Design and testing of a transducer for measuring the loads on the rollers of a crane carriage.

Atanasiu, Costica ; Iliescu, Nicolae ; Pastrama, Stefan Dan 等

1. INTRODUCTION

The paper presents the design, testing and practical use of a transducer used to measure the load on the rollers of a crane carriage. The elastic element of the transducer is described extensively by Iliescu and Atanasiu (2006). It was conceived to measure loads up to 200 kN with accurate sensitivity. For the measurement range, the design of the elastic element was made to obtain a variation of the strain with the applied load as close to a linear one. Also, the maximum stress was limited to a value of 0.75 of the yield limit [[sigma].sub.[gamma]].

2. THE LOAD CELL

The chosen material was a Romanian chromium alloy steel 13CN35 with a yield limit of 670 MPa.

The elastic element which is a simply supported beam is presented in Fig. 1 and has the following geometry:

--Span: L = 150 mm;

--Height of the cross section: h = 40 mm in the 40 mm length middle part and [h.sub.1] = 35 mm in the rest of the length;

--width of the cross section: W = 60 mm (it was chosen taking into account the width of the track rail of the roller).

As one can see in Fig. 1, the upper face of the middle part was machined with a cylindrical surface and has two arms on which the roller is supported. In this way, a fixed position on the surface of the element is ensured.

Four strain gauges were glued on the elastic element (Fig. 1) at the distance c = 40 mm from the supports. Two gauges were placed on the upper face (denoted as [T.sub.1] and [T.sub.3]) and the other two ([T.sub.2] and [T.sub.4])--on the lower face with their axis in the longitudinal central plane (Fig. 1).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The load cases and the corresponding bending moment diagrams are presented in Fig. 2. The measured load may be applied either in the middle of the beam, equally distributed on the two arms or eccentrically with respect to the middle.

The normal stress due to the bending of the elastic element under load is determined with the well known Navier formula (Timoshenko & Goodier, 1970):

[sigma] = M/[I.sub.y] x Z (1)

where M is the bending moment, [I.sub.y] is the second moment of area of the cross section and z is the coordinate of a point in the cross section with respect to the system of axes that passes through the centroid.

In order to verify the limitation of the stress imposed by design, the maximum stress values were calculated for the three load cases.

In the central section of the elastic element, the stress has the following values:

--For the case from Fig. 2, a:

[[sigma].sub.max] = 6 x 37.5P/W [h.sup.2] = 2.34 x [10.sup.-3] P (2)

--for the case from Fig. 2, b:

[[sigma].sub.max] = 6 x 30P/W [h.sup.2] = 1.875 x [10.sup.-3] P (3)

Since the diameter of the roller is bigger than the diameter of the cylindrical zone of the elastic element, the load is applied on the two arms, as in load case b.

In the section where the height of the cross section is changed, the maximum stress from load case a. has a lower value than in the middle:

[[sigma].sub.max] = 6 x 27.5P/W [h.sup.2] = 2.25 x [10.sup.-3] P (4)

A maximum value of the stress [[sigma].sub.max] = 450 MPa is obtained for a measured load of 200 kN, meaning that the condition imposed by design ([[sigma].sub.max] < 0.75 [[sigma].sub.[gamma]]) is fulfilled.

In order to measure the loads using the designed transducer, the stress must be calculated in the points where the strain gauges are placed.

From the bending moment diagram from Fig. 2, b and using equation (1), one can calculate the value of the stress as:

[[sigma].sub.max] = 6 x 20P/W [h.sup.2] = 1.63 x [10.sup.-3] P (5)

while the strain is:

[epsilon] = [sigma]/E = 7.76 x [10.sup.-9] P (6)

If the strain gauges are connected in full bridge (Theocaris et al., 1976), the strain read by the measurement equipment is:

[[epsilon].sub.measured] = 4[epsilon] = 31.04 x [10.sup.-9] P (7)

When the two arms take over different parts of the load, and the overall load is eccentric to the center of the beam (Fig. 2, c) the strains indicated by the gauges are: --For gauges [T.sub.1] and [T.sub.2]:

[[epsilon].sub.1,2] = [+ or -] 6Pbc/LEW [h.sup.2] (8)

--For gauges [T.sub.3] and [T.sub.4]:

[[epsilon].sub.3,4] = [+ or -] 6Pac/LEW [h.sup.2] (9)

For the connection of the gauges in full bridge, the strain measured in this case is:

[[epsilon].sub.measured] = [[epsilon].sub.1] - [[epsilon].sub.2] + [[epsilon].sub.3] - [[epsilon].sub.4] = 12Pc/EW [h.sup.2] = kP (10)

where k = 31.04 x [10.sup.-9].

From eq. (10) it can be noticed that the obtained strain is proportional with the load and does not depend on the eccentricity. In this way, deviations from the load symmetry of the elastic element do not influence the values of the strain and eq. (6) is recovered in the case of eccentric load.

[FIGURE 3 OMITTED]

2. CALIBRATION AND TESTING OF THE TRANSDUCER

For the four rollers of the crane carriage ([V.sub.1], ..., [V.sub.4]), four transducers were manufactured and placed on the track rails, under the rollers. Since the accuracy of machining is not the same for each transducer, they should be calibrated in order to determine the relationship between the strain e and the applied load P (Sandu & Sandu, 1999).

For calibration, the transducers were loaded with known forces and the strains were measured with the strain gauge device. Before the calibration process, each transducer was loaded and unloaded in order to check the feed-back of the strain gauges and to avoid unwanted local permanent strains of the material. After the final measurements, the transducers were again calibrated. The differences between the initial and final calibrations were very small.

Finally, tests were performed in order to verify the behavior of the transducers under load. They were used to measure the load on the rollers of a crane carriage (Fig. 3). The maximum load that can be lifted by the crane is 25 kN. The experimental tests were necessary in order to perform a verification of strength structure of the crane.

The measurements were performed for two loading cases:

Case I: own weight of the carriage and the arm of the crane at 90[degrees] with respect to the axis of the track rail;

Case II: a load of 25kN at the hook of the crane (applied using another crane) and the arm of the crane at 90[degrees] with respect to the axis of the track rail.

3. RESULTS AND CONCLUSIONS

The loads on each roller of the carriage were determined using the measured strains from eq. (10) and the calibration curves for each transducer. The obtained results are presented in Table 1.

From Table 1, the following data can be obtained by adding the loads on the rollers for each loading case separately:

--For loading case I, the own weight of the carriage is calculated as: [G.sub.own] = 257100 N.

--For loading case II, the own weight of the carriage and the weight in the hook is [G.sub.total] = 282900 N.

The obtained results can be verified by determining the weight in the hook as [G.sub.hook] = [G.sub.total] - [G.sub.own] = 25800 N.

The difference between the obtained weight and the real one (25kN) is 1.2%, showing thus that the accuracy of the designed transducers is very good and they can be used further to measure elevated loads with precision.

4. REFERENCES

Iliescu, N. & Atanasiu, C. (2006), Metode tensometrice in inginerie (Strain gauge measurements in engineering), AGIR Publishing House, Bucharest (in Romanian).

Sandu, M. & Sandu, A. (1999), Captoare cu traductoare rezistive. Proiectare. Aplicatii (Strain gauge transducers. Design. Applications), Printech Publishing House, Bucharest, (in Romanian).

Theocaris, P., et al. (1976), Analiza experimentala a tensiunilor (Experimental stress analysis), Vol. 1, Technical Publishing House, Bucharest (in Romanian).

Timoshenko, S.P. & Goodier, J.N. (1970)--Theory of Elasticity, McGraw-Hill Kogakusha, Ltd, New York. [1].

Tab. 1 The obtained results

Loading Obtained loads on each roller [N]
 case
 [V.sub.1] [V.sub.2] [V.sub.3] [V.sub.4]

 I 80000 36700 49200 91200
 II 33300 92000 106200 51400