# The Reduction of Rotating Conveyor Roller Vibrations via the Use of Plastic Brackets

^{*}

## Abstract

**:**

## 1. Introduction

^{–1}] [9], or acceleration a(t) [m·s

^{–2}] (1).

_{RMS}[m·s

^{–2}] can be expressed as (2).

## 2. Materials and Methods

_{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 a 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.

_{RMS}[m·s

^{−1}] was carried out 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].

^{®}Premium 2012 × 64, 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,YASKAWA Electric Europe GmbH, Schwalbach am Taunus, Germany, 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 ϕ24 mm (with a tight key of 8 × 7 × 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 × 2513 La L = L). The revolutions of the electric motor n

_{e}[min

^{−1}] are controlled by an electric inverter (type YASKAWA VS-606 V7, YASKAWA Electric Europe GmbH, Schwalbach am Taunus, Germany).

_{r}[mm] (133, 108 and 89), at the same circumferential speeds v

_{r}[m·s

^{−1}] of their casings.

_{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 are controlled by a frequency converter.

_{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 400/230 V with a frequency of 50 Hz is used. In North America, it is a phase distribution system of 120 V at a frequency of 60 Hz) and the frequency f

_{i}[Hz] set on the display of the frequency converter.

_{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.

_{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.

_{(*)RMS(fi)}[mm·s

^{−1}] in the range of 10–1 × 10

^{4}Hz (this frequency range is applied in the ISO 10816-3 standard [49]). The 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.

## 3. Results

_{(*)RMS(fi)}[mm·s

^{−1}] for a rotating conveyor roller with a diameter D

_{r}[mm] were carried out using a laboratory machine, see Figure 3, under the same technical conditions, on two types of fixed conveyor idlers (where the 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.

**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.

_{(*)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 Figure 4a and Figure 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

_{(*)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).

_{(*)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.

_{(*)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. The measured courses of the effective values of the vibration velocities v

_{(*)RMS(fi)}[mm·s

^{−1}] are listed in the appendix with the title “Measured data” [53].

_{(*)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.

_{(*)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.

_{(*)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 plastic brackets.

_{(*)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.

_{(*)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.

_{(*)RMS(fi)}[mm·s

^{−1}], measured at points A to D grow with the increasing speed v

_{r}[m·s

^{−1}] of the conveyor roller rotation with a plastic casing, the axle of which is mounted in a plastic support.

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

_{(*)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 at measuring points A and B of the conveyor idler with plastic brackets on our laboratory device.

_{(*)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. The measured courses of the effective values of the vibration velocities v

_{(*)RMS(fi)}[mm·s

^{−1}] are listed in the appendix with the title “Measured data” [53].

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)RMS(fi)}[mm·s

^{−1}], measured at points B and D of the steel casing, the axis of which is stored in a plastic support.

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

_{(*)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 at measuring points A and B of a fixed conveyor idler with steel trestles, see Figure 10a, of the laboratory device (Figure 11).

_{(*)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 this paper, the measured graphs of the effective values of the 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}. The measured courses of the effective values of the vibration velocities v

_{(*)RMS(fi)}[mm·s

^{−1}] are listed in the appendix with the title “Measured data” [53].

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)RMS(fi)}[mm·s

^{−1}], measured at points A to D grow with the increasing speed v

_{r}[m·s

^{−1}] of the conveyor roller rotation with a plastic casing, the axle of which is mounted in a steel support.

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

_{(*)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.

_{(*)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. The measured courses of the effective values of the vibration velocities v

_{(*)RMS(fi)}[mm·s

^{−1}] are listed in the appendix with the title “Measured data” [53].

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)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.

_{(*)RMS(fi)}[mm·s

^{−1}], measured at points B and D with speed v

_{r}= 2.5 m·s

^{−1}of the conveyor roller rotation with a steel casing, the axis of which is stored in a plastic support.

## 4. Discussion

^{−1}, with the help of the DEWESoft X software, the effective values for the vibration velocities were determined, and these are listed in Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18, Table 19, Table 20, Table 21, Table 22, Table 23, Table 24, Table 25 and Table 26.

_{(*)RMS(fi)}[mm·s

^{−1}] in the coordinate axes (x, y, z). For more information, see Section 3.1, Section 3.2, Section 3.3 and Section 3.4.

_{(*)RMS(fi)}[mm·s

^{−1}] reach the conveyor roller with an 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 the vibration in each direction are described.

_{r}= 825 min

^{−1}and the roller axle placement of the conveyor with an 89 mm diameter into plastic brackets (see Figure 11 part B), the effective value of the vibration velocity v

_{(*)RMS(fi)}[mm·s

^{−1}] in axis “z” reaches 37.4% of the value v

_{(*)RMS(fi)}[mm·s

^{−1}], compared to placing this roller in a steel trestle.

_{(*)RMS(fi)}[mm·s

^{−1}] in the “z” axis reaches 40% of the value v

_{(*)RMS(fi)}[mm·s

^{−1}], unlike when placed in a steel trestle.

_{(*)RMS(fi)}[mm·s

^{−1}] reach the conveyor roller with a ϕ108 mm diameter placed in the steel trestle of a fixed conveyor idler, and that is in the “z” axis (vertical direction).

_{r}= 442 min

^{−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 v

_{(*)RMS(fi)}[mm·s

^{−1}] in axis “z” reaches 41.9% of the value v

_{(*)RMS(fi)}[mm·s

^{−1}], compared to placing this roller in a steel trestle.

_{(*)RMS(fi)}[mm·s

^{−1}] in the “z” axis reaches 46.9% of the value v

_{(*)RMS(fi)}[mm·s

^{−1}], unlike when placed in a steel trestle.

_{(*)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 idler, and these are reached in the “z” axis direction (vertical direction).

_{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 v

_{(*)RMS(fi)}[mm·s

^{−1}] in axis “z” reaches 66.7% of the value v

_{(*)RMS(fi)}[mm·s

^{−1}], compared to placing this roller in a steel trestle.

_{(*)RMS(fi)}[mm·s

^{−1}] in the “z” axis reaches 57.5% of the value v

_{(*)RMS(fi)}[mm·s

^{−1}], unlike when placed in a steel trestle.

_{(*)RMS(fi)}[mm·s

^{−1}] for the rotating conveyor rollers measured at the points A to D, of which the plastic or steel casing of a 133 mm diameter rotates at a 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.

_{(*)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.

_{(*)RMS(fi)}[mm·s

^{−1}] were measured at 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).

_{(*)RMS(fi)}[mm·s

^{−1}] for the rotating conveyor rollers measured at the points A to D, of which the plastic or steel casing of a 108 mm diameter rotates at a 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.

_{(*)RMS(fi)}[mm·s

^{−1}] for the rotating conveyor rollers measured at the points A to D, of which the plastic or steel casing of an 89 mm diameter rotates at a 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.

## 5. Conclusions

_{r}[mm], see Figure 5. This assembly consists of a flange, with screw connections attaching a pulley with the calculated diameter of 141.5 mm.

- −
- The experimental measurement of the vibration velocities v
_{(*)RMS(fi)}[mm·s^{−1}] was carried out in a central roller (horizontally placed roller in a fixed idler). - −
- 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. - −
- Using two acceleration sensors, the vibrations of the rotating conveyor roller positioned in the trestle were detected (B or D) 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).
- −
- 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. - −
- One or two so-called “V-belt pulley assembly” units were placed onto the tested conveyor roller (with a steel or plastic casing) with a diameter of D
_{r}= 133 mm (or 108 mm or 89 mm). This assembly consists of a flange, with screw connections attaching a pulley with the calculated diameter of D_{w}= 153 mm. - −
- The vibrations of the transport rollers were measured at the speed of rotation v
_{r}= 3.84 m·s^{−1}, 2.5 m·s^{−1}, and 1.25 m·s^{−1}.

_{(*)RMS(fi)}[mm·s

^{-1}], which are listed in Section 3 in Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18, Table 19, Table 20, Table 21, Table 22, Table 23, Table 24, Table 25 and Table 26, are listed in the appendix entitled “Measured data” [53].

## Author Contributions

## Funding

## Data Availability Statement

_{(*)RMS(fi)}[mm·s

^{−1}], listed from Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16, Table 17, Table 18, Table 19, Table 20, Table 21, Table 22, Table 23, Table 24, Table 25 and 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

## Conflicts of Interest

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**Figure 1.**The endless loop of a conveyor belt supported by conveyor rollers. 1—conveyor line, 2—conveyor rollers, 3—conveyor belt.

**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, 9—threaded rod.

**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 ϕ133 mm conveyor roller, (

**d**) manufactured V-belt pulley assembly. 1—V-belt pulley, 2—flange, 3—screw M4 × 16 DIN 912, 4—screw M4 × 10 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 M4 × 16 DIN 912, 4—screw M4 × 25 DIN 912 (screw M4 × 35 DIN 933).

**Figure 6.**Conveyor roller (

**a**) steel, (

**b**) rubberized, (

**c**) a 3D model of a conveyor roller fitted with two pieces of the V-belt pulley assembly. 1—V-belt pulley, 2—flange, 3—screw M4 × 16 DIN 912, 4—screw M4 × 10 (25) DIN 912 (M4 × 35 DIN 933), 5—ϕ133 mm conveyor roller (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 M4 × 16 DIN 912, 4—screw M4 × 10 (25) DIN 912 (M4 × 35 DIN 933), 5—ϕ133 mm conveyor roller (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 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}], ϕ89 mm plastic roller, 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}], ϕ89 mm steel roller, the circumferential speed of the roller v

_{r}= 3.84 m·s

^{−1}, plastic trestle, (

**a**) measuring point A, (

**b**) measuring point B.

**Figure 14.**Effective vibration values v

_{(*)RMS(fi)}[mm·s

^{−1}], ϕ89 mm plastic roller, the circumferential speed of the roller v

_{r}= 3.85 m·s

^{−1}, steel trestle, (

**a**) measuring point A, (

**b**) measuring point B.

**Figure 15.**Effective vibration values v

_{(*)RMS(fi)}[mm·s

^{−1}], ϕ89 mm steel roller, the circumferential speed of the roller v

_{r}= 3.84 m·s

^{−1}, steel trestle, (

**a**) measuring point A, (

**b**) measuring point B.

**Figure 16.**The effective vibration values v

_{(*)RMS(fi)}[mm·s

^{−1}] of conveyor rollers with an 89 mm diameter, at revolutions of 825 min

^{−1}. Measuring point as in Figure 11 (

**a**) A, (

**b**) C, (

**c**) B, (

**d**) D.

**Figure 17.**The effective vibration values v

_{(*)RMS(fi)}[mm·s

^{−1}] of conveyor rollers with a 108 mm diameter, at revolutions of 442 min

^{−1}. Measuring point as in Figure 11 (

**a**) A, (

**b**) C, (

**c**) B, (

**d**) D.

**Figure 18.**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 19.**The effective vibration values v

_{(*)RMS(fi)}[mm·s

^{−1}] of ϕ133 mm conveyor rollers at different revolutions when red line is plastic trestle, roller casing—steel, blue line is steel trestle, roller casing—steel, fialová line is plastic trestle, roller casing—plastic, and green line is steel trestle, roller casing—plastic. Measuring point as in Figure 11 (

**a**) B, (

**b**) D, (

**c**) A, (

**d**) C.

**Figure 20.**The effective vibration values v

_{(*)RMS(fi)}[mm·s

^{−1}] of ϕ108 mm conveyor rollers at different revolutions when red line is plastic trestle, roller casing—steel, blue line is steel trestle, roller casing—steel, fialová line is plastic trestle, roller casing—plastic, and green line is steel trestle, roller casing—plastic. Measuring point as in Figure 11 (

**a**) B, (

**b**) D, (

**c**) A, (

**d**) C.

**Figure 21.**The effective vibration values v

_{(*)RMS(fi)}[mm·s

^{−1}] of ϕ89 mm conveyor rollers at different revolutions when red line is plastic trestle, roller casing—steel, blue line is steel trestle, roller casing—steel, fialová line is plastic trestle, roller casing—plastic, and green line is steel trestle, roller casing—plastic. 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].

B | 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” | ||||
---|---|---|---|---|---|---|---|---|

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.25 | 0.13 | 0.40 | 0.14 | 0.93 |

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.14 | 0.13 | 0.25 | 0.10 | 0.34 |

13.4 | 220 | 1.24 | 0.09 | 0.08 | 0.06 | 0.08 | 0.05 | 0.17 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.12 | 0.07 | 0.21 | 0.09 | 0.34 |

13.4 | 220 | 1.24 | 0.11 | 0.06 | 0.06 | 0.09 | 0.10 | 0.15 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.21 | 0.09 | 0.24 | 0.13 | 0.58 |

10.9 | 179 | 1.25 | 0.07 | 0.11 | 0.06 | 0.10 | 0.08 | 0.18 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.20 | 0.09 | 0.27 | 0.13 | 0.68 |

10.9 | 179 | 1.25 | 0.08 | 0.09 | 0.06 | 0.10 | 0.08 | 0.19 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.18 | 0.26 | 0.43 | 0.28 | 0.46 |

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.11 | 0.07 | 0.20 | 0.12 | 0.32 |

13.36 | 220 | 1.25 | 0.12 | 0.08 | 0.08 | 0.10 | 0.08 | 0.14 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.14 | 0.15 | 0.26 | 0.12 | 0.30 |

13.37 | 220 | 1.25 | 0.11 | 0.12 | 0.09 | 0.08 | 0.07 | 0.13 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.12 | 0.07 | 0.21 | 0.13 | 0.26 |

10.89 | 179 | 1.25 | 0.19 | 0.09 | 0.07 | 0.14 | 0.09 | 0.16 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.11 | 0.14 | 0.13 | 0.09 | 0.23 |

10.89 | 179 | 1.25 | 0.11 | 0.07 | 0.08 | 0.08 | 0.06 | 0.14 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.37 | 0.15 | 0.77 | 0.27 | 1.04 |

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.26 | 0.14 | 0.78 | 0.20 | 0.81 |

13.34 | 220 | 1.24 | 0.08 | 0.13 | 0.06 | 0.17 | 0.10 | 0.32 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.24 | 0.11 | 0.63 | 0.18 | 0.64 |

13.35 | 220 | 1.24 | 0.08 | 0.13 | 0.06 | 0.14 | 0.09 | 0.32 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.25 | 0.14 | 0.35 | 0.21 | 0.61 |

10.84 | 179 | 1.24 | 0.08 | 0.12 | 0.09 | 0.16 | 0.09 | 0.20 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.23 | 0.12 | 0.38 | 0.18 | 0.57 |

10.84 | 179 | 1.24 | 0.11 | 0.15 | 0.09 | 0.21 | 0.10 | 0.19 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.36 | 0.26 | 0.79 | 0.18 | 1.15 |

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 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.16 | 0.09 | 0.44 | 0.10 | 0.50 |

13.30 | 219 | 1.24 | 0.06 | 0.10 | 0.05 | 0.14 | 0.08 | 0.25 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.20 | 0.14 | 0.52 | 0.12 | 0.59 |

13.32 | 220 | 1.24 | 0.07 | 0.10 | 0.07 | 0.13 | 0.07 | 0.21 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.13 | 0.08 | 0.26 | 0.09 | 0.39 |

10.87 | 179 | 1.25 | 0.10 | 0.06 | 0.11 | 0.14 | 0.09 | 0.18 |

**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” | ||||
---|---|---|---|---|---|---|---|---|

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 | 0.15 | 0.10 | 0.23 | 0.10 | 0.40 |

10.87 | 179 | 1.25 | 0.10 | 0.14 | 0.09 | 0.11 | 0.09 | 0.18 |

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## Share and Cite

**MDPI and ACS Style**

Hrabovský, L.; Nováková, E.; Pravda, Š.; Kurač, D.; Machálek, T.
The Reduction of Rotating Conveyor Roller Vibrations via the Use of Plastic Brackets. *Machines* **2023**, *11*, 1070.
https://doi.org/10.3390/machines11121070

**AMA Style**

Hrabovský L, Nováková E, Pravda Š, Kurač D, Machálek T.
The Reduction of Rotating Conveyor Roller Vibrations via the Use of Plastic Brackets. *Machines*. 2023; 11(12):1070.
https://doi.org/10.3390/machines11121070

**Chicago/Turabian Style**

Hrabovský, Leopold, Eliška Nováková, Štěpán Pravda, Daniel Kurač, and Tomáš Machálek.
2023. "The Reduction of Rotating Conveyor Roller Vibrations via the Use of Plastic Brackets" *Machines* 11, no. 12: 1070.
https://doi.org/10.3390/machines11121070