The Reduction of Rotating Conveyor Roller Vibrations by the Use of Plastic Brackets

The paper presents the basic structural parts, a 3D model and the overall design of a laboratory machine, which was created to detect vibrations generated by the casing of a conveyor roller ro-tating at different speeds. The intention of the authors was to verify whether plastic brackets in-serted into the structurally modified trestles of a fixed conveyor idler can reduce the vibration values transmitted from the rotating conveyor roller to the trestle of a fixed idler. Experimental vibration measurements taken on the non-rotating parts of conveyor rollers, performed on a laboratory machine according to ISO 10816, are suitable for characterizing their operating condi-tions with regard to trouble-free operation. The aim of this paper is to detect the vibrations of a rotating conveyor roller on a laboratory machine in the defined places of a fixed conveyor idler and also on the steel frame of a laboratory machine that represents the supporting track of a belt conveyor. Vibrations detected by piezoelectric acceleration sensors were recorded by a measur-ing apparatus and displayed in the environment of Dewesoft X software. The measurements show that the vibration values grow with the increasing speed of the conveyor roller rotation. Experimental measurements have proven the correctness of the assumption that the vibrations transmitted to the trestle of a fixed conveyor idler are lower by up to 40% when using plastic brackets into which the axle of the conveyor roller is attached, compared to the solution where the axle of the conveyor roller is inserted into the notches of a steel trestle.

Keywords:

Subject: Engineering - Civil Engineering

1. Introduction

Vibration [1,2] is defined as a process during which a material body oscillates around its equilibrium position. Vibration [3] is described by amplitude and phase at a given point in time. Since in real situations, a body cannot be described as a single point of mass, the oscillation through the body spreads gradually from one particle to another—this phenomenon is called waves. Waves can be classified as non-periodic and periodic. Periodic waves [4] (harmonic vibrations) have a sinusoidal waveform and can be described by their speed, acceleration and deflection. These three quantities are the basis for the description and measurement of vibrations [5]. We use speed mainly to determine the energy of vibrations, acceleration to determine the high-frequency components of vibrations, and deflection is used for low-frequency components.

The CSN ISO 10816 standard [6] establishes the general rules for measuring and evaluating machine vibrations, and these vibrations are measured on non-rotating parts (especially on bearings). The standard [6] stipulates that the measurement is generally broadband in order to cover the entire frequency range of a particular machine being measured. According to the standard [6], the measured values are the vibration deflection, vibration velocity and vibration acceleration. In practice, the effective value of vibration velocity is mainly used for vibration evaluation due to its relationship with the energy of these vibrations. Two criteria are decisive for the assessment of vibration strength (the highest measured value from a set of vibrations performed at multiple locations and in multiple directions). The first is the magnitude of the vibration, and the second is the magnitude of the change in vibration [7].

By vibrations [8] we mean the mechanical oscillation of a body or elastic medium, where the individual points of the body/medium oscillate around an equilibrium position. The motion of the individual points of a body subjected to vibrations can be described by the time course of its deflection y(t) [m], velocity v(t) [m·s^–1] [9] or acceleration a(t) [m·s^–2] (1).

a (t) = \frac{d^{2} y (t)}{{dt}^{2}} = \frac{d^{2} A \cdot \sin (ω \cdot t)}{{dt}^{2}} = \frac{d v (t)}{dt} = \frac{d A \cdot ω \cdot \cos (ω \cdot t)}{{dt}^{2}} = - A \cdot ω^{2} \cdot \sin (ω \cdot t) [m \cdot s^{- 2}],

(1)

The effective value of vibration acceleration a_RMS [m·s^–2] can be expressed as (2).

a_{RMS} = \sqrt{\frac{1}{T} \cdot \int_{0}^{T} |a^{2} (t)| \cdot d t} = \frac{|a_{\max}|}{\sqrt{2}} \approx 0 . 707 \cdot A \cdot ω^{2} [m \cdot s^{- 2}],

(2)

In the article [10], by the authors Perun and Opasiak, vibration measurements of the cylinder shell installed on a laboratory stand were made. It contains the results of the assessment of the technical condition of the rollers of belt conveyors after a specified period of operation.

Klimenda et al. [11] deals with the measurement of noise and vibration of rollers for belt conveyors. In this article is described and individual rollers types which were measured. Process of noise and vibration measurement of the individual rollers types is given. Part of the article is noise and vibration measurement evaluation. Three the highest acceleration values in depending on the frequency of vibration in individual directions (x, y, z) are given.

In the article [12] Svoboda et al. deal with measuring vibrations on the stand of a roller conveyor. Difference between individual set of rollers is in used of semi-finished product of the outer shell, the design of the rollers is the same. One set has a shell from convectional tube and the second set from accuracy tube. The vibrations were measured by six-channel analyser Brüel & Kjær (PULSE). Acceleration and natural frequency were measured by using a three-axis accelerometer. In the conclusion of the article is an evaluation of vibration. Three the highest acceleration values in depending on the frequency of vibration in individual directions are given. From this evaluation are selected rollers with minimal and maximal acceleration.

In the article [13] Bortnowski et al. created a device for a wireless measuring device that moves with the conveyor belt along of the route, which records the signal of transverse vibrations of the belt.

The roller is an important part of the belt conveyor in sand carrier at sea, presented by Peng et al in the article [14]. They in this paper, a novel intelligent fault diagnosis method for rollers is proposed by using audio wavelet packet decomposition and Convolutional Neural Networks (CNN).

Article by M. Svoboda et al. [15] deals with the measurement of vibrations on the stand of a roller conveyor. Acceleration and natural frequency were measured by using a three-axis accelerometer. In the conclusion of the article is an evaluation of vibration. Three the highest acceleration values in depending on the frequency of vibration in individual directions are given.

In many branches of industry, bulk materials are transported over short, medium and long transport distances using continuously working conveyor systems, the so-called belt conveyors [16,17,18]. The conveyor belt, see Figure 1, consists of a conveyor line 1 (assembled from steel assembled parts), which is fitted with conveyor rollers 2 [19] that support the conveyor belt 3 [20]. The endless loop of the conveyor belt circulates between two end drums. As a rule, on the upper surface of the conveyor belt, guided in the upper run of the belt conveyor [21], the conveyed material is transported towards the driving station.

On the drive drum of a conveyor belt driving station, the conveyor belt is carried away by frictional forces acting on the contact surface between the surface of the drive drum casing and the surface of the conveyor belt. The solution of the force ratios acting on the driving drums is based on the basic Euler (Eytelwein) relation [22,23]. The transmission capability [24,25] between the drive drum and the conveyor belt depends on the angle of wrap, the coefficient of friction between the belt and the drive drum, and the belt tension (which generates the tension force of the conveyor belt).

Belt conveyor drives must be designed in such a way that the belt on the driving drums does not slip in the individual movement phases (start-up, steady running, and run-down phases). It is possible to increase the transmission capacity of belt conveyor drives by a number of technical measures, including e. g. increasing the coefficient of friction between the belt and the drive drum, increasing the preload of the conveyor belt and increasing the angle of wrap (the implementation of two-drum and three-drum driving stations).

The disadvantage of both two-drum (Figure 2ab) and three-drum drives is that the working run of the conveyor belt touches the casings of the conveyor rollers in the return run of the belt conveyor. An insufficiently cleaned surface of a conveyor belt from the adhered grains of the transported material causes the material to stick to the casings of the conveyor rollers, see Figure 2c. These then vibrate as a result of the unbalanced mass when the rollers rotate.

In Figure 2a to Figure 2d, the red arrows indicate the working surface of the conveyor belt, i.e. the surface on which the conveyed material is carried in the working (upper) run of the conveyor belt. In the return run of the conveyor belt, this dirty surface of the conveyor belt meets the casings of the conveyor rollers [26]. Despite the intensive brushing of dirt and adhered material grains from the working surface of the conveyor belt with devices called cleaners [27,28,29,30], dirt often remains on the surfaces of the conveyor belts, which accumulates on the rotating casings of the conveyor rollers.

Authors J Eliasson et al. in article [31] they present an Internet of Things (IoT) architecture suitable for large scale sensor networks for condition monitoring. The developed technology has been applied and demonstrated for rotating conveyor belt rolls.

Authors R. Li et al. propose in the article [32] to use radial grating vibration sensing technology for both belt conveyor roller vibration monitoring. This can then be used to predict the fault state in the roller and its position, using distributed optical fibber temperature measurement technology which can be used for “hot spot monitoring”.

This paper [33] presents a recent review of acoustic and vibration signal-based fault detection for belt conveyor idlers using ML models. It also discusses major steps in the approaches, such as data collection, signal processing, feature extraction and selection, and ML model construction.

Article [34] by X Liu et al. describes a test device for detecting vibration of conveyor belt rollers.

Machine learning-based techniques for condition monitoring and fault diagnosis of industrial equipment were used in the paper [35] by authors J. Soares et al. Therefore, this paper presents a machine learning-based method for fault diagnosis in belt conveyor idlers.

2. Materials and Methods

The article is a follow-up to the article [9], in which the effective values of the vibration velocity v_RMS [m·s^-1] were measured in three mutually perpendicular planes of a rotating (circumferential speed v_r = 1.28 to 6.93 m·s^-1) conveyor roller (with the casing diameter of 133 mm). The effective values of the vibration velocity v_RMS [m·s^-1] were measured for two different fittings of the conveyor roller axles. One is the traditional placement of the flattened ends of the roller axle in the notches of the trestles, see Figure 3b on the fixed conveyor idler. The second way is to position these flattened ends of the roller axle in plastic brackets inserted into the specially designed steel trestles of the fixed conveyor idler.

The measurement of the effective values of vibration velocity v_RMS [m·s^-1] was done using a laboratory machine, see Figure 3a, which is located in a laboratory at the Department of Machine and Industrial Design, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava. This device was designed by DvB-AF s.r.o., with its registered office at Meleček 227, 747 41 Hradec nad Moravicí, Žimrovice. A laboratory stand designed to measure the noise of a rotating roller is described in [36,37].

Researches on idlers were rather focused on rolling resistance, their energy consumption, load distribution, and failure analysis until now [38,39,40,41].

A 3D structural model of a laboratory machine created in SolidWorks®Premium 2012x64, SP5 is shown in Figure 3. The laboratory machine consists of a steel frame 1, to which a vertically sliding drive support frame is mechanically attached 7, see Figure 3c. The supporting device of the electric motor 8 is attached to the supporting frame of the drive 7, to which the electric motor is attached by screw connections (type 1AL90L-4, power engine P_e = 1.5 kW, revolutions n_e = 1445 min^-1). A V-belt pulley with a calculated diameter of d_w = 81.5 mm, is positioned onto the shaft of an electric ϕ 24 mm (with a tight key 8 x 7 x 40 mm). This pulley transmits the pulling force of the drive by friction to one (or two) V-belts 5 [42] (type SPZ 2500 Lw 9.7 x 2513 La L=L). The revolutions of the electric motor n_e [min^-1] is controlled by an electric inverter (type YASKAWA VS-606 V7).

Laboratory measurements were carried out on conveyor rollers with various diameters D_r [mm] (133, 108 and 89), at the same circumferential speeds v_r [m·s^-1] of their casings.

In Table 1, it is possible to read the required circumferential speed v_r [m·s^-1] of the conveyor roller, the required revolutions n_r [min^-1] of a roller with diameter D_r [m] and frequency f_i [Hz], by which the revolutions n_r [min^-1] of a conveyor roller is controlled by a frequency converter.

The theoretical magnitude of rotational speed n_r [m·s^-1] of the conveyor roller with diameter D_r [m] can be expressed based on knowing the transmission ratio i_w [-] and the constant c_i [-] according to the relation (3). The transmission ratio i_w [-] is defined by the ratio of the calculated diameter of the drive pulley d_w [m] and the diameter of the driven pulley D_w [m]. The constant c_i [-] expresses the ratio of the frequency value of f = 50 Hz (in Europe a unified distribution grid of 400/230V with a frequency of 50 Hz is used. In North America, it is a phase distribution system of 120V at a frequency of 60 Hz) and the frequency f_i [Hz] set on the display of the frequency converter.

n_{r} {= n}_{e} \cdot i_{w} \cdot c_{i} {= n}_{e} \cdot \frac{d_{w}}{D_{w}} \cdot \frac{f}{f_{i}} {[s}^{- 1}]

(3)

One or two so-called “V-belt pulley assembly” units are placed onto the tested conveyor roller (with a steel, plastic or rubberized casing) with a diameter of D_r = 133 mm (or 108 mm or 89 mm), see Figure 4a. This assembly consists of a flange 2, with screw connections 3 attaching a pulley 1 with the calculated diameter of D_w = 153 mm. Prevention of this flange displacement 2 along the length of the conveyor roller casing, and prevention of flange rotation in relation to the circumference of the conveyor roller casing, is secured via screw connections 4.

An electric motor [43], on the shaft of which a V-belt is slid (calculated diameter d_w = 81.5 mm), sets the V-belt into motion [42]. The V-belt rotates the test conveyor roller at a revolution n_r [min^-1], corresponding to the circumferential velocity v_r [m·s^-1] of the conveyor roller, see Table 1.

The design dimensions of flange 2 slid onto the ϕ108 mm conveyor roller is shown in Figure 5b, and the design dimensions of flange 2 slid onto the ϕ89 mm conveyor roller is shown in Figure 5e.

Steel casing, see Figure 6a, or rubberized, see Figure 6b, conveyor roller (ϕ133, ϕ108 or ϕ89 mm) rotates relative to the stable axle of the roller ϕ20 mm on 2 pcs of radial ball bearings 6204-2RS [44].

In the article [45] the authors M. Vasić et al. analysed failures of belt conveyor tension roller bearings. The article also examines the effects of tensioner pulley mounting position on bearing damage.

Plastic casing, see Figure 7a, of the conveyor roller (ϕ133, ϕ108 or ϕ89 mm) rotates relative to the roller axle ϕ20 mm on 2 radial ball bearings 6204-2RS [44].

The axle of the tested conveyor roller is inserted into a cut-out in the steel (Figure 3b) or plastic (Figure 8d) trestle of the fixed conveyor idler, which is screwed to the top surface of the steel frame of the laboratory machine (Figure 3).

The vibrations generated by the rotating conveyor roller, transmitted to the sleeper of the fixed roller idler and the steel frame of the laboratory machine, were detected by two acceleration sensors PCE KS903.10 [46], see Figure 9. Signals from acceleration sensors were recorded by Dewesoft SIRIUSi-HS 6xACC, 2xACC+ [47] measuring apparatus during experimental measurements. Time records of the measured vibration values were used by the Dewesoft X [48] measuring program and transformed into effective vibration velocity values v_(*)RMS(fi) [mm·s^-1] in the range of 10÷1·10⁴ Hz (this frequency range is applied in the ISO 10816-3 standard [49]). Effective velocity values v_(*)RMS(fi) [mm·s^-1] (where * presents the x, y or z axis of the coordinate system) with periodic courses were displayed using a PS monitor in the environment of the Dewesoft X measuring software.

The speed of the conveyor roller was scanned by an optical laser sensor DS-TACHO-3 [50,51].

3. Results

The aim of this paper is to specify an academic contribution, which is one of the possible recommendations to reduce the vibrations transmitted to the supporting structure of the belt conveyor excited by the rotating casing of the conveyor roller.

Experimental measurements of vibration velocities v_(*)RMS(fi) [mm·s^-1] for a rotating conveyor roller with a diameter D_r [mm] were done using a laboratory machine, see Figure 3, under the same technical conditions, on two types of fixed conveyor idlers (where basic dimensions comply with the standard CSN ISO 1537 [52]), see Figure 10a. The fixed roller idler support consists of rollers with diameter D_r [mm], with their axles firmly embodied in the cut-outs of trestles 1, placed on a sleeper 2 made of a tube with a circular cross-section.

Interventionary studies involving animals or humans, and other studies that require ethical approval, must list the authority that provided approval and the corresponding ethical approval code.

The experimental measurement of vibration velocities v_(*)RMS(fi) [mm·s^-1] was carried out in a central roller (horizontally placed roller in a fixed idler), see Figure 10a, of our laboratory machine. A conveyor roller of a given diameter D_r [mm] fitted with a V-belt pulley assembly, see Figures 4a and 5a,d, was rotated by means of a V-belt [42] with revolutions n_r [min^-1] (see Table 1). Using two acceleration sensors [46] the vibrations of the rotating conveyor roller positioned in the trestle were detected (B or D), see Figure 11, in the fixed conveyor idler and at the point of the mechanical attachment of the roller support to the upper beam of the steel frame of the laboratory machine (A or C), see Figure 11.

3.1. The plastic Trestle of a Fixed Conveyor idler, the Plastic Casing of the Conveyor Roller

Table 3 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 89 mm plastic casing at the measuring points A and B for a fixed conveyor idler with plastic brackets (Figure 8) of our laboratory machine (Figure 11).

Figure 12 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 3.84 m·s^-1 for a conveyor roller with a plastic casing of 89 mm diameter.

With regard to the scope of the paper, the measured graphs of the effective values of vibration velocities v_(*)RMS(fi) [mm·s^-1] are not presented in this paper for circumferential speeds v_r = 2.5 m·s^-1 and v_r = 1.25 m·s^-1 for conveyor rollers with a diameter of 89 mm. In case of interest in these measured vibration waveforms, the author of this paper can supply the measured data sets with the graphic records of the measured vibration values for the conveyor rollers (with a steel or plastic casing), whose axles are placed in plastic brackets, Figure 10c, or on a steel trestle, Figure 10b, of the fixed conveyor idler.

Table 4 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 89 mm plastic casing at the measuring points C and D for a fixed conveyor idler with plastic brackets.

Figure 13 shows the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in three mutually perpendicular axes of the coordinate system (Figure 11) at circumferential speed v_r = 3.84 m·s^-1 of the conveyor roller with a plastic casing diameter 89 mm. Vibration sensors have been placed at measuring points C and D.

Table 5 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 89 mm plastic casing at the measuring points C and D for a fixed conveyor idler with plastic brackets.

Figure 14 shows the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in three mutually perpendicular axes of the coordinate system (Figure 11) at circumferential speed v_r = 2.5 m·s^-1 of the conveyor roller with a plastic casing diameter 108 mm. Vibration sensors have been placed at measuring points A and B.

In this paper, the measured graphs of the effective values of vibration velocities v_(*)RMS(fi) [mm·s^-1] are not presented for the circumferential speeds of the conveyor rollers (with diameter 108 mm and 133 mm.) other than v_r = 2.5 m·s^-1. As mentioned above, if you are interested in these measured vibration waveforms, it is necessary to ask the authors of this article via e-mail for documentation of the measured vibration records of the conveyer rollers taken at various circumferential speeds v_r [m·s^-1].

Figure 15 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a plastic casing of 108 mm diameter.

Table 7 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm plastic casing at the measuring points A and B for a fixed conveyor idler with plastic brackets.

Figure 16 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a plastic casing of 133 mm diameter.

Table 8 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm plastic casing at the measuring points C and D for a fixed conveyor idler with plastic brackets.

Figure 17 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a plastic casing of 133 mm diameter.

3.2. The Plastic Trestle of a Fixed Conveyor Idler, the Steel Casing of the Conveyor Roller

Table 9 displays the effective vibration velocity values v_(*)RMS(fi) [mm·s^-1] that were read from the DEWESoft X measurement software provided for the vibration measurements of a steel casing roller with a diameter of 89 mm. These were taken in measuring points A and B of the conveyor idler with plastic brackets on our laboratory device.

Figure 18 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 3.84 m·s^-1 for a conveyor roller with a steel casing of 89 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 10 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 89 mm steel casing at the measuring points C and D for a fixed conveyor idler with plastic brackets.

Figure 19 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 3.84 m·s^-1 for a conveyor roller with a steel casing of 89 mm diameter. Vibration sensors have been placed at measuring points C and D.

Table 11 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 108 mm steel casing at the measuring points A and B for a fixed conveyor idler with plastic brackets.

Figure 20 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a steel casing of 108 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 12 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 108 mm steel casing at the measuring points C and D for a fixed conveyor idler with plastic brackets.

Figure 21 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a steel casing of 108 mm diameter. Vibration sensors have been placed at measuring points C and D.

Table 13 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm steel casing at the measuring points A and B for a fixed conveyor idler with plastic brackets.

Figure 22 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a steel casing of 133 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 14 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm steel casing at the measuring points C and D for a fixed conveyor idler with plastic brackets.

3.3. The steel Trestle of the Fixed Conveyor Idler, the Plastic Casing of the Conveyor Roller

Table 15 lists the effective vibration velocity values v_(*)RMS(fi) [mm·s^-1] that were read from the DEWESoft X measurement software for the vibration values of a conveyor roller with a diameter of 89 mm plastic casing taken in measuring points A and B of a fixed conveyor idler with steel trestles, see Figure 10a, of the laboratory device (Figure 11).

Figure 24 shows the measured RMS values for the vibration velocity v_(*)RMS(50) [mm·s^-1] in axes “x“, “y“ and “z“ for the selected coordinate system at circumferential speed v_r = 3.84 m·s^-1 of the conveyor roller with a plastic casing with an 89 mm diameter. With regard to the scope of the paper, the measured graphs of the effective values of vibration velocities v_(*)RMS(fi) [mm·s^-1] are not presented in this paper for circumferential speeds v_r = 2.5 m·s^-1 and v_r = 1.25 m·s^-1.

Table 16 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 89 mm plastic casing at the measuring points C and D for a fixed conveyor idler with steel brackets.

Figure 25 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 3.85 m·s^-1 for a conveyor roller with a plastic casing of 89 mm diameter. Vibration sensors have been placed at measuring points C and D.

Table 17 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 108 mm plastic casing at the measuring points A and B for a fixed conveyor idler with steel brackets.

Figure 26 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a plastic casing of 108 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 18 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 108 mm plastic casing at the measuring points C and D for a fixed conveyor idler with steel brackets.

Figure 27 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a plastic casing of 108 mm diameter. Vibration sensors have been placed at measuring points C and D.

Table 19 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm plastic casing at the measuring points A and B for a fixed conveyor idler with steel brackets.

Figure 28 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a plastic casing of 133 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 20 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm plastic casing at the measuring points A and B for a fixed conveyor idler with steel brackets.

Figure 29 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a plastic casing of 133 mm diameter. Vibration sensors have been placed at measuring points C and D.

3.4. The steel Trestle of the Fixed Conveyor Idler, the Steel Casing of the Conveyor Roller

Table 21 lists the effective vibration velocity values v_(*)RMS(fi) [mm·s^-1] that have been read from the DEWESoft X software for the vibration values measured on the 89 mm diameter conveyor roller with the steel casing at the measuring points A and B of the fixed conveyor idler. The flattened ends of the conveyor roller axle are supported in the steel trestles of the fixed conveyor idler.

Figure 30 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 3.84 m·s^-1 for a conveyor roller with a steel casing of 89 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 22 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 89 mm steel casing at the measuring points A and B for a fixed conveyor idler with steel brackets.

Figure 31 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 3.84 m·s^-1 for a conveyor roller with a steel casing of 89 mm diameter. Vibration sensors have been placed at measuring points C and D.

Table 23 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 108 mm steel casing at the measuring points A and B for a fixed conveyor idler with steel brackets.

Figure 32 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a steel casing of 108 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 24 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 108 mm steel casing at the measuring points C and D for a fixed conveyor idler with steel brackets.

Figure 33 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a steel casing of 108 mm diameter. Vibration sensors have been placed at measuring points C and D.

Table 25 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm steel casing at the measuring points A and B for a fixed conveyor idler with steel brackets.

Figure 34 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a steel casing of 133 mm diameter. Vibration sensors have been placed at measuring points A and B.

Table 26 indicates effective vibration velocity values v_(*)RMS(fi) [mm·s^-1], which have been read from the DEWESoft X measurement software, for the vibration measurements of a conveyor roller with a diameter of 133 mm steel casing at the measuring points A and B for a fixed conveyor idler with steel brackets.

Figure 35 indicates the measured effective values of the vibration speed v_(*)RMS(50) [mm·s^-1] in the “x“, “y“ and “z“ axes of the selected coordinate system at circumferential speed v_r = 2.5 m·s^-1 for a conveyor roller with a steel casing of 133 mm diameter. Vibration sensors have been placed at measuring points C and D.

4. Discussion

The aim of this paper was to detect vibrations transmitted by the rotating casing of the conveyor roller to the fixed conveyor idler and also to the steel frame of the laboratory machine to which the fixed conveyor idler is attached. The measurement of the vibrations of the roller casing installed on a laboratory stand, and an assessment of the technical condition of the belt conveyor rollers after the specified operating time, were also carried out in [33]. In the conclusions of the vibrations measurement of the conveyor roller done by both laboratory machines similar results were achieved.

From the measured time curves of the vibration value (see Figure 12 to Figure 35) for conveyor rollers of 89 mm, 108 mm and 133 mm diameters rotating at circumferential speeds 1.25, 2.5 and 3.85 m·s^-1, with the help of the DEWESoft X software, the effective values for vibration velocities were determined, and these are listed in Table 3 to Table 26.

The vibration values of the conveyor rollers show that the effective values of the vibration velocity increase with the increasing speed (circumferential speed) of the conveyor roller casings. This assumption is confirmed in the findings presented in the article [9] by Klimenda et al., who deal in their article [11] with the measurement of the noise and vibration of rollers designed for belt conveyors. The three highest acceleration values depending on the frequency of the vibration in each direction (x, y, z) correspond to the measured effective vibration values v_(*)RMS(fi) [mm·s^-1] in coordinate axes (x, y, z). For more information, see Chapters 3.1 to 3.4.

Figure 36(c) and Figure 36(d) show that the highest effective values of the vibration velocity v_(*)RMS(fi) [mm·s^-1] reach the conveyor roller with ϕ89 mm diameter placed in the steel trestle of a fixed conveyor idler, and that is in the “z“ axis (vertical direction). This fact can be traced in the article [12], in which the three highest values of acceleration depending on the frequency of vibration in each direction are described.

At the revolutions of the steel casing conveyor roller n_r = 825 mim^-1 and the roller axle placement of the conveyor with a 89 mm diameter into plastic brackets (see Figure 11 part B), the effective value of the vibration velocity is v_(*)RMS(fi) [mm·s^-1] in axis “z“ is reaching 37.4 % of the value v_(*)RMS(fi) [mm·s^-1], compared to placing this roller in a steel trestle.

When the axle of the steel conveyor roller ϕ89 mm is fitted into the plastic brackets (see Figure 11 part D), the effective value of the vibration velocity v_(*)RMS(fi) [mm·s^-1] in the “z“ axis reaches 40 % of value v_(*)RMS(fi) [mm·s^-1], unlike when placed in a steel trestle.

Figure 37c,d show that the highest effective values of the vibration velocity v_(*)RMS(fi) [mm·s^-1] reach the conveyor roller with ϕ108 mm diameter placed in the steel trestle of a fixed conveyor idler, and that is in the “z“ axis (vertical direction).

At the revolutions of the steel casing conveyor roller n_r = 442 mim^-1 and the roller axle placement of the conveyor with a 108 mm diameter into plastic brackets (see Figure 11 part B), the effective value of the vibration velocity is v_(*)RMS(fi) [mm·s^-1] in axis “z“ is reaching 41.9 % of the value v_(*)RMS(fi) [mm·s^-1], compared to placing this roller in a steel trestle.

When the axle of the steel conveyor roller ϕ108 mm is fitted into the plastic brackets (see Figure 11 part D), the effective value of the vibration velocity v_(*)RMS(fi) [mm·s^-1] in the “z“ axis reaches 46.9 % of value v_(*)RMS(fi) [mm·s^-1], unlike when placed in a steel trestle.

From Figure 38c,d, it is clear that the biggest differences in the effective values of the vibration velocity v_(*)RMS(fi) [mm·s^-1] are reached by the conveyor rollers with a 133 mm diameter, when these are placed in the fixed trestle of a conveyor idle, and these are reached in the “z“ axis direction (vertical direction).

At the revolutions of the steel casing conveyor roller n_r = 361 mim^-1 and the roller axle placement of the conveyor with a 108 mm diameter into plastic brackets (see Figure 11 part B), the effective value of the vibration velocity is v_(*)RMS(fi) [mm·s^-1] in axis “z“ is reaching 66.7 % of the value v_(*)RMS(fi) [mm·s^-1], compared to placing this roller in a steel trestle.

When the axle of the steel conveyor roller ϕ133 mm is fitted into the plastic brackets (see Figure 11 part D), the effective value of the vibration velocity v_(*)RMS(fi) [mm·s^-1] in the “z“ axis reaches 57.5 % of value v_(*)RMS(fi) [mm·s^-1], unlike when placed in a steel trestle.

In Figure 39, we can see the effective vibration values v_(*)RMS(fi) [mm·s^-1] for the rotating conveyor rollers measured in the points A to D, of which the plastic or steel casing of a 133 mm diameter rotates at circumferential speed of v_r = 5.74 (3.84, 2.5 or 1.25) m·s^-1, provided that the flattened ends of the conveyor roller axles are fitted into the steel or plastic trestle of the fixed conveyor idler.

Graphs (a) to (d) show that the effective vibration values v_(*)RMS(fi) [mm·s^-1] of the rotating conveyor rollers reach the highest values at higher frequencies set on the frequency converter (the speed of the driving electric motor was controlled by a frequency converter) corresponding to the revolutions of the conveyor rollers.

Research by K. Hicke at al. [53] focuses on monitoring the acoustic condition and detection of roller faults in industrial conveyor belts.

Graphs (a) to (d) also show that higher effective vibration values v_(*)RMS(fi) [mm·s^-1] that were measured in points A to D, in the case when the axles of the conveyor rollers were placed in a steel trestle (green and blue curves) than when the axles of the conveyor rollers were positioned in plastic brackets (purple and red colour curves).

In Figure 40, we can see the effective vibration values v_(*)RMS(fi) [mm·s^-1] for the rotating conveyor rollers measured in the points A to D, of which the plastic or steel casing of a 108 mm diameter rotates at circumferential speed of v_r = 4.66 (3.84, 2.5 or 1.25) m·s^-1, provided that the flattened ends of the conveyor roller axles are fitted into the steel or plastic trestle of the fixed conveyor idler.

In Figure 41, we can see the effective vibration values v_(*)RMS(fi) [mm·s^-1] for the rotating conveyor rollers measured in the points A to D, of which the plastic or steel casing of a 89 mm diameter rotates at circumferential speed of v_r = 3.84 (2.5 or 1.25) m·s^-1, provided that the flattened ends of the conveyor roller axles are fitted into the steel or plastic trestle of the fixed conveyor idler.

The provided vibration measurements of the rotating conveyor rollers with their axles fitted in the steel or plastic trestles of the fixed conveyor idler, performed on the non-rotating parts of our laboratory machine is sufficient to appropriately characterize operating conditions with regard to trouble-free operation. Measurements were made with regard to ISO 10816-1 [6], which specifies the general conditions and procedures for the measurement and evaluation of vibration by means of measurements carried out on non-rotating parts. The general evaluation criteria, which are presented in the form of both magnitude and vibration change, apply to both in-service monitoring and acceptance tests. The criteria were set primarily with regard to ensuring the reliable, safe and long-term operation of the machine (i.e., a belt conveyor) while minimizing the adverse effects on the connected equipment.

Vibrations lead to fatigue failure or damage which is harmful to engine supporting structures [54].

5. Conclusions

This paper presents a design solution of an experimental machine on which the vibrations of a rotating casing of a conveyor roller can be detected in laboratory conditions. The laboratory machine was created to confirm the theoretical assumption that the magnitude of vibration decreases when the axles of the conveyor roller are placed in plastic brackets. These plastic brackets were attached to the structurally modified trestles of a fixed conveyor idler. This theoretical assumption stated in the article was proved.

The authors of the article carried out experimental measurements based on the measurement of the vibrations of the rotating conveyor roller on the non-rotating parts, i.e., on the trestle of the fixed conveyor idler and in the place of the mechanical attachment of the conveyor idler to the steel frame of the laboratory machine. Vibrations were detected by acceleration sensors, recorded by a measuring apparatus and displayed on a PC monitor in the environment of Dewesoft X software. With the help of software, the measured vibration values were converted into the effective values of the vibration speed, and these were recorded in tables (see Table 3 ÷ Table 26).

The measured instantaneous values of the vibrations at time t [s] were presented in graphs (see Figure 12 ÷ Figure 35). Due to the limited space for the article, in Chapter “3. Results“ only the selected measurements records are presented (In case of interest, all records are available from the authors of the article).

The article also describes the design modification of the fixed conveyor idler, the result of which is the installation of plastic brackets in the places where the flattened end parts of the conveyor roller axles are inserted into the notches created in the steel trestle of the traditional fixed conveyor idler. This modified fixed conveyor idler is characterized by two plastic brackets with notches, into which the flattened end parts of the conveyor roller axles are inserted.

The evaluation of the measured data made it possible to conclude that the use of plastic brackets can reduce the vibration values transmitted from the rotating casings of the conveyor rollers into the supporting structure of the belt conveyor. Vibrations generated by the rotating casings of the conveyor rollers in industrial plants with their casings covered with dirt produce excessive secondary noise, which is undesirable in the production hall.

Vibrations and noise are adversely manifested with the higher speed of the conveyor belt, which corresponds directly to the higher revolutions and circumferential speed of the conveyor rollers.

Author Contributions

Conceptualization, L.H. and S.P.; methodology, L.H.; software, S.P.; validation, E.N., T.M. and D.K.; formal analysis, L.H.; investigation, L.H.; resources, D.K.; data curation, E.N.; writing—original draft preparation, L.H.; writing—revie and editing, L.H.; visualization, L.H. and E.N.; supervision, T.M.; project administration, L.H.; funding acquisition, L.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by “Research and innovation of modern processes and technologies in industrial practice”, grant number SP2023/003” and was funded by MŠMT ČR (Ministry of education youth and sports).

Data Availability Statement

Measured data of effective vibration speed values v_(*)RMS(fi) [mm·s^-1], listed from Table 3 to Table 26 and processed using DEWESoft X software, can be sent in case of interest, by prior written agreement, in *.XLSX (Microsoft Excel) format.

Acknowledgments

In this section, you can acknowledge any support given which is not covered by the author contribution or funding sections. This may include administrative and technical support, or donations in kind (e.g., materials used for experiments).

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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Figure 1. The endless loop of a conveyor belt supported by conveyor rollers.

Figure 2. Two-drum driving station (a) type Ω, (b) type C, (c) without a boom, (d) type S, (e) transported material stuck on the casing of the conveyor roller. 1—conveyor roller, 2—drive drum, 3—dump drum, 4—transmission drum, 5—conveyor belt.

Figure 3. (a) Structural 3D design of a laboratory machine—front view, (b) conveyor roller placed in the trestle of a fixed conveyor idler, (c) drive frame, (d) laboratory machine—rear view. 1—steel frame, 2—fixed conveyor idler, 3—conveyor roller, 4—driven pulley, 5—V-belt, 6—plastic bracket, 7—drive support frame, 8—electric motor support device.

Figure 4. (a) A 3D model of V-belt pulley assembly, (b) the dimensions of the pulley, (c) the dimensions of the flange for the conveyor roller ϕ133 mm, (d) manufactured V-belt pulley assembly. 1—V-belt pulley, 2—flange, 3—screw M4x16 DIN 912, 4—screw M4x10 DIN 912.

Figure 5. (a) A 3D model of the V-belt pulley assembly, (b) flange dimensions for ϕ108 mm conveyor roller, (c) manufacture V-belt pulley assembly, (d) a 3D model of the V-belt pulley assembly, (e) flange dimensions for ϕ89 mm conveyor roller, (f) manufactured V-belt pulley assembly. 1—V-belt pulley, 2—flange, 3—screw M4x16 DIN 912, 4—screw M4x25 DIN 912 (screw M4x35 DIN 933).

Figure 6. Conveyor roller (a) steel, (b) rubberized, (c) a 3D model of a conveyor roller fitted with two pieces V-belt pulley assembly. 1—V-belt pulley, 2—flange, 3—screw M4x16 DIN 912, 4—screw M4x10 (25) DIN 912 (M4x35 DIN 933), 5—conveyor roller ϕ133 mm (or ϕ108 mm or ϕ89 mm).

Figure 7. (a) plastic conveyor roller, (b) conveyor roller fitted with two pieces of a V-belt pulley assembly, (c) roller axle placed in a plastic bracket. 1—V-belt pulley, 2—flange, 3—screw M4x16 DIN 912, 4—screw M4x10 (25) DIN 912 (M4x35 DIN 933), 5—conveyor roller ϕ133 mm (or ϕ108 mm, or ϕ89 mm), 6—plastic bracket to hold the roller axles.

Figure 8. Plastic bracket for the conveyor roller axle inserted into a modified trestle of a fixed roller idler (a) 3D structural design, (b) 3D structural design, (c) the implemented solution of the plastic bracket, plastic holder, (d) conveyor roller mounted in the trestle of a fixed roller idler. 1—conveyor roller, 2—plastic bracket.

Figure 9. Measuring chain for detecting and recording the vibrations of rotating rollers on a laboratory machine.

Figure 10. (a) fixed conveyor idler—basic dimensions (in Table 2), (b) roller support with traditional trestles, (c) conveyor idler with plastic brackets in trestles. 1—trestle, 2—sleeper, 3—plastic bracket.

Figure 11. (a) A laboratory machine used to measure the vibrations of the conveyor rollers; (b) measuring points A, B, C, and D on a fixed conveyor idler where accelerometers are placed.

Figure 12. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ89 mm, the circumferential speed of the roller v_r = 3.84 m·s^-1, plastic trestle, (a) measuring point A, (b) measuring point B.

Figure 13. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ89 mm, the circumferential speed of the roller v_r = 3.84 m·s^-1, plastic trestle, (a) measuring point C, (b) measuring point D.

Figure 14. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point A, (b) measuring point B.

Figure 15. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point C, (b) measuring point D.

Figure 16. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point A, (b) measuring point B.

Figure 17. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point C, (b) measuring point D.

Figure 18. Effective vibration values v_(*)RMS(fi) [mm·s^-1], stell roller ϕ89 mm, the circumferential speed of the roller v_r = 3.84 m·s^-1, plastic trestle, (a) measuring point A, (b) measuring point B.

Figure 19. Effective vibration values v_(*)RMS(fi) [mm·s^-1], stell roller ϕ89 mm, the circumferential speed of the roller v_r = 3.84 m·s^-1, plastic trestle, (a) measuring point C, (b) measuring point D.

Figure 20. Effective vibration values v_(*)RMS(fi) [mm·s^-1], stell roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point A, (b) measuring point B.

Figure 21. Effective vibration values v_(*)RMS(fi) [mm·s^-1], stell roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point C, (b) measuring point D.

Figure 22. Effective vibration values v_(*)RMS(fi) [mm·s^-1], stell roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point A, (b) measuring point B.

Figure 23. Effective vibration values v_(*)RMS(fi) [mm·s^-1], stell roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, plastic trestle, (a) measuring point C, (b) measuring point D.

Figure 24. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ89 mm, the circumferential speed of the roller v_r = 3.85 m·s^-1, steel trestle, (a) measuring point A, (b) measuring point B.

Figure 25. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ89 mm, the circumferential speed of the roller v_r = 3.85 m·s^-1, steel trestle, (a) measuring point C, (b) measuring point D.

Figure 26. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point A, (b) measuring point B.

Figure 27. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point C, (b) measuring point D.

Figure 28. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point A, (b) measuring point B.

Figure 29. Effective vibration values v_(*)RMS(fi) [mm·s^-1], plastic roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point C, (b) measuring point D.

Figure 30. Effective vibration values v_(*)RMS(fi) [mm·s^-1], steel roller ϕ89 mm, the circumferential speed of the roller v_r = 3.84 m·s^-1, steel trestle, (a) measuring point A, (b) measuring point B.

Figure 31. Effective vibration values v_(*)RMS(fi) [mm·s^-1], steel roller ϕ89 mm, the circumferential speed of the roller v_r = 3.85 m·s^-1, steel trestle, (a) measuring point C, (b) measuring point D.

Figure 32. Effective vibration values v_(*)RMS(fi) [mm·s^-1], steel roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point A, (b) measuring point B.

Figure 33. Effective vibration values v_(*)RMS(fi) [mm·s^-1], steel roller ϕ108 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point C, (b) measuring point D.

Figure 34. Effective vibration values v_(*)RMS(fi) [mm·s^-1], steel roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point A, (b) measuring point B.

Figure 35. Effective vibration values v_(*)RMS(fi) [mm·s^-1], steel roller ϕ133 mm, the circumferential speed of the roller v_r = 2.5 m·s^-1, steel trestle, (a) measuring point C, (b) measuring point D.

Figure 36. The effective vibration values v_(*)RMS(fi) [mm·s^-1] of conveyor rollers with a 89 mm diameter, at revolutions 825 min^-1. Measuring point as in Figure 11 (a) A, (b) C, (c) B, (d) D.

Figure 37. The effective vibration values v_(*)RMS(fi) [mm·s^-1] of conveyor rollers with a 108 mm diameter, at revolutions 442 min^-1. Measuring point as in Figure 11 (a) A, (b) C, (c) B, (d) D.

Figure 38. The effective vibration values v_(*)RMS(fi) [mm·s^-1] of conveyor rollers with a 133 mm diameter, at revolutions 361 min^-1. Measuring point as in Figure 11 (a) A, (b) C, (c) B, (d) D.

Figure 39. The effective vibration values v_(*)RMS(fi) [mm·s^-1] of ϕ133 mm conveyor rollers at different revolutions. Measuring point as in Figure 11 (a) B, (b) D, (c) A, (d) C.

Figure 40. The effective vibration values v_(*)RMS(fi) [mm·s^-1] of ϕ108 mm conveyor rollers at different revolutions. Measuring point as in Figure 11 (a) B, (b) D, (c) A, (d) C.

Figure 41. The effective vibration values v_(*)RMS(fi) [mm·s^-1] of ϕ89 mm conveyor rollers at different revolutions. Measuring point as in Figure 11 (a) B, (b) D, (c) A, (d) C.

Table 1. Calculated values of the rotational speed n_r [min^-1] of a conveyor roller with a given diameter D_r [m] for circumferential speed v_r [m·s^-1] of the conveyor roller casings.

D_r [mm]	89			108				133
f_i [Hz]	v_r [m·s^-1]	n_r [s^-1]	n_r [min^-1]	f_i [Hz]	v_r [m·s^-1]	n_r [s^-1]	n_r [min^-1]	f_i [Hz]	v_r [m·s^-1]	n_r [s^-1]	n_r [min^-1]
50	3.58	12.81	768.7	50	4.35	12.82	769.2	50	5.35	12.80	768.3
34.9	2.5	8.94	536.5	41.2	3.58	10.55	633.1	33.4	3.58	10.41	624.7
17.4	1.25	4.47	268.2	28.8	2.5	7.37	442.1	23.4	2.5	5.98	359.0
-	-	-	-	14.4	1.25	3.68	221.0	11.7	1.25	2.99	179.5

Table 2. Basic dimensions of the conveyor idler according to [52].

	E	D = D_r	L	a	b	t	o	s	h	f	α	weight
[mm]											[deg]	[kg]
1200	1600	89, 108, 133	465	35	140	100	18	14	85	175	20	18.5

Table 3. Roller axle placement—plastic trestle, measuring points A and B, roller casing—plastic, D_r = 89 mm.

f_i	n_r	v_r	Measuring point „A“			Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]			[mm·s^-1]
50	825	3.84	0.93 ¹	0.31 ¹	0.21 ¹	0.47 ²	0.17 ²	0.92 ²
32.5	536	2.50	0.23	0.21	0.10	0.52	0.14	0.62
16.2	268	1.25	0.14	0.10	0.07	0.14	0.08	0.22

¹ see Figure 12a, ² see Figure 12b.

Table 4. Roller axle placement—plastic trestle, measuring points C and D, roller casing—plastic, D_r = 89 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]			[mm·s^-1]
50	825	3.84	0.87 ¹	0.25 ¹	0.13 ¹	0.40 ²	0.14 ²	0.93 ²
32.4	535	2.49	1.61	0.20	0.12	1.03	0.12	0.65
16.2	267	1.25	0.12	0.12	0.08	0.26	0.06	0.23

¹ see Figure 13a, ² see Figure 13b.

Table 5. Roller axle placement—plastic trestle, measuring points A and B, roller casing—plastic, D_r = 108 mm.

f_i	n_r	v_r	Measuring point “A”			Measuring point “B”
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	824	4.66	0.92	0.26	0.25	0.46	0.22	0.70
41.3	681	3.85	0.88	0.36	0.22	0.53	0.29	1.03
26.8	442	2.5	0.60 ¹	0.14 ¹	0.13 ¹	0.25 ²	0.10 ²	0.34 ²
13.4	220	1.24	0.09	0.08	0.06	0.08	0.05	0.17

¹ see Figure 14a, ² see Figure 14b.

Table 6. Roller axle placement—plastic trestle, measuring points C and D, roller casing—plastic, D_r = 108 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	824	4.66	0.55	0.23	0.11	0.36	0.21	0.72
41.3	681	3.85	0.52	0.33	0.09	0.41	0.26	0.96
26.8	442	2.5	0.56 ¹	0.12 ¹	0.07 ¹	0.21 ²	0.09 ²	0.34 ²
13.4	220	1.24	0.11	0.06	0.06	0.09	0.10	0.15

¹ see Figure 15a, ² see Figure 15b.

Table 7. Roller axle placement—plastic trestle, measuring points A and B, roller casing—plastic, D_r = 133 mm.

f_i	n_r	v_r	Measuring point „A“			Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	824	5.74	0.70	0.37	0.21	0.51	0.29	0.89
33.7	555	3.86	0.46	0.36	0.15	0.50	0.28	0.85
21.8	360	2.51	0.20 ¹	0.21 ¹	0.09 ¹	0.24 ²	0.13 ²	0.58 ²
10.9	179	1.25	0.07	0.11	0.06	0.10	0.08	0.18

¹ see Figure 16a, ² see Figure 16b.

Table 8. Roller axle placement—plastic trestle, measuring points C and D, roller casing—plastic, D_r = 133 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	825	5.75	0.46	0.46	0.19	0.66	0.43	1.11
33.7	555	3.86	0.73	0.35	0.11	0.55	0.34	0.88
21.8	360	2.50	0.18 ¹	0.20 ¹	0.09 ¹	0.27 ²	0.13 ²	0.68 ²
10.9	179	1.25	0.08	0.09	0.06	0.10	0.08	0.19

¹ see Figure 17a, ² see Figure 17b.

Table 9. Roller axles placement—plastic trestle, measuring points A and B, roller casing—steel, D_r = 89 mm.

f_i	n_r	v_r	Measuring point “A”			Measuring point “B”
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)		v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	823	3.84	0.54 ¹	0.20 ¹	0.11 ¹		0.33 ²	0.36 ²	0.46 ²
32.3	533	2.48	1.93	0.46	0.16		1.32	0.60	0.56
16.1	266	1.24	0.22	0.10	0.08		0.24	0.12	0.21

¹ see Figure 18a, ² see Figure 18b.

Table 10. Roller axles placement—plastic trestle, measuring points C and D, roller casing—steel, D_r = 89 mm.

f_i	n_r	v_r	Measuring point “C”			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	823	3.84	1.09 ¹	0.18 ¹	0.26 ¹	0.43 ²	0.28 ²	0.46 ²
32.3	533	2.48	0.81	0.51	0.22	0.70	0.52	0.52
16.12	266	1.24	0.17	0.10	0.09	0.11	0.07	0.18

¹ see Figure 19a, ² see Figure 19b.

Table 11. Roller axles placement—plastic trestle, measuring points A and B, roller casing—steel, D_r = 108 mm.

f_i	n_r	v_r	Measuring point “A”			Measuring point “B”
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	826	4.67	0.75	0.24	0.15	0.39	0.19	0.48
41.4	682	3.86	0.36	0.31	0.12	0.32	0.18	0.56
26.84	442	2.5	0.60 ¹	0.11 ¹	0.07 ¹	0.20 ²	0.12 ²	0.32 ²
13.36	220	1.25	0.12	0.08	0.08	0.10	0.08	0.14

¹ see Figure 20a, ² see Figure 20b.

Table 12. Roller axles placement—plastic trestle, measuring points C and D, roller casing—steel, D_r = 108 mm.

f_i	n_r	v_r	Measuring point “C”			Measuring point “D”
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	826	4.67	1.40	0.20	0.31	0.38	0.19	0.44
41.34	681	3.85	1.27	0.25	0.28	0.61	0.19	0.52
26.85	443	2.5	0.67 ¹	0.14 ¹	0.15 ¹	0.26 ²	0.12 ²	0.30 ²
13.37	220	1.25	0.11	0.12	0.09	0.08	0.07	0.13

¹ see Figure 21a, ² see Figure 21b.

Table 13. Roller axles placement—plastic trestle, measuring points A and B, roller casing—steel, D_r = 133 mm.

f_i	n_r	v_r	Measuring point “A”			Measuring point “B”
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	825	5.75	0.47	0.24	0.11	0.35	0.24	0.55
33.64	554	3.86	0.64	0.17	0.10	0.48	0.18	0.37
21.92	361	2.52	0.23 ¹	0.12 ¹	0.07 ¹	0.21 ²	0.13 ²	0.26 ²
10.89	179	1.25	0.19	0.09	0.07	0.14	0.09	0.16

¹ see Figure 22a, ² see Figure 22b.

Table 14. Roller axles placement—plastic trestle, measuring points C and D, roller casing—steel, D_r = 133 mm.

f_i	n_r	v_r	Measuring point “C”			Measuring point “D”
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	825	5.75	0.49	0.24	0.18	0.27	0.19	0.48
33.67	555	3.87	0.32	0.18	0.17	0.30	0.14	0.31
21.87	361	2.51	0.21 ¹	0.11 ¹	0.14 ¹	0.13 ²	0.09 ²	0.23 ²
10.89	179	1.25	0.11	0.07	0.08	0.08	0.06	0.14

¹ see Figure 23a, ² see Figure 23b.

Table 15. Roller axles placement—steel trestle, measuring points A and B, roller casing—plastic, D_r = 89 mm.

f_i	n_r	v_r	Measuring point „A“			Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]			[mm·s^-1]
50	824	3.84	0.25 ¹	0.40 ¹	0.24 ¹	0.77 ²	0.24 ²	1.13 ²
32.33	533	2.48	0.92	0.25	0.17	1.02	0.14	0.81
16.14	266	1.24	0.09	0.14	0.15	0.28	0.13	0.32

¹ see Figure 24a, ² see Figure 24b.

Table 16. Roller axles placement—steel trestle, measuring points C and D roller casing—plastic, D_r = 89 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	826	3.85	0.28 ¹	0.37 ¹	0.15 ¹	0.77 ²	0.27 ²	1.04 ²
32.35	533	2.48	0.26	0.28	0.12	0.89	0.17	0.79
16.15	266	1.24	0.11	0.17	0.13	0.31	0.14	0.33

¹ see Figure 25a, ² see Figure 25b.

Table 17. Roller axles placement—steel trestle, measuring points A and B roller casing—plastic, D_r = 108 mm.

f_i	n_r	v_r	Measuring point „A“			Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	825	4.66	0.44	0.53	0.36	0.66	0.32	2.16
41.24	680	3.84	0.28	0.41	0.22	0.76	0.32	1.33
26.73	441	2.50	0.33 ¹	0.26 ¹	0.14 ¹	0.78 ²	0.20 ²	0.81 ²
13.34	220	1.24	0.08	0.13	0.06	0.17	0.10	0.32

¹ see Figure 26a, ² see Figure 26b.

Table 18. Roller axles placement—steel trestle, measuring points C and D roller casing—plastic, D_r = 108 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	823	4.65	0.58	0.86	0.23	0.61	0.45	2.54
41.29	681	3.85	0.66	0.48	0.18	0.76	0.40	1.30
26.68	440	2.49	0.35 ¹	0.24 ¹	0.11 ¹	0.63 ¹	0.18 ¹	0.64 ¹
13.35	220	1.24	0.08	0.13	0.06	0.14	0.09	0.32

¹ see Figure 27a, ² see Figure 27b.

Table 19. Roller axles placement—steel trestle, measuring points A and B roller casing—plastic, D_r = 133 mm.

f_i	n_r	v_r	Measuring point „A“			Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	825	5.75	0.44	0.66	0.41	0.76	0.41	2.31
33.48	552	3.84	0.46	0.43	0.20	0.57	0.38	0.97
21.83	360	2.51	0.13 ¹	0.25 ¹	0.14 ¹	0.35 ²	0.21 ²	0.61 ²
10.84	179	1.24	0.08	0.12	0.09	0.16	0.09	0.20

¹ see Figure 28a, ² see Figure 28b.

Table 20. Roller axles placement—steel trestle, measuring points C and D roller casing—plastic, D_r = 133 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	824	5.74	0.69	0.68	0.23	0.95	0.39	1.94
33.56	553	3.85	0.49	0.38	0.16	0.63	0.27	0.92
21.84	360	2.51	0.18 ¹	0.23 ¹	0.12 ¹	0.38 ²	0.18 ²	0.57 ²
10.84	179	1.24	0.11	0.15	0.09	0.21	0.10	0.19

¹ see Figure 29a, ² see Figure 29b.

Table 21. Roller axles placement—steel trestle, measuring points A and B roller casing—steel, D_r = 89 mm.

f_i	n_r	v_r	Measuring point „A“			Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]			[mm·s^-1]
50	825	3.84	0.46 ¹	0.38 ¹	0.17 ¹	0.82 ²	0.20 ²	1.23 ²
32.4	534	2.49	0.92	0.57	0.13	0.96	0.57	0.80
16.17	267	1.24	0.09	0.11	0.07	0.21	0.07	0.24

¹ see Figure 30a, ² see Figure 30b.

Table 22. Roller axles placement—steel trestle, measuring points C and D roller casing—steel, D_r = 89 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	826	3.85	0.92 ¹	0.36 ¹	0.26 ¹	0.79 ²	0.18 ²	1.15 ²
32.4	534	2.49	0.92	0.57	0.13	0.96	0.57	0.80
16.17	267	1.24	0.09	0.11	0.07	0.21	0.07	0.24

¹ see Figure 31a, ² see Figure 31b.

Table 23. Roller axles placement—steel trestle, measuring points A and B roller casing—steel, D_r = 108 mm.

f_i	n_r	v_r	Measuring point „A“						Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)			v_(y)RMS(fi)		v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)			v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	823	4.65		0.61	0.35		0.15		0.83		0.24	0.94
41.25	680	3.85		0.35	0.36		0.11		0.90		0.24	1.12
26.73	441	2.49		0.38 ¹	0.16 ¹		0.09 ¹		0.44 ²		0.10 ²	0.50 ²
13.30	219	1.24		0.06	0.10		0.05		0.14		0.08	0.25

¹ see Figure 32a, ² see Figure 32b.

Table 24. Roller axles placement—steel trestle, measuring points C and D roller casing—steel, D_r = 108 mm.

f_i	n_r	v_r	Measuring point „C“			Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)	v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	823	4.66	1.14	0.30	0.28	0.99	0.24	0.84
41.20	679	3.84	1.19	0.40	0.33	1.03	0.33	1.10
26.73	441	2.49	0.46 ¹	0.20 ¹	0.14 ¹	0.52 ²	0.12 ²	0.59 ²
13.32	220	1.24	0.07	0.10	0.07	0.13	0.07	0.21

¹ see Figure 33a, ² see Figure 33b.

Table 25. Roller axles placement—steel trestle, measuring points A and B roller casing—steel, D_r = 133 mm.

f_i	n_r	v_r	Measuring point „A“				Measuring point „B“
f_i	n_r	v_r	v_(x)RMS(fi)		v_(y)RMS(fi)	v_(z)RMS(fi)	v_(x)RMS(fi)	v_(y)RMS(fi)			v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	826	5.75	0.29	0.29		0.13	0.46		0.18	0.87
33.66	555	3.86	0.43	0.21		0.11	0.49		0.14	0.68
21.89	361	2.51	0.14 ¹	0.13 ¹		0.08 ¹	0.26 ²		0.09 ²	0.39 ²
10.87	179	1.25	0.10	0.06		0.11	0.14		0.09	0.18

¹ see Figure 34a, ² see Figure 34b.

Table 26. Roller axles placement—steel trestle, measuring points C and D roller casing—steel, D_r = 133 mm.

f_i	n_r	v_r	Measuring point „C“						Measuring point „D“
f_i	n_r	v_r	v_(x)RMS(fi)		v_(y)RMS(fi)			v_(z)RMS(fi)	v_(x)RMS(fi)		v_(y)RMS(fi)		v_(z)RMS(fi)
[Hz]	[min^-1]	[m·s^-1]	[mm·s^-1]
50	824	5.74		0.33		0.30	0.17			0.42	0.20	0.83
33.59	554	3.86		0.26		0.21	0.12			0.33	0.14	0.59
21.87	361	2.51		0.23 ¹		0.15 ¹	0.10 ¹			0.23 ²	0.10 ²	0.40 ²
10.87	179	1.25		0.10		0.14	0.09			0.11	0.09	0.18

¹ see Figure 35a, ² see Figure 35b.

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