SOFTWARE GSPARALW - Version C USER MANUAL
Contents
1. This option draws the surface of contact and the teeth in the transverse plane The teeth can be moved within a cycle to examine the meshing necessary informations are given through the Help in line BEARING LOADS Distances L1 2 3 4 are measured from centre plane of gear to bearing 1 2 3 or 4 See Help in line 11 It is important to enter these distances as positive or negative in accordance with the figures obtained with the Help in line Bearings below the centre plane of gears involve negative values of L The direction of rotation and helix hand applie to the pinion When the wheel is driving speed increaser reverse the direction of rotation GSPARALW displays for each direction of rotation and helix hand the load applied to each bearing for a unity torque at the pinion Multiply the figures displayed by the actual torque to obtain the actual load GSPARALW also displays the load angle dec degrees for each bearing as measured from the centre line 12 Tolerances NFE 23 006 Tolerances according to the french standard are easily accessible as well for the pinion as for the wheel Allowances can be applied either to the span dimensions W K teeth or to the tooth normal thickness Some comments follows Most standard allowances are negative in order to provide backlash If they were applied to the span dimensions W K teeth of internal gears the result would be seizure instead of backlash This is why the appl2. Fig 1 When the difference between the pinion and wheel numbers of teeth is too small this specific interference may occur In this case the pinion or shaper tooth tip trims the wheel tooth tip This type of interference is advised and the amount of trimming is given as well for the pinion as for the shaper With a pressure angle of 20 a dif ference of 8 teeth between pinion or shaper and wheel is usually sufficient to prevent interference 8 Radial engagement Fig 1 When the difference between the pinion and wheel numbers of teeth is not sufficient it may not be possible to engage the pinion radially in the wheel but only axially In the case of a shaper it is clearly impossible to make axial engagement and consequently trimming of the teeth would result This is advised as well for the pinion as for the shaper In this latter case the amount of trimming is given 9 Interference at tooth bottom When the shaper addendum is not sufficient to generate the wheel profile to the necessary height an interference may occur when meshing with the pinion This is exactly the same type of interference as that existing at the tip but now at the bottom GSPARALW advises this type of interference Another shaper can then be selected or alternatively reduce the pinion tip diameter by an amount equal to two times the interference All these calculations are carried on from the nominal dimensions If some backlash is provided by the
3. angle beta helix angle betab base helix angle delta 1 2 3 4 angle of load F1 2 3 4 See Help in line epsilon oe transverse contact ratio 1 epsilon overlap axial ratio Should be gt 1 to provide full advantage of helical gearing When epsilon the load capacity of helical gears is impaired Increase helix angle or face width or choose a smaller module to make epsilon 2 AUTOMATIC DETERMINATION SHIFT COEFFICIENTS The option automatic determination of rack shift coefficients not only prevents undercutting but optimises the rack shift coefficients to balance exactly the slide roll ratios of pinion and wheel 3 This option is accessible as well with free or imposed centre distance for external or internal gears For the latter it is however quite satisfactory to give both pinion and wheel a positive coefficient of 0 4 to 0 5 normal module Incidentally the slide roll ratio the value of which is displayed characterises the resistance to wear the closer it is to zero the closer the contact is to pure rolling and therefore the smaller is the wear The balance results in an equal sharing of wear between pinion and wheel EXTERNAL GEARING 4 When the data entered number of teeth helix angle rack shift coefficient lead to undercutting with rack cutter or hob it is advised It is then possible either to continue with undercutting or to go back to modify one or more parameter s and cancel unde
4. axial modification such as crowning or tip easing or semi topping the profile must be free of any kind of undercutting or interference no service factor is taken into account The designer should therefore appreciate and apply it to the results DATA SYMBOLS AND UNITS Unless otherwise specified all dimensions are in mm loads in Newton torques in N m and powers in kW Subscript refers to pinion 2 to wheel b face width of the narrowest element E modulus of elasticity N mm See Help in line HB Brinell hardness ball dia 10 3000 Kg See Help in line M1 allowable pinion torque nl pinion speed r p m power z2C operating number of teeth in rack When variable enter an average number 15 Life it is the value hours which can be reasonnably expected Because of the unavoidable dispersion in manufacture it should not be considered as absolutely certain but as a reasonnable figure to be expected Since a global life figure has been entered it is not necessary to enter daily working time there is indeed no difference between ten years at 12 hours day and five years at 24 hours day 16 Shared torque when one single pinion drives two wheels 17 Intermediate wheel idler or jockey wheel It is free on its shaft is driven by pinion and drives another pinion or wheel METHOD NFE 23 015 This method is the french proposal to ISO TC The simplified method as found at the end of the standard
5. is used here It is not aplicable to internal gearing ISO quality number should be from 5 to 8 18 It introduces a reliability factor for application where more failures are accepted or conversely when high reliability is required The number Fi to be entered corresponds to a failure probability of 1 Fi For example if Fi 100 is entered as it is in usual commercial applications 1 failure out of 100 is to be expected It is a modern method well suited to commercial applications as usually encountered Datas and symbols sigmaF basic stress factor for strength N mm See Help in line sigmaH basic stress factor for pitting N mm See Help in line NM material number See Help in line ISO quality number from 5 to 8 METHOD AGMA 2001 B88 It is probably the most advanced but however the most difficult to use The new standard 2001 B88 has super seded the former standard 218 01 The new standard provides a considerably wider range of values for Sac and Sat vs the material physical data some 15 pages In order to simplify the selection the old tables of 218 01 have been retained in this leaflet their values for Sac Sat are indeed a little more conservative and quite sufficient for commercial applications Clearly the new standard can be referred to when necessary or wished The determination of the load distribution factors Cm Km is difficult when using the analytical method it is indeed uneasy to appreciate a true
6. sun with the sun driving and the crown fixed Number of teeth The numbers of teeth in sun and crown which determine the train ratio are normally entered The normal corresponding number of teeth in planets is automatically displayed When necessary for example to cure undercutting it can be reduced or increased by one unit In order to ensure equidistant location of planets the sum number of teeth in sun number of teeth in crown divided by the number of planets must be an integer If the entered numbers of teeth do not comply with this rule they refused Automatic basic rack shift When this option is selected the sun and planets rack shifts are optimised by equalling their slide roll ratios The crown rack shift is then determined from the planet one The sun planet meshing is preferred because the load capacity of the planet crown meshing is normally largely in excess of the other one Recording The train data are saved separately from those of conventionnal gears in a file named PlanetW dat located in the directory named GSREPER EXTENSION LOAD CAPACITY Epicyclic trains The displayed load capacities take in account the total number of planets It is assumed that the load is perfectly shared by the planets this of course being never achieved It is the responsibility of the designer to reduce the values displayed in accordance with the actual degree of misbalance having in mind that a satisfactory sharing can be obtained
7. value for the lead mismatch et The alternative empirical method is easier to handle and has therefore been introduced Both external and internal gears can be dealt with and a reliability factor can be introduced IMPORTANT the AGMA quality number to be entered is not the same as the ISO one but is specified in AGMA 390 There is no strict correspondance between the ISO and AGMA systems however an approximate equivalence can be found on Help in line The load distribution factors Km Cm can be determined from the methods described in the standard Some comments and explanations are given below 10 19 Empirical method to be preferred when possible The following conditions are required face width should be smaller than or equal to 2 x pinion reference pitch diameter both elements should lie between the bearings no overhanging maximum face width 1016 mm 40 the contact under load must spread over the full face width Dimensions S1 and 5 are shown on Help line Applications are to be classified in four categories open gearing commercial enclosed gear units precision enclosed gear units extra precision enclosed gear units AGMA does not give any further information or comment regarding these categories but clearly the usual commercial applications are to be classified in the second one 20 Analytical method Due to unavoidable errors in elements assembly and leads distorsion the light l
8. SOFTWARE GSPARALW Version USER MANUAL Georges STEVENS 6 Impasse d Ossau 64140 LONS France T l et Fax 33 5 59 32 29 65 27 03 2006 INSTALLATION AND SURVEY Installation Insert the CD in its drive If its contents do not self display open it with Windows Explorer To install GSPARALW on your hard disc double click on the installation programme InstalParalW It will create a folder named GSREPER if not yet existing and will copy in it the software It will also copy six auxiliary files named ParalWD1 4 dat and ParalWN1 2 dat containing the tolerances per NF and DIN In addition it will create short cut and its icon on your computer desktop you will just have to double click on the icon to run GSPARALW If convenient the file gsparalw exe can be moved manually anywhere on your hard disc Surve The organigram of GSPARALW is visible from all pages except Help pages by clicking on the red button O located in the upper left corner From it you can see where you are in the software and where to go Help in line is available when necessary by clicking on menu Help In addition some datum fields provide a specific help when passing over them with the cursor the mention F1 Help is displayed Focus now the field by clicking on it and press key F1 IMPORTANT 17 11 2006 This software cannot be transferred or copied to the benefit of any other company or people without the Author s permis
9. e field to focus it and press key F1 On the DATA page the menu Help gives access to an option allowing a predetermination of the numbers of teeth and module for a given torque to be transmitted When a gear or a pair of gears has been designed GSPARALW allows recording on disc of all dimensions and tolerances for a future recall With the extension LOAD CAPACITY it determines the torque and power capacity according to NFE 23 015 french standard AGMA 2001 B88 american standard of September1989 With possible application of the Miner rule for variable loadings ISO 6336 method of G HENRIOT proposed in his book TRAITE THEORIQUE ET PRATIQUE DES ENGRENAGES GSPARALW makes them easily accessible to engineers who not specialized in gearing and will certainly prove helpful even to specialists LIMITS GSPARALW is suitable only for involute parallel axis gears either spur or helical and spur internal Low tooth external gears as STUB are accepted RUNNING GSPARALW GSPARALW is protected by two codes the first one referring to the dimensional section the second one to the extension LOAD CAPACITY If you are in trial period and therefore do not know the codes you however have access to all functions and options of GSPARALW including the extension LOAD CAPACITY but only odd number of teeth will be accepted When numbers in parenthesis are displayed they refer to the corresponding paragraphs of this
10. erent versions of its method denoted from A to D the first one being the most sophisticated but however the most difficult to use The simplified version D is used here sufficient for usual commercial applications More details and instructions can be obtained from the Help in line Intermediate factors The main intermediate factors used in the calculataions can be displayed for the four standards and a calculation sheet can be printed LIS Fig 1 INTERNAL GEARS TROCHOIDAL INTERFERENCE AND CUTTER TRIMMING Spin Hardening Induction Coil Induction Coil or Flame Head j or Fiame Head a ns 2 Type B Type Flank Hardening Inductor or Flame Head f Inductor or Flame Head Type B Flank and Root Hardening Inductor or Flame Head Type Fig 4 INDUCTION OR FLAME HARDENING
11. hest point of the tooth when a single pair of teeth is carrying all the load Less accurate spur gears having errors that prevent two pairs of teeth from sharing the load may be most heavily stressed when the load is applied at the tip See Help in line This question is omitted with helical gears with overlap ratio gt 1 Miner s rule The Miner s rule although being not a part of the american standard AGMA 2001 B88 is however described and recommended in its appendix B It provides an efficient way to determine the expectable life of a pinion and wheel set loaded by a repeated or single cycle incorporating several periods each of them of different torque and or speed including uniformly variable torque and or speed This option is only applicable in conjunction with the AGMA 2001 B88 method More details and instructions are given by clicking on Help of the corresponding form METHOD HENRIOT It is very popular in France owing to the notoriety of its author It is very similar to NFE 23 015 although somewhat simplified It is however quite reliable in most cases as usually encountered It allows treatment of both external and internal gears but does not introduce a reliability factor Datas and symbols ISO quality number 5 through 12 sigmaH allowable surface stress N mm See Help in line sigmab allowable bending stress N mm See Help in line METHOD ISO 6336 D The standard ISO 6336 proposes four diff
12. ication to the span dimensions is possible only with external gears If the application is selected to the circular thickness backlash is obtained as well with external as internal gears It will be noticed that when the application is selected to the thickness the allowances have not the same values on the form tolerances or dimensions This is because in the former case they apply to the thickness while in the latter they apply to the span dimensions and are therefore multiplied by the cosine of the normal pressure angle For the same reason the signs are different in the case of internal gears a reduction of the thickness results in an increase of the span dimensions 13 Tolerances DIN 3962 August 1978 Tolerances according to the german standard are easily accessible as well for the pinion as for the wheel Translation of the german terms are given hereunder without any liability Profil Formabweichung ff profile shape error Profil Winkelabweichung fHalpha profile angle error Profil Gesamtabweichung Ff profile total error Teilungs Einzelabweichung fp individual pitch error Eingriffsteilungs Abweichung fpe gear pitch error Teilungssprung fu pitch error Teilungs Gesamtabweichung Fp pitch total error Teilungs Spannenabweichung tiber 1 8 Umfang Fpz 8 pitch error on 1 8 revolution Rundlaufabweichung Fr radial runout error Zahndickenschwankung Rs allowance on tooth thickness Flankenlinien Gesamtabweich
13. le Each element can be identfied by a reference 30 characters a number 8 characters and an index These identications will be used for a later recall RECORDING ON DISC Each time a new case has been dealt with or when an existing case has been modified GSPARALW will ask if you wish to record for a later use When the case dealt with comprises two elements pinion and wheel each one is recorded under its own identificators but when one of them is later recalled its mating element is also read If you omitted the reference and number they will be asked for before recording If you just have modified an existing case it will be recorded under the former reference and number READING FROM DISC In case of options 2 3 and 5 GSPARALW displays a selecting grid Sorting is carried out either with alphabetic references or increasing numbers or increasing modules On each line can be seen the reference the number the index if any the normal module the number of teeth followed by the letter I if internal gear the helix angle followed by the letter R or L according to the helix hand the number of teeth of the mating gear if any followed by the letter I when internal or rack if a rack When the record comprises two elements both are read DIMENSIONAL SECTION DATA SYMBOLES AND UNITS All dimensions in mm unless otherwise specified loads in Newton torques in N m powers in kW and angles in decimal degrees Subscri
14. manual After having choosen either conventionnal gears or epicyclic train a first menu is displayed with the following options anew case to be selected to deal with a new problem Recording will be possible for later recall read from disc with modifications allows reading of a previously recorded case with possible modification of data read from disc without modifications allows reading of a previously recorded case without modification of data replace worn out gears to determine the dimensions to be given to gears to replace existing worn out delete on disc to delete an element or train previously recorded If the element to be deleted has been recorded with a mating element both will be deleted save the file dat it is recommended to save periodically the files PARGEARW dat and PLANETW dat containing the records If necessary it will be then possible to reload the records from the disquette to the directory GSREPER exit GSPARALW if a case has been dealt with GSPARALW will ask if you wish to record it before leaving In case of option 1 you will have to choose between one external or internal gear or two external or internal gears In case of options 1 and 2 GSPARALW displays an editing page Select first the type of gear s then the desired options then fill the other fields With Stub teeth the options Manual rack shift and Free centre distance are only accessib
15. oad contact is punctual Under load the contact spreads over as a line and should normally spread over the whole face width GSPARALW advises when it does not and displays the ratio Fm b where Fm is the actual loaded width of contact The ratio Fm b depends basically on the value of mismatch et explained below When calculating the strength capacity the tooth thickness reduction to provide the necessary backlash is taken in account Datas and symbols et total lead mismatch between mating teeth It represents the combined effects of the influences listed below except hertzian contact and bending deformation at the tooth surface errors of lead in machining errors in the alignment of the shafts elastic deflections of mounting elements under load such as shafts bearings housings foundations etc bearing clearances thermal expansion centrifugal forces The value of et is very difficult to estimate and require very careful consideration the calculated load capacity depends indeed widely on it It therefore requires all the designer wisdom and experience Fm loaded width of contact See above 11 Qv AGMA quality number Does not correspond to ISO quality number See Help in line Sac allowable contact stress for pitting See Help in line Sat allowable bending stress N mm See Help in line 22 Load sharing accurate spur gears develop the most critical stress when the load is applied at the hig
16. pt refers to pinion subscript 2 to wheel and subscript 0 to tool Aw centre distance at zero backlash When the algebraic sum external gears or difference internal gears of the basic rack shift coefficients is not zero it is taken into account When the pinion is associated to a rack a 15 the distance from the pinion centre to the rack reference line b face width d reference pitch diameter da tip diameter When the sum external gears of the basic rack shift coefficients is not zero this dimension may be slightly reduced to maintain the bottom clearance It may similarly be slightly increased with internal gears to prevent interference db base diameter dw operating pitch diameter F1 2 3 4 load on bearing 1 2 3 4 See Help in line number of teeth for span gauging L1 2 3 4 distance from centre plane to bearing 1 2 3 4 Help in line mn normal module rt0 tip radius coefficient of cutting tool See Help in line sna normal crest thickness When the data entered lead to a value smaller than 0 3 mn it is advised When they lead to a negative value sharp crest it is rejected See later W span gauging over K teeth x basic rack shift coefficient It is positive when the basic rack reference line does not intersect the reference pitch circle diameter negative when it does This definition is applicable to both external and internal gears 0 tool addendum coefficient See Help in line alphan normal pressure
17. rcutting Clearly this last option is strongly recommended If however undercutting is accepted it is suggested to draw the tooth section to appreciate its amount 5 When the data entered lead to a tip thickness smaller than 0 3 mn it is advised This value is normally a minimum especially with case hardened gears 6 When the data entered lead to a negative tip thickness sharp crest it is rejected INTERNAL GEARS Internal gears are subject to specific restrictions or interferences examined below Limitation of tip diameter da2 When the flank of the mating pinion is generated by a rack or hob the involute profile extends downward to a definite radius depending on the rack shift coefficient the tool addendum and the tool tip radius But if the wheel tooth total height is held normal 2 normal module it may require that the arc of involute of the pinion tooth flank extends lower than actually generated In this case GSPARALW automatically increases da2 by a small amount just preventing the interference In the case of a shaper GSPARALW gives the radius to which the arc of involute should extend to generate the wheel profile down to its tip these calculations are carried from nominal dimensions When some backlash is provided by the wheel the shaper is fed slightly deeper The result is a slight easing at the wheel tooth tip which is negligible and does not affect the wheel behaviour 7 Trocho dal interference
18. sion Its use is subject to your acceptance of the conditions accessible from the first page of the software FOREWORD GSPARALW Version C is an efficient software to deal with all the problems involved in parallel gearing spur or helical external or internal including simple epicyclic trains It allows quick and accurate determination of the following dimensions reference and operating pitch diameters tip and root diameters base diameters and helix angle minimum operating radius when engaged with another element transverse contact and overlap axial ratios span dimensions and dimensions over pins tolerances as per french standard NFE 23 006 german standard DIN 3062 and ISO 1328 1 and 2 In addition it advises all kinds of interference or undercutting allows automatic determination of optimum basic rack shift coefficients to prevent undercutting and exactly balance the slide roll ratios of pinion and wheel checks the full suitability of a shaper to cut an internal wheel draws and prints the section of the pinion and wheel tooth calculates the bearing loads determines the cutting times allows to visualize the meshing cycle Help in line is available whenever possible and necessary Click on Menu Help or button In addition a specific help in line is available for certain capture fields These fields are advised by a bubble F1 Help displayed when the cursor passes over the field Click on th
19. ung Fbeta flank line helix error Flankenlinien Winkelabweichung FHbeta flank line helix angle error Flankenlinien Formabweichung Fbetaf flank line helix shape error Teilungs Spannenabweichung Fpk pitch error over N teeth ISO Tolerances ISO 1328 1 and 2 Tolerances according to ISO are easily accessible as well for the pinion as for the wheel 14 IMPORTANT Values displayed are those found in the standard issued by the french Association Fran aise de normalisation AFNOR under reference E 23 007 1 et 2 However this document incorporates two mistakes 1 Total pitch error Fp for 1600 lt dia lt 2500 40 lt mod lt 70 precision class 11 The wrong value given by the standard is 603 when the correct value is 630 2 Total profile error Falpha for 6000 lt dia lt 8000 16 lt mod lt 25 precision class 9 The wrong value given by the standard is 113 when the correct value is 133 GSPARALW displays the correct values not those given by the french edition GSPARALW displays the cumulative pitch tolerance for all teeth and for half the circle Normally it is however checked on only 1 8 of the total number of teeth EPICYCLIC TRAINS Details to use this option are accessible on line by clicking on menu Help or when existing on icon Following are some comments regarding this type of gearing Number of teeth in crown Ratio of train It is equal to 1 Number of teeth in
20. wheel the shaper is engaged slightly deeper and some safety margin will result ALLOWANCE ON SPAN DIMENSIONS W K TEETH Allowances on dimension W K teeth controling the backlash are entered on the editing form If preferred they can alternatively be entered from the form tolerance NFE 23 006 The corresponding dimensions over rollers are displayed Note that negative allowances provide backlash with external gears but positive allowances are required with internal gears 10 DRAWING OF NORMAL TOOTH SECTION External gears GSPARALW draws the section in a normal plane as generated by a rack or hob The fillet shape is true and it is possible to appreciate the effect of undercutting For helical gears the section is that of the spur gear having the virtual equivalent number of teeth Errors involved are negligible and always smaller than the screen resolution Drawing and printing of several teeth are available only with spur gears For helical gears indeed it would be necessary to draw the transverse section which would not be representative of the form and resistance to failure Internal gearing GSPARALW draws only the arc of involute the fillet is not drawn since widely depending on the shaper data It is in addition of no interest since the bending strength of an internal wheel is never critical In both cases the reference pitch circle is drawn Printing Enter the enlargement factor scale of printed tooth MESHING CYCLE
21. with 2 and still more 3 planets but that with more planets the sharing can be only very poor The calculations are based on the relative speeds of the elements All indeed behave as if the planet carrier was fixed and the sun speed being that relative to the sun carrier This relative speed is equal to 1 Nrelative 1 where is the train ratio as determined above Account is of course taken of the sun and crown number of meshings multiplied by the number of planets and of the number of planet meshings multiplied by 2 The four methods proposed for the evaluation of the torque and power capacity of parallel axis gears are appli cable either to internal except NFE 23 006 or external spur or helical with involute profile The gear capacity is limited either by surface stress pitting resistance or wear or bending stress bending strength The load capacity of a pair of gears should therefore be determined using four calculations for pitting and for bending of both pinion and wheel These four methods do not allow calculation of bending strength of internal gears since this type of gear is normally not subject to this kind of bending failure GSPARALW allows easy determination in few seconds of the corresponding ratings with however the follo wing limitations the working height of the tooth must be 2 normal modules Low tooth such as STUB are not allowed the profile must be involute without transverse or
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