Milling Simulation

The simulation system calculates the engagement conditions of the milling cutter for each time ... A more economical and more flexible ... The limited dynamic.
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Milling Simulation An Adaptive Approach to Increase Simulation Accuracy Klaus Weinert, Patrick Damm Department of Machining Technology University of Dortmund Baroper Strasse 301 44227 Dortmund

ABSTRACT. One of the most important trends in manufacturing of dies and molds for casting and forming is to shorten the process chain by direct HSC-milling into quenched steel. The development of modern cutting materials, coatings and milling cutter geometries allows to substitute the electric discharge machining in more and more fields of application. In order to take full advantage of the HSC-technology, the process must be reliable and the machining accuracy must be predictable. These demands are in contrast to the complex and ever changing engagement conditions during the milling process. This is the core problem in machining sculptured surfaces. One opportunity to ensure high process reliability while decreasing contour-faults at the same time lies in the simulation based offline-optimization of the milling process as developed by the Department of Machining Technology (ISF), Dortmund, Germany. The simulation system calculates the engagement conditions of the milling cutter for each time period of the process. This geometric information and additional process characteristics (e.g. the moving direction of the tool) are joined to an 'equivalent tool load'. Depending on these predicted values, the feed rates are adapted to get a regular tool load in the real milling process. In order to increase the accuracy of the simulation further the system is now equipped with an 'adaptive' database which compares the predicted values for tool loads with the real values which are measured during machining time. The measured and the predicted values are compared and the results are used to adjust the rules of the simulation. KEY WORDS: NC-Machining, Milling Simulation, Process Optimization

1.

Introduction

Form tools are necessary for a wide range of production technologies, e.g. dropforging, die casting and injection molding. A more economical and more flexible way to manufacture such molds – compared to EDM (electric discharge machining) technologies – is direct HSC-milling of quenched steel [Bie 91]. This technology has been developed to practical usability, actively supported by research efforts in the areas of machine tools, motion controls systems and milling cutters. There are two remaining major problems concerning this manufacturing process: • •

poor process reliability poor contour accuracy

The process reliability is considerably influenced by the risk of tool breakage or the damage of the tools cutting edge which leads to contour faults and rough surfaces. The most important reason for tool breakage is that the process forces exceed the tools capability due to changing engagement conditions caused by varying overmeasures. Contour faults are basically caused by two major influences. The limited dynamic capability of the HSC-milling machine and the deformation of the milling cutter. The first effect can be reduced by continuously aligned milling paths and the integration of intelligent algorithms like ‘feed-forward’ or ‘look-ahead’ into the motion control system. The second effect, what is responsible for contour faults, i.e. cutter deformations, is caused by varying process forces due to changing engagement conditions, local surface-overmeasures and the tools moving direction. These problems have to be minimized in order to take full advantage of the greater productivity of the HSC-milling process. Milling cutter deformation

Premachining roughing

semi-finishing

programed overmeasure

vf

unwanted overmeasure

Figure 1.

Problems in the machining of sculptured surfaces

There are different ways to improve the process reliability and the machining accuracy: •

Milling in discrete steps with reduced surface overmeasure in order to reduce process forces.



Milling with an overall reduced feed rate in order to reduce the process forces generally.



Milling with continuously adjusted feed rates, that depend on the actual process forces.

The first and the second method can be implemented without problems. The disadvantage of these methods is a significant increase in machining time and with it a corresponding loss of economy. The third method requires the capability of analyzing the process forces. To perform this task there are two basically different methods, whose advantages and disadvantages will be discussed in the following paragraph.

2.

Online- vs. Offline- Process-Optimization

To adjust feed rates continuously, depending on the actual process conditions, it is necessary to have a ‘tool’ which is capable of analyzing the relevant characteristic values.

2.1.

Online-Process-Optimization

One possibility is to measure the tool loads during the milling process and to adjust the feed rates online by using an adaptive control circuit. The main advantage of this method is, that it is not necessary to obtain any deeper knowledge of the cutting process, because the system simply orients itself by the measured values read by the sensors. On the other hand there are a series of disadvantages which let this procedure seem to be impractical for everyday life. The two most important reasons therefore are: •

Every machine has to be equipped with a bulky and expensive measuring and adaptive control equipment.



The control circuit must be extremely fast to avoid a serious tool impairment.

The first aspect normally leads to very high costs for the introduction and operation of that technology. If the spreading of such systems in the market would be extensive enough, this argument could possibly be weakened.

Vf,1

Vf,2

low over-measure

high over-measure

earliest time for the adaptive control system to reduce the feed rate 10

vf,1

feed rate vf

m/min

6

4

2

vf,2 -11,7

0

Figure 2.

0

-25

-20

-15

-10 -5 time t

0

ms

10

Restriction of an adaptive motion control by the machines dynamic

But the second point listed above is related to a technological property all control circuits own. They are not capable of prognosticating a situation – they only can respond to a change in the measured values. This means that the time such a system needs for its reaction must be short enough to prevent the milling cutter from an engagement condition which exceeds its capability. Figure 2 and figure 3 illustrate the problem for control circuits. The milling cutter runs from an area with a low overmeasure into an area with a high overmeasure. Supposing the feed rate has to be decreased from vf,1 = 8m/min to vf,2 = 1m/min and the machine provides a maximum acceleration capability of 1g, the whole deceleration process needs about 11.7ms and a path length of 0.88mm. During this brake path the tools is operated with a varying overload, according to its position. Scaling down this problem to a deceleration from vf,1 = 4m/min to vf,2 = 1m/min there is still a brake path of about 0.21mm. Furthermore has to be kept in mind that this calculation assumes an ‘ideal’machine tool which means, that the motion control cycle has no delay time and that there is no jerk limitation.

10

feed rate vf

m/min

vf,1

6

4

vf,2

2 -11,7

0 0 -25 -20 -15 -10 -5 time t

0

ms 10

0,5

path length s

0

-0,5

0,21 0,88

-1

mm

-2

Figure 3.

2.2.

Length of brake path for different deceleration processes.

Offline-Process-Optimization

Instead of measuring the relevant values during the milling process the necessary information for an adequate feed rate adaptation can be obtained by a calculation based on a simulation model. The optimized feed rates are provided to the motion control system by a modified motion control dataset to which the necessary instructions sets are added. Such a system combines the following advantages: •

Only one installation is needed to serve a series of machines.



Neither the machine tools nor the milling cutters or any other expensive equipment has to be modified.



The simulation results can be stored, reused and evaluated at any time and as often as necessary. The simulation is capable to prognosticate changing engagement conditions.



Adaptive Control Control Circuit

Standard Control Dataset

+

Process

H(f)

Process Database

fitnessfunction Φ (K1, K2,.., Kn )

+

K1 K2

-

Kn +-

Process Database

Kn

process characteristic parameters Ki

Offline- Process Optimization

Standard Control Dataset

Figure 4.

K1 K2

H(f)

Process Optimized Control Datasets

Control Circuit + H(f) -

Optimization of the Motion Control Data

K1...Kn = K1, opt … Kn, opt

Adaptive control vs. offline-process-optimization.

The first two aspects refer to the economical advantage of those systems. The third issue offers a new possibility for the analysis of the milling process in special situations and helps to obtain more detailed information of the general process. The most important property of an offline-milling simulation is its ability to prognosticate machining situations. By predicting engagement conditions in an offline procedure, the simulation system is not only able to simply reduce the feed rate in areas with high overmeasures but also to take the dynamic parameters of the machine tool into account (fig. 4). This means that a necessary deceleration of the machine can be brought into play early enough to operate with a low feed rate even when the milling cutter enters the critical areas. In the late nineties the Department of Machining Technologies (ISF), Dortmund (Germany) developed a milling simulation, which will be introduced in the following paragraph.

3.

A Milling Simulation for the Increase of Process Reliability and Manufacturing Accuracy

Several papers have shown, that accuracy, process reliability and the time required for the milling process can be improved significantly when using different cutting process models to determine the cutting conditions [Alt 96, YK 94]. The crucial aspect is that for all models the engagement conditions have to be known. In principle a simulation system as discussed here has to perform two main tasks:



computation of all necessary information to represent the manufacturing process adequately.



evaluation of the information with respect to the given objective (e.g. homogenization of process forces by means of a feed rate adaptation).

These two tasks determine the main components of the simulation system: •

an information processor which is capable of calculating all demanded process information based on the given boundary conditions (NC-paths, tool geometry, etc.)



a process model which is capable of interpreting the distributed information into a realistic result, which can be evaluated with respect to given objectiv

3.1.

The information processor

The information processor, commonly designated as ‘simulation kernel’, has to distribute all relevant geometric information about the process. For the milling of sculptured surfaces this means, that the simulation kernel has to calculate the engagement conditions for any given position of the milling cutter during the machining period – which is generally a very complex and therefore time consuming job. One general advantage of the calculation method developed at the ISF is its efficiency and the slight demand for hardware performance. The solution which has been chosen is a discrete approach similar to the methods used in [Hui 94] and [YK 94]. The work piece can be imagined as a regular ‘pin grid array’ whose nails are shortened by the milling cutter (fig. 5). The main idea is to

Figure 5.

The discrete approach works as an pin grid aray whose nails are shortened by the milling cutter.

scan-convert the cutter path as well as the surface of the cutter. The scan-converted cutter is placed at each sample point along the cutter path and the z-values of the work piece grid are decreased according to the respective values for the scanconverted cutter surface. The accumulation of all lengths by which the nails have been shortened represents the amount of material removed by the milling cutter. In addition to the geometry oriented pin grid array explained above, the information processor includes some routines which work directly on the given NC-sets and provide the process model with some kinematical aspects like the angle of inclination of the tool movement.

3.2.

The process model

In the second step the information delivered by the simulation kernel has to be linked together by means of a process model which prescribes how a certain parameter has an effect on the systems behavior. In the conventional milling simulation of the ISF this process model is a heuristically generated set of rules which subsumes all single aspects in a so called ‘virtual depth of cut’ tv. The basis for the calculation of tv is the true average depth of cut t, which is the average length of all nails cut off [WMF 97, WEA 97]. To take cutting process specific effects into account, t is modified by a set of correction factors. The calculation of tv and the corresponding phenomena considered in the different terms are discussed in the following subsections. 3.2.1. Upcut milling / down-cut milling To gain an influence over the differences between upcut milled areas and down-cut milled areas, the accumulation of the cut nails is separated into two parts, so that t is calculated as: t = tupcut+ tdown-cut This allows to introduce a weigh factor σupcut for upcut material. The virtual depth of cut tv is now calculated as:

tv = σupcut ⋅tupcut+ tdown-cut 3.2.2. Inclination angle of tool path Since the tool load for downward directed cutting paths (plunge cutting) is noticeably higher than in the case of an upward directed path, a correction factor σα for the path inclination is defined as follows (fig. 6):

σα σα,max

α>0 α tv,max

It has to kept in mind that the usefulness of the calculated results depends on a lot of parameters, the user has to provide (table 1)[WAG 98]. To estimate adequate values, a very skillful specialist is required. Especially the overall limits vf,min and vf,max has to be adjusted conscientiously. This problematic nature was the motivation to extend the system with an ‘integrated milling expert’, a module which is capable of automatically adjusting proper simulation parameters.

Table 1.

Parameters to be given by the user for a feed rate adaptation.

Parameter

vf,min, vf,max tv,min, tv,max σα,max σα,min αmin αmax αlt, αht smin σu,max σupcut

4.

Description Minimum and maximum resulting feed rate. Minimum and maximum virtual depths of cut. For values which exceed these limits, the feed rate is not further increased or decreased. Maximum correction factor for material cut in an downward directed cutting path. Minimum correction factor for material cut in an upward directed cutting path If the path inclination falls short of this value the cut material is weighed by the value σα,max. If the path inclination exceeds this value the cut material is weighed by the value σα,min. Limits within the amount of cut material is weighed by 1. Limit for asymmetry correction. Above this value no asymmetry is taken into account. Maximum correction factor for an asymmetric engagement. Correction factor for material which is removed by upcut milling.

Adaptive Milling Simulation

The quality of the results of the conventional milling simulation is mainly limited by the following two aspects: •

The operator does not provide the optimum set of simulation parameters.



The set of linear functions, which make up the heuristic process model, do not exactly represent the realistic process environment.

The approach to work against both items is to involve the realistic process information in the simulation system by means of an additional comparison- and adaptation cycle (fig. 8). The process parameter which is actually used for the comparison between the real process and the simulated process is the resultant force Fa,real in conjunction with the corresponding feed rate vf and the desired resultant force Fa,desired at vf,desired which was previously adjusted by the feed rate adaptation. Fa,real can be measured at the machine by means of a 3-axes force measuring unit. If Fa,real is greater then Fa,desired, then vf,real was too high and vice versa.

4.1.

Architecture and working principle

The functional structure of the adaptive simulation system is shown in fig. 9. Two identical simulation kernels predict feed rates in the manner described in paragraph 3. The primary simulation is actually used to manipulate the feed rate information for the NC-file and the secondary simulation is used for the comparison of

CAD/CAM

NC-milling

milling simulation NCpaths

simulationkernel

load estimation

optimized NCpaths

adaptation

comparison

milling simulation simulationkernel

Figure 8.

load estimation

Adaptive milling simulation – basic structure.

the predicted values and the measured values. In addition to the conventional calculation, the results are multiplied by a correction value k which is deposited with an adaptation database. In the beginning this multi dimensional database is initialized with the value ‘1’ in all entries (details of the adaptation database are discussed in 4.2.1 and 4.2.2). In the subsequent comparisons, improved correction values k’are generated according to the following rules: Case 1: vf < vf,desired ∧ Fa,real < Fa,desired The real feed rate is below the simulated feed rate and the true resultant force is even lower then the desired force. For this constellation no proper correction value can be calculated, because the measured force has no relation to the simulated feed rate. k’= k

Figure 9.

Architecture and working principle of the adaptation system

Case 2: vf < vf,desired ∧ Fa,real > Fa,desired In this situation the new correction value is based on the feed rate quotient: k’= k ⋅vf / vf,desired Case 3: vf > vf,desired This situation is only theoretical, because the machines motion control system should not exceed the programmed feed rate vf,desired. Case 4: vf ≈vf,desired This is the standard constellation. The machine moves approximately with the programmed feed rate. The correction value is derived from the resultant forces. k’= Fa,desired / Fa,real

4.2.

Learning- and Adaptation Structure

With a review of section 3.2, the calculations of correction values k are made to improve the quality of the formula: tv = σu ⋅σα ⋅(σupcut ⋅tupcut+ tdown-cut) k depends on all parameters of the right side of the above expression: k = Φ (σu , σα , σupcut , tupcut , tdown-cut) This means that the data structure in which the k-values are stored is at least fivedimensional. The disadvantage, that the complex process conditions are reduced to a set of one-dimensional values, still exists. In order to reduce the dimension of the data structure and to improve the quality of the simulation results, the new criterion chip relief is introduced. The chip relief S is defined as the normalized contour which the length of all cut nails make up in an two-dimensional system of coordinates (fig. 10). Inside this criterion most of the effects discussed in 3.2 are encapsulated, so that k can be written as: k = Φ (S, α, ta) ta is the average depth of cut, which is calculated as the average length of all cut nails. Because of the normalization of S, which does not allow to value the absolute depth of a cut, it is necessary to make use of ta.

cutting edge

pins removed by the milling cutter

chip relief

1

0

-5

0

5

pin grid array

Figure 10. Calculation of chip relief S. There are two different tasks the correction value database is used for: • •

Storage of correcting values k, calculated for a certain combination of S, α and ta. Finding a proper correcting value k to a given set of S, α and ta.

The main differences lay in the search order of these jobs. To optimally meat the different requirements, the database is implemented twice with different internal structures. 4.2.1. Learning structure The learning structure is made up as a two-dimensional array Aα,ti in the path inclination α and the index ti (fig. 11). ti is calculated as: ti = g ⋅ta / tmax g is the size of A and tmax is the maximum depth of cut, a constant of the simulation

chip relief S

correction value k

depth of cut ta inclination angle α

Figure 11. Learning structure

correction value k

depth of cut ta

chip relief S

inclination angle α

Figure 12. Adaptaion stucture kernel. The bigger g the more accurate is the learning and adaptation behavior. The entries are pointer to lists. Each list contains a series of chip reliefs S and the according correcting value k. 4.2.2. Adaptation structure In contrast to the learning structure the adaptation structures main task is to provide the simulation kernel with an efficient solution to obtain correction values for a given set of parameters. Therefore the adaptation structure is made up as a onedimensional Array Aα in the inclination angle α (fig. 12). The entries are lists of chip reliefs and each chip relief itself includes a list of correction values, sorted by the size of the according value for ta. If the simulation kernel ‘asks’ for a ta which does not already exist, the correction value k is calculated as the average between adjacent entries.

4.3.

Operation cycle of the Adaptive simulation system

According to fig. 9 a typical NC-path optimization by means of the adaptive milling simulation can be subdivided into four phases which are periodically entered. Primary phase During the first phase the primary simulation optimizes NC-path based on the current database (adaptation structure). The optimized motion control sets are provided to the machine tool via a reserved storage area (NC-buffer) which is accessible by

the secondary simulation. The primary phase is stopped when the NC-buffers storage capacity is reached. Machining phase When the NC-buffer is filled by the primary simulation, the machine starts/continues operating with the optimized NC-data until the buffer is empty. While the machine is milling, the measured forces are written to adaptation kernel together with the according milling cutter positions and feed rates. Secondary phase After the machine has worked off the control sets provided via the NC-buffer the secondary simulation starts to process the information collected in the adaptation kernel as described in 4.1. For a better performance the improved correction values are not directly written to the adaptation structure but deposited with the learning structure. Adaptation phase In the fourth phase the data which are collected in the learning structure have to be transferred to the adaptation structure. For this, each entry is provided to the adaptation structure with the belonging to it α and ta value. Then the list of chip reliefs which is connected to the entry Aα is searched for a matching shape. If such a chip relief entry can be found, the improved tupel (α, ta) is stored directly, if not, a new list for this chip relief is generated first. After all entries are processed, the buffers (measured values, optimized NC-paths) and the learning structure is cleared. Every time the operating cycle starts from the beginning, the knowledge base for the new feed rate adaptation includes the experiences from the last iteration(s) in the form of more accurate correction values. To show the convergence property of the complete system, some examples are given in the next chapter

5.

Application examples

5.1.

Reciprocal milling with varying depths of cut

For the evaluation of the adaptive milling simulation the machine is replaced by a another conventional milling simulation with a default behavior. This offers the possibility to directly compare the adaptation results with the ‘real’ machining properties. The function for the calculation of the resultant force Fa,real is:

Figure 13. Testgeometry and NC-paths for reciprocal milling. Fa,real = (ta+0.3) ⋅(dupcut+1) ⋅0.0392 ⋅vf + 26.71

resultant force Freal [N]

dupcut is the share of the cut material which is removed by upcut milling. The inclination angle is constant for the complete machining process, so that α does not appear as an extra parameter in the formula. The desired resultant force Fa,desired is set

feed rate vf [mm/min]

path length [mm]

Figure 14. Reciprocal milling – feed rate and forces in the course of several learning and adpatation phases.

feed rate vf [mm/min] learned behavior feed rate vf [mm/min]

learned behavior

ideal behavior

feed rate vf [mm/min] feed rate vf [mm/min]

ideal behavior

Figure 15. Different chip reliefs and the adapted feed rate behavior.

le

to 140 N. Figure 14 shows the adapted feed rates and the resultant forces for the overall adaptation process. It can be seen that the maximum force converges against 140 N, as expected. Figure 15 shows the feed rates learned by the adaptation structure for four different chip reliefs. The dashed lines show the ideal feed rates derived from the above formula for the resultant force.

5.2.

Circular milling of a freeform surface

For this milling procedure the inclination angle is not considered to be constant. The formula for the resultant force Fa,real is: Fa,real = (-2α / 90 + 1) ⋅(ta+0.3) ⋅(dupcut+1) ⋅0.0392 ⋅vf + 26.71

for α ≤ 0

Fa,real = (-α / 90 + 1) ⋅(ta+0.3) ⋅(dupcut+1) ⋅0.0392 ⋅vf + 26.71

for α > 0

resultant force Freal [N]

The milling cutter starts to cut on the innermost contour and moves outwards. The desired resultant force is set to 140 N again. Figure 16 shows the adaptation results and the corresponding milling cutter path for different phases of the process.

path length [mm]

Figure 16. Circular milling of a freeform surface – cutter path and resultant forces.

5.3.

Quality improvement to the conventional milling simulation

To compare the calculation expenses and the calculation accuracy of the adaptive milling simulation with the conventional milling simulation, a benchmark was run on both systems. While the needed calculation time of the adaptive system is noticeable higher (tab. 2) the machining time can be reduced because of the better exploitation of the milling cutters capability of 140 N (fig. 17). Table 2.

Parameters to be given by the user for a feed rate adaptation. Conventional Milling Simulation

Time for simulation

52 sec

Adpative Millling Simulation 198 sec

Time for machining

138 sec

117 sec

resultant force Freal [N]

Task

resultant force F real [N]

path length [mm]

Figure 17. Comparison between the conventional milling simulation and the adaptive milling simulation. The feed rates optimized by the adaptive system lead to an even better exploitation of the milling cutters capacity.

6.

References

[Alt 96]

Altintas, Y: A General Mechanics and Dynamics Model for Helical End Mills, Annals of the CIRP, Vol. 45/1 (1996), pp. 59-64.

[Bie 91]

Bieker, R.: NC-Fräsen von Stahlhohlformen. VDI, Düsseldorf, 1991.

[Ens 99]

Enselmann, A.: HSC-Fräsen von Formen und Gesenken – Technologie, Wirtschaftlichkeit, Optimierung, Vulkan, Essen, 1999.

[Hui 94]

Hui, K.C.: Solid Sweeping in Image Space-Application in NC-Simulation, The Visual Computer, Vol. 10 (1994), pp. 306-316.

[WAG 98] Weinert, K., Albersmann, F., Guntermann, G.: Adaptive Milling Simulation for Optimization of the HSC-milling process, Proceedings of the International Seminar on Improving Machine Tool Performance (Vol. 1), San Sebastian, Spain, July 6-8, pp. 435-444, (1998). [WE 96]

Weinert, K. and Enselmann, A.: A Model for Computer-Based Contour-Fault Prediction and Compensation when Milling Sculptured Surfaces, Flexible Automation and Intelligent Manufacturing (FAIM), Begell House inc., New York, pp. 915-928. (1996)

[WEA 97] Weinert, K., Enselmann, A.. and Albersmann, F.: Feed-Rate Adaption, ContourFault Prediction and Compensation for Optimisation of the HSC-Milling Process, Proceedings of the European Conference on Integration in Manufacturing, Technical University of Dresden, Germany, 1997, pp. 301-312. [WMF 97] Weinert, K.; Müller, H.; Friedhoff, J.: Efficient Discrete Simulation of 3-AxisMilling for Sculptured Surfaces. Production Engineering, Vol. III/2, 1997. [YK 94]

Yazar, Z.; Koch, K. et. al.: Feed-Rate Optimization Based on Cutting Force Calculations in 3-Axis Milling of Dies and Molds with Sculptured Surfaces, Int. J. Mach. Tools. Manufact., Vol. 34 (1994), pp. 365-377.

[YM 93]

Yang, B. and Menq, C.:Compensation for Form Error of End-Milled Sculptured Surfaces Using Discrete Measurement Data, Int. J. Mach. Tools Manufact., Vol. 33 (1993), pp.725-740.