Olivier Vidal
email: olivier.vidal@cnam.fr

Keywords: Earnings management, earnings distribution, experiment, accounting threshold

In asserting that the number of firms reporting small profits is abnormally high, thus suggesting that earnings management has taken place, accounting researchers assume that the distribution of reported earnings should be smooth for unmanaged earnings. This has never in fact been demonstrated. This article seeks to confirm this assumption through a laboratory experiment, and also sets out to identify the general distribution pattern to be expected for unmanaged earnings. Normal distribution does not appear to be a good fit. The study's results also highlight the existence of downward management of earnings by firms with higher-than-average profits.

INTRODUCTION

Since the late 1990s, one stream of accounting literature has focused on the distribution of earnings reported by firms. It is also referred to as the literature on accounting thresholds, or earnings management to meet an objective. Researchers estimate that every year the number of firms reporting small profits is abnormally high, and the number of firms reporting small losses is abnormally low. This suggests that a significant number of firms manage their accounts every year to avoid reporting a loss (Hayn, 1995;[START_REF] Burgstahler | Earnings management to avoid earnings decreases and losses[END_REF][START_REF] Degeorge | Earnings Management to Exceed Thresholds[END_REF]. All the studies carried out so far appear to confirm this.

In reaching this conclusion, this stream of research has relied on a fundamental premise concerning earnings distribution patterns: if earnings are not managed, the distribution pattern should be smooth [START_REF] Burgstahler | Earnings management to avoid earnings decreases and losses[END_REF]. This basic premise has never yet been demonstrated, as observation of unmanaged earnings is in practice impossible. The only earnings that can be observed are the earnings actually reported, which may have been managed. The "real" earnings cannot be found in any database. The smooth distribution premise therefore results from deductive reasoning [START_REF] Vidal | Gestion du résultat et seuils comptables : impact des choix méthodologiques et proposition d'un instrument de mesure des irrégularités[END_REF]. Researchers can find no explanation why distributions of earnings, if unmanaged, display discontinuities, especially around the zero profit mark. This paper presents a study which proposes to demonstrate this assumption empirically for the first time. It uses an experiment-based approach in which business game participants simulate the management of a fictitious firm competing with other firms. They make management decisions, but can under no circumstances interfere with the accounts. Accounting manipulation is a decision made with the sole objective of modifying the earnings after they have been calculated or estimated. In the experimental protocol, earnings are calculated absolutely impartially by a software, using the same rules for all firms. One thousand six hundred and twenty annual earnings figures are analyzed in this way. The first finding of this study confirms the fundamental premise and thus supports the assumption that earnings are managed to avoid reporting losses. Secondary findings concerning the distribution pattern show that the Normal distribution does not appear to be a good fit for earnings distributions. benchmark distribution considered "regular"1 . Comparison of an empirical distribution2 with the expected distribution may reveal differences that are interpreted as irregularities.

However, it is impossible to observe distributions of unmanaged earnings. The benchmark distribution pattern is therefore unknown. Researchers have adopted a prudent approach in addressing this problem, leading to non-parametric measures of the irregularities, although some authors still refer more or less explicitly to a Gaussian distribution pattern. A few authors have attempted to introduce parametric measurement approaches, making explicit reference to a specific distribution [START_REF] Vidal | Gestion du résultat et seuils: les montants manipulés sont-ils marginaux ? CAAA annual conference[END_REF].

Studies not based on a specific distribution law

The first approach used to examine irregularities in the reported earnings distributions is very much the dominant approach in the accounting literature [START_REF] Burgstahler | Earnings management to avoid earnings decreases and losses[END_REF][START_REF] Degeorge | Earnings Management to Exceed Thresholds[END_REF][START_REF] Brown | A Temporal Analysis of Earnings Surprises: Profit versus Losses[END_REF][START_REF] Burgstahler | Earnings Management to Avoid Losses and Earnings Decrease: Are Analysts Fooled?[END_REF][START_REF] Das | Rounding-up in reported EPS, behavioral thresholds, and earnings management[END_REF][START_REF] Dechow | Why Are Earnings Kinky? An Examination of the Earnings Management Explanation[END_REF][START_REF] Holland | Do Australian companies manage earnings to meet simple earnings benchmarks[END_REF][START_REF] Leuz | Earnings Management and Investor Protection: An International Comparison[END_REF][START_REF] Mcnichols | Discussion of "Why are Earnings Kinky? An Examination of the Earnings Management Explanation[END_REF][START_REF] Bisson | Les entreprises non cotées manipulent-elles leurs résultats ?, 3ème colloque international : gouvernance et juricomptabilité[END_REF][START_REF] Glaum | The Extent of Earnings Management in the US & Germany[END_REF][START_REF] Mard | Les sociétés françaises cotées gèrent-elles leurs chiffres comptables afin d'éviter les pertes et les baisses de résultats ?[END_REF][START_REF] Brown | A Temporal Analysis of Earnings Management Thresholds: Propensities and Valuation Consequences[END_REF][START_REF] Coppens | An analysis of earnings management by European private firms[END_REF][START_REF] Burgstahler | The Importance of Reporting Incentives: Earnings Management in European Private and Public Firms[END_REF][START_REF] Daske | The distribution of earning relative to targets in the European Union[END_REF][START_REF] Roychowdhury | Earnings management through real activities manipulation[END_REF][START_REF] Beaver | An Alternative Interpretation of the Discontinuity in Earnings Distributions[END_REF]. In this approach, known as "non-parametric", the parameters of the overall distribution law are unknown. However, whatever law applies, the researchers assume that if earnings have not been managed the distribution should be "smooth". This approach calls for several comments:

• It is easy to implement because it uses very few mathematical tools. Irregularities are measured without reference to the distribution parameters, using local estimations based on the observed numbers in the classes surrounding the interval studied.

• It is robust, for the underlying conditions involve very few restrictions. Only discontinuities (the "peaks" or "breaks") in the distribution are taken into consideration. A "strange-looking" distribution pattern will not be considered irregular as long as it remains "smooth". For example, a uniform earnings distribution pattern (a totally flat line) would be considered regular. The notion of irregularity is restricted to discontinuities.

Figure 1: Example of smooth irregular distribution

Non-parametric measures have the advantages associated with their drawbacks: they are straightforward and robust, but nonetheless imprecise (Chen, [START_REF] Lin | Detecting the Frequency and Magnitude of Earnings Management ; A Parametric Model and Empirical Analysis[END_REF][START_REF] Vidal | Gestion du résultat et seuils comptables : impact des choix méthodologiques et proposition d'un instrument de mesure des irrégularités[END_REF]. The reason the non-parametric approach is the most commonly used is that researchers are prudent. As they are unable to observe the distributions of unmanaged earnings, they do not take the risk of inventing the mathematical parameters of those distributions.

Are the distributions Gaussian?

Although researchers generally avoid the risk of explicitly proposing a distribution law for corporate earnings, several studies are based on an implicit assumption: distribution of earnings should follow a Gaussian pattern, i.e. Normal distribution. This is particularly true of [START_REF] Burgstahler | Earnings management to avoid earnings decreases and losses[END_REF] who measure irregularities by symmetry. Measuring irregularities by symmetry requires a hypothesis regarding at least one of the parameters of the distribution. [START_REF] Mard | Les sociétés françaises cotées gèrent-elles leurs chiffres comptables afin d'éviter les pertes et les baisses de résultats ?[END_REF] goes further, adjusting the estimations by explicit reference to a Normal distribution. Yet paradoxically, in both these cases, the authors highlight the asymmetrical nature of the empirical distributions observed. [START_REF] Jeanjean | La théorie positive de la comptabilité : une revue des critiques[END_REF] writes "Theoretically, in a sufficiently large sample, scaled earnings distribution should be normal". These references to Normal distribution result from the frequent use of this law to reflect economic phenomena. They assume that corporate earnings are (a) data with random distribution and/or (b) that as there are large numbers of them in databases, the central limit theorem can be applied.

(a) Corporate earnings are not random data. They depend on the firm's actual business activity and its managers' strategic decisions, which may vary in suitability. Business activity generates returns that are not random 3 . Independently of the risk factor that is omnipresent in almost all decisions, to rephrase Einstein, "businesses do not play dice". Every year, the earnings distribution of a population of firms will therefore present characteristics that cannot be assumed in advance.

3 Even if earnings were random, they would not necessarily follow a Normal distribution.

The distribution is uniform (flat line)

A non-parametric approach detects no irreglarities, because the distribution is smooth .

And yet this distribution of reported earnings appears totally impossible.

(b) The central limit theorem teaches that when a large number of drawings of a variable following the same law are aggregated, the aggregate distribution approaches Normal distribution. To attain such a normal distribution, a large number of drawings need to be aggregated -in other words, we need to examine the distribution of corporate earnings in a given country over several hundred years. This is currently impossible, as no such data are available. In fact it will always be impossible, since the components of the population studied, and the economic context, undergo changes on such a scale over such a long period that we cannot accept the idea that the distribution of earnings will remain unchanged over the very long term. In other words, the central limit theorem cannot apply here. Whether or not they are aggregated over several years, the distribution law for earnings is unknown.

Studies based on an explicit distribution law

Chen, Lin, Wang and Wu (2005) paper stand out for its attempt to measure irregularities in distribution by using a mathematical law for earnings distribution. This paper posit (without explanatory arguments) that earnings should follow a mixed normal distribution. The most interesting aspect of these parametric approaches deserves emphasis: if the distribution law is known, then "parametric" measures can be introduced for irregularities. In other words, irregularities are measured by calculating the surface separating the expected distribution from the observed distribution. These measures are more precise than non-parametric measures, and make it possible to assess the total number of firms in an irregular position and the amounts that have been "managed". These advantages, however, come with associated drawbacks: they depend on the relevant distribution law, which is as yet unknown.

Research questions

Ultimately, a dual research question is addressed. Observing the distribution of unmanaged earnings, the study has two objectives:

(1) It seeks to verify the premise that an unmanaged earnings distribution is smooth (without discontinuities). If supported, this initial point will confirm the relevance of all the research on accounting thresholds since 1995.

(2) It seeks to identify the mathematical distribution law for earnings reported by firms. This second point opens up the field of research to parametric methodologies for measuring irregularities.

PART 2: OBSERVATION OF REPORTED EARNINGS DISTRIBUTIONS

Before presenting the results of our experimental research, it is useful to observe the distributions of earnings as reported (and therefore potentially manipulated) by firms, and review the specificities of these distributions.

To identify and discuss any irregularities (other than local discontinuities), a benchmark pattern is needed. Since the relevant theoretical distribution is unknown, it is presumably impossible to identify irregularities. To get around this problem, we work on the reductio ad absurdum assumption that a Normal distribution pattern should apply. The comparison between the actual distribution and the normal distribution identifies zones of potential irregularities which are discussed.

Differences between observed distributions and Normal distribution

Most studies on earnings distributions observe the earnings variable scaled by a size variable such as total assets. However, it is of some value to begin by first observing the distribution pattern for unmanaged earnings.

Unscaled earnings distribution

The graphs below (see Figure 2) show the earnings distribution for French listed companies from 1992 to 2004 as reported in the Compustat Global Vantage database. Comparison of the distribution for the earnings variable with a Normal distribution having the same mean and standard deviation shows the following differences:

• The empirical distribution is dissymmetrical, whereas the Normal distribution is symmetrical. The empirical distribution has thicker distribution tails (particularly on the left) than the Normal distribution. Finally, the mode for the empirical distribution lies not on the mean nor the median, but on the zero earnings mark.

• The empirical distribution is more highly concentrated (leptokurtic) than the Normal distribution. Rather than being bell-shaped, it is shaped like an upturned funnel. There is a upward phase then a downward phase, but no "flat" summit.

Scaled earnings distribution

The earnings of French listed firms from 1992 to 1994 have been scaled by the "total assets" variable. The distribution is shown below (Figure 4). Except for the mode, which no longer lies around zero but around the mean (mean and median are practically the same), the differences observed in the unscaled earnings distribution are also observed in the scaled earnings distribution.

Discussion of the observed differences

Dissymmetry

Reported earnings follow a dissymmetrical distribution. The dissymmetry observed in France is also noted by [START_REF] Burgstahler | Earnings management to avoid earnings decreases and losses[END_REF] in 76,000 observations for US firm earnings. More specifically, three sources of dissymmetry are observed: large losses, a thickness in the distribution to the left, and smaller numbers of firms to the left of the mean.

(a) Large losses

There is no economic limit to a loss, but there is a limit to earnings increases. The effect of competition in a market economy means that a competitive advantage cannot generate economic rents indefinitely. Competitors will try to copy the resources that generate exceptional rents. Generating income necessarily requires a resource-consuming activity which itself generates charges. Value cannot be created out of nothing.

However, this constraint applicable to an increase does not exist for a downward trend. It is technically possible to incur expenses indefinitely without generating income, and this automatically leads to infinite losses. The market constraint will make such a firm disappear rapidly, but for a few years (at least one), the firm may report very significant losses. In general, a firm caught up in a spiral of deficit can make extremely large losses. We cannot thus consider high losses as a distribution irregularity due solely to earnings management practices.

(b) Thickness of the distribution on the left

The conservatism principle may explain this dissymmetry. For Givoly and Hayn ( 2002), the broad tail in the distribution reflects accounting distrust (the conservatism principle) of highrisk firms, whereas the low spread to the right results from a reluctance to translate good performance into accounting terms. Even so, can the dissymmetry be attributed to accounting conservatism alone? If all firms are subject to the conservatism principle in the same way, we would expect to see a shift towards the left hand side of the earnings distribution curve, but not necessarily any dissymmetry.

But firms are not necessarily faced with risk in similar ways, and firms with worse results than their peers have to cope more with unfavorable events. Therefore, these firms (whose earnings are below the median) are more likely to suffer the consequences of the conservatism principle and their earnings are weighed down more by provisions. This may explain why the left hand side of the curve shows a steeper slope and spreads out further to the left. The conservatism principle can therefore legitimately explain a dissymmetry that apparently cannot be considered solely as an expression of accounting manipulation.

(c) The low numbers "just to the left" of the mean

As we have just seen, the steeper slope to the left of the mean can be explained by the conservatism principle. Also, considering that firms manage a portfolio of activities, they are likely to discontinue their least profitable activities first, in order to concentrate their efforts and resources on the most profitable activities. In other words, even if accounting conservatism alone does not fully explain the dissymmetry, a process of economic adjustment leads firms to leave the left hand part of the earnings curve by managing their portfolio of activities in such a way as to approach the central part of the distribution curve. The theory of effort [START_REF] Dechow | Why Are Earnings Kinky? An Examination of the Earnings Management Explanation[END_REF]) supports this explanation. All this suggests there is may be nothing abnormal about observing dissymmetry.

High concentration

The earnings show a "pointed" distribution pattern typical of high concentration. This concentration is located around the median and/or the mean when the variable is scaled, but when the variable is unscaled it lies around the zero earnings point. This observation raises questions as to the economic nature of the phenomenon observed: the earnings.

(d) Concentration around the peak

If a Normal distribution is assumed, high concentration must be considered as an irregularity.

In other words, firms manage their accounts so they can report earnings that are close to the mean (median). The annual mean (median) of reported earnings could thus be interpreted as a new threshold that has not yet been considered in the literature.

Explanations for this hypothesis can be imagined: publishing close-to-average earnings enables the firm to convey a picture of relative health, and it is not impossible that reporting results that are lower than competitors' earnings involves a cost. This could encourage managers to aim for that level. But the concentration phenomenon could also be explained by the non-random nature of earnings distribution. (1) There is a certain inertia in profit levels. A firm that is highly profitable one year is very unlikely to make a significant loss the following year. It will go through increasingly difficult years before reaching a disastrous situation. (2) Also, in a competitive economic universe, firms are under market law pressure that tends to homogenize their performances.

(3) The theory of effort [START_REF] Dechow | Why Are Earnings Kinky? An Examination of the Earnings Management Explanation[END_REF] can also provide an explanation for the concentration.

It is thus natural to see high concentration around the mean in earnings distributions, and this phenomenon cannot be attributed solely to accounting manipulation.

(e) Concentration around the zero earnings mark

In the unscaled earnings distribution (Figure 3), there is high concentration around zero. This is largely explained by the sample composition. The sample contains many small firms and few large firms. The small firms are achieving results commensurate with their investments, whether they are losses or profits. It may appear normal that small unscaled earnings should be concentrated around zero. However, there is a break in the distribution between slightly negative earnings and zero earnings, and this discontinuity cannot be explained by the sample composition. Small size should have the same effect on both the negative and positive side, but here the concentration is not symmetrical.

In short, the size effect makes it difficult to interpret the unscaled earnings distribution -but this does not justify the high concentration of exclusively positive earnings above zero.

Summary

In the first section we saw that it is impossible to apply the central limit theorem in order to posit a Gaussian distribution pattern for earnings. Observation of published results shows that every year, earnings distributions have recurring characteristics (upturned funnel curve, dissymmetry, and concentration). These characteristics cannot apparently be attributed solely to accounting manipulations. For all these reasons, aggregate earnings distributions cannot be considered to follow a Normal distribution pattern. Until it becomes possible to observe a distribution of unmanaged earnings, accounting researchers will be obliged to advance with great caution.

PART 3: THE EXPERIMENTAL PROTOCOL

In an ideal business world, managers take their management decisions, and accountants translate the effects of those decisions on the life of the firm into the financial statements with total impartiality. In reality, managers, who oversee publication of the accounts, may have motives for orienting the information disclosed to the public (Healy and Whalen, 1999;Breton and Stolowy, 2003). In such cases there is a presumption of earnings management. More specifically, accounting manipulation is considered to have taken place when there is a deliberate intent not to report the "real" earnings calculated or estimated impartially under accounting rules, but to release a different earnings figure justified by management through the selected accounting options (provisions, useful lives etc) or management decisions that they would not have made in normal circumstances (delaying or advancing investments, granting or refusing extended payment terms, etc).

In a business game that simulates running an organization, it is possible to restrict participants to management decisions alone, in total isolation from the production of financial statements.

But to arrive at a statistically relevant earnings distribution, the experimental protocol requires a very large number of simulations. The research in this paper is based on a timely opportunity: from the archives of an introduction to management course involving the use of business games, it is possible to establish the distribution of 1,641 unmanaged annual earnings figures.

Presentation of the business game

The Win-Firme business game, a teaching software developed in 1995, is used in some fifty schools and universities, mostly in France4 . The way it works is typical of this kind of business game software. Participants are put into teams. Each team runs a fictitious firm that manufactures and sells products. Participants take operational decisions (product manufacturing quantities, sale price, communication and quality budgets, staff hiring and pay, and the research and development budget for marketing new products). These decisions are entered into a computer, and the software compares them with competing firms' decisions and allocates consumers according to predefined parameters.

Two aspects of the game should be highlighted. The first is that this simulation excludes chance. There is no random event. Yet it remains impossible to predict the future, since competitors' decisions are unknown. The second important aspect is that sales are allocated essentially on the basis of relative decisions by the different firms. There is no right or wrong decision, because the algorithm is not looking for a standard solution. Therefore, whatever the demand parameters are, firms adjust their budgets and prices to generate profits. In other words, firm profitability does not depend on the game parameters but on the coherence of the team's decisions compared to its competitors. Consequently, whatever the scenario, the earnings distribution cannot be predicted.

43 games were scrutinized to develop the database used for this study (see Table 1). A game lasts an average 5 to 6 rounds (and a round generally lasts 2 hours), corresponding to 2 to 4day business game seminars. The number of competing teams generally ranges from 5 to 8, and seminars are attended by thirty to forty students. In all, 1,620 annual earnings were entered to form the database. The size variables (total assets and sales) were also entered. Total assets (sales) amounted to zero in six (four) cases. After eliminating these data from the base, the scaled results provide 1,614 (1,616) observations. The 43 game seminars contributing to the database took place in 23 different schools and universities between 2004 and 2009. Participants are students, in both scientific fields (mostly first-year students at engineering schools) and economic disciplines (management and/or economics degree students). 5 seminars were attended by students with more diverse backgrounds (adults on in-service training, students from other course types) as part of their masters qualifications in research or vocational subjects. While all participants were students when they attended the seminar, the mixed range of profiles avoids the bias of an overhomogeneous population that is frequent in experimental protocols. In all, nearly 1,200 participants contributed to data collection. Excluding the time needed for data recovery and entry, the duration of the experimental protocol can be estimated at 800 hours.

The advantage of experiments

Using laboratory-type experiments to study earnings distributions offers an enormous advantage: the "reported" earnings in the game are calculated by the software, without the participants (managers) being able to take any accounting decision. The software plays the role of a totally independent accountant. In the business game, earnings are not managed because no accounting choices are included in the game. The same rules apply for all firms.

The accounts are a purely technical result of the firms' business decisions.

However, accounting options are not the only lever for earnings management. Managers may also use the timing of certain investment decisions to achieve an earnings objective. Degeorge, Patel and Zeckhauser (1999) use the term "direct managing", Glaum, Lichtblau and Lindemann ( 2004) talk of "manipulation of cash flows", [START_REF] Roychowdhury | Earnings management through real activities manipulation[END_REF] refers to "real activities manipulation", and [START_REF] Burgstahler | The Importance of Reporting Incentives: Earnings Management in European Private and Public Firms[END_REF] refer to "Business Management". [START_REF] Graham | The economic implications of corporate financial reporting[END_REF] show that these practices are in fact dominant in business. In a business game, managers are arguably able to influence earnings through their R&D, communication and quality budgets. But the game is a simplified model of reality, and time is divided into rounds. Decisions are taken irrevocably at the start of the round. In other words, it is as if the decisions for year N were taken in the night of December 31, N-1 to January 1, N. This makes it impossible to adjust budgets during the year when the first earnings estimates are calculated. Manipulation of cash flows to achieve an earnings objective is thus impossible.

For all these reasons, use of simulations to study earnings management is particularly judicious.

The limitations of experiments

While an experiment can isolate the accounting process from attempts at opportunistic earnings management, it diverges from reality in that it is based on economic modeling, and furthermore is implemented in a teaching context. These two factors may lead to divergences between the earnings distribution resulting from the game and the theoretical distribution of actual earnings. They are reviewed below to examine how far they can be controlled for.

Economic modeling

In a simulation, the participants are players whose decisions are risk-free, as they will not actually experience the effects (on their pay or their career) simulated in the game. This may lead them to adopt different behaviors from those seen in real life.

This bias is limited by the fact that the software makes no assumption about performance, and the duration of each seminar obliges the "firms" to introduce long-term strategies. If firms reduce their price in the face of higher pressure from competitors, the average firm performances will be lower and firms will have to take the initiative of adjusting their strategy to improve their lot. This can come about through a downturn in competitive pressure or disappearance of the weakest competitors. In other words, if the competitors take greater risks, the effects on results should ultimately lead to compensating adjustments by participants, since a balance is reached without any intervention by the facilitator, or alteration of the software settings.

Other possible phenomena are radical optimization strategies at the end of the game, or underassertive decisions at the start of the game when participants have not yet assimilated the way the game works. To control for this bias, the earnings distribution is also traced after eliminating the first and last year of the game from the database.

Teaching context

The simulations used to construct this study were originally developed for an educational purpose. It is interesting to examine the possible biases associated with this purpose. First of all, the scenarios are generally constructed such that firms are identical at the start of the game. Their markets generally grow in the first few rounds, so that students are not under too much pressure in the learning phase of the game. Generally, the industries simulate a maturity phase from the third or fourth round, which increases the competitive pressure and has a damaging effect on firm performance. While crisis phases happen in real life, their effects on earnings distributions are smoothed by the fact that a large number of sectors exist, and firms manage more diversified product portfolios than in the game. However, this bias is offset by the large number of games studied, and partly controlled for by eliminating the first year of the game.

The game facilitator's role can also introduce bias. Firms in difficulty generally receive help from the facilitator, who does not want participants to give up before the seminar is over. In other words, in situations where a struggling firm would go out of business in real life, in the game, the facilitator tends to delay that outcome as far as possible. He provides assistance in the form of subsidies, or advice, or possibly artificially keeping the firm alive when in reality its financial position would be untenable (long-term negative equity, zero industrial assets, astronomical debts, etc). Such situations remain infrequent, and generally only happen at the end of a seminar. Nonetheless, this intervention could result in overrepresentation of lossmaking firms (thick tails on the left of the distribution) in earnings distributions. This bias is limited by eliminating the final year of the game.

Impact of methodological limitations on the object of the study

Given the two objectives of this study, the limitations identified may reduce the relevance of the answer it provides for the second objective. It is possible that teaching constraints and economic modeling may, despite the controls applied, influence the earnings distribution pattern. The results of the research on the question of the distribution pattern of "real" earnings must thus be considered in perspective. But there is no reason why these limitations should have any influence on discontinuities. In other words, whatever the limitations of the study, the answer it provides to the first question of whether or not there is any discontinuity around the zero earnings level can be considered reliable.

PART 4: OBSERVATION OF THE DISTRIBUTION PATTERN OF UNMANAGED EARNINGS

This fourth section presents the results of the study. The two research questions are addressed successively: (1) are there any discontinuities around the zero earnings mark in unmanaged earnings distributions? and ( 2) what do unmanaged earnings distributions look like?

Unmanaged distributions show no discontinuities

Figure 5 shows corporate earnings distributions derived from business games, scaled successively by the total assets and sales variables. Unscaled earnings distributions are not shown, as they are not relevant to this study. In the simulations, the 43 business games do not all have identical parameters. There may be considerable differences in the orders of magnitude used by different facilitators. For example, in one game quantities may be expressed in units and prices in euros, while in another with similar parameters for production cost and sales development structure, the production unit may be a batch of 1,000 products, with prices expressed in thousands of euros. In other words, value data are not comparable between games, as there is a possibility they are not expressed in the same units. The overall pattern of the distributions is similar for both denominators. Both these distributions are more concentrated than a Normal distribution (kurtosis > 3) and dissymmetrical (skewness < 0). Although they contain data from 43 games, i.e. 43 independent drawings, this is not a large enough number to apply the central limit theorem.

Simple visual observation5 shows that there is no discontinuity around the zero earnings mark.

This provides an answer to the first research question. To show this result more clearly, the earnings distributions for French, UK and German listed firms from 1992 to 2004 as reported in the Compustat Global Vantage base are traced in Figure 7. All three distributions of reported (and therefore potentially managed) earnings display a large discontinuity at the zero earnings level. There is a clear contrast with the simulated earnings distributions. The unmanaged earnings distributions resulting from business game simulations do have some things in common with the reported earnings distributions. They are more concentrated or "pointier" (kurtosis > 3) than Normal distributions, and dissymmetrical with a steeper slope on the left than the right, and more negative values (negative skewness). But despite these similarities, the simulated earnings distributions are more spread out than the reported earnings distributions. This difference may be caused by the smaller number of earnings figures generated by the simulations (1,614 compared to 6,879 to 14 028), but it could also result from the biases identified in section 3 above. Game participants may take more risks in simulations than in real life, and this may lead to overrepresentation of extreme results.

But the most significant difference for the purposes of our study remains the absence of discontinuities in unmanaged earnings distributions, while all the reported earnings distributions show such discontinuities.

Finally, as a control, the simulated earnings distributions are traced after elimination of the first and last year of the game. The distribution pattern (Figure 9) is no different, although it is less smooth because of the smaller number of observations (1,054 against 1,614).

Unmanaged earnings distributions do not follow a Gaussian shape

The similarities observed (Figure 5 and Figure 7) between the distributions of unmanaged earnings and published earnings confirm the relevance of using simulated earnings distributions in seeking to identify the appropriate theoretical distribution law for earnings. Mathematically, identification of a theoretical law of distribution based on an empirical distribution is called "distribution fitting". There are many distribution fitting softwares that do this. Each one contains a catalogue of laws. For each law, they measure a goodness-of-fit indicator (Kolmogorov-Smirnov distance, Anderson-Darling distance, and Chi-square distance). The laws are ranked, and it is possible to deduce a theoretical distribution (from the laws in the catalogue) that is the best fit to the empirically-observed distribution.

But the fit cannot be determined from our aggregate distribution of (scaled) unadjusted earnings, because the law we are looking for is the distribution law for unmanaged annual earnings. Every year, firms' earnings correspond to an independent "drawing". The mathematical process must therefore be conducted in a situation where all other factors are equal, i.e. after eliminating environmental influences on economic performance. The proposed solution is to standardize the annual distributions before aggregating them [START_REF] Vidal | Gestion du résultat et seuils comptables : impact des choix méthodologiques et proposition d'un instrument de mesure des irrégularités[END_REF]. This part of the study thus requires modification of the database. Each earnings figure is centered on the mean and reduced by the standard deviation for the source annual earnings 6 .

6 Centering is on the mean rather than the median despite the fact that the mean is more sensitive to extreme values, because the number of firms is relatively small in each game (generally 5 to 8). This means that when there is an uneven number of firms (twenty cases), the median is equal to the earnings of one of the firms and as a result the class located exactly in the centre of the distribution after centering on the median would be overrepresented. In black: Distribution of the 1,641 earnings figures resulting from the standardized simulations.

In grey: Normal distribution fit for parameters N(0; 0,92194). In black: Distribution of the 1,616 earnings figures resulting from the standardized simulations.

In grey: Normal distribution fit for parameters N(0; 0.922).

Two distributions are shown in Figure 11. The first relates to earnings scaled by total assets, and the second earnings scaled by sales. The fit to Normal distribution is illustrated by the curve superimposed over each graph. Two facts are clearly visible.

The first is that the two distributions are almost perfectly identical, whichever variable is used for scaling. There is strong dissymmetry, but the pattern is much less concentrated than in unstandardized distributions.

The second is that the Normal distribution is not a good fit for these distributions, an observation confirmed by statistical tests (p-value is nearer to 0 than 1). The Best Fit7 software used for distribution fitting (checking against all laws) ranks the best fits as shown in Table 5. The proposed distribution laws are ranked according to the Kolmogorov-Smirnov test, which gives more weight to the central portion of the distribution. No law offers a statistically good fit. The Weibull distribution is the best fit, whichever test is used (the value of distance "s" between the fitted distribution and the empirical distribution is almost half the distance measured using Normal distribution), but the significance level remains low. This distribution, bounded to the left, is generally used to study lifetimes (positive values). Its asymmetrical aspect is what makes it a better fit than the Normal distribution, but it remains conceptually ill-suited because it is bounded to the left.

The Logistic distribution comes second in the ranking of fits. It ranks above Normal distribution due to its more concentrated (pointier) shape. But its symmetry (like the Normal distribution) cannot properly reflect the observed pattern of distributions.

Finally, a graphic representation of the standardized (scaled) earnings distribution of French listed firms is drawn up (Figure 8). This distribution shows significant differences from the simulated earnings distributions. First of all, the simulated earnings distributions are less "smooth". This is explained by the smaller number of observations. Simulated distributions are considerably less pointed, due to the strong discontinuity observed around the zero earnings mark in reported earnings, which reinforces concentration (the non-standardized distributions in Figure 5 confirm this). In black: Distribution of the earnings published by French firms from 1992 to 2004, standardized (7,737 observations).

In grey: Normal distribution for parameters N (0; 1)

The final aspect noted is the high dissymmetry in simulated earnings. The peak of the distribution is clearly located among the positive values, whereas it tends to lie around zero (and therefore the median used to center distributions) for reported earnings. In the context of our study this is an unexpected finding, and deserves further exploration. It is as if, in reality, the excess number of firms making very small profits resulted from two separate avoidance mechanisms: avoidance of losses (which leads to the discontinuity at the zero earnings level), and avoidance of above-median earnings (which leads to understatement of results when they are good). This study thus confirms the intuition that firms build up "cushions" in profitable periods and use them when they fall on harder times [START_REF] Degeorge | Earnings Management to Exceed Thresholds[END_REF].

CONCLUSION

This study is original, being the first time a laboratory experiment has been presented for analysis of earnings management practices to meet thresholds.

Its principal finding is the confirmation of a hypothesis that had not been demonstrated before: unmanaged earnings distributions should not present any discontinuities, and should follow a smooth curve.

The second important result of this study is the confirmation that earnings distributions do not appear to follow a Normal distribution. The theoretical distribution pattern is more concentrated, and dissymmetrical. The Weibull distribution (dissymmetrical) and Logistic distribution (concentrated) provide a better fit, but that fit is still imperfect. These results

Figure

  Figure 2: Distribution of earnings reported by French firms

Figure

  Figure 3: Distribution of earnings scaled by Total Assets

Figure

  Figure 4: Earnings distribution (simulation)

Figure 6 :

 6 Figure 6: Earnings distribution (simulation) after elimination of the first and last year of the game

Figure

  Figure 7: Earnings distribution (simulation) after standardization

Figure

  Figure 8: Earnings distribution (reported) after standardization

Table 1 : Characteristics of games in the database

 1

		Number of firms	Game duration	Number of games Number of observations
	Mean	6.5	5.7 rounds	43	1,620
	Maximum	9	9 rounds
	Minimum	4	3 rounds

Table 2 : Characteristics of experiment participants

 2

		Science students	Economics and/or	Other
			management students
	2 years' higher	3	1		4
	education
	3 years' higher	7	8		15
	education/Degree
	level
	4 years' higher	1	3		4
	education/Master 1
	5 years' higher	7	12		19
	education/Master 2
	Other			1	1
		18	24	1	43

Figure 5: Distribution of earnings reported by French, German and UK firms

	12
	10
	8										France: Distribution of 7,742 earnings (scaled
	6										by total assets) reported by French
											listed firms from 1992
	4										to 2004 (source:
											Compustat Global
	2										Vantage database).
	0
	-1	-0,8	-0,6	-0,4	-0,2	0	0,2	0,4	0,6	0,8	1
	10
	8
											United Kingdom:
											Distribution of 14,028
	6										earnings (scaled by
											total assets) reported
	4										by UK listed firms
											from 1995 to 2004
											(source: Compustat
	2										Global Vantage
											database).
	0
	-1	-0,8	-0,6	-0,4	-0,2	0	0,2	0,4	0,6	0,8	1
	16
	14
	12										Germany: Distribution
	10										of 6,879 earnings
	8										(scaled by total assets) reported by German
	6										listed firms from 1995
											to 2004 (source:
	4										Compustat Global
	2										Vantage database).
	0
	-1	-0,8	-0,6	-0,4	-0,2	0	0,2	0,4	0,6	0,8	1

Table 3 : Fitting the annual earnings distribution (simulation)

 3

	Function	Input	Weibull	Logistic	BetaGeneral Normal
	Shift		-4.11594
	Parameter 1		5.216468	4.59E-02	5.433517	9.29E-12
	Parameter 2		4.476426	0.534046	4.732276	0.921938
	Parameter 3				-3.3036
	Parameter 4				2.863938
	Minimum	-2.4894	-4.1159	-∞	-3.3036	-∞
	Maximum	2.6583	+ ∞	+ ∞	2.8639	+ ∞
	Mean	0.0000	0.004224	0.045906	-0.00711	0.0000
	Mode	-1.4629 [est] 0.18153	0.045906	0.044991	0.0000
	Median	0.13908	0.056762	0.045906	0.007369	0.0000
	Std. Deviation	0.92194	0.90787	0.96865	0.92066	0.92194
	Variance	0.84944	0.82422	0.93829	0.84762	0.84997
	Skewness	-0.3271	-0.2831	0	-0.076	0
	Kurtosis	2.5993	2.9133	4.2	2.5523	3
	A-D Test Value (« s »)		4.588	10.89	8.25	10.6
	P Value		N/A	< 0.005	N/A	< 0.005
	Rank		1	4	2	3
	K-S Test Value (« s »)		0.04638	0.05681	0.05861	0.06848
	P Value		N/A	< 0.01	N/A	< 0.01
	Rank		1	2	3	4
	Chi-Sq Test Value (« s »)		93.12	189.8	123.7	153.1
	P Value		3.56E-07	0	0	0
	Rank		1	4	2	3

Also known as the "expected distribution" or "theoretical distribution".

Or "real" or "observed" distribution.

The website www.winfirme.com describes the software and how it works.

Visual observation is clear enough to rule out the need for a statistical test, which would be problematic to implement since it requires a non-parametric measure of irregularity, and several methodological limitations have been highlighted in respect of such measures[START_REF] Glaum | The Extent of Earnings Management in the US & Germany[END_REF][START_REF] Durtschi | Earnings Management ? The shapes of the Frequency Distributions of Earnings Metrics Are Not Evidence Ipso Facto[END_REF].

This software published by Palisade has been totally integrated into the @risk software since 2008 and is no longer available separately.

WHAT SHOULD AN UNMANAGED EARNINGS DISTRIBUTION LOOK LIKE?


Kwamiwi Mawussi

Laurent Pierre Tapie

Bernardin Mawussi

A Knowledge base model for complex forging die machining

Keywords: Machining feature, CAD, CAM, machining process preparation

Recent evolutions on forging process induce more complex shape on forging die. These evolutions, combined with High Speed Machining (HSM) process of forging die lead to important increase in time for machining preparation. In this context, an original approach for generating machining process based on machining knowledge is proposed in this paper. The core of this approach is to decompose a CAD model of complex forging die in geometric features. Technological data and topological relations are aggregated to a geometric feature in order to create machining features. Technological data, such as material, surface roughness and form tolerance are defined during forging process and dies design. These data are used to choose cutting tools and machining strategies. Topological relations define relative positions between the surfaces of the die CAD model. After machining features identification cutting tools and machining strategies currently used in HSM of forging die, are associated to them in order to generate machining sequences. A machining process model is proposed to formalize the links between information imbedded in the machining features and the parameters of cutting tools and machining strategies. At last machining sequences are grouped and ordered to generate the complete die machining process. In this paper the identification of geometrical features is detailed. Geometrical features identification is based on machining knowledge formalization which is translated in the generation of maps from STL models. A map based on the contact area between cutting tools and die shape gives basic geometrical features which are connected or not according to the continuity maps. The proposed approach is illustrated by an application on an industrial study case which was accomplished as part of collaboration.

Introduction

Design of forged part and forging die is obtained by the study of metal flow from the die cavities to the gutter and flash through the parting surface. This type of study was performed in different sections of the functional part using a wire-frame model [START_REF] Bagard | Tooling and complex shapes: technical-economic reports between high speed machining[END_REF][START_REF] Mawussi | Modèle de représentation et de définition d'outillages de forme complexe. Application à la génération automatique de processus d'usinage[END_REF][START_REF] Sun | Operation decomposition for freeform surface features in process planning[END_REF]. Then models of forged part and forging die are designed by machining assistant who is generally in charge of the definition of the final shapes and the generation of the machining process. In this approach, the final shapes of forged parts and forging dies was obtained according to the know-how of the machining assistant and the available machining resources.

Today, die designers define forged part according to the whole shape of the functional part. Therefore design of the final shapes of dies and forged parts is transferred to engineering and design department. This evolution is closely linked with the development of powerful software tools which allow simulating metal flow in the 3D model of die cavities (TRANSVALOR, Material forming simulation, http://www.transvalor.com; [START_REF] Kulon | A knowledge-based engineering design tool for metal forging[END_REF]. The die model obtained in the engineering and design department is processed by the machining assistant.

Today, die models have more complex shape. Indeed, the introduction of close die forging process (Fig. 1) increases the complexity and the finishing requirements of die shapes in order to limit machining operation [START_REF] Doege | Closed die technology for hot forging[END_REF].

Fig. 1. Conventional versus close die forging process

Because of the evolution of die shapes, the machining assistant must now elaborate the machining process starting from die model given by the engineering and design department. This model is considered in most of the cases as a void geometry, since it involves poor technological and topological information required by machining assistant. So, machining process preparation involves the analysis of geometrical and topological information of the die shape in order to associate machining information. At this step of the elaboration of the machining process, the machining assistant chooses machining strategy and resources according to die shape with respect to the minimal machining time, the part quality and surface roughness. Integration of High Speed Machining (HSM) technology is also crucial for the processing of technical and economical constrains.

In the die machining context, HSM does not only mean high cutting speeds and/or high feed rates. It should be considered as a machining process where operations are realised with specific methods and equipment (machining strategies, machine tool, cutting tools, spindle…) and involves machining process modifications (SANDVIK Coromant, Die & Mould Making, Application Guide, http://www. coromant.sandvik.com, 2010). Electro Discharged Machining (EDM) step is significantly reduced and often eliminated from die machining process. Heat treatment after die semi finishing machining can be avoided thanks to improvement in cutting tools manufacturing and preparation. As the machining of forging die is performed on high heat treated stocks (45-60 Hrc) several technical and economical reports highlight productivity and part quality increases with the introduction of HSM [START_REF] Kranjnik | Modern machining of die and mold tools[END_REF][START_REF] Toh | Design, evaluation and optimisation of cutter path strategies when high speed machining hardened mould and die materials[END_REF][START_REF] Altan | Manufacturing of Dies and Molds[END_REF]. These evolutions must lead to a better part quality for HSM than conventional machining if an efficient machining planning is associated to a relevant choice of cutting conditions and tools. In this context the tasks carried out are very difficult to automate owing to the complexity of the die shape and involve high skilled worker intervention realising time expensive operations.

Current forging die machining process is decomposed in three main steps: roughing, semi-finishing and finishing. Roughing operation objective is to reach as close as possible the desired rough shape with high level of cutting material flow and tool path series as smooth as possible. Associated machining features for this operation are pockets or cavities. Semi-finishing operation objective is to warrant a constant depth of cut or constant tool engagement during finishing operation. Finishing operation objective is to obtain the final die shape up to the geometrical quality specified. The die geometry and topology must be taken into account during this final operation with a high levelled refinement to reach this objective.

The work presented in this paper is devoted to finishing operation of die cavity. According to the industrial context, the finishing process is based on standard machining resources (3-axes high speed machine tools, end mill, ball nose and corner rounded end mill cutting tools) and common Computer Aided Machining (CAM) strategies (parallel planes, Z level, parallel curve guidance). These common CAM strategies presented in several works [START_REF] Toh | Design, evaluation and optimisation of cutter path strategies when high speed machining hardened mould and die materials[END_REF][START_REF] Dragomatz | A classified bibliography of literature on NC milling path generation[END_REF] are integrated in a very wide CAM and Computer Aided Process Planning (CAPP) software.

Technical and economical studies highlighted the importance of CAM preparation in the die machining process. During this preparation step, the experience and know how of the machining assistant has a great influence on the part quality. Thus, the tasks carried out must be adapted to this technical and economical context which involves evolutions on CAD models, CAM strategies and machining strategies (HSM). This adaptation depends mainly on the good suitability between die shape and HSM process.

CAM preparation is based on machining feature recognition from the CAD model of the part. Several approaches for machining features recognition are proposed in different works: syntactic pattern recognition [START_REF] Abouel Nasr | A new methodology for extracting manufacturing features from CAD system[END_REF][START_REF] Sundararajan | Volumetric feature recognition for machining components with freeform surfaces[END_REF], graph-based recognition (Lee, Jhee, Park, 2007), rule-based recognition [START_REF] Choi | C-space based CAPP algorithm for freeform die-cavity machining[END_REF][START_REF] Zhang | A surface based approach to recognition of geometric features for quality freeform surface machining[END_REF][START_REF] Sridharan | Recognition of multi-axis milling features: Part II: Algorithms & implementation[END_REF]. These approaches are based on a well known machining feature data base and a topological analysis of the CAD model geometry. Yet, the topological analysis of the CAD model must be closely link with the machining process specificities. [START_REF] Sunil | Automatic recognition of features from freeform surface CAD models[END_REF] highlight that efficient machining feature recognition is always carried out by the formalisation of knowledge used by machining process expert. [START_REF] Sun | Operation decomposition for freeform surface features in process planning[END_REF] propose 3 axis machining feature recognition based on cutting tool tip geometry and topological analysis of the slope angle of the part. Some approaches are developed for 3-5 axes HSM of aeronautical structural parts illustrated in Fig. 2.a [START_REF] Derigent | 3D digitising strategy planning approach based on a CAD Model[END_REF](Derigent et al., , 2010;;[START_REF] Yu | Slicing recognition of aircraft integral panel generalized pocket[END_REF]. Topological analysis of shapes denotes that forging dies are composed of several cavities having very different shapes and depths Fig. 2.b compared to pockets of aeronautical parts. Beyond this difference, no machining features data base is formalised in industrial practices for forging die machining even though for aeronautical parts machining features recognition is based on a well-known machining features data base.

b. Forging dies a. Structural aeronautical parts

Fig. 2. Complex shaped parts with cavities

The work presented in this paper is aimed to transform a complex shaped CAD model to a CAM model towards an efficient identification of machining features. The main objective of the approach presented is to define machining features suitable for HSM process from the die model (3D CAD model). First, a machining process model integrating the machining feature concept is presented. Then, based on this model the knowledge useful for the machining feature identification on forging die CAD model are detailed.

Machining process

Traditional machining process generation is conducted towards four main steps Fig. 3. In the first step, the CAD model is analyzed in order to collect geometrical, topological and technological information (Fig. 3 step 1). The results of this analysis are associated and then used to create geometrical features. This step states the decomposition of the part into several geometrical features. In the second step machining strategies and cutting tools are selected for each geometrical feature (Fig. 3 step 2). The parameters of these resources are defined based on the analysis carried out in the first step. Several CAM software allow computing tool paths. According to the machining strategies and cutting tools parameters defined in the second step, the appropriate module is selected from the CAM software in order to generate machining sequences (Fig. 3 step 3). At last, machining sequences are grouped and planed in order to obtain the machining process (Fig. 3 step 4). This planning process is also based on the results of the topology analysis. Step 1

Step 2

Step 3

Step 4

Fig. 3. Machining process generation

This paper is focused on the geometrical and technological analysis of the CAD model. To ensure the completeness of the geometrical and technological analysis, a machining process model which is structured towards the four main steps presented in Fig. 3 is proposed. Knowledge carried out in step 2 are formalized in the following in order to link the different components of the machining process model given at the last part of this section. The new approach developed on the basis of the knowledge formalized in this paper allows extracting machining features for step 3.

Geometrical and technological analyses

To generate a machining process by using any CAM software, it is necessary to identify the surface or the portion of surface to be machined and to specify the machining limits on the CAD model of the part. This task is performed starting from a geometrical data analysis with respect to the technological data defined by the designer. Typically, information on material, form tolerance and roughness defined as functional requirements by the engineering department are considered as a part of technological data. Currently, surface to be machined does not correspond to all the surface of the part. The machining process must be adapted in order to satisfy the cutting conditions which depend on the technological data.

The machining data such as the scallop height and the machining tolerance defined in this level starting from the technological data are associated with surface to be machined in order to create a machining feature (Fig. 4). A machining feature is defined as the set made up of a geometrical feature and its technological data to which it is possible to associate a well-known machining process. A similar definition was given in [START_REF] Bourdet | La Gamme Automatique en usinage[END_REF] for prismatic parts.

Geometry in proximity

Geometry in relationship

Material 32

Form tolerance Roughness

Surface to be machined

Machining boundary

Fig. 4. Machining feature

When the machining feature is created, the tool paths are computed by considering the other geometrical shapes located in its environment. Analysis of the geometry and the topology of the part thus make it possible to avoid interferences with the part in the zones where the material should not be removed.

Geometrical and topological analyses

During machining process generation, it is necessary to analyse the geometry of the part according to several topological data. The different types of topological and geometrical data considered allow distinguishing the geometrical shapes in contact and the proximity relation of the surface to be machined (Fig. 4).

All the topological relationships are not detailed in this paper. The examples presented on figure 5 show the three main situations in which the computation of the tools paths takes account of the topological relations and the type of shapes with which they are associated. In Fig. 5.a, the surface to be machined has topological relations with concave surfaces. The cutting tool can move along the initial surface without any deviation of the tool paths. In Fig. 5.b the surface to be machined has topological relations with convex surfaces. The cutting tool cannot move entirely along the initial surface. The tool path must be modified to avoid interference with the convex surfaces. In Fig. 5.c the surface to be machined has a contact topological relation with a concave surface and a proximity topological relation with a convex surface. The cutting tool can move along the initial surface on the top of the concave surface but the tool paths must be modified to avoid interference with the convex surface.

Fig. 5. Influence of topology on tool paths

To integrate all the topological situations in the machining process generation it is necessary to build the complete model of the topological relations. This is done in our work and the results will be presented further. When the two phases of the geometrical analysis are completed the tool paths can be computed thanks to the selection of cutting tools and machining strategies.

Machining strategy

To define a machining strategy, four parameters must be set. The first parameter is the feed direction which corresponds to the sweeping direction of the machining feature by the cutting tool. Three types of feed direction can be defined. In Fig. 6.a the direction is given by a curve to which the tool paths are parallel. When this type of strategy is selected, the difficulty is to determine the curve which makes it possible to obtain a most constant feed rate as possible. The solution consists in extracting the curve starting from the geometry of the machining feature. For the two other types of direction, the tools paths are located in plans parallel with that selected for the strategy. This plan can contain the tool axis or be perpendicular to it Fig. The second parameter of the machining strategy is the cutting mode which defines the correspondence between the direction of rotation of the cutting tool and that of its feed rate Fig. 7.a. Two modes can be defined: downward and upward. When the upward mode is chosen, the teeth of the cutting tool in contact with the material advance in opposite direction of the machining direction. So they start with the maximal chip thickness and finish with a null chip thickness. The downward mode is the reverse of the upward mode. For the machining of the complex shapes and thus of our machining features, the parameter is set to the upward mode because it facilitates the cutting conditions. The two last parameters are linked to the dimensional quality of the surface machined. The pitch parameter which represents the radial depth of cut defines the scallop height (Fig. 7.b). The scallop height defined in CAM tools used in our work is directly linked to the surface roughness (Rt criteria). If the criteria defined in the technological data are different from the Rt, tables available in the literature to establish conversion are used.

The machining tolerance parameter defines the maximal deviation between the tool path and the machined surface (Fig. 7.c.). It is directly declared by transposing the form tolerance defined in the technological data.

Once the parameters of the machining strategy are defined, it is necessary to associate them with the different elements of the machining feature in order to integrate the results of the analyses into the machining preparation tasks. The structure of the associations is presented in Fig. 8. Only the associations of the machined surface with the sweeping mode and the feed direction are detailed in section 3. Associations relating to the topological relations and the machining boundary which are also important will be developed in another communication. Fig. 8. Machining features and strategies links

Cutting tools

Selection of cutting tools follows the same steps of the machining strategies. It is based on the parameters which define the tool tip and the geometry of its body and attachment which is necessary to check the accessibility of the machined surfaces. From the APT model considered for the definition of the tool tip (Fig. 9a) three types of tools used generally in the machining processes of complex shapes parts are identified (Fig. 9b). Only two types "ball nose" and "corner end mill" are used in finishing operations. The flat end mill is generally used in roughing operations but it can be appropriate for the finishing of some convex shapes with plane surfaces. To avoid the interference between the tool and the part, the dimensions OL and TL (Fig. 9c) are checked for their compatibility with the depth of the cavities. The material of the cutting tool is also an important parameter. It is directly determined from the material of the part. Associations of the cutting tool parameters with the different elements of the machining feature are presented in Fig. 10. The relation between the roughness and the tool tip corresponds directly to that which was established with the pitch parameter of the machining strategy (Fig. 8). Indeed, the geometry of the tool tip determines the scallop height according to the pitch. The tool tip can be more finely defined according to the machining boundary. As specified here before, this association will not be detailed in this paper. The determination of the tool will thus be done through its type.

Surface to be machined Fig. 10. Machining features and cutting tool links

Machining sequence

Tool paths can be generated when the machining strategies are defined and the types of cutting tools are selected. For a given machining feature, the machining sequence is aimed to gather its tool paths. It is thus defined as an uninterrupted and organised series of machining trajectories computed with a unique cutting tool, a unique approach and a unique clearance (Fig. 11). Through this organization, a given machining sequence is composed of (in this order) an initial trajectory, one or several intermediate trajectories and a final trajectory. Each trajectory is also composed of an approach path, a machining path and a clearance path. In addition, the initial and final trajectories have respectively a fast initial approach and a fast final clearance. The most important part of a machining sequence is the set of machining tool paths along which the cutting conditions must be respected in order to obtain the final part. Then, parameters chosen or defined for the cutting tools and the machining strategies must be compatible with the performances of the machine tool in terms of axis kinematics and Numerical Controlled Unit (NCU) capacities. The example presented in Fig. 12 shows some problems related to this compatibility. This result was obtained by using "performance viewer" which is a simulation tool developed during our research works (Tapie, Mawussi, Anselmetti, 2007a, 2007b). It highlights feed rate reductions: the set point of the feed rate is not respected or reached. The significant feed rate reduction 2 is induced by the small radius of curvature of the portion of the surface to be machined. Feed rate reductions 4 and 5 are induced by the topological relationship between the machined surface and two limit surfaces. Finally, the feed rate reduction 1 is also related to a topological relation but as the surface is convex, the tool paths can be extended in order to limit this reduction. The generation of the machining sequences is carried out thanks to the association of the machining strategies and the cutting tools to the machining features. The association process (Fig. 13) comprises five tasks. Approach/initial paths and clearance/final paths are respectively generated during tasks 1 and 2. Their basic shape depends in most cases on the body geometry of the cutting tool, the machining strategy (sweeping mode and feed direction) and the surface to be machined of the machining feature. This basic shape must be adapted according to the attachment geometry of the cutting tool and the topological relationships of the machining feature in order to avoid collisions. Transition paths are generated in the same way during task 3. The cutting mode and the pitch parameter determine which machining paths have to be linked up by transition paths and how. The generation of these machining paths during task 4 is mainly based on the tip geometry of the cutting tool and all elements of the machining strategy. As the parking point must allow avoiding collisions, it is defined during task 5 from the body and attachment geometries of the cutting tool and the topological relationships of the machining feature.

Machining process model

The generation of the machining process is made from the ordered gathering of the machining sequences. Data used during this generation are linked ones to the others. These links have been modelled using UML language (Fig. 14). Clustering of topological and technological data to the basic geometric shape in order to create the machining feature is presented in the left of the data structure. Then the association of the cutting tools parameters and the machining strategies elements in parallel to each machining feature created previously make it possible to generate the machining sequence. Finally all machining sequences are clustered in the machining process of the part towards a planning task which takes into account topological relationships between the machining features and of which objective is to reduce the machining time. In the following part only the knowledge formalization during the generation of the machining sequences is presented.

Knowledge integration

Extraction of the different geometrical features starting from CAD model of the part is an important task insofar as it must make it possible to isolate areas of the part to which are associated the cutting tools and the machining strategies. Therefore the approach developed in this paper is aimed to integrate the know-how of the machining assistant in the decomposition of the part shape into geometrical features.

In industrial practices of forging die machining, no machining features data base is formalised. Indeed, the CAD model is not sufficient to associate a well known machining process to a part area. The difficulty is to identify a machining feature (in particular the surface to be machined) suitable with a machining process.

The proposed approach is to associate machining data to the part surfaces in order to create machining features. The part geometry is analyzed according to machining criteria in order to define surfaces to be machined (Fig. 15). Two machining criteria are mainly developed in this section: cutting tool type and machining strategy. Surface to be machined

Machining boundary

Functional data

Machining data

Fig. 15. Machining process generation with knowledge integration

Contact area on cutting tools

One of the main difficulties during high speed machining of complex shape parts is to maintain the cutting speed set point because the contact area between cutting tool and the shape of the part changes every time (Fig. 16). Maintaining the cutting speed is a key factor in the cutting mechanism [START_REF] Tapie | Decomposition of forging die for high speed machining[END_REF]. This machining difficulty is closely linked with the tool type and the geometry of the part. Indeed, to machine a horizontal plane and to maintain the cutting speed, a flat or corner end mill is more appropriate than a ball nose end mill. Thresholds of the color limits between the different types of area are fixed by the machining assistant according to technological data. In the map shown in Erreur ! Source du renvoi introuvable..b they are fixed to 0.15 for the draft contact area and 0.8 for the flat contact area. These values can be adjusted by the machining assistant according to the machining strategies used to generate tool paths. Contact areas extracted at this level of the decomposition process give information useful for associating cutting tools to elementary geometrical features and to predict the effective cutting speed. Yet, this information is not sufficient to choose the machining strategy. A second map based on the analysis of the machining continuity is developed for the final choice of machining strategies.

Continuity in machining feed direction

As it is depicted previously, the choice of a machining strategy for machining tool path generation has two main objectives: avoid significant federate loss and reducing as possible machining time. To achieve these goals, the machining assistant often associates to a standard 3 axes HSM two types of machining strategies widely used in CAM software for the machining of forging dies:

parallel planes strategy : the machining feed direction is defined by parallel planes containing the tool axis; -Z-level strategy: the machining feed direction is defined in parallel planes perpendicular to the tool axis Several machining experimental works on inclined planes [START_REF] Kang | Characteristics of inclined planes according to the variation of cutting direction in high-speed ball-end milling[END_REF][START_REF] Kecelj | Speciality of HSC in manufacturing of forging dies[END_REF]Toh, 2004aToh, , 2004b) ) or complex shape parts [START_REF] Baptista | Three and five axis milling of sculptured surfaces[END_REF][START_REF] Vivancos | Optimal machining parameters selection in high speed milling of hardened steels for injection moulds[END_REF] have been performed. Analysis of the results of these experimentations underlines the fact that geometrical features must be grouped according to the same direction sequences -equivalent to the feed direction -in order to limit cutting mechanical deteriorations and thermal problems. Parallel planes strategy allows reducing machining time by covering large areas of machined parts. Priority is given to the application of this strategy towards the second type of map developed. The principle of this second map belongs to the ability of the normal vector of different adjacent facets to hold on the same plane along a machining tool path. This ability can be evaluated from the projection of the contact area indicator in the feed direction (Erreur ! Source du renvoi introuvable..a.) which characterizes the continuity indicator of parallel planes strategy. Indeed, when the normal vectors of several adjacent facets hold on the same plane containing the tool axis direction and the feed direction, their projections on the plane H must be equal to the contact area indicator defined previously (see Erreur ! Source du renvoi introuvable..a). If the continuity for parallel planes is not obtained for several adjacent facets but the values of the contact area indicators are the same, the resulting machining condition corresponds to continuity in the plane H which becomes the Z-level plane. For this reason the contact area indicator becomes the Z-level indicator in this stage (Erreur ! Source du renvoi introuvable..a.). This Z-level indicator characterizes the ability of the normal vectors of different adjacent facets to turn around the feed direction with the same contact area. Then, the contact map generated previously also allows determining the Z-level continuity for the final geometric features extracted.

Analyzing the results obtained from maps generated for several forging dies, 3 machining continuity cases can be distinguished:

-Indifferent feed direction (Erreur ! Source du renvoi introuvable..b.): it corresponds to flat areas for which the normal vectors of several adjacent facets are hold on a same plane whatever is the selected feed direction.

-Oriented feed direction (Erreur ! Source du renvoi introuvable..c.): it corresponds to the continuity of planar or quasi-planar areas for which only one feed direction is found.

-Undefined feed direction (Erreur ! Source du renvoi introuvable..d.): it corresponds to transition areas or blend surfaces for which there is no privileged feed direction.

A fourth case can be highlighted. It corresponds to draft surfaces for which the Z-level strategy continuity indicator is constant in several adjacent facets. This case is equivalent to the draft area identification from the contact area map. In practice continuities in parallel planes are searched by testing several feed directions. Ten directions are systematically tested between 0 ° and 90 ° with a step of 10 °. In the example of Erreur ! Source du renvoi introuvable., only one oriented feed direction is identified on the first map. To be efficient, tested directions must be determined from the characteristics of the contact areas and the main directions of the rough shape of the part. Variations of the feed direction around these directions can be small. Geometrical features are finally identified from areas obtained by bringing closer maps corresponding to tool orientation and machining feed direction continuity. The maps combination is carried out toward their complementarities. Indeed, the tool map orientation, realised first, integrates knowledge about cutting tool choice and cutting conditions and enables to obtain elementary geometrical features. The machining strategy continuity maps, built in a second stage, enable to group or not elementary geometric features and then integrate relevant knowledge for machining strategy choice.

Application introduced afterwards shows a complete identification of areas as well as different associations of cutting tools and machining strategies.

Application

The proposed method is applied to the generation of the machining process of the industrial die of which the CAD model is presented in Fig. 20.a. This die is composed of a deep and complex shape cavity which has a topological relationship with a central slot. The STL model (Fig. 20.b.) used to build maps is created thanks to a standard meshing tool of the CAD software CATIA ® . With basic parameters (deviation of 0,2mm and maximum edge length of 1mm) the meshing process leads to 13450 facets. The accuracy of the geometric features extraction can be improved by increasing the number of facets thanks to the modification of the parameters but it will also increase the processing time. Since this improvement does not have influence on the maps, the initial number of facets is maintained. Two maps are generated for the industrial die from the STL model (Fig. 21). The first map associated with the cutting speed shows three types of areas (Fig. 21a). Areas of types 1 which are located at the centre of the cutting tool spread over the broad part of the die. Areas of type 2 located on the flank of the cutting tool are linked up to the first by intermediate areas of type 3. The second map which allows searching for directions pointed out for a sequence of several surfaces is generated according to nine directions. For this industrial die, this map brings any other relevant information for the decomposition of geometric shape. Analysis of the types of areas and their relative positions (topology) allows us to define the geometric features presented in Fig. 22. The main area of type 1 located on the top of the die represents its parting plane. The die cavity is composed of three main features: the flank surface and the bottom surface which includes a protrusion. The protrusion includes several contact areas with the cutting tool and it is not easily identifiable as much as it appears on the map through several colours. This is the main element for the recognition of revolution features composed of a rounded crest and several rings. The protrusion is linked to the bottom of the die cavity by transition features. It is also the case of the die cavity which is entirely linked to the parting plane by transition features. The height of the protrusion is such as its rounded crest does not exceed the parting plane which can therefore be machining without taking into account the protrusion. This information expresses the importance of topological relations. As a result, each machining feature is created from a form feature which embeds technological data (material, roughness, form tolerance) and topological data (example: "the protrusion does not exceed the parting plane"). At this stage of the generation of the machining process of the die, machining features are entirely identified. Cutting tools and machining strategies associated to them according to knowledge defined in the maps (Erreur ! Source du renvoi introuvable. and Erreur ! Source du renvoi introuvable.) and methods presented in the association graphs (Fig. 8 and Fig. 10) are shown in Fig. 23. Two cutting tools and two machining strategies are necessary and sufficient for all machining features of the die. As the protrusion feature is particular, it is machined by two cutting tools because the roughness allows it (16 µm). If the junction between the rounded crest and the flank (the set of rings) of the protrusion feature owed to the change of cutting tool is not compatible with the form tolerance (0.1 mm), it is necessary to consider the use of the only corner end mill. Machining with the only corner end mill will make it possible to reach the set point of the cutting speed on the rounded crest but will increase the machining time. It will also fix only one machining strategy which will be Z-level.

Conclusions

Application of a unique standard machining strategy and a choice of one cutting tool for the machining of a whole surface of a given forging die are generally unsatisfactory because of the variations of cutting speed and feed rate. Approach presented in this paper is aimed to decompose the die geometry in several machining area in order to limit the variations of cutting speed and feed rate. The decomposition process represents the CAD/CAM integration in the field of the machining of forging dies and it can be extended to complex shape parts.

The generation of the machining process of dies by the machining assistant is based on several expert knowledge which are linked to technological and topological data, machining strategies, cutting tools and machining sequence components. The detailed analysis of these expert knowledge made it possible to highlight their relations and associations to the different information being able to be processed during the decomposition of the forging die shape. The data handled at this stage as their relations were gathered in the machining process model which was used as a basis for machining knowledge formalization and integration. Knowledge formalization in the machining process generation has been carried out at two stages starting from the representation of the CAD model of die by STL facets. In the first stage the difficulty linked to the variation of cutting speed contact areas between cutting tools and the shape of the die have been analysed. Knowledge formalization at this stage leads to the generation of contact area map which is based on the orientation of the normal vector of each facet of the STL model compared to the tool axis direction. The decomposition of the normal vector by projection respectively to the tool axis direction and the plane H perpendicular to this tool axis direction defines the orientation indicator and the contact area indicator. These two indicators are useful for the integration of knowledge associated to cutting tools. The second stage of knowledge formalization is based on the difficulty to keep the orientation of the normal vectors of several facets in the same plane. When a plane parallel to the tool axis direction exists, it defines a machining continuity and corresponds to the basic plane for the parallel planes strategy. Maps generated at this stage for the search of continuity planes are based on a continuity indicator defined according to a given machining direction. The continuity indicator provided information for the integration of knowledge associated to machining strategies. Extraction of geometrical features from the combination of the two types of maps is not automatic. This is one of the points which must be developed in next work. The knowledge integration being based on several expert rules, the geometric feature extraction process must be based on artificial intelligence approaches like neural network.

The industrial case study presented in the final part of the paper shown a complete application of the knowledge formalization for the decomposition of the die shape into geometrical features. The machining features created by associating cuttings tools and machining strategies to the geometrical features can be used by a machining assistant to generate the machining sequences.

Fig. 6 .

 6 Fig. 6. Machining types and parameters

  Fig. 7. Machining quality requirements

  Fig. 9. Cutting tool parameters

  Fig. 11. Machining sequence components

  Fig. 12. Feed rate reductions

Fig. 13 .

 13 Fig. 13. Links between machining process components

Fig. 14 .

 14 Fig. 14. Machining process model

  Fig. 16. Examples of contact areasThe orientation of a given facet of the STL model of the die compared to the tool axis (or machining direction) makes it possible to locate the contact area between tool tip and the machined surface and to estimate its size. Two types of significant information can be extracted from the analysis of this orientation: indication about the range of the contact area (closely linked with the area size) and evaluation of the effective radius of the tool tip which determines the effective cutting speed. The principle of building the contact map is based on the evaluation of the tool orientation obtained by the projection of the unite vector representing the STL facet normal on the tool axis direction. The orientation indicator resulting from projection (Erreur ! Source du renvoi introuvable..a) defines the location of the contact area between tool and part. Indeed, when the contact area moves from the center of a ball en mill tool to its external diameter, the orientation indicator takes a value which varies from 0 to 1. Inversely to the orientation indicator, the projection of the unite vector representing the STL facet normal on a plane H perpendicular to the tool axis direction defines a contact area indicator (Erreur ! Source du renvoi introuvable..a) which represents the size of the contact area. Orientation or contact area map is generated according to the two indicators highlighted previously. The map presented in Erreur ! Source du renvoi introuvable..b is obtained by assigning a color to the contact area indicator of each STL facet. The color scale is the one provided by MATLAB ® . Analyzing the results obtained from maps generated for several forging dies, three types of contact areas can be identified (Erreur ! Source du renvoi introuvable..c). Flat contact area, which is the first type, characterizes planar or quasi planar surface portions. Usually this type of area defines cavity bottoms and die parting planes. Draft area, which is the second type, characterizes drafted surfaces (vertical or quasi vertical) representing cavity flanks. Between the colors of the two first types of contact area, several surface portions are associated to graduated colors. The transition contact areas associated to these colors characterize transition or blend surfaces located between flat and drafted surfaces.

  Fig. 17. Elementary geometrical feature identification

Fig. 18 .

 18 Fig. 18. Continuity in machining feed direction

  Fig. 19. Machining continuity maps

  Fig. 20. Industrial case study

  Fig. 21. Maps generation

Fig. 22 .

 22 Fig. 22. Geometric features extraction

Fig. 23 .

 23 Fig. 23. Association of cutting tools and machining strategies

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