# New Method for Determining the Machine-Hand Welding Times Using Ultrasonic Welding Machines with Rotary Sonotrode

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Some Basic Principles of the Reaction Model according to Möller during Sewing

_{w1}, x

_{w2}, x

_{w3}.

_{ar}—normal time of machine-hand technological sub-operations (s); l

_{s}—length of the sewn segment of the seam (cm); G

_{u}—specific density of sewn stitches (cm

^{−1}); v

_{n}—nominal stitching speed of the sewing machine (min

^{−1}); R

_{p}–necessary reaction abilities; R

_{max}—maximum reaction abilities; D—addition for activating the pedal and for transient acceleration and braking of the electric motor of the sewing machine.

_{p}depending on the characteristic group and the radius of curvature r

_{z}, the joining accuracy x

_{w1}and the method of guiding the workpiece. W. Möller defined only three groups of seam curvature (straight or slightly with radius ≥ 60 cm, medium with radius ≥ 30 to 60 cm and strongly curved with radius to 30 cm) and specified which of the characteristic seams joining in the parts of the garments belong to which group.He added three groups of permissible tolerances of 1, 2 and 3 mm for each group of characteristic seams and gave numerical values of the required reactions.

_{p}and R

_{max}, which is an integral part of the expression. The extension of the sewing time will be greater with reducing the radius of curvature of the seam and with the required accuracy of joining these seams (R

_{p}values) and because sewing will be performed by machines with higher nominal sewing speeds and lower specific stitch densities (R

_{max}values).

_{ef}using the reaction factors R

_{p}and R

_{max}(3).

_{ef}—effective stitching speed of the sewing machine (min

^{−1}).

## 3. Development of a New Reaction Model for Ultrasound Welding with Rotary Sonotrode

^{−1}to 13.6 m min

^{−1}. The thickness of the welded composite polymer material may range from 50 µm to 2 mm, and can be varied with an accuracy of 20 µm and a welding force of up to 800 N. The linear speed of the sonotrode circumference and thus the displacement of the material, i.e., the welding speed, depends on the radius of the sonotrode and the angular speed of its rotation. During the rotation of the sonotrode, the layers of the polymer material are guided manually in such a way that the welding is performed by guiding the workpiece along the required trajectory of the weld, taking care of the permissible deviation tolerance. In this way, the simultaneous work of the machine and the worker is performed, the so-called machine-hand work, whereby the machine supplies the required energy of ultrasonic vibrations and moves the workpiece, and the worker aligns the edges of the material and manually guides the workpiece along the seam trajectory with occasional corrections in accordance with the permissible tolerance.

#### 3.1. Technical, Technological and Ergonomic Parameters of the New Model

- radius of ultrasonic rotary sonotrode r
_{s}in cm; - angular speed of rotation of the ultrasonic sonotrode, ω
_{s}in rad s^{−1}; - maximum possible angular speed of sonotrode rotation, ω
_{max}in rad s^{−1}; - linear speed of the sonotrode circumference, i.e., the speed of workpiece displacement, vs. in cm s
^{−1}; - nominal welding speed or maximum possible circumferential speed in ultrasonic welding with rotary sonotrode—v
_{max}in cm s^{−1}; - critical radius of curvature of the weld above which the highest welding speed of the machine can be used, r
_{krit}in cm; - delay time of the beginning of welding due to the heating of the beginning of the weld, t
_{dy}in s; and - critical radius of curvature of the weld, r
_{zk}in cm.

- length of the ultrasonic weld of a segment until the tolerance of the weld accuracy is reached, w
_{x}in cm; - total length of the ultrasound weld, l
_{s}in cm; - radius of curvature of the segment of the weld seam, r
_{z}in cm; - permissible tolerance of deviation of the set and actual seam trajectory, x
_{w1}in cm; - machine time of welding all segments of the seam with ultrasonic rotary sonotrode without correction due to the reaction abilities of the worker, t
_{t}in s; - total welding time of all segments with added times of activating the machine pedal and delay of the beginning of welding, t
_{tot}in s; - recommended linear speed of the sonotrode circumference, v
_{prep}in cm s^{−1}; and - recommended angular speed of the ultrasonic sonotrode, ω
_{prep}in rad s^{−1}.

- latent reaction time of the worker, t
_{reak}in s; - number of required reactions of the worker R
_{p}; - number of maximum possible reactions of the worker R
_{max}; - machine-hand seam welding using the rotary sonotrode based on human reactions, tar in s;
- recommended speed of ultrasonic welding with regard to reaction abilities of the worker, v
_{prep}in cm s^{−1}; - number of interruptions in the weld, i.e., number of welding segments in the ultrasonic weld; and
- activation time of the machine pedal, t
_{fm}in s.

#### 3.2. Relationship between Model Parameters

_{t}is increased by the reaction abilities R

_{p}and R

_{max}(4):

_{s}and the angular speed of the rotation of the sonotrode ω

_{s}(5):

_{t}can be expressed by the usual mathematical expression for calculating machine work as the ratio of the total length of the ultrasonic weld ls and nominal welding speed or maximum possible circumferential speed of ultrasonic welding with rotary sonotrode—v

_{max}(6).

_{max}by expression (7):

_{max}(8).

_{max}can be calculated by expression (9):

_{max}depends on the type of the ultrasonic machine with rotary sonotrode, or sonotrode radius and the highest possible angular speed of the sonotrode rotation.

_{p}it is necessary to define the deviation between the nominal and actual ultrasonic weld observed by the worker during the ultrasonic welding as shown in Figure 4. This figure shows a layout of welding two layers of polymer materials with a rotary sonotrode showing important technological welding parameters: radius of curvature of the segment r

_{z}, permissible tolerance of deviations of the nominal and actual seam trajectory x

_{w1}and the length of the ultrasonic weld of one segment until reaching the tolerance of the weld accuracy w

_{x}.

_{x}until reaching the given tolerance of the welding accuracy x

_{w1}for some radius of curvature of the weld x

_{w1}can be calculated by expression (13):

_{z}and the permissible tolerance of the nominal and actual trajectory of the ultrasonic weld x

_{w1}, is calculated by expression (14) taking into account the geometry of parameters in Figure 4:

_{prep}can be determined by expression (16):

_{prep}(17):

_{z}and the permissible tolerance of deviations of the nominal and actual seam trajectory x

_{w1}.

_{prep}is calculated by expression (18).

_{p}in tabular form on the basis of operational measurements of groups of welds with different radii of curvature and tolerances of trajectory deviations, as in Möller, but they are determined mathematically for any radius of curvature and specified tolerance. In addition, the defined expressions also show a mathematical correlation of all 23 process parameters relevant for determining the time of the ultrasonic welding based on human reactions, which is favourable for future studies of various high-tech welding methods in industrial manufacturing processes.

_{x}according to Figure 4 and reaching the permissible welding tolerance x

_{w1}(specified welding accuracy), the operator stops the rotation of the sonotrode by releasing the machine pedal, whereby the ultrasonic generator is switched off. The worker then repositions the workpiece and activates the pedal to make the other segment of the weld. The procedure is repeated until all segments of the weld have been made on the entire length of the weld ls. As there are usually several such segments, the activation and releasing time of the pedal should not be neglected. The number of seam interruptions n in the seam, i.e., the number of seam welding segments is calculated by expression (19):

_{fm}and the delay time of the beginning of welding due to heating of the beginning of the weld, t

_{dy}at the beginning of the weld when the sonotrode is idle, and the ultrasonic generator works and heats the beginning of the weld. After the delay time for the start of the sonotrode rotation has expired, the sonotrode rotation mechanism is automatically switched on.

_{zk}. If v

_{max}is inserted into expression (17) instead of v

_{prep}and r

_{zk}is excluded, (21) is obtained:

#### 3.3. Methodological Application Steps of the New Model

- length of the ultrasonic weld of a segment w
_{x}until reaching the specified tolerance of the accuracy of the ultrasonic weld according to expression (13); - number of welding interruptions n in the ultrasonic weld, i.e., number of welding segments according to expression (19);
- number of required reactions of the worker R
_{p}according to expression (14); - number of maximum possible reactions of workers R
_{max}, according to expression (12); - recommended speed of ultrasonic welding with regard to the reaction ability of the worker, v
_{prep}in cm s^{−1}, according to expression (16) or (17); - machine-hand welding time with ultrasonic rotary sonotrode based on human reactions, tar in s, according to expression (15) or (8);
- total welding time of all segments with the added activation times of the machine pedal and the delay of the beginning of welding, t
_{tot}according to expression (20) and; - critical radius of curvature r
_{zk}according to expression (21).

## 4. Results and Discussion

_{prep}, and taking into account the reaction ability of the worker, their values were calculated for the lengths of curved welds up to 120 mm and for curvature radii up to 160 mm. These values are often found in ultrasound welding of waterproof clothing, thermal insulation chambers on clothing and other items made of technical textiles. The calculation was performed for three groups of permissible tolerances of deviation of the nominal and actual seam trajectories x

_{w1}of 2, 4 and 6 mm. For each permissible tolerance, a diagram of the dependence of machine-hand times on the length and radius of curvature of the weld and a diagram of the dependence of the recommended welding speed on the length and radius of curvature of the weld were made. Figure 5, Figure 6 and Figure 7 show diagrams of the mentioned dependencies. It can be seen that the maximum machine-hand time will be required for ultrasonic welding of long welds with small radius of curvature, and the least amount of machine-hand time for welding short welds with large radius of curvature. At the same time, the machine-hand welding time decreases as the permissible welding tolerance increases, Figure 5a, Figure 6a and Figure 7a.

_{prep}on the radius of curvature of the weld for the degree of welding accuracy of 2, 4 and 6 mm. These are in fact the highest welding speeds that can be applied with regard to possible reaction abilities of the worker and according to them the ultrasonic machine should be programmed when the radius of curvature of the weld and the required welding accuracy is known. It can be seen that the recommended welding speeds are low when it comes to strongly curved welds and high accuracy, and they increase as the curvature of the welds and welding accuracy decrease.

_{zk}on the radius of curvature r

_{z}for an ultrasonic machine with a nominal welding speed of 23 cm s

^{−1}and a sonotrode diameter of 105 mm. The critical radius decreases with the increasing welding accuracy. This diagram applies only to machines with the same maximum welding speed and sonotrode diameter and cannot be used for other machines with different technical characteristics.

_{p}according to Möller for the welding accuracy of 1, 2 and 3 mm and according to the mathematical model presented for the same welding accuracies. It can be seen that Möller’s change in the required reactions is erratic.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Maynard, H.B. Industrial Engineering Handbook, 1st ed.; McGraw-Hill Book Company, Inc.: New York, NY, USA, 1956; pp. 59–78. [Google Scholar]
- Möller, W. Realistische Prozesszeit für das Maschinennähen. Bekleidungstechnik
**1990**, 36, 30–32. [Google Scholar] - Troughton, M.J. Ultrasonic Welding. In Book Handbook of Plastics Joining: A Practical Guide, 2nd ed.; William Andrew Inc.: Norwich, NY, USA, 2008; pp. 15–17. [Google Scholar]
- Coverall, Gowns and Surgical Gowns Part of the Broader Needs. Available online: https://euratex.eu/covid-19/protective-garments/coverall-gowns-and-surgical-gowns/ (accessed on 24 November 2021).
- Heckner, R. Zeitwertkartei und Proceßzeitberechnung für die Näherei. Bekleid. Wäsche
**1975**, 27, 1081–1084. [Google Scholar] - Krowatschek, F.; Nestler, F. Bessere Nahtqualität durch Langsamnähen. Bekleid. Wear
**1994**, 36, 25–27. [Google Scholar] - Krowatschek, F.; Ludemann, P. Der Nähvorgang als Kybernetisches System. In Band 5, Forschnunggemeinschaft, Bekleidungsindustrie; Systemdruck: Berlin, Germany, 1974; pp. 82–89. [Google Scholar]
- Kumbhar, O.; Sizikova, E.; Majaj, N.; Pelli, D. Anytime Prediction as A Model of Human Reaction Time. 2020. Available online: https://www.researchgate.net/publication/346373453_Anytime_Prediction_as_a_Model_of_Human_Reaction_Time (accessed on 6 June 2021).
- Kroemer, K.H.E. Fitting the Human; CRC Press: Boca Raton, FL, USA, 2017. [Google Scholar]
- Schmidtke, H. Ergonomie; Carl Hanser Verlag GmbH & Co. KG: Deutschland, Germany, 1993. [Google Scholar]
- Bullinger, H.J. Ergonomie, Produkt-und Arbeitsplatzgestaltung; Teubner, B.G., Ed.; Verlag: Deutschland, Germany, 1994. [Google Scholar]
- Vujasinović, E.; Rogale, D. Properties and performance of welded or bonded seams. In Joining Textiles: Principles and Applications; Woodhead Publishing: Sawston, UK, 2013; pp. 435–461. [Google Scholar]
- Leśnikowski, J. Research into the Textile-Based Signal Lines Made Using Ultrasonic Welding Technology. AUTEX Res. J. Available online: https://content.sciendo.com/view/journals/aut/ahead-of-print/article-10.2478-aut-2020-0025/article-10.2478-aut-2020-0025.xml?language=en (accessed on 22 October 2021). [CrossRef]
- Firšt Rogale, S.; Dragčević, Z.; Rogale, D. Determining Reaction Abilities of Sewing Machine Operators in Joining Curved Seams. Int. J. Cloth. Sci. Technol.
**2003**, 15, 179–188. [Google Scholar] [CrossRef]

**Figure 2.**Control circuits A, B and C and permissible deviation tolerances x

_{w1}, x

_{w2}and x

_{w3}during guiding the workpiece when joining seams on garment parts.

**Figure 3.**Ultrasonic welding zone of polymer materials, rotary sonotrode and engraved counter-roller of the ultrasonic machine.

**Figure 4.**Layout of welding two layers of polymer materials with rotary ultrasonic sonotrode together with the specified technological welding parameters.

**Figure 5.**Dependency diagrams for a permissible welding tolerance of 2 mm: (

**a**) machine-hand times on the length and radius of curvature of the weld; (

**b**) recommended welding speeds on the length and radius of curvature of the weld.

**Figure 6.**Dependency diagrams for a permissible welding tolerance of 4 mm: (

**a**) machine-hand times on the length and radius of curvature of the weld; (

**b**) recommended welding speeds on the length and radius of curvature of the weld.

**Figure 7.**Dependency diagrams for a permissible welding tolerance of 6 mm: (

**a**) machine-hand times on the length and radius of curvature of the weld; (

**b**) recommended welding speeds on the length and radius of curvature of the weld.

**Figure 8.**Machine-hand welding time with ultrasonic rotary sonotrode based on human reactions for a 120 mm long weld seam and for a welding accuracy of 2, 4 and 6 mm according to the model (blue curve) and experimental measurements (red curve).

**Figure 9.**Machine-hand welding time with ultrasonic rotary sonotrode based on human reactions for an 80 mm long weld seam and for a welding accuracy of 2, 4 and 6 mm according to the model (blue curve) and experimental measurements (red curve).

**Figure 10.**Machine-hand welding time with ultrasonic rotary sonotrode based on human reactions for a 40 mm long weld seam and for a welding accuracy of 2, 4 and 6 mm according to the model (blue curve) and experimental measurements (red curve).

**Figure 11.**Dependency of the recommended speed of ultrasonic welding in relation to the reaction abilities of the worker, v

_{prep}on the radius of curvature of the weld for the degree of welding accuracy of 2, 4 and 6 mm.

**Figure 12.**Dependence of the critical radius of curvature r

_{zk}on the radius of curvature r

_{z}for an ultrasonic machine with a nominal welding speed of 23 cm s

^{−1}and a sonotrode diameter of 105 mm.

**Figure 13.**Dependence of the required number of reactions R

_{p}on the radius of curvature r

_{z}according to Möller for a welding accuracy of 1, 2 and 3 mm and according to the mathematical model presented for the same welding accuracy.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rogale, D.; Rogale, S.F.; Knezić, Ž.; Fajt, S. New Method for Determining the Machine-Hand Welding Times Using Ultrasonic Welding Machines with Rotary Sonotrode. *Machines* **2021**, *9*, 330.
https://doi.org/10.3390/machines9120330

**AMA Style**

Rogale D, Rogale SF, Knezić Ž, Fajt S. New Method for Determining the Machine-Hand Welding Times Using Ultrasonic Welding Machines with Rotary Sonotrode. *Machines*. 2021; 9(12):330.
https://doi.org/10.3390/machines9120330

**Chicago/Turabian Style**

Rogale, Dubravko, Snježana Firšt Rogale, Željko Knezić, and Siniša Fajt. 2021. "New Method for Determining the Machine-Hand Welding Times Using Ultrasonic Welding Machines with Rotary Sonotrode" *Machines* 9, no. 12: 330.
https://doi.org/10.3390/machines9120330