**Selection of standard ****weights for calibration of weighing instruments**

**T****EUVO**** ****L****AMMI**

**The Finnish Association of Technology for ****Weighing, Helsinki, Finland**

*Abstract*

*This paper deals with the selection of standard weights or test loads for the calibration of single-interval weighing **instruments. Four **tables are given for the selection of **weights of at most 50 kg. The tables contain information about the accuracy of the weights and the instruments to be calibrated. According to the accuracy of the instrument a table is chosen; with its aid the weights are selected so that their accuracy is appropriate in relation to that of the **instrument.*

1 Introduction

The weights dealt with here are those given in OIML Recommendations:

R 111, “Weights of classes E1, E2, F1, F2, M1, M2, M3” (1994) [1] or

R 47, “Standard weights for testing of high capacity weighing machines” (1979–1978) [2]

R 111 covers weights of at most 50 kg and R 47 those from 50 kg to 5000 kg. Their errors are measured in connection with either the calibration or the verification of the weights. In both these cases the following conditions are supposed to be met:

- The errors of the weights comply with the maximum permissible errors (mpe’s) given in the Recommenda- tions;

- The measurement uncertainty of the error of each weight is a fractional part of the mpe of the weight (usually at most 1/3 ´ mpe). This uncertainty is the uncertainty of the weight.

A generally accepted principle for selecting the weights for calibrating an instrument is that the accuracy of the weights should be appropriate in relation to that of the instrument and the influence of the errors of the weights on the calibration results should be controlled.

One way to achieve this is to select the weights for each applied load so that the quotient of the error of the weights and a certain error of the instrument specified by its user (maximum tolerable error) is not greater than a chosen fraction.

Usually, the value of the fraction chosen is 1/3, but sometimes it is 1/6. The idea of using 1/6 is explained in 4.2.2.

The user can specify the maximum tolerable errors,

e.g. by giving maximum differences between the indications of the instrument and the corresponding true values, as determined by the weights. In other words, he gives limits for the errors of the instrument obtained by means of calibration, and his expectation is that the errors are within the limits, the maximum tolerable errors. This is dealt with in more detail in Section 2.

In Section 3 the general rules for selecting R 111 and R 47 weights for the calibration of instruments are given, though these have been dealt with previously in the author’s publication *Calibration of Weighing **Instruments and Uncertainty of Calibration *[3]*. *However, the main subject of this paper is to select the weights of class E2 to M3 of R 111 (class E1 is not dealt with here) using the tables given at the end of Section 4.

2 Maximum tolerable errors (MTEs) of instruments

Suppose that the user of an instrument has selected an error f representing the accuracy of the instrument or the accuracy of weighing with it (compare f with e in OIML R 76-1, T.3.2.3, 2.2 and 3.5.1 [4]). f may equal the scale interval of the instrument or a multiple thereof (OIML R 76-1, T.3.2.2). With the aid of f the user can define the maximum tolerable errors (MTEs) of the instrument. The MTEs can be:

± f for all the loads, or

± 0.5 f or ± f for certain “small” loads but ± f or ± 2 f for the larger loads, or

± 0.5 f or ± f for “small” loads, ± f or ± 2 f for certain “medium” loads and ± 1.5 f or ± 3 f for larger loads.

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In the following the absolute values êMTEú of the MTEs are used. The cases:

1) êMTEú = 0.5 f, f & 1.5 f; 0.5 f & f, or only f and

2) êMTEú = f, 2 f & 3 f, or f & 2 f are dealt with separately.

The “small” and “medium” loads expressed in terms of f are defined in 4.3.

- General rules for selecting the weights used for calibrating instruments

The quotient Max/f, where Max is the maximum weighing capacity of the instrument, plays an important role. It is used in the tables in Section 4 but also in one of the following rules based on the requirement of R 76-1, 3.7.1 concerning standard weights for the verifi- cation of instruments.

**Verified weights**

*Weights of at most 50 kg (R 111)*

The sum of the absolute values of the mpe’s (sum of

êmpe÷ ’s) of the weights shall not be greater than 1/3 or 1/6 of the êMTEú of the instrument for the applied load (1/3 is used in R 76-1).

*Weights from 50 kg to 5000 kg (R 47)*

For these weights, rule 3.1.1 with the fraction 1/3 can be considered to be met if Max/f of the instrument is equal to or less than the n marked on the weights.

**Calibrated weights**

*Errors of the indications of the instrument are not**corrected for the errors of the weights*

The sum of the absolute values of the errors of the weights shall not be greater than 1/3 or 1/6 of the êMTEú of the instrument for the applied load. However, on the basis of condition 1) in “Introduction” this rule is replaced with rule 3.1.1 here.

*Errors of the indications of the instrument are**corrected for the errors of the weights*

The sum of the absolute values of the uncertainties of the weights shall not be greater than 1/3 of the êMTEú of the instrument for the applied load. The fraction 1/6 is not used here for this case.

**Rules 3.1.1 to 3.2.2 only approximately met**

Sometimes it is reasonable to allow the previous rules to be met only approximately. For example, 3.1.1 with the fraction 1/3 is approximately met if the sum of the

êmpeú ’s of the weights exceeds the limit 1/3 ´ êMTEú and the quotient of the excess and the limit is less than or about 1/10 for the applied load. This is applied similarly to the other rules too.

**Tables for selecting weights of class E****2****to M****3****(R 111) according to Max/f of the instrument**

**General**

*Scope*

Tables 1, 2, 3 and 4 at the end of this section cover the selection of the weights of class E_{2} to M_{3} of R 111 according to Max/f of the instrument to be calibrated. The tables are compiled so that the weights selected with their aid meet rule 3.1.1 above without any further action, however, with the exception of the weights for instruments/balances with “very” high Max/f.

The weights dealt with here are normally verified weights, but under the practice of 3.2.1 calibrated weights may also be concerned. The weights for the balances with “very” high Max/f are calibrated weights of class E_{2} which meet rule 3.2.2, if applicable. This is one of the two procedures to be dealt with in the tables.

*Differences between the tables*

In Tables 1 and 2 the values of êMTEú are: 0.5 f, f & 1.5 f or 0.5 f & f, or only f, and in Tables 3 and 4: f, 2 f & 3 f or f & 2 f (if êMTEú only takes on the value f, Table 1 or 2 is referred to). The fraction is 1/3 in Tables 1 and 3 and 1/6 in Tables 2 and 4.

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*Selection**of**a**table,**its**use,**groups**1), 2), 3) and 4)**of the instruments and procedures*

The table is selected according to êMTEú and the frac- tion 1/3 or 1/6. Then Max/f of the instrument/ balance is calculated and, following the instructions given in the tables, it is assigned to one of the following groups (compare the groups with the accuracy classes for instruments/balances in R 76-1, 3.1.1 and 3.2):

Group 1): Special balances (Max/f is unlimited, special accuracy)

Group 2): Laboratory or precision balances (Max/f

£ 100 000, high accuracy)

Group 3): Instruments for industrial weighing (Max/f

£ 10 000, medium accuracy)

Group 4): Instruments for industrial weighing (Max/f

£ 1 000, low accuracy)

On the basis of Max/f and the group of the instru- ment/balance the accuracy class of the weights, or the procedure to be applied (see 4.1.1), is obtained from the table chosen.

The procedures are:

- “Apply 3.2.2” or “No calibration”. If Max/f is high enough, they are applied for some balances of Group 1).
- “Apply 3.2.2” means that calibrated weights of class E
_{2}are selected applying 3.2.2 and “No calibration” means that some balances are not calibrated with the weights dealt with here. The procedure “Apply 3.2.2” is used for Tables 1 and 3. It cannot be used for Tables 2 and 4 because the fraction is 1/6 for them. Due to this fraction rule 3.2.2 is excluded. Therefore, the procedure “No calibration” has to be used for Tables 2 and 4 instead of “Apply 3.2.2”. Note that the highest value of Max/f dealt with in the tables is 650 000. More information about the use of the tables is given in the text below each table.

If weights £ 50 g are selected, problems caused by these weights are explained in 4.4. The application of the tables to the selection of the weights for verification of instruments/balances is dealt with in 4.5.

The use of Tables 1, 2, 3 and 4 is illustrated in 4.2.1 to

4.2.4 by means of examples. In order to use the tables properly the “small” and “medium” loads for which the values of êMTEú are given in Section 2 should be defined. This is done in 4.3.

*Table**1*

This table is for êMTEú = 0.5 f, f & 1.5 f; 0.5 f & f or only f and for the fraction 1/3. Table A in 4.3 shows in which cases the values of êMTEú are used. According to Max/f and the group of the instrument/balance the accuracy class E_{2} to M_{3} of the weights (3.1.1 or 3.2.1) or the procedure “Apply 3.2.2” is obtained from Table 1.

*Example 1: Group 4): Instruments for industrial **weighing **(Max/f *£ *1 000, low accuracy)*

- If Max/f £ 660, weights of class M
_{3}are selected irres- pective of the possible values of êMTEú . (Consider an instrument with Max 6 600 g, f = 10 g and Max/f = 660. Let the weights for the Max load be 5 kg, 1 kg , 500 g and 100 g of class M_{3}. Their êmpeï’s are 2.5 g, 0.5 g, 0.25 g and 0.05 g respectively.- Let êMTEïassume the value f = 10 g for all the loads. For the Max load the sum of the êmpeï’s of the weights is Sêmpeï = (2.5 + 0.5 + 0.25 + 0.05) g = 3.3 g » 1/3 ´ êMTEï » 3.3 g.

- Let êMTEïassume the values 0.5 f = 5 g, f = 10 g & 1.5 f = 15 g so that êMTEï= 0.5 f is used for the loads a) from 0 to 50 f (the loads are expressed in terms of f), ïMTEï = f for the loads,

- > 50 f but £ 200 f and ïMTEï = 1.5 f for the loads, c) over 200 f to Max. Let us investigate the sums S êmpeï of the weights (the test loads) which can be used at the greatest loads of the ranges a), b) and c) respectively. For the greatest load of the range a) Sïmpeï = 0.25 g < 1/3 ´ 0.5 f » 1.7 g, for that of

b) Sï mpe ï = 1 g < 1 / 3 ´ f » 3.3 g and for that of

c) Sïmpeï = 3.3 g < 1/3 ´ 1.5 f = 5 g).

b) If 660 < Max/f £ 1 000

- and êMTEú takes on the values 0.5 f, f & 1.5 f, the class is M
_{3} - the class is M
_{2}if êMTEú takes on the values 0.5 f & f or only f.

*Example 2: Group 3): Instruments for industrial weighing (Max/f *£ *10 000, medium **accuracy)*

If 2 200 < Max/f £ 3 300

- and êMTEú takes on the values 0.5 f, f & 1.5 f, the class is M
_{2} - the class is M
_{1}if êMTEú takes on the values 0.5 f & f or only f.

*Example 3: Group 2): Laboratory or precision balances*

(*Max/f *£ *100 000*, *high accuracy)*

Max/f = 6 500 (also see 4.4)

- Consider a balance with Max 650 g and f = 0.1 g

– let êMTEú be 0.5 f = 0.05 g for loads £ 500 g and f = 0.1 g for > 500 g to 650 g. The quotient L/(0.5 f)

= 500/0.05 has to be compared with Max/f = 6 500. Because 500/0.05 > 6 500 (L/(0.5 f) > Max/f), class

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F2 has to be used. Note that M1 would be suitable for the load 650 g but not for 500 g. (For 650 g the sum of theïmpeï’s for weights of class M_{1} is (25 + 5 + 3) mg = 33 mg

» 1/3 ´ ïMTEï= 1/3 ´ 0.1 g » 33 mg but for 500 g it is 25 mg > 1/3 ´ ïMTEï = 1/3 ´ 0.05 g » 16.7 mg).

– M_{1} would be suitable if the choice of the values of

êMTEú were made so that êMTEú = 0.5 f is used for loads £ 300 g and ïMTEï= f for > 300 g to 650 g (*thus L/(0.5 f) = 300 g/(0.5 f) < Max/f *), or if êMTEú

= f for all loads.

- Consider a balance with Max 65 g and f = 10 mg. Obviously, the weights used are £ 50 g and they should be of class F
_{2}irrespective of the possible values of êMTEú .

*Example 4: Group 1): Special balances*

*(Max/f unlimited, special accuracy)*

a) If 65 000 < Max/f £ 200 000 (also see 4.4)

- and êMTEú assumes the possible values 0.5 f & f or only f, weights of class E
_{2}are selected- exceptionally, if weights of £ 50 g are used, 170 000

< Max/f < 200 000 and f = 1 mg, *calibrated *weights of class E_{2} are selected applying 3.2.2, i.e., the procedure “Apply 3.2.2” is used. Such a balance might have Max 190 g, f = 1 mg, Max/f = 190 000. However, if f > 1 mg (e.g., Max 380 g, f = 2 mg, Max/f = 190 000), weights (3.1.1 or 3.2.1) of class E_{2} are used.

b) If 200 000 < Max/f £ 300 000 (also see 4.4)

- and êMTEú = 0.5 f, f & 1.5 f, the class of the weights is E
_{2}. (Consider a balance with Max 290g, f = 1mg, Max/f = 290 000 and ïMTEï = 0.5 f, f & 1.5 f. Let the weights for the Max load be 200 g, 50 g and two of 20 g of class E_{2}. The sum of their ïmpeï’s is (0.30 + 0.10 + 2 ´ 0.080) mg = 0.56 mg which exceeds 1/3 ´ ïMTEï = 1/3 ´ 1.5 mg = 0.5 mg by 0.06 mg. This excess is neglected (3.3) because 0.06 mg/0.5 mg is near to 1/10).- if êMTEú = 0.5 f & f or only f,
*calibrated*weights of class E_{2}are selected applying 3.2.2, i.e., the pro- cedure “Apply 3.2.2” is used.

- if êMTEú = 0.5 f & f or only f,

*Table 2 and the idea of using the fraction 1/6*

In this table êMTEú = 0.5 f, f & 1.5 f; 0.5 f & f or only f as in Table 1 but the fraction is 1/6. Table A in 4.3 shows in which cases the values of êMTEú are used. According to Max/f and the group of the instrument/balance the accuracy class E_{2} to M_{3} of the weights (3.1.1 or 3.2.1) or the procedure “No calibration” is obtained from Table 2.

- If the weights are within the mpe’s, as they should be, the sum of their êmpeú’s is £ 1/6 ´ êMTEú of the instrument/balance for the applied load. The sum reveals the influence of the errors of the weights on the calibration results.
- Suppose that due to wear and tear the weights are not within the mpe’s. However, if their errors can be estimated to be within the mpe’s multiplied by 2, the weights can conditionally be used for the calibration of instruments/balances. The sum of the doubled

êmpe÷’s of the weights is £ 1/3 ´ êMTEú . So the

influence of the errors of the weights on the calibration results is twice that in 1) and thus at most 1/3 ´ êMTEú . If this is accepted, the calibration with these weights can be regarded as correct.

- In case 2), the increase of the influence of the errors of the weights from £ 1/6 ´ êMTEú to £ 1/3 ´ êMTEú has to be accepted. In principle this is not difficult because £ 1/3 ´ êMTEú is a generally accepted in- fluence. Because the errors of the weights may exceed the limits of the mpe’s even by 100 %, the period of readjustment of the weights can be extended. This is a considerable advantage. From this angle there are reasons to apply the fraction 1/6.
- If the aim is to minimize the uncertainty of the calibration of instruments/balances, the influence of the errors of the weights should be kept as small as possible. £ 1/6 ´ êMTEú could be suitable. Therefore, the errors of the weights should strictly be within the mpe’s as in 1) and the fraction 1/6 should be applied.

Note 1: In R 111 mpe’s on initial verification (mpe’s in 1) above) and in service are given. The latter are twice the mpe’s on initial verification. The mpe’s in service can be used in situations similar to the following. Parties concerned by weighings with legally controlled instruments/balances (e.g., non-self- indicating instruments) in which balance (the position of equilibrium) is obtained with the aid of weights, want to check whether the weights used are “acceptable”. The weights were adjusted to be within the mpe’s on initial verification. Now the errors of the weights are acceptable if they are within the mpe’s in service. One could say that the mpe’s in service give the user of the instrument protection against complaints about the incorrectness of the results of the instrument as far as the weights are concerned.

Note 2: Notwithstanding 2) above the weights, the errors of which are within the mpe’s in service, are not for calibration, verification or testing of instruments/balances.

*Example 5: Group 3): Instruments for industrial weighing *(*Max/f *£ *10 000, medium **accuracy)*

If 1 100 < Max/f £ 3 300, the class is M irrespective of

When the weights of class E2 to M3 selected by

êMTEú .

1

(Consider an instrument with Max 6 000 g, f = 2 g,

means of Table 2 (with the fraction 1/6) are used for the calibration of instruments/balances, the consequences of their errors could be as follows.

Max/f = 3 000 and ïMTEï = f = 2 g for all the loads. Let the weights for the Max load be 5 kg and 1 kg of class M_{1}. The sum of their

ïmpeï’s is (250 + 50) mg = 0.30 g < 1/6 ´ ïMTEï = 1/6 ´ 2 g » 0.33 g).

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*Example 6: Group 2): Laboratory or precision balances **(Max/f *£ *100 000, high accuracy)*

Max/f = 6 500 (6 000 < Max/f £ 11 000; also see 4.4)

- Consider a balance with Max 650 g and f = 0.1 g. Let

êMTEú be 0.5 f = 0.05 g for loads £ 500g and f = 0.1 g for > 500 g to 650 g. Weights of class F_{2} are selected.

- Consider a balance with Max 65 g and f = 10 mg. Obviously, the weights used are £ 50 g and they should be of class F
_{1}irrespective of the possible values of êMTEú .

*Example 7: Group 1): Special balances*

*(Max/f unlimited, special accuracy)*

If Max/f £ 60 000 (also see 4.4)

- and the weights are > 50 g, calibration is per- formed with the weights of class E
_{2} - if the weights are £ 50 g and êMTEú = 0.5 f & f, calibration is not performed with the weights dealt with here, i.e., the procedure “No calibration” is used. However, calibration is performed with the weights £ 50 g of class E
_{2}if êMTEú = f for all the loads.

*Table**3*

Table 3 is for êMTEú = f, 2 f & 3 f or f & 2 f and for the fraction 1/3. If êMTEú = f for all the loads, apply Table 1. Table B in 4.3 shows in which cases the values of êMTEú are used. According to Max/f and the group of the instrument/balance the accuracy class E_{2} to M_{3} of the weights (3.1.1 or 3.2.1) or the procedure “Apply 3.2.2” is obtained from Table 3.

*Example 8: Group 2): Laboratory or precision balances **(Max/f *£ *100 000*, *high accuracy)*

Max/f = 6 500 (also see 4.4)

- Consider a balance with Max 650 g and f = 0.1 g. Let

êMTEú be f = 0.1 g for loads £ 500 g and 2 f =0.2 g for

> 500 g to 650 g. Weights of class M_{1} are selected.

- Consider a balance with Max 65g and f = 10 mg. Let

êMTEú be f = 10 mg for loads £ 50 g and 2 f = 20 mg for > 50 g to 65 g. Weights of class M_{1} are selected.

*Table**4*

Table 4 is for êMTEú = f, 2 f & 3 f or f & 2 f and for the fraction 1/6. If êMTEú = f for all the loads, apply Table 2. Table B in 4.3 shows in which cases the values of êMTEú are used. According to Max/f and the group of the

instrument/balance the accuracy class E_{2} to M_{3} of the weights (3.1.1 or 3.2.1) or the procedure “No calibra- tion” is obtained from Table 4.

The consequences of using the fraction 1/6 are the same as in 1) and 2) in 4.2.2.

*Example 9: Group 2): Laboratory or precision balances **(Max/f *£ *100 000, high accuracy)*

Max/f = 6 500 (also see 4.4)

- Consider a balance with Max 650 g and f = 0.1 g
- let êMTEú be f = 0.1 g for loads £ 500 g and 2 f =

0.2 g for > 500 g to 650 g. The class is F_{2} because L/f = 500 g/0.1 g = 5 000 > 3 000 (e.g. F_{2} is necessary for the load 500 g)

- if êMTEú = f = 0.1 g for loads £ 300 g and 2 f = 0.2 g for >300 g to 650 g, then L/f = 300 g/0.1 g = 3 000. So weights of class M
_{1}are selected. - Consider a balance with Max 65 g and f = 10 mg. Let

êMTEú be f = 10 mg for loads £ 50 g and 2 f = 20 mg for > 50 g to 65 g. Because the weights for this balance are £ 50 g their class is F_{2}.

**Values of**ê**MTE**ú**for Tables 1, 2, 3 and 4**

The following auxiliary tables A and B give the values of

êMTEú which are to be used when selecting weights for the calibration of instruments/balances with the aid of Tables 1, 2, 3 and 4. Table A (for Tables 1 and 2) and B (for Tables 3 and 4) are patterned on the model of R 76-1, 3.5.1.

*Definition 1: *“Small” loads for an instrument/ balance (expressed in terms of f) are those less than or equal to some chosen load which is not greater than 50 000 f, 5 000 f, 500 f

or 50 f for groups 1), 2), 3) or 4) res- pectively. For example, for a balance of group 2) the “small” loads can be from 0 to 5 000 f or from 0 to a load less than 5 000 f, say, 3 000 f. 5 000 f or 3 000 f is the greatest “small” load L.

*Example 10: *If Max of a balance of group 2) equals 15 000 f, then Max/f = 15 000 and thus

< 20 000. If the greatest “small” load L is 3 000 f, then according to Table A êMTEú is 0.5 f for the loads from 0 to 3 000 f and f for the loads over 3 000 f to Max. êMTEú can also be chosen to be only f from 0 to Max.

*Definition 2: *“Medium” loads for an instrument/ balance (expressed in terms of f) are those

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**Table A **The values of êMTE ê = 0.5 f, f & 1.5 f, or 0.5 f & f, or only f in relation to Max/f and the group of an instrument/balance for Tables 1 and 2 (the groups are defined in 4.1.3)

Max/f of an instrument/balance in: Group 1) Group 2) Group 3) Group 4) | êMTE ê | |||

£ 50 000 | £ 5 000 | £ 500 | £ 50 | only f 1) |

£ 200 000 2) | £ 20 000 2) | £ 2 000 2) | £ 200 2) | 0.5 f & f, or only f 3) |

> 200 000 | > 20 000 | > 2 000 | > 200 | 0.5 f, f &1.5 f, or 0.5 f & f, or only f 4) |

1**) **from 0 to the greatest “small” load L (see Definition 1). In this case L = Max for the instrument/balance.

2**) **but greater than L/f in the same group.

3**) **0.5 f for the “small” loads and f for larger loads, or only f for all the loads (see Example 10).

4**) **0.5 f for the “small” loads, f for the “medium” loads (see Definition 2) and 1.5 f for the larger loads but êMTE ê can also be chosen to be 0.5 f for the “small” loads and f for larger loads, or only f for all the loads.

**Table B **The values of êMTE ê = f, 2 f & 3 f, or f & 2 f in relation to Max/f and the group of an instrument/balance for Tables 3 and 4 (the groups are defined in 4.1.3). (If for an instrument/ balance êMTE ê = f for all the loads, then according to 4.2.3 and 4.2.4 Table 1 or 2 is used instead of Table 3 or 4 respectively.)

Max/f of an instrument/balance in: Group 1) Group 2) Group 3) Group 4) | êMTE ê | |||

£ 200 000 1) | £ 20 000 1) | £ 2 000 1) | £ 200 1) | f & 2 f 2) |

> 200 000 | > 20 000 | > 2 000 | > 200 | f, 2 f & 3 f, or f & 2 f 3) |

1**) **but greater than L/f in the same group (L = the greatest “small” load, see Definition 1).

2**) **f for the “small” loads and 2 f for larger loads.

3**) **f for the “small” loads, 2 f for the “medium” loads (Definition 2) and 3 f for the larger loads but êMTE ê can also be chosen to be f for the “small” loads and 2 f for larger loads (see Example 11 below).

greater than the greatest “small” load L but not greater than 200 000 f, 20 000 f,

2 000 f or 200 f for groups 1), 2), 3) or 4) respectively. For example, if the “small” loads for an instrument of group 3) are from 0 to 300 f, the “medium” loads are in the interval over 300 f to 2 000 f. *Note***: **The lower limit of the “medium” loads is not predetermined because it depends on the choice of the greatest “small” load L. However, the corresponding upper limit is. It takes on the values 200 000 f to 200 f in the different groups respectively.

*Example 11: *If Max of an instrument of group 3) equals 2 500 f, then Max/f = 2 500 and thus

> 2 000. Let the greatest “small” load L be 400 f. According to Table B êMTEú is f for the loads from 0 to 400 f, 2 f for the “medium” loads over 400 f to 2 000 f and

3 f for the loads over 2 000 f to Max.

êMTEú can also be chosen to be f from 0 to 400 f and 2 f for the loads over 400 f to Max = 2 500 f.

**Weights of nominal values**£**50 g**

There are problems when selecting weights for balances in group 1) or 2), especially if weights of £ 50 g are to be used for the Max load.

In order to explain the nature of the problems consider Max 65 kg and Max 65 g balances both in group

1) with Max/f = 65 000. For the Max 65 kg balance the sum of the êmpeú ’s of class F_{1} weights of > 50 g is slightly below the limit 1/3 ´ êMTEú for the Max load (3.1.1), but for the Max 65 g balance the corresponding sum of the class F_{1} weights of £ 50 g exceeds the limit.

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In the tables the above problem is solved by giving two accuracy classes for some balances in group 1) or 2). One class is for weights > 50 g for balances with certain Max/f ’s and “large” Max loads (e.g: F_{1}, Max/f = 65 000, Max 65 kg,), and the other for weights £ 50 g for balances with the same Max/f ’s as above and “small” Max loads respectively (e.g.: E_{2}, Max/f = 65 000, Max 65 g).

*Note: *For a “large” Max load, e.g. 650 g there is no problem with a single weight of £ 50 g (i.e., weights of > 50 g are dominating) but for a “small” Max load, e.g. Max near to 100 g there may be.

In the column “Instruments/balances” of the tables several intervals of the values of Max/f are given. When using only weights > 50 g for balances of group 1) and 2) the upper limits of the intervals could be higher than those given in the tables. For example, in Table 1 the upper limits 20 000 (6 500 < Max/f £ 20 000) and 300 000

(200 000 < Max/f £ 300 000) could be raised to 22 000 and 330 000 respectively. But if weights £ 50 g were selected using the tables with the higher limits, their accuracy would not be suitable in all cases. Since weights £ 50 g are important for the calibration of the balances in question the limits have not been raised. As a result of this weights > 50 g selected using the tables may sometimes be more accurate than necessary.

**Use of the tables to select weights for verification of instruments/balances**

Table 1 or 2 ( êMTEú = 0.5 f, f &1.5 f; 0.5 f & f, or f) can be applied to select the weights for the verification of instruments/balances. Then “ f ” is replaced with “e”, “MTE” with “MPE”(maximum permissible error for instruments/balances), the “groups 1), 2), 3) and 4)” of the instruments/balances with the “accuracy classes I, II, III and IIII” respectively and “calibration” with “verifica- tion”. If in Table 1 or 2:

- only one accuracy class of weights is given for instruments/balances with a certain n = Max/e, then the correct class is obtained from the tables without any further action.
- two accuracy classes of weights are given for instruments/balances with a certain n = Max/e, then to choose the right class the OIML requirements in R 76-1, 3.2 and 3.5.1 have to be taken into account. This is elucidated in the following.

*4.5.1 *÷ *MPE*÷ *= 0.5 e, e & 1.5 e*

For certain instruments/balances in Table 1 and 2 the accuracy classes of the weights are given in the form

e.g.: *M**2** *(*M**1** **if *ï *MTE*ï *= 0.5 f & f or f*) or *F**2 **(F**1 **if *ï *MTE*ï *= 0.5 f & f or f*).

Use the replacements for êMTEú , f and groups 1) to 4) as given above. These accuracy classes are for instruments/balances with n = Max/e > 200 000 in class I, n > 20 000 in class II, n > 2 000 in class III or n > 200 in class IIII. Thus the values of the ÷MPE÷ ’s to be applied are 0.5 e, e & 1.5 e. According to the informa- tion on the use of the tables (given in the text below the tables) the accuracy class of the weights given first (M_{2} or F_{2} in the above examples) is used. The second accuracy class given in parentheses is to be ignored because the condition “*if*÷ *MPE*÷ *= 0.5 e & e or e*” is not in accordance with the OIML requirements for the instruments/balances in question.

*4.5.2 *÷ *MPE*÷ *= 0.5 e & e*

For some balances in Table 1 and 2 there are accuracy classes of the weights in the form e.g.: *M**1 *(*F**2 if **1)*. *F**2 if*

ï *MTE*ï *= 0.5 f & f and L/(0.5 f) > Max/f …*), *F**2** *(*F**1** **if **1)*)

or *E**2 *(*No calibration if **1) **and *ï*MTE*ï*= 0.5 f & f )*. 1) refers to the use of weights of £ 50 g. Use the replacements for

êMTEú, f, groups 1) to 4) and calibration. This concerns class I balances with n = Max/e £ 200 000 but n > 50 000 and class II balances with n £ 20 000 but n > 5 000. The values of the êMPEú ’s to be applied are 0.5 e & e. Accuracy classes of the weights similar to those in the above examples, and in advice under the heading “Exception” in Table 1, can be used. However, one has to check that only those instructions in the tables are followed which are or lead to results which are compatible with the OIML requirements (also see 4.5.4).

*4.5.3 *÷ *MPE*÷ *= 0.5 e*

In the case where êMPEú = 0.5 e is used for all the loads (e.g., n = Max/e = 50 000 and e ³ 1 mg for class I balances or n = 5 000 and e ³ 0.1 g for class II balances), Table 1 or 2 is exceptionally applied so that the weights are chosen according to Max/f where f = 0.5 e.

*4.5.4 Restriction concerning balances of class II*

The sections of Tables 1 and 2 which are intended for class II balances (originally intended for group 2) balances) can be used for the selection of weights only if for the balances e ³ 10 mg. So if 1 mg £ e £ 5 mg (R 76-1, 3.2) for class II balances with êMPEú ’s of 0.5 e & e, or only 0.5 e, the weights cannot be obtained correctly from the tables in all cases.

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Table 1 Max/f and accuracy classes E_{2} to M_{3} of weights or procedure to be applied

- ïMTEï of the instrument/balance takes on the values: 1) 0.5 f, f & 1.5 f or 2) 0.5 f & f or 3) only f (the values are chosen following the instructions in Table A in 4.3)
- The fraction is 1/3 (the error of the weights shall not be greater than 1/3 ´ ïMTE÷ for the applied load)

Instruments/balances Max/f | Weights Accuracy class or procedure |

Group 1): Special balances (Max/f unlimited, special accuracy); f ³ 1 mg, e.g. f = 1 mg, 2 mg, 5 mg, 10 mg, 20 mg, etc. | |

300 000 < Max/f £ 650 000 200 000 < Max/f £ 300 000 65 000 < Max/f £ 200 000 Max/f £ 65 000 | Apply 3.2.2 E_{2} (Apply 3.2.2 if ïMTEï = 0.5 f & f or f) E2 Exception: Apply 3.2.2 if 1), 170 000 < Max/f < 200 000 and f = 1 mg (E_{2} if f >1 mg) F1 (E2 if 1). E2 if ïMTEï = 0.5 f & f and L/(0.5 f ) > Max/f 2); L is the greatest “small” load (4.3) for which ïMTEï = 0.5 f) |

Group 2): Laboratory or precision balances (Max/f £ 100 000, high accuracy); f ³ 10 mg, e.g., f = 10 mg, 20 mg, 50 mg or ³ 0.1 g. | |

65 000 < Max/f £ 100 000 30 000 < Max/f £ 65 000 20 000 < Max/f £ 30 000 6 500 < Max/f £ 20 000 Max/f £ 6 500 | F1 (E2 if ïMTEï = 0.5 f & f or f) F1 F2 (F1 if ïMTEï = 0.5 f & f or f) F2 Exception: F1 if 1) , 17 000 < Max/f < 20 000 and f = 10 mg (F_{2} if f > 10 mg) M1 (F2 if 1). F2 if ïMTEï = 0.5 f & f and L/(0.5 f ) > Max/f 3); L is the greatest “small” load (4.3) for which ïMTEï= 0.5 f) |

Group 3): Instruments for industrial weighing | |

(Max/f £ 10 000, medium accuracy); | |

f ³ 1 g, e.g., f = 2 g or 20 kg. | |

6 600 < Max/f £ 10 000 | M1 (F2 if ïMTEï = 0.5 f & f or f) |

3 300 < Max/f £ 6 600 | M1 |

2 200 < Max/f £ 3 300 | M2 (M1 if ïMTEï = 0.5 f & f or f) |

Max/f £ 2 200 | M2 |

Group 4): Instruments for industrial weighing (Max/f £ 1 000, low accuracy); f ³ 5 g, e.g., f = 50 g or 50 kg. 660 < Max/f £ 1 000 Max/f £ 660 | M3 (M2 if ïMTEï = 0.5 f & f or f) M3 |

1) Weights of £ 50 g are used (4.4).

2) F_{1} if L/(0.5 f) £ Max/f, or if ïMTEï = f for all the loads. Weights of > 50 g are used/dominating (4.4).

3) M_{1} if L/(0.5 f) £ Max/f, or if ïMTEï = f for all the loads. Weights of > 50 g are used/dominating (4.4).

In the column “Weights” the accuracy classes of the weights (3.1.1 or 3.2.1) and the procedure “Apply 3.2.2” (4.1.3) are given for the instruments/balances to be calibrated.

If there is only one accuracy class corresponding to a Max/f, it can be used irrespective of the values of êMTEú given in 1), 2) or 3) above. Frequently, another accuracy class along with conditions for its use is given in parentheses. This class must be applied if the conditions are met, e.g., if êMTEú = 0.5 f & f or f . Otherwise if êMTEú = 0.5 f, f & 1.5 f, the class given first is used.

This scheme is analogously applied to the case where the procedure “Apply 3.2.2” is used. For example, if only “Apply 3.2.2 ” is given, it is applied irrespective of the values of êMTEú .

Advice under the heading “Exception” is for certain special cases.

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Table 2 Max/f and accuracy classes E_{2} to M_{3} of weights or procedure to be applied

- ïMTEï of the instrument/balance takes on the values: 1) 0.5 f, f & 1.5 f or 2) 0.5 f & f or 3) only f (the values are chosen following the instructions in Table A in 4.3)
- The fraction is 1/6 (the error of the weights shall not be greater than 1/6 ´ ïMTE÷ for the applied load)

Instruments/balances Max/f | Weights Accuracy class or procedure |

Group 1): Special balances (Max/f unlimited, special accuracy); | |

f ³ 1mg, e.g. f = 1 mg, 2 mg, 5 mg, 10 mg, 20 mg, etc. | |

Max/f > 110 000 | No calibration |

60 000 < Max/f £ 110 000 | E2 (No calibration if 1) ) |

Max/f £ 60 000 | E2 (No calibration if 1) and ïMTEï = 0.5 f & f 2) ) |

Group 2): Laboratory or precision balances | |

(Max/f £ 100 000, high accuracy); | |

f ³ 10 mg, e.g., f = 10 mg, 20 mg, 50 mg or ³ 0.1 g. | |

50 000 < Max/f £ 100 000 | E2 |

30 000 < Max/f £ 50 000 | F1 (E2 if ïMTEï= 0.5 f & f or f) |

11 000 < Max/f £ 30 000 | F1 |

6 000 < Max/f £ 11 000 | F2 (F1 if 1)) |

Max/f £ 6 000 | F2 (F1 if 1) and ïMTEï = 0.5 f & f 3) ) |

Group 3): Instruments for industrial weighing | |

(Max/f £ 10 000, medium accuracy); | |

f ³ 1 g, e.g., f = 2 g or 20 kg. | |

5 000 < Max/f £ 10 000 | F2 |

3 300 < Max/f £ 5 000 | M1 (F2 if ïMTEï = 0.5 f & f or f) |

1 100 < Max/f £ 3 300 | M1 |

Max/f £ 1 100 | M2 |

Group 4): Instruments for industrial weighing | |

(Max/f £ 1 000, low accuracy); | |

f ³ 5 g, e.g., f =50 g or 50 kg. | |

500 < Max/f £ 1 000 | M2 |

330 < Max/f £ 500 | M3 (M2 if ïMTEï = 0.5 f & f or f) |

Max/f £ 330 | M3 |

1) weights of £ 50 g are used (4.4).

2) E2 if 1) and ïMTEï= f for all the loads or if weights of > 50 g are used/dominating (4.4).

3) F2 if 1) and ïMTEï= f for all the loads or if weights of > 50 g are used/dominating (4.4).

In the column “Weights” the accuracy classes of the weights (3.1.1 or 3.2.1) and the procedure “No calibration” (4.1.3) are given for the instruments/ balances to be calibrated.

If there is only one accuracy class corresponding to a Max/f, it can be used irrespective of the values of êMTEú given in 1), 2) or 3) above. Sometimes, another accuracy class along with conditions for its use is given in parentheses. This class must be applied if the conditions are met, e.g., if 1) (if weights of £ 50 g are used). Otherwise if the weights are > 50 g, the class given first is used.

This scheme is analogously applied to the case where the procedure “No calibration” is used. For example, consider “E_{2} (No calibration if 1) )”. If the weights are £ 50 g, calibration is not performed with the weights dealt with here. Otherwise, if the weights are > 50 g, calibration is performed with weights of class E_{2}.

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Table 3 Max/f and accuracy classes E_{2} to M_{3} of weights or procedure to be applied

- ïMTEï of the instrument/balance takes on the values: 1) f, 2 f & 3 f or 2) f & 2 f (the values are chosen following the instructions in Table B in 4.3). If ïMTEï = f for all the loads, apply Table 1
- The fraction is 1/3 (the error of the weights shall not be greater than 1/3 ´ ïMTE÷ for the applied load)

Instruments/balances Max/f | Weights Accuracy class or procedure |

Group 1): Special balances | |

(Max/f unlimited, special accuracy); | |

f ³ 1 mg, e.g., f = 1 mg, 2 mg, 5 mg, 10 mg, 20 mg etc. | |

400 000 < Max/f £ 650 000 | E_{2} (Apply 3.2.2 if ïMTEï= f & 2 f) |

130 000 < Max/f £ 400 000 | E2 |

65 000 < Max/f £ 130 000 | F1 (E2 if 1)) Exception: F1 if 1) , Max/f = 70 000 or 105 000 |

and L = 50 000 f 2) | |

Max/f £ 65 000 | F1 |

Group 2): Laboratory or precision balances | |

(Max/f £ 100 000, high accuracy); | |

f ³ 10 mg, e.g., f = 10 mg, 20 mg, 50 mg or f ³ 0.1 g. | |

65 000 < Max/f £ 100 000 | F1 |

40 000 < Max/f £ 65 000 | F_{2} (F_{1} if ïMTEï= f & 2 f) |

13 000 < Max/f £ 40 000 | F2 |

6 500 < Max/f £ 13 000 | M1 (F2 if 1)) Exception: M1 if 1) , Max/f = 7 000 or 10 500 |

and L = 5 000 f 3) | |

Max/f £ 6 500 | M1 |

Group 3): Instruments for industrial weighing | |

(Max/f £ 10 000, medium accuracy); | |

f ³ 1 g, e.g., f = 2 g or 20 kg. | |

6 600 < Max/f £ 10 000 | M1 |

4 400 < Max/f £ 6 600 | M_{2} (M_{1} if ïMTEï= f & 2 f) |

1 300 < Max/f £ 4 400 | M2 |

Max/f £ 1 300 | M3 |

Group 4): Instruments for industrial weighing (Max/f £ 1 000, low accuracy); f ³ 5 g, e.g., f = 50 g or 50 kg. Max/f £ 1 000 | M3 |

1) weights of £ 50g are used (4.4).

2) L is the greatest “small” load for which ïMTE÷ = f (see Definition 1 in 4.3).

3) L is the greatest “small” load for which ïMTE÷ = f (see Definition 1 in 4.3).

In the column “Weights” the accuracy classes of the weights (3.1.1 or 3.2.1) and the procedure “Apply 3.2.2” (4.1.3) are given for the instruments/balances to be calibrated.

If there is only one accuracy class corresponding to a Max/f, it can be used irrespective of the values of êMTEú given in 1) or 2) above. Sometimes, another accuracy class along with conditions for its use is given in parentheses. This class must be applied if the conditions are met, e.g., if êMTEú = f & 2 f. Otherwise if êMTEú = f, 2 f & 3 f, the class given first is used.

This scheme is analogously applied to the case where the procedure “Apply 3.2.2” is used. For example, consider “E_{2} (Apply 3.2.2 if êMTEú = f &2 f )”. If êMTEú = f & 2 f , *calibrated *weights of class E_{2} are used applying 3.2.2. Otherwise, if êMTEú = f, 2 f & 3 f, weights (3.1.1 or 3.2.1) of class E_{2} are used.

Advice under the heading “Exception” is for certain special cases.

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Table 4 Max/f and accuracy classes E_{2} to M_{3} of weights or procedure to be applied

- ïMTEïof the instrument/balance takes on the values: 1) f, 2 f & 3 f or 2) f & 2 f (the values are chosen following the instructions in Table B in 4.3). If ïMTEï = f for all the loads, apply Table 2
- The fraction is 1/6 (the error of the weights shall not be greater than 1/6 ´ ïMTE÷ for the applied load)

Instruments/balances Max/f | Weights Accuracy class or procedure |

Group 1): Special balances | |

(Max/f unlimited, special accuracy); | |

f ³ 1mg, e.g. f = 1 mg, 2 mg, 5 mg, 10 mg, 20 mg etc. | |

Max/f > 300 000 | No calibration |

200 000 < Max/f £ 300 000 | E_{2} (No calibration if ôMTEô= f & 2 f ) |

65 000 < Max/f £ 200 000 | E2 Exception: No calibration if 1), 170 000 < Max/f < 200 000 and |

f = 1 mg (E_{2} if f > 1 mg) | |

Max/f £ 65 000 | F1 (E2 if 1). E2 if L/f > 30 000 2); L is the greatest “small” load |

(4.3) for whichôMTEô = f) | |

Group 2): Laboratory or precision balances (Max/f £ 100 000, high accuracy); f ³ 10 mg, e.g., f = 10 mg, 20 mg, 50 mg or ³ 0.1 g. | |

65 000 < Max/f £ 100 000 30 000 < Max/f £ 65 000 20 000 < Max/f £ 30 000 6 500 < Max/f £ 20 000 Max/f £ 6 500 | F_{1} (E_{2} ifôMTEô= f & 2 f) F1 F_{2} (F_{1} if ôMTEô= f & 2 f) F2 Exception: F1 if 1), 17 000< Max/f < 20 000 and f = 10 mg (F_{2} if f > 10 mg) M1 (F2 if 1). F2 if L/f > 3 000 3); L is the greatest “small” load (4.3) for whichôMTEô = f) |

Group 3): Instruments for industrial weighing | |

(Max/f £ 10 000, medium accuracy); | |

f ³ 1 g, e.g., f = 2 g or 20 kg. | |

6 600 < Max/f £ 10 000 | M_{1} (F_{2} if ôMTEô= f & 2 f) |

3 300 < Max/f £ 6 600 | M1 |

2 200 < Max/f £ 3 300 | M_{2} (M_{1} if ôMTEô= f & 2 f) |

Max/f £ 2 200 | M2 |

Group 4): Instruments for industrial weighing (Max/f £ 1 000, low accuracy); f ³ 5 g, e.g., f = 50 g or 50 kg. 660 < Max/f £ 1 000 Max/f £ 660 | M_{3} (M_{2} if ôMTEô= f & 2 f) M3 |

1) weights of £ 50g are used (4.4).

2) F1 if L/f £ 30 000. Weights of > 50 g are used/dominating (4.4).

3) M1 if L/f £ 3 000. Weights of > 50 g are used/dominating (4.4).

In the column “Weights” the accuracy classes of the weights (3.1.1 or 3.2.1) and the procedure “No calibration” (4.1.3) are given for the instruments/ balances to be calibrated.

If there is only one accuracy class corresponding to a Max/f, it can be used irrespective of the values of êMTEú given in 1) or 2) above. Frequently, another accuracy class along with conditions for its use is given in parentheses. This class must be applied if the conditions are met, e.g., if L/f > 3 000 (a balance in group 2) with Max/f £ 6 500). Otherwise if L/f £ 3 000, the class M_{1} given first is used.

This scheme is analogously applied to the case where the procedure “No calibration” is used. For example consider “E_{2} (No calibration if

êMTEú = f & 2 f)”. If êMTEú = f & 2 f, calibration is not performed with the weights dealt with here. Otherwise, if êMTEú = f, 2 f & 3 f, calibration is performed with weights of class E_{2}.

Advice under the heading “Exception” is for certain special cases.

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References

- OIML Recommendation R 111, Weights of classes E1, E2, F1, F2, M1, M2, M3 (1994)
- OIML Recommendation R 47 Standard weights for testing of high capacity weighing machines (1979-1978)
- T. Lammi: Calibration of Weighing Instruments and Uncertainty of Calibration. OIML Bulletin Volume XLII,

Number 4, October 2001

- OIML Recommendation R 76-1, Nonautomatic weighing instruments. Part 1: Metrological and technical requirements – Tests (1992)

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