# Interdependence of Technical and Technological Parameters in Polymer Ultrasonic Welding

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- (a)
- Parameters of the polymer material to be ultrasonically welded:
- material thickness (d, mm)
- specific material density of the polymer material to be welded (ρ
_{1}, kgm^{−3}) - speed of ultrasound propagation in the polymer material to be welded (c
_{1}, ms^{−1}) - acoustic damping factor of the material (μ
_{A}, m^{−1}) - acoustic impedance of the polymer material to be welded (Z
_{1}, kg/m^{2}s) - heating the material from room temperature to melting temperature (Q
_{H}, J) - melting heat of the material (Q
_{L}, J) - (specific melting heat) latent heat of melting the material (L, J/kg)
- specific heat of the material to be welded (c, J/m
^{3}K) - initial temperature of the material before welding ((T
_{1}, K) - melting temperature of the material (T
_{2}, K) - breaking force of ultrasonic welded joints (F
_{p}, N)

- (b)
- Acoustic parameters:
- intensity of ultrasonic oscillations (I, W/m
^{2}) - coefficient of reflection of ultrasound pressures (r)
- ultrasound intensity absorption coefficient (α)
- ultrasound intensity reflection coefficient between the material to be welded and the counter roller (R)
- ultrasound intensity reflection coefficient between the ultrasonic rotary sonotrode and the material to be welded (R
_{1}) - ultrasound intensity absorption coefficient on the discontinuity of the sonotrode/material (α
_{1}) - ultrasound intensity absorption coefficient on the material/counter roller discontinuity (α
_{2}) - functional dependence of the decrease in ultrasound pressure in the material to be welded depending on the distance (thickness) of the material (p(x))
- ultrasound pressure (p, Pa)
- functional dependence of the decrease in ultrasound intensity in the material with distance (thickness) of the material (I(x), W/m
^{2}) - coefficient of reflection of ultrasound intensities on the discontinuity (R)

- (c)
- Technological parameters (depending on the machine):
- frequency of ultrasonic vibrations of the sonotrode (f, Hz)
- declared electrical power of the machine’s ultrasonic generator (P
_{d}, W) - electrical power of the ultrasonic generator of the machine at which the maximum breaking force of the ultrasonic welded joint appears (P
_{dmax}, W) - effective power of the ultrasonic rotary sonotrode (P
_{α}, W) - force with which rotary ultrasonic sonotrodes act on two layers of thermoplastic polymer materials with total thickness (P
_{s}, N) - specific density of sonotrode material (ρ
_{0}, kg/m^{3}) - speed of ultrasound propagation in the sonotrode (c
_{0}, ms^{−1}) - sonotrode vibration amplitude (A
_{0}, m) - acoustic impedance of the ultrasonic rotary sonotrode (Z
_{0}, kg/m^{2}s) - specific material density from which the counter-roller is made (ρ
_{2}, kgm^{−3}) - speed of ultrasound propagation of the backing material for welding (c
_{2}, ms^{−1}) - acoustic impedance of the backing material (table) for welding (Z
_{3}, kg/m^{2}s) - sonotrode ultrasound intensity (I
_{0}, W/m^{2}) - radius of the ultrasonic rotary sonotrode (r
_{s}, m) - width of the ultrasonic rotary sonotrode (w
_{s}, m) - length of the imprint of the rotary sonotrode on the material (l
_{s}, m) - angular velocity of the rotation of the ultrasonic sonotrode (ω
_{s}, rad/s). If the linear velocity of the sonotrode edge and the radius of the rotary ultrasonic sonotrode are given, the angular velocity is calculated by the expression ω_{s}= v_{s}/r_{s} - linear speed of the edge of the ultrasonic rotary sonotrode, i.e., speed of the movement of the workpiece v
_{s}, cm/s). If the angular velocity and the radius of the rotary ultrasonic sonotrode are given, the linear velocity is calculated by the expression v_{s}= ω_{s·}r_{s}. - ultrasonic welding time depending on the ratio of the length of the imprint of the ultrasonic rotary sonotrode and the linear speed of the sonotrode edge, i.e., the speed of the workpiece movement (t
_{s}, s) - ultrasonic welding time calculated according to the mathematical model (t
_{m}, s) - delay time of the start of welding due to heating the beginning of the welded joint (t
_{dy}, s).

## 2. Acoustic Mathematical Model of Ultrasonic Welding Time

_{0}from which it is made and the speed of sound waves c

_{0}in it. The polymer material has a specific material density ρ

_{1}and the speed of sound waves c

_{1}in it. At the bottom of the welder there is a counter-roller that has a specific density of the material ρ

_{2}from which it is made and the speed of sound waves c

_{2}within it. Ultrasonic vibrations of intensity I

_{0}occur in the rotary ultrasonic sonotrode, which are intended to induce heat into the polymer material. Since reflection occurs on each discontinuity of acoustic impedances encountered by an ultrasonic wave, an ultrasonic wave of intensity I

_{0}is also partially reflected on the discontinuity (sonotrode/material) with an intensity I

_{r0}, while a larger part penetrates the material with an intensity of I

_{1}. Due to the absorption of the material and the conversion of the ultrasonic wave into heat, the intensity of the wave weakens, so that it takes on the intensity of I

_{12}at the contact surface between the lower part of the material and the counter roller. Since it is the second discontinuity (material/counter roller), there is a reflection of intensity I

_{r1}, which returns part of the ultrasonic energy into the material, while the other part with an intensity of I

_{2}goes into the counter roller, representing a loss of ultrasonic energy.

_{r1}, gradually becomes of intensity I

_{21}. Back-reflection of I

_{r2}on the discontinuity (material/sonotrode) causes a portion of the ultrasonic energy to return to the material and a portion of the ultrasonic wave with an intensity of I

_{3}to reach the sonotrode.

_{0}, i.e., the average power of the ultrasonic wave, as determined by E. Dieulasaint and D. Royer [16], can be expressed by Equation (1):

_{0}is defined as the product of the specific density of the material ρ

_{0}from which the ultrasonic rotary sonotrode is made and the speed of the sound wave c

_{0}in it in accordance with Equation (2):

_{1}and the counter roller Z

_{2}are defined according to equations:

_{r}and direct ultrasound pressure p

_{d}) is defined by Equation (5):

_{d}of ultrasound intensity) is defined by Equation (6):

_{r}and direct I

_{d}of ultrasound intensity) is defined by Equation (8):

_{0}i and material Z

_{1}is defined by Equation (12):

_{1}and the counter roller Z

_{2}is defined by Equation (13):

_{α}

_{1}in the thermoplastic polymer material, the temperature of the material rises and the ultrasonic wave penetrating through the material weakens in intensity, so that it drops from the initial I

_{1}to the intensity I

_{12}at the bottom of the layer of the welded material. In this way, the absorption value of the injected ultrasonic wave from the sonotrode can be calculated in the polymer material:

_{α}

_{1}, which is converted into heat, is shown in Figure 1.

_{r1}on the discontinuity (2) (material/counter roller) returning to the polymer material is defined by the equation:

_{21}at the end of its path, near the top of the material layer:

_{1}developed in the polymer material:

_{0}, which is directed towards the thermoplastic polymer material according to its effect. When the ultrasound wave reaches the discontinuity (1) at the boundary of the sonotrode and the upper layer of the material being welded, a reflection occurs, whereby a part of the ultrasonic wave I

_{r}

_{0}is reflected back into the sonotrode. The weakened ultrasonic wave with intensity I

_{1}continues to penetrate the polymer material. As the ultrasonic wave penetrates the polymer material, the ultrasonic energy I

_{α}

_{1}is absorbed, causing the intensity of the ultrasonic wave to decrease so that it assumes intensity I

_{12}immediately adjacent to the second discontinuity (2) at the boundary between the bottom layer of the material and the counter roller. When the ultrasonic wave reaches the discontinuity (2), a back-reflection occurs, where part of the ultrasonic wave of intensity I

_{r}

_{1}is reflected back into the polymer material and the other part of intensity I

_{α}

_{2}is transferred to the counter roller, where part of the energy of the ultrasonic wave

_{2}is irreversibly lost. The ultrasonic wave reflected from the discontinuity (2) propagates towards the sonotrode, where it weakens because it returns a large part of its energy to the material I

_{α}

_{3}. The weakened reflected wave finally reaches the sonotrode, i.e., the discontinuity (1), so that part of the wave is reflected back into the material with an intensity of I

_{r}

_{2}, while a part is transmitted to the sonotrode I

_{r}

_{3}.

_{2}and into the sonotrode I

_{3}as well as the influence of the back reflection of the reflected wave Ir

_{3}are neglected in this analysis, as their influence is small when the influence of the other parameters is taken into account.

_{α}developed in the polymer material is calculated by the product of the intensity of ultrasonic waves that are converted into the heat of the polymer material and the area of action of the sonotrode consisting of the width of the sonotrode w

_{s}and the length of the sonotrode imprint on the polymer material l

_{s}:

_{s}, the length of the sonotrode imprint on the polymer material l

_{s}, the specific heat of the material c, and the difference between the melting temperature and the initial temperature are the factors that determine the energy needed to reach the melting temperature of the ultrasonic material:

_{L}is equal to the product of the density of the material ρ, the thickness of the two layers of material with individual thickness d, the width of the sonotrode w

_{s}, the length of the imprint of the sonotrode on the polymer material l

_{s}and the latent heat of the material L:

_{T}required for welding polymer materials is the sum of specific heating and latent melting heat, so the addition of Equations (29) and (30) gives Equation (31):

_{T}= P

_{α}·t, then t = Q

_{T}/P

_{α}. Thus, if Equations (31) and (28) are inserted into this expression, an equation is obtained for calculating the required welding time t during the action of ultrasound on thermoplastic polymer materials:

_{α}

_{4}, etc.), Equation (32) is still of high accuracy in terms of practical application. Equation (32) has a complicated structure that indicates there are many factors that affect how polymer materials weld. The most important parameters are the welding times and the power of the ultrasonic generator, expressed by the amplitudes of the ultrasonic rotary sonotrode. These are also the most frequently set parameters in ultrasonic welding. The aforementioned equation and all of its derivations, which completely describe and reveal its origin, very thoroughly reveal the intricate interdependencies of the technical and technological parameters of the ultrasonic welding of polymer materials.

## 3. Measuring Methods and Materials

_{0}and the welding time are parameters that can change. Other parameters do not change during joining in this case. The machine manufacturers do not specify the parameter value for the amplitude, but allow that the power of the ultrasonic generator P

_{d}can be adjusted. Therefore, it is important to check the value of the amplitude of the ultrasonic rotary sonotrode at the declared power of the ultrasonic generator.

_{0}and their dependence on the indicated declared power of the ultrasonic generator, which is typically displayed on the microcomputer screen of the ultrasonic machine, were measured to verify the mathematical model of ultrasonic welding time presented in Section 3 of this paper and in mathematical expressions (1) to (32). The declared power of the ultrasonic generator have been determined for Pfaff Model 8310 [17] ultrasonic machine with rotary sonotrode for welding polymer materials, Figure 3. A rotary sonotrode, Figure 4, with a welding speed of 0.6 to 13.6 m/min is a component of the ultrasonic machine. The ultrasonic generator has an adjustable power range of 200 to 400 W and runs at a frequency of 35 kHz. It sends the vibrations to a circular sonotrode with a 105 mm diameter and a 10 mm width.

^{3}J/mm

^{3}K, at the melting temperature T2 of 485 K and the ambient temperature T

_{1}of 289 K. The specific melting heat L is 163 × 10

^{3}J/kg, and the specific density of the polymer material ρ is 1.4 × 10

^{3}kg/m

^{3}.

^{2}measuring specimens. The aforementioned ultrasonic machine, which has an adjustable electrical power of the ultrasonic generator of 50 to 100%, or converted to a power of 200 to 400 W, was used to weld the test specimens. For this experiment, six power levels of 200 W, 244 W, 280 W, 320 W, 356 W, and 400 W were chosen. Seven welding speeds were also used, including 0.077 m/s, 0.097 m/s, 0.113 m/s, 0.125 m/s, 0.147 m/s, 0.167 m/s, and 0.227 m/s. To calculate the breaking force of the ultrasonic welds for each of the specified materials, 42 groups of 20 test specimens were created in line with the aforementioned information and evaluated on a strength tester.

_{0}was 4.1 × 10

^{7}kg/m

^{2}s, the acoustic impedance of the material to be welded (acoustic impedance of the material), Z

_{1}, was 3.2 × 10

^{6}kg/m

^{2}s. The acoustic damping factor of the material μ

_{A}was 0.37 m

^{−1}.

_{1}amount to 0.73.

## 4. Results

#### 4.1. Results of Analysing the Rotary Sonotrode’s Vibration Amplitude in Relation to the Ultrasonic Generator’s Set Electrical Power

_{0}= 0.484 + 0.3383·P

_{d}.

#### 4.2. Results of Testing Specimens of Ultrasonic Welds for Breaking Forces

- A.
- Weld with a nice appearance, Figure 7a
- B.
- Weld with scarcely noticeable damage symptoms, Figure 7b
- C.
- Weld with substantial weld damage, Figure 7c.

**Figure 7.**The visual appearance of a weld with a nice appearance (

**a**) and its cross-sectional view (

**d**), weld with scarcely noticeable damage symptoms (

**b**) and its cross-sectional view (

**e**), weld with substantial weld damage (

**c**) and and its cross-sectional view (

**f**).

- D.
- Separation of the material layers at the weld
- E.
- Material tearing inside the weld
- F.
- Material tearing along the weld’s edge.

- for a welding speed of 0.077 m/s for the declared power of the ultrasonic generator of 200 W
- for a welding speed of 0.097 m/s for the declared power of the ultrasonic generator of 250 W
- for a welding speed of 0.113 m/s for the declared power of the ultrasonic generator of 268 W
- for a welding speed of 0.125 m/s at the declared power of the ultrasonic generator of 272 W.

#### 4.3. Verification of Mathematical Model Results

_{0}= 0.484 + 0.3383·P

_{d}, for the declared power of the ultrasonic generator of 200 W, the oscillation amplitude of the rotary ultrasonic sonotrode was determined to be 68.1 µm, for a power of 250 W the amplitude was 85.1 µm, for a power of 268 W the amplitude was 91.1 µm and for a power of 272 W the amplitude was 92.5 µm.

_{m}that was introduced in the paper’s introduction. Additionally, the actual times t

_{s}are displayed, which are derived from the linear speed of the rotary sonotrode circumference (t

_{s}= l

_{s}/v

_{s}) and the 0.02 m imprint value of the rotary sonotrode.

## 5. Discussion

_{0}= 0.484 + 0.3383 -Pd for each of the four determined declared powers of the ultrasonic generator at which the maximum breaking force occurs. The sonotrode’s real vibration amplitude can be found in values of 68.1, 85.1, 91.1, and 92.5 µm in Table 2 for the powers at which the highest breaking force occurs (200 W, 250 W, 268 W, and 272 W). The mathematical model’s expression (28) can then be used to determine the ultrasonic sonotrode’s effective power, Pα (Table 2). The calculated effective power of the sonotrode is significantly lower than the declared power when the declared power of the ultrasonic generator and the effective power of the ultrasonic rotary sonotrode are compared. This discrepancy results from the utilization coefficient of the ultrasonic circuit (eclectic losses of the piezoelectric plates and other mechanical losses).

## 6. Conclusions

- A list of 44 characteristics has been put together and separated into three subgroups that are crucial for ultrasonic welding of polymer materials. There are 12 parameters in the first subgroup that are dependent on the polymer material being ultrasonically welded, 11 general acoustic and electroacoustic characteristics in the second subgroup, and 21 technical parameters in the third subgroup that are dependent on the ultrasonic welding equipment. Future research on ultrasonic welding of polymer materials may benefit from the systematization and cataloguing of these characteristics.
- The new creation of comprehensive a mathematical model and the associated drawings are provided, further demonstrating the reliance of numerous significant parameters.
- A suitable original measuring method and apparatus are described for calculating the vibration amplitudes of an ultrasonic rotary sonotrode.
- The laboratory determination of breaking forces of test specimens welded by the ultrasonic welding method for polymer materials of various characteristics is described, together with the necessary measuring equipment due to the verification of the mathematical model.
- The creation of calibration diagrams of the relationship between the ultrasonic rotary sonotrode’s vibration amplitude and the declared power of the ultrasonic generator is also explained in order to get pertinent and realistic data needed for the implementation of the mathematical model presented.
- Breaking forces were examined for 42 sets of test specimens that were welded at various welding speeds and welding powers on the basis of which the welding times were determined for the compounds with the maximum braking force and compared with the calculated ultrasonic welding times according to the mathematic model.
- The area of the best welding parameters also was identified, along with typical variations in the functional dependency of breaking forces on the ultrasonic energy injected into the weld. The diagrams show areas where too little ultrasonic energy was applied, resulting in low breaking forces, optimal areas with ultrasonic energy applied, resulting in maximum joint breaking forces, and areas with too much ultrasonic energy applied. This resulted in deterioration of the welds.
- The new developed mathematical model and the experimental data showed good agreement, with differences that are not important for practical application.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bhudolia, S.K.; Gohel, G.; Leong, K.F.; Islam, A. Advances in Ultrasonic Welding of Thermoplastic Composites: A Review. Materials
**2020**, 13, 1284. [Google Scholar] [CrossRef] [PubMed] - Jone, I. Ultrasonic and dielectric welding of textiles. In Joining Textiles—Principles and Applications, 1st ed.; Jones, I., Stylios, G.K., Eds.; Woodhead Publishing: Cambridge, UK, 2013; pp. 374–398. [Google Scholar]
- Kuo, C.-C.; Tsai, Q.-Z.; Li, D.-Y.; Lin, Y.-X.; Chen, W.-X. Optimization of Ultrasonic Welding Process Parameters to Enhance Weld Strength of 3C Power Cases Using a Design of Experiments Approach. Polymers
**2022**, 14, 2388. [Google Scholar] [CrossRef] - Kayar, M.; Mistik, S.I.; Inan, D. Analysing effect of the factors on ultrasonic seam tensile properties of nonwoven fabrics by Nested Anova Design. Int. J. Cloth. Sci. Technol.
**2015**, 27, 803–817. [Google Scholar] [CrossRef] - Gomer, A.; Zou, W.; Grigat, N.; Sackmann, J.; Schomburg, W.K. Fabrication of Fiber Reinforced Plastics by Ultrasonic Welding. J. Compos. Sci.
**2018**, 2, 56. [Google Scholar] [CrossRef] - Sancaktar, E. Polymer adhesion by ultrasonic welding. J. Adhes. Sci. Technol.
**1999**, 13, 179–201. [Google Scholar] [CrossRef] - Shi, W.; Little, T. Mechanisms of ultrasonic joining of textile materials. Int. J. Cloth. Sci. Technol.
**2000**, 12, 331–350. [Google Scholar] [CrossRef] - Kiss, Z.; Temesi, T.; Bitay, E.; Bárány, T.; Czigány, T. Ultrasonic welding of all-polypropylene composites. J. Appl. Polym. Sci.
**2020**, 137, 48799. [Google Scholar] [CrossRef] - Nguyen, T.-H.; Thanh, L.Q.; Loc, N.H.; Huu, M.N.; Van, A.N. Effects of Different Roller Profiles on the Microstructure and Peel Strength of the Ultrasonic Welding Joints of Nonwoven Fabrics. Appl. Sci.
**2020**, 10, 4101. [Google Scholar] [CrossRef] - Atalay, O.; Kalaoglu, F.; Bahadir, S.K. Development of textile-based transmission lines using conductive yarns and ultrasonic welding technology for e-textile applications. J. Eng. Fibers Fabr.
**2019**, 14, 1558925019856603. [Google Scholar] [CrossRef] - Makwana, A.M.; Patel, V.R. Experimental Investigation of Ultrasonic Welding on Thermoplastic Material—A Review. Int. J. Eng. Res. Technol.
**2017**, 6, 350–352. [Google Scholar] - Palardy, G.; Villegas, I.F. On the effect of flat energy directors thickness on heat generation during ultrasonic welding of thermoplastic composites. Compos. Interfaces
**2017**, 24, 203–214. [Google Scholar] [CrossRef] [Green Version] - Chinnadurai, T.; Prabaharan, N.; Saravanan, S.; Karthigai, P.; Pandiyan, P.; Alhelou, H.H. Prediction of Process Parameters of Ultrasonically Welded PC/ABS Material Using Soft-Computing Techniques. IEEE Access
**2021**, 9, 33849–33859. [Google Scholar] [CrossRef] - Petriceanu, S.; Rontescu, C.; Cicic, D.; Bogatu, A. Ultrasonic characterization of the PVC welded materials. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, UK, 2018; Volume 849, pp. 1–8. [Google Scholar]
- Khmelev, V.N.; Abramov, A.D. Model of Process and Calculation of Energy for a Heat Generation of a Welded Joint at Ultrasonic Welding Polymeric Thermoplastic Materials. In Proceedings of the 8th Siberian Russian Workshop and Tutorial on Electron Devices and Materials, Novosibirsk, Russia, 1–5 July 2007. [Google Scholar]
- Dieulesaint, E.; Royer, D. Elastic Waves in Solids, 1st ed.; John Wiley & Sons: Hoboken, NJ, USA, 1980; pp. 239–240. [Google Scholar]
- Pfaff Industrial. PFAFF 8310 -041/002 with Sonotrode from Top, Feed-off-the-Arm Version (from Side). Available online: https://www.pfaff-industrial.com/en/portfolio/welding-machines/ultrasonic-sealing-machines/pfaff-8310-042-sontrode-unten (accessed on 7 August 2022).
- InfinitiVision 3000A X-Series Oscilloscopes, Data Sheet. Available online: http://www.keysight.com/ (accessed on 7 August 2022).
- Fiber Optic MTI 2100 Fotonic Sensor. Available online: https://mtiinstruments.com/products/non-contact-measurement/fiber-optic-sensors/fiber-optic-mti-2100-fotonic-sensor/ (accessed on 7 August 2022).
- Silva Girão, P.; Postolache, O.; Faria, J.B.; Pereira, J. An Overview and a Contribution to the Optical Measurement of Linear Displacement. Sens. J. IEEE
**2002**, 1, 322–331. [Google Scholar] [CrossRef] - Sauter model HF 500, Scales and Measuring Instruments. Available online: https://scales-measuring.com/en/force-measurement/2172-digital-force-gauge-sauter-fh-500.html (accessed on 7 August 2022).
- Sauter Electrical Horizontal Test Stand THM 500N500N. Available online: https://www.kern-sohn.com/shop/en/measuring-instruments/force-gauges/THM/ (accessed on 7 August 2022).

**Figure 1.**Machine components and acoustic parameters used in the ultrasonic welding process utilizing the rotary sonotrode ultrasonic welding machine.

**Figure 2.**A symbolic author’s presentation of the intensity, propagation, reflection and absorption of ultrasonic waves, suitable for production engineering.

**Figure 5.**The measuring system for measuring breaking forces of an ultrasonic welded joint (

**a**), test clamps with a test specimen after tearing (

**b**).

**Figure 6.**Dependence of the vibration amplitude of the rotary ultrasonic sonotrode on the declared power of the ultrasonic generator.

**Figure 8.**A diagram showing the functional relationships between the breaking forces of ultrasonic welds and the speed at which specimens are welded using a rotary ultrasonic sonotrode in relation to the declared electrical power of the ultrasonic generator.

**Table 1.**The results of breaking force values and standard deviations of specimens of ultrasonic welds and visual observation grades of ultrasonic welds before and after tearing.

v_{s}, m/s | Testing Elements | P_{d}, W | |||||
---|---|---|---|---|---|---|---|

200 | 244 | 280 | 320 | 356 | 400 | ||

0.077 | Visual observation grades of ultrasonic welds before tearing | A | A | A | C | C | C |

Breaking force of ultrasonic welded joint F [N] | 33.80 | 30.80 | 23.90 | - | - | - | |

Standard deviation | 4.66 | 6.2 | 3.12 | - | - | - | |

Visual observation grades of ultrasonic welds after tearing | D, E | E | E | - | - | - | |

0.097 | Visual observation grades of ultrasonic welds before tearing | A | A | A | B | C | C |

Breaking force of ultrasonic welded joint F [N] | 28.24 | 32.24 | 31.21 | 27.75 | - | - | |

Standard deviation | 1.46 | 4.02 | 4.09 | 3.01 | - | - | |

Visual observation grades of ultrasonic welds after tearing | D | D, E | E | E, F | - | - | |

0.113 | Visual observation grades of ultrasonic welds before tearing | A | A | A | B | C | C |

Breaking force of ultrasonic welded joint F [N] | 23.14 | 31.00 | 32.34 | 26.00 | - | - | |

Standard deviation | 2.95 | 3.00 | 3.95 | 2.10 | - | - | |

Visual observation grades of ultrasonic welds after tearing | D | D | D, E | E, F | - | - | |

0.125 | Visual observation grades of ultrasonic welds before tearing | A | A | A | A | C | C |

Breaking force of ultrasonic welded joint F [N] | 21.20 | 30.15 | 33.50 | 24.14 | - | - | |

Standard deviation | 5.49 | 2.41 | 2.63 | 3.07 | - | - | |

Visual observation grades of ultrasonic welds after tearing | D | D | D, E | F | - | - | |

0.147 | Visual observation grades of ultrasonic welds before tearing | A | A | A | A | C | C |

Breaking force of ultrasonic welded joint F [N] | 15.32 | 24.66 | 28.48 | 30.94 | - | - | |

Standard deviation | 2.87 | 2.05 | 3.12 | 2.64 | - | - | |

Visual observation grades of ultrasonic welds after tearing | D | D | D | D | - | - | |

0.167 | Visual observation grades of ultrasonic welds before tearing | A | A | A | A | C | C |

Breaking force of ultrasonic welded joint F [N] | 12.30 | 22.12 | 26.00 | 28.60 | - | - | |

Standard deviation | 1.38 | 1.62 | 2.93 | 4.01 | - | - | |

Visual observation grades of ultrasonic welds after tearing | D | D | D | D | - | - | |

0.227 | Visual observation grades of ultrasonic welds before tearing | - | - | A | A | A | A |

Breaking force of ultrasonic welded joint F [N] | - | - | 5.40 | 14.33 | 21.40 | 26.30 | |

Standard deviation | - | - | 3.41 | 3.21 | 2.91 | 3.12 | |

Visual observation grades of ultrasonic welds after tearing | - | - | D | D | D | D |

**Table 2.**Values of the vibrations, effective power, speed and welding time achieved by the ultrasonic rotary sonotrode depend on the specified electrical power.

P_{dmax}, W | A_{0}, µm | P_{α}, W | v_{s}, m/s | t_{m}, s | t_{s}, s | Δ (t_{m} − t_{s}), s |
---|---|---|---|---|---|---|

200 | 68.1 | 126.5 | 0.077 | 0.288 | 0.259 | 0.029 |

250 | 85.1 | 197.5 | 0.097 | 0.184 | 0.206 | −0.022 |

268 | 91.1 | 226.3 | 0.113 | 0.161 | 0.177 | −0.016 |

272 | 92.5 | 233.4 | 0.125 | 0.156 | 0.160 | −0.004 |

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## Share and Cite

**MDPI and ACS Style**

Rogale, D.; Fajt, S.; Firšt Rogale, S.; Knezić, Ž.
Interdependence of Technical and Technological Parameters in Polymer Ultrasonic Welding. *Machines* **2022**, *10*, 845.
https://doi.org/10.3390/machines10100845

**AMA Style**

Rogale D, Fajt S, Firšt Rogale S, Knezić Ž.
Interdependence of Technical and Technological Parameters in Polymer Ultrasonic Welding. *Machines*. 2022; 10(10):845.
https://doi.org/10.3390/machines10100845

**Chicago/Turabian Style**

Rogale, Dubravko, Siniša Fajt, Snježana Firšt Rogale, and Željko Knezić.
2022. "Interdependence of Technical and Technological Parameters in Polymer Ultrasonic Welding" *Machines* 10, no. 10: 845.
https://doi.org/10.3390/machines10100845