The paper presents a description of test stands and the methodology ofdetermining the static characteristics of a metal coupling of high torsional flexibility. In addition, the paper presents preliminary tests results which enable to determine the above characteristics

Krzysztof FILIPOWICZ

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TRANSPORT PROBLEMS                                                                                                               2008 PROBLEMY TRANSPORTU                                                                                          Tom 3 Zeszyt 1     Krzysztof FILIPOWICZ Silesian University of Technology, Faculty of Mining and Geology, Institute of Mining Mechanisation Akademicka 2, 44-100 Gliwice, Poland Corresponding author. E-mail: krzysztof.filipowicz@polsl.pl    THE STATIC CHARACTERISTICS OF A TORSIONALLY FLEXIBLE METAL COUPLING  Summary. The paper presents a description of test stands and the methodology of determining the static characteristics of a metal coupling of high torsional flexibility. In addition, the paper presents preliminary tests results which enable to determine the above characteristics.    CHARAKTERYSTYKI STATYCZNE METALOWEGO SPRZĘGŁA PODATNEGO SKRĘTNIE  Streszczenie. W pracy przedstawiono budowę nowego rozwiązania konstrukcyjnego metalowego  sprzęgła  o  duŜej  podatności  skrętnej  oraz  opis  stanowisk  badawczych  i metodykę wyznaczania jego charakterystyk statycznych. Zaprezentowano takŜe uzyskane wstępne wyniki badań, pozwalające na wyznaczenie wymienionych charakterystyk.   1. INTRODUCTION  The  conditions  of  work  of  power  transmission  systems  used  in  building,  road  and  mining machines where the transferred torque is in most cases randomly variable require the use of couplings of  high  torsional  flexibility.  Such  couplings  are  resistant  to  specific  loads.  The  proper  torsional flexibility may be achieved by means of a solution developed in the Institute of Mining Mechanisation at the Silesian University of Technology. The patented construction of a torsionally flexible metal coupling has been described in literature [2,3,4]. A torsionally flexible coupling is characterised by specific elastic and damping features, which have a basic influence on the performance of the power transmission system due to the change of run and stabilisation of torsional vibration and the load torque. The use of torsionally flexible couplings of unknown  characteristics  may  lead  to  the  incorrect  performance  of  the  whole  power  transmission system. Thus, it is vital to determine the static and dynamic characteristics of torsionally flexible coupling.  Such  knowledge  will  ensure  the  correct work  of  the  power  transmission  system  of  the working machine. The constructive analysis of torsionally flexible couplings, the majority of which has a complex construction and contains flexible connectors of physico-chemical features hard to define, leads to the conclusion that the most proper and advantageous way of determining the characteristics of torsionally flexible couplings is to carry out tests with the use of proper testing stands.  70                                                                                                                                          K. Filipowicz  2. RESEARCH AREA  The  tests  were  carried  out  on  one  of  the  constructive  proposals  of  a  new,  one-directional torsionally flexible metal coupling (Fig.1), where the torque is transmitted from the active to the passive by means of a nut with two screw joints. The screw joints are placed between the externally threaded input shaft (1) and the nut (2), which also has a screw thread on the external cylindrical surface. The external screw thread co-operates with the internal screw thread in the housing (4). Both screw joints have different directions and pitches. The pitches of multiple threads are big enough so that the lead angle is bigger than the friction angle for the screw and nut materials [3, 4]. The  resistance  of  a  properly  chosen  set  of  disk  springs  (Fig.1,  position  3)  and  the  rotary movement  of  the  input  shaft  makes  the  springs  press  the  nut.  This  leads  to  the  increase  of  the component of force in the circumferential direction on the screw thread. The increase of this force causes the increase of the torque, and when it reaches the running torque of the machine, its rotary movement, which is at the same time the working movement begins.   Fig. 1. The prototype of one-way flexible torsional coupling, a – view of the coupling, b – depositional drawing of the coupling, where: 1 – driveshaft, 2 – screw nut with inside and outside thread, 3 – disc springs set, 4 – inner thread housing, 5 – left cover, 6 – output cover, 7 – regulatory ring, 8 – disk sealing up, 9 – seal, 10 – cone bearings, 11 – thrust bearing, 12 – cone bearings, 13 – sealing ring Rys. 1. Prototyp jednokierunkowego sprzęgła podatnego skrętnie z dwoma gwintami, gdzie: 1 – wał wejściowy, 2 – nakrętka z gwintem wewnętrznym i zewnętrznym, 3 – zespół spręŜyn talerzowych, 4 – obudowa z gwintem wewnętrznym, 5 – pokrywa lewa, 6 – piasta wyjściowa, 7 – pierścień regulacyjny, 8 – tarcza uszczelniająca, 9 – uszczelnienia, 10 – łoŜysko stoŜkowe, 11 – łoŜysko wzdłuŜne, 12 – łoŜysko stoŜkowe, 13 – pierścień uszczelniający  Temporary overloads of the working machine causes the additional compression of the elastic elements, and underloads lead to their elastic recovery. When the power transmission system is turned off, the nut pressed by the springs returns to its preliminary position on the input shaft. When the preliminary compression of the nut is big enough and the system has been turned off, the nut returns to its initial position. The torsional angle of the coupling elements caused by the nominal load between the input and output may be quite significant and reaches e.g. the full turn of the input shaft (active) before the output  shaft  (passive)  begins  its  rotary  motion.  The  construction  of  a  torsionally  flexible  metal coupling has been described in previous papers and the patent description [3, 4]. The tests were carried out with the use of couplings with four different sets of disc springs. The choice of these sets was based on the analysis of disc springs characteristics arranged in packs and forming sets. The sets were chosen so that with the maximum torque moment Mmax = 100 Nm, the springs would work below the accepted working range, that is 75% of the maximum deflection. The static characteristics of a torsionally flexible metal coupling                                                          71  Table 1 contains the data regarding the disc springs used in the coupling and the sets that were placed in it.                                                                                                                                                    Tab. 1 The sets of the disc springs used in the coupling  Coupling Number Type of disc springs DIN 2093 The number of springs in the pack The arrangement of the pack 1  40 x 20,4 x 2,5  5  <<<<< >>>>> 2  40 x 20,4 x 2,5  4  <<<< >>>> 3  40 x 20,4 x 2,25  4  <<<< >>>> 4  40 x 20,4 x 2  4  <<<< >>>>   3. DETERMINING THE STATIC CHARACTERISTICS OF THE COUPLING  The static characteristic of a flexible coupling is a dependency of the torque Mobr, which turns the coupling by the specific angle of rotation j between the active and the passive element of the coupling. The changes of the torque in this case should be very slow.                        Mobr = f (φ)                                                                        (1)  where: Mobr – the torque moment on the flexible coupling, Nm, φ - relative angle of rotation of the coupling elements, radian or degrees.  The shape of the static characteristics depends on the construction of the coupling, the material used  for  the  flexible  connecting  link  i.e.  the  elastic-damping  system  and  the  very  shape  of  the connecting link. In case of couplings with flexible rubber elements or elastomers which are most commonly used in power transmission systems of working machines, the characteristic is nonlinear with damping which makes it hard to choose the proper coupling for the power transmission system [1,5,8].  3.1. The testing stand and methodology of determining the static characteristics of a flexible  coupling  The testing stand used to determine the static characteristics of a coupling is used to test the mechanical couplings built in the Institute of Mining Mechanisation at the Silesian University of Technology, as shown in Fig.2. The  electric  motor  (1)  powered  by  the  inverter,  which  enables  the  smooth  regulation  of  the rotational speed from 0 ÷ 1700 min-1, is connected with the tensometric torque meter (5) used to test the torque moment Mobr = Mstat. The value of the measured torque is read and recorded by means of a computerised measuring apparatus (7) of type SCXI produced by National Instruments. One of the elements of the tested flexible metal coupling - the housing (2) is directly attached to the output shaft of the torque meter. The other element of the coupling - the output shaft - is attached to the hydraulic disc brake (3) which is controlled from the pressure supply system (4). The output shaft of the coupling i.e. the passive element of the coupling is attached to the rotary disc with an angular scale 0°÷360° (6). An indicating needle attached to the coupling housing was used to read the relative angular displacement of the elements j = jstat. 72                                                                                                                                          K. Filipowicz  When the coupling is secured at the testing stand by means of a fully blocked hydraulic brake, one of the elements of the flexible clutch may no longer turn. The electric motor is activated by means of an inverter and the static torque Mstat is gradually increased. The torque moment changes every 10 Nm in order to reach the maximum Mmax = 100Nm. At the same time the relative angular displacement of the coupling elements φstat on the angular scale of the disc is read by means of an indicating needle attached to the movable housing. The precision of the reading is ± 1º. The readings of the dependency of the torque Mstat on the relative angular displacement φstat is carried out with and without the load. The  aim  of  this  procedure  is  to  determine  the  histeresis  loop  which  presents  the  value  of  the mechanical energy damping in the coupling.  Fig. 2.  The testing stand used to test the mechanical couplings, where: 1 – electric motor, 2 – tested flexible coupling, 3 – hydraulic disc brake, 4 – control system of hydraulic brake, 5 – torque meter, 6 – disc with an a angular scale, 7 – measuring-recording set Rys. 2. Stanowisko do badania sprzęgieł mechanicznych, gdzie: 1 – silnik elektryczny, 2 – badane sprzęgło podatne, 3 – tarczowy hamulec hydrauliczny, 4 – układ sterowania hamulcem hydraulicznym, 5 – momentomierz tensometryczny, 6 – tarcza z podziałką kątową, 7 – aparatura pomiarowo-rejestrująca  3.2. The static characteristics of a torsionally flexible metal coupling  The tests enabled to determine the basic static characteristics of the four options of a torsionally flexible metal coupling for spring sets as shown in table 1. Figures 3 are the graphic illustration of the determined  static  characteristics  of  different  options  of  the  coupling.  The  determined  static characteristics  of  the  torsionally  flexible  metal  coupling  are  linear  with  damping  of  coefficient r = 0,98. When the coupling characteristics are linear as those obtained in the tests, we can determine the coefficient called the torsional rigidity of the coupling k for each of them. For the determined linear static characteristics, the dependency is expressed as follows:                                                                           statstat Mkj=                                                           (2) where:  Mstat  – the static torque moment on the coupling, Nm φstat – the corresponding relative  angular displacement of the coupling elements,  radian or degrees. The static characteristics of a torsionally flexible metal coupling                                                          73  a)                         b) 0 30 60 90 120 150 180 210 240 270Relative angular displacement   jstat , °0102030405060708090100110120Static torque moment  Mstat ,  NmNr 1   2,5 x <<<<< 5AsAr      0 30 60 90 120 150 180 210 240 270Relative angular displacement   jstat , °0102030405060708090100110120Static torque moment  Mstat ,  NmNr 2   2,5 x <<<< 4AsAr  c)                        d) 0 30 60 90 120 150 180 210 240 270Relative angular displacement   jstat , °0102030405060708090100110120Static torque moment  Mstat ,  NmNr3   2,25 x <<<< 4AsAr     0 30 60 90 120 150 180 210 240 270Relative angular displacement   jstat , °0102030405060708090100110120Static torque moment  Mstat ,  NmNr 4   2 x <<<< 4ArAs      Fig. 3.  The illustration of some static characteristics of torsionally flexible metal coupling, where: a – coupling nr 1, b – coupling nr 2, c – coupling nr 3, d – coupling nr 4 Rys. 3.  Ilustracja charakterystyk statycznych czterech opcji metalowego sprzęgła podatnego skrętnie, gdzie: a – sprzęgło nr 1, b – sprzęgło nr 2, c – sprzęgło nr 3, d – sprzęgło nr 4 The flexible metal coupling is not only rigid but it also absorbs energy. The histeresis loop was obtained during loading and unloading and it presented the histeresis losses of the mechanical energy in the coupling called damping.  In the flexible metal coupling damping is achieved by means of constructive friction in screw joints mainly. The  value  of  the  mechanical  energy  damping  in  the  coupling  is  specified  by  the  damping coefficient that is determined as follows:          srAA= y                                                              (3) 74                                                                                                                                          K. Filipowicz  where:  Ar – damping during one working cycle, Nm × degrees,  As – elastic strain during one work cycle, Nm × degrees. The  obtained  torsional  rigidity  coefficients  as  well  as  the  damping  coefficient  for  the  tested options of the torsionally flexible metal clutch are presented in Table 2.                                                                                                                                                     Tab. 2 The obtained torsional rigidity coefficient k and  the damping coefficient y Coupling Number  Type of disc springs The torsional rigidity coefficient  k,  Nm/° The damping coefficient  y  1  40 x 20,4 x 2,5  1,77  0,20 2  40 x 20,4 x 2,5  0,80  0,33 3  40 x 20,4 x 2,25  0,67  0,45 4  40 x 20,4 x 2  0,45  0,47    4. SUMMARY  The preliminary tests carried out to determine the static characteristics of a torsionally flexible metal coupling lead to the following general conclusions: -  The proposed testing stands as well as the methodology of the static characteristics test enable to quickly  and  correctly  determine  the  static  characteristics  with  acceptable  precision  and repeatability of the achieved measurements results. -  The determined static characteristics of the torsionally flexible coupling are linear with damping of linear correlation coefficient r = 0,98. -  The  position  and  slope  of  the  static  characteristics  and  values  of  the  torsional  rigidity  and damping  coefficients  are  strictly  linked  with  the  application  of  the  disc  springs  sets  in  the coupling, the more rigid the springs the greater torsional rigidity of the coupling and the lower the damping coefficient. -  The coupling characteristics can be shaped by the proper choice of disc springs sets, though one has to take into consideration the condition of the proper performance of the spring i.e. up to 75% of its maximum strain. -  The torsionally flexible metal coupling enables to obtain significant angles of the relative angular displacement  of  the  elements  even  up  to  a  few  hundred  degrees;  the  obtained  angles  are determined by the applied sets of disc springs.  The presented conclusions clearly indicate the advantageous features of the presented constructive solution of the flexible coupling. None of the mechanical couplings which have been used so far in road, building and mining machinery has the above characteristics and the static characteristics as those mentioned above. Classic flexible couplings enable to obtain angles of mutual torsion only up to a few degrees, in most cases with difficulty to describe nonlinear characteristics.  The static characteristics of a torsionally flexible metal coupling                                                          75  Bibliography  1.  Dietrich M. (red.), Markusik S.: Podstawy konstrukcji maszyn. Tom III, wyd. 3. WNT, Warszawa, 1999. 2.  Kowal A.: Sprzęgło mechaniczne. Patent RP: PL 190945 B1 i PL-191092 B1, 2006. 3.  Kowal A.: Konstrukcja metalowego sprzęgła podatnego skrętnie. Biblioteka TEMAG. Trwałość Elementów i Węzłów Konstrukcyjnych Maszyn Górniczych, Gliwice-Ustroń, 2005, s.107-116. 4.  Kowal A., Filipowicz K.: Metalowe sprzęgła podatne skrętnie. Górnictwo i Geologia. T.1, Z.2, Wydawnictwo Politechniki Śląskiej, Gliwice, 2006. 5.  Markusik S.: Sprzęgła mechaniczne. WNT, Warszawa, 1979. 6.  Opasiak T.: Metody wyznaczania charakterystyk statycznych i dynamicznych sprzęgieł podatnych. Maszyny Dźwigowo-Transportowe. 2, 2000, s.5-15. 7.  Opasiak T.: Badania charakterystyk statycznych i dynamicznych sprzęgieł nierozłącznych podatnych oponowych. Praca doktorska, Katowice, 2004. 8.  Osiński Z.: Sprzęgła i hamulce. PWN, Warszawa, 1985.   Received 17.02.2008; accepted in revised form 22.04.2008 

The static characteristics of a torsionally flexible metal coupling

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