)

To reduce simulation time, a cut off line is implemented which only allows trajectories with maximum depth lower than the line to be simulated. The cut off line is based on the sum of the radius of the grinding wheel and 125% of the average protrusion height. This method of simulation is only accurate in producing two-dimensional workpiece surfaces and assuming all the trajectories lie in the same x-height plane. When the simulation is applied to predict a three-dimensional workpiece surface, a workpiece topography with sharp edges is produced as shown in Fig.5. Compared to a realistic workpiece surface finish produced by CBN grinding, the simulated workpiece surface indicates inaccuracy. A realistic workpiece surface finish depicts a smoother surface with curved edges instead of sharp and straight edges.

For an accurate kinematic simulation of the full stochastic wheel topography, a novel approach is used to produce a three-dimensional surface profile illustrated in Fig.6.

306 Mohammad Rabiey et al. / Procedia CIRP 77 (2018) 303–3064 Author name / Procedia CIRP 00 (2018) 000–000

Fig.5. Predicted 3D workpiece surface using kinematic simulation method

In addition to merging of the trajectories of the cutting edges, the geometries of the individual cutting edges must be taken into account. The single-line trajectories as shown in Fig.4 only reflects the center of the cutting edge and they lie in different x-height planes depending on the z-positions of the cutting edge on the grinding wheel. The rounded geometries of each spherical grain and their respective z-positions are first merged with their determined trajectories.

Fig. 6. 3D Simulation of workpiece surface topography (upper figure showing surface facing x-axis and lower figure showing surface facing z-axis)

Next, the newly merged three-dimensional trajectories of all the cutting edges are merged together and trimmed to form the three-dimensional surface illustrated in Fig.6. The different

sized spherical shape of the cutting edges is reflected in Fig. 6 facing the z-axis where the trajectories are perpendicular to the z-axis.

The maximum height resulted from simulation (which will be correspondent to Rz) is 8 µm which is higher than the Rz in case of grinding of steel 100Cr6 with the same grinding parameter as simulated (Rz. of the real case is 4 µm). The reason of considerable difference between the simulation and real case is the ploughing process which happens in the reality encompassed with plastic deformation of the metal. In real grinding, all the grains will not cut the surface but lots of them just rub and plough the surface.

Next step of the simulation will be merging of rubbing and ploughing process into the algorithm of the program which makes the simulation much closer to the reality results.

4. Summary

The mathematical method discussed in this paper provides an algorithm not only to simulate the wheel surface topography but also the grinding process and the surface topography achieved after the grinding. The simulation results demonstrate the topography of electroplated bond wheel and by randomize grain size and grain distance. The simplified assumption of the simulation is that all the grains which come to contact do cutting process.

References

[1] Nguyen, T., & Butler, D. Simulation of precision grinding process, part 1: generation of the grinding wheel surface. International Journal of Machine Tools and Manufacture, 2005, 45(11); p 1321-1328

[2] Chen, X., & Rowe, W. B. Analysis and simulation of the grinding process. part I: generation of the grinding wheel surface International Journal of Machine Tools and Manufacture, 36 (8) ,1996:871-882

[3] Koshy, P., Jain, V., & Lal, G. Stochastic simulation approach to modelling diamond wheel topography. International Journal of Machine Tools and Manufacture, 1997; 37(6): 751-761.

[4] Darafon, A., Warkentin, A., & Bauer, R. 3D metal removal simulation to determine uncut chip thickness, contact length, and surface finish in grinding. The International Journal of Advanced Manufacturing Technology, 2012;66(9-12):1715-1724.

[5] Liu, Y., Warkentin, A., Bauer, R., & Gong, Y. Investigation of different grain shapes and dressing to predict surface roughness in grinding using kinematic simulations. Precision Engineering, 2013; 37(3):758-764.

[6] Mcdonald, A., Mohamed, A. O., Warkentin, A., & Bauer, R. J. Kinematic simulation of the uncut chip thickness and surface finish using a reduced set of 3D grinding wheel measurements. Precision Engineering, 2017;49: 169-178.

[7] Rabiey, M.: Dry grinding with CBN Wheels, The Effect of Structuring, Dissertation, University of Stuttgart, (2010).

[8] Tawakoli, T., & Rabiey, M. Macro-topography effects on dry grinding with CBN wheels. International Journal of Mechatronics and Manufacturing Systems, 2008;1(4):415.

[9] Klocke, F.; Konig, W.: Schleifen, Honen, Lappen; Fertigungsverfahren Band 2, Springer Verlag, (2005).

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Simulation of workpiece surface roughness after flat