1、UDC 621.833 : 001.4 DEUTSCHE NORMEN December 1976 General Definitions and Specification Factors for Gears, Gear Pairs and Gear Trains - DIN 868 Allgemeine Begriffe und Bestimmungsgrssen fr Zahnrder, Zahnradpaare und Zahnradgetriebe Il C c D .- - m O 3 f g ?.z - : H L 3 $ c .- D 8 c c .- E Q 2 - 5 3
2、O a r p .z m 2 g -? c ._ o -= c O .jt 50 8; gg a?- CD .= - BE 2; 3 al mal This Standard contains the general definitions and symbols for gears, gear pairs and gear trains as well as the definitions of their parameters. The content of this Standard has been brought into line with the recommendation I
3、SO/R 1122 - 1969 issued by the International Organization for Standardization (ISO) ; for this purpose the Swiss Standard VSM 15 522 - 1974 has also been used as a source, so that extensive agreement with international standardization has been achieved. The quantities contained in ISO/R 1122 - 1969
4、have been supplemented in this Standard by further terms and parameters which have appeared important in connection with gear tooth geometry. The symbols used agree with DIN 3999. Specific terms relating to particular gear tooth systems are dealt with in separate Standards. $1 :2 2.1 2.2 2.3 2.3.1 2
5、.3.2 2.3.3 2.3.4 2.3.5 2.4 2.5 2.6 2.7 2.8 2.8.1 2.8.2 2.9 2.9.1 2.9.2 63 3.1 3.1.1 3.1.2 3.1.3 3.1.4 3.2 3.2.1 3.2.2 3.2.3 Contents Page Symbols and designations. 3 3.2.4 General terms relating to a gear . 3 3.3 Tooth 3 3.4 Gear . 3 3.5 Gear tooth system . 3 3.5.1 Tooth 1, tooth 2 etc., tooth k 3 3
6、.5.2 Tooth spaces . 3 3.5.3 Pitch p; right pitch, left pitch; designation . . 3.5.4 Angularpitchr . 4 3.5.5 Modulem . 4 3.6 Numberof teeth z . 4 3.7 Gearaxis 4 3.7.1 Datum surface, reference surface 4 3.7.2 Plane tooth system . 4 3.7.3 Axial boundary . 4 3.7.4 End surfaces of the gear tooth system.
7、4 3.8 Position of the gear tooth system relative to the gear body . 5 External gear teeth, external gear 5 Internal gear teeth, internal gear 5 4 Facewidth b . 4 3.8.1 3.8.2 3.8.3 3.8.4 3.8.5 General terms concerning gear pairs 5 3-85 Gearpair 5 3.8.7 Gear and mating gear. . 5 3-9 Pinion (small gear
8、) and wheel (large gear) . . 5 3*9*1 Driving and driven gear 5 3.9.2 Gear train . 5 Geartransmission 5 4 Singlestage gear transmission 5 4.1 Multi-stage gear transmission . 5 4.2 Fixed-axis gear transmission . 5 4.3 Page Epicyclic or planetary gear transmission (gear train) 5 External gear pair 6 In
9、ternal gear pair 6 Gear axes of a gear pair 6 Axial plane 6 Crossing line, crossing points 6 Mid-planes., . 6 Centre distance a (offset) . 6 . Shaft angle E . 7 Gearratiou 7 Transmission ratio i. 7 True-angle ratio 7 True-torque ratio 7 Speed-reducing ratio 7 Speed-increasing ratio . 7 Engagement. .
10、 7 Point of contact . 7 Contact line. . 7 Plane of action 7 Zone of action 7 Path of contact . 7 Length of path of contact 7 Meshing interference 7 Types of tooth system . 8 Individual tooth system 8 Paired tooth system; X-zero tooth system . . 8 . Kinematic terms . 8 Instantaneous axis . 8 Function
11、al surfaces . 8 Rolling type gear transmissions . 8 Continued on pages 2 to 20 I Sole sale rights of German Standards (DIN-Normen) are with Beuth Verlag GmbH, Berlin 30 and Kln 1 DIN 868 engl. Preisgr. I Vertr.-Nr. O1 11 03.81 DIN 868 Page 2 4.3.1 4.3.2 4.3.3 4.3.4 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.4.
12、1 Page Rolling axis 8 Plane gear transmissions. spherical gear trans- missions 8 Pitch point C 8 Pitch surface; pitch cylinder. pitch cone . 8 Helical rolling type gear transmissions . 8 Helix axis . 9 Helix point S . 9 Helical pitch surfaces 9 Parameters at the helix point S . 9 Relative angular ve
13、locity wE1 9 4.4.4.2 Velocity of sliding ugs . 9 4.4.4.3 Reduced lead (parameter) p, of the helical motion 10 4.4.5 Working point W 10 4.4.6 Parameters at the working point W . 10 4.4.6.1 Relative angular velocity wE1 10 4.4.6.2 Velocity of sliding u, . 10 4.5 5 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.2
14、 5.2.1 5.2.2 5.2.3 5.2.4 5.3 6 6.1 6.2 6.3 6.4 7 7.1 I Pure helical type gear transmissions 11 Types of gears and gear pairs . 11 Gears and gear pairs for rolling type gear transmissions . 11 Rack; rack and pinion pair 11 Bevel gear; bevel gear pqir . 11 Plane bevel gear; plane bevel gear pair . 11
15、Contrate gear pair; crown wheel Il Gears and gear pairs for helical rolling type gear transmissions 11 Cylindrical worm gear set (worm gear set); cylindrical worm (worm). wormwheel 11 Hyperboloid gear pair . 12 Crossed helical gear pair (cylindrical crossed helical gear pair); crossed helical gears
16、(cy1 indrical crossed helical gears). crossed helical worm gear 12 Hypoid gear pair (helical bevel gear pair); hypoid gears (helical bevel gears) 12 Double enveloping worm gear set; double enveloping worm. double enveloping worm- wheel 12 Crest and root surfaces I 3 Crest 13 Tip surface 13 Bottom of
17、 tooth space . 13 Root surface . 13 Tooth flanks and tooth profiles . 13 Tooth flanks . 13 Cylindrical gear; cylindrical gear pair . 11 7.2 7.3 7.3.1 7.3.2 7.3.3 7.4 7.5 7.5.1 7.5.2 7.5.3 7.5.4 7.5.5 7.5.6 7.6 7.6.1 7.6.2 7.6.3 7.6.4 7.6.5 7.7 7.7.1 7.7.2 7.7.3 7.7.4 7.7.5 7.7.6 7.8 7.8.1 7.8.2 7.8.
18、3 7.8.4 8 8.1 8.2 8.2.1 8.2.2 8.2.3 8.2.4 8.3 Page Datum tooth trace. tooth trace. reference tooth trace . 13 Gear tooth profile. tooth profile. flank profile 13 Transverse profile; transverse section . 13 Normal profile; normal section . 13 Axial profile; axial section 13 Standard basic rack tooth
19、profile 13 Types of tooth flank 13 Mating flanks . 13 Right flank. left flank . 13 Corresponding flanks 13 Opposite flanks . 13 Working flanks 13 Non-working flanks . 13 Partsof flanks 13 Addendum flank. dedendum flank . 13 Usable flank; usable tip circle. usable root circle 14 Active flank 14 Fille
20、t surface. root radiusing . 14 Tooth tip . 14 Tooth flank modifications Tip relief Ca. root relief C, . vertical crowning C, 14 Longitudinal crowning C, (tooth trace relief) . 14 End relief . 14 Tooth tip chamfer . 14 Grinding relief 15 Cutter interference . 15 Flank profiles of cylindrical gears .
21、15 I nvolute gear teeth . 15 (flank corrections) . 14 Cycloidal gear teeth 15 Point tooth system. cylindrical lantern tooth system . 16 Circular arc gear teeth . 17 Backlash and clearance between mating tooth systems 17 Bottom clearance c . 17 Backlash j . 17 Circumferential backlash jt 17 Normal ba
22、cklashj, . 17 Radial backlash j, 17 Axial backlash i, 17 Entry clearance je 17 Alphabetical index 19 DIN868 Page3 1 Symbols and designations The following symbols and designations are used in this Standard: Centre distance Facew idth Width of crowning Bottom clearance Datum surface diameter Effectiv
23、e diameter Transmission ratio Backlash Entry clearance Normal back I ash Radial backlash Circumferential backlash Axial play Number of teeth or pitch number Module Speed (rotational frequency) Pitch Lead Datum surface radius Gear ratio Velocity of sliding Number of teeth Pitch point End relief Tip r
24、elief Tooth trace relief Root relief Prof i le modif cat ion Helix point Working point Helix angle reference cone half angle Angular pitch Angular velocity Shaft angle The above symbols may be supplemented by the follow- ing subscripts or auxiliary symbols: a b for the driven gear f m for a mean val
25、ue n s t w x C red for reduced parameters re1 for relative parameters 1 2 - for scalar parameters +. for vector parameters for the driving gear or for parameters at the tip circle for parameters at the root surface for parameters in the normal section for parameters at the helix point for parameters
26、 in the transverse section for parameters at the working point for parameters in the axial section for parameters referred to end relief for parameters relating to the smaller gear of a gear pair for parameters relating to the larger gear of a gear pair For further symbols relating to gear teeth see
27、 DIN 3999. Symbols are also dealt with in the following Standards: DIN 1302 Mathematical signs and symbols, DIN 1304 General symbols for use in formulae, DIN 1313 Method of writing physical equations in the natural sciences and technology. 2 General terms relating to a gear 2.1 Tooth A tooth is an e
28、lement projecting from a gear body and possessing a shape permitting the transmission of force and motion to the teeth of a mating gear (see Section Figure 1. Tooth 2.2 Gear A gear is a mechanical element rotatable about an axis and consisting of the gear body with its bearing surfaces and the teeth
29、 projecting from the gear body. Figure 2. Gear 2.3 Gear tooth system The tooth system of a gear comprises the totality of its teeth. 2.3.1 Tooth 1, tooth 2 etc., tooth k For designating individual teeth, tooth 1, tooth 2 etc. are to be so marked on a transverse surface of the gear tooth system (see
30、Section 2.8.1) that the teeth are numbered in ascending order in the counting direction. A tooth isgenerally designated by the letter symbol k. The next higher tooth in the counting direction is then designated by k + 1 and the next lower tooth in the counting direction by k - 1, see Fig. 3. In the
31、case of gear pairs with parallel axes (see Section 3.5) the transverse surfaces used for designating the teeth shall be visible from the same viewing direction; normally this is the direction in which the force is imparted to the driving gear, or some other specific, assumed direction. In the case o
32、f gear pairs with intersecting axes (see Section 3.5) the viewing direction for both gears is generally towards the point at which the axes intersect. In the case of gear pairs with non-parallel non-intersect- ing axes (see Section 3.5) the transverse surfaces general- ly used for designating the te
33、eth are those which are visible from the drive side in the case of the driving gear and from the driven side in the case of the driven gear. 2.3.2 Tooth spaces The tooth spaces are the intervals between the teeth into which the teeth of the mating gear (see Section 3.1 .I) enter during the rotary mo
34、tion. Page 4 DIN 868 Figure 3. Designation of teeth 2.3.3 Pitch p; right pitch, left pitch; designation A pitch p (single pitch) is the datum surface arc (see Section 2.6) in a given section of the gear tooth system (see Section 7.3) between the corresponding flanks (see Section 7.5.3) of two adjace
35、nt teeth. The pitch between two right flanks (see Section 7.5.2) is termed a right pitch and that between two left flanks (see Section 7.5.2) a left pitch. The pitches in the case of crown wheels the end surfaces are normally cylinders about the gear axis. 2.8.2 Facewidth b The facewidth b is the di
36、stance between the two end surfaces on the datum surface of a gear tooth system, see Fig. 6. Figure 6. Facewidth b DIN 868 Page 5 2.9 Position of the gear tooth system relative to the gear body 2.9.1 External gear teeth, external gear With external gear teeth the teeth project outwards from the gear
37、 body (away from the gear axis). A gear with external teeth is termed an external gear or externally-toothed gear. In calculations the number of teeth of an external gear is entered in the equations as a positive quantity. Figure 7. External gear 2.9.2 Internal gear teeth, internal gear With interna
38、l gear teeth the teeth project inwards from the gear body (towards the gear axis). A gear with internal teeth is termed an internal gear or internally-toothed gear. In calculations the number of teeth of an internal gear is entered in the equations as a negative quantity. This means that all quantit
39、ies derived from it - e. g. all dia- meters and radii, angular pitch, gear ratio and centre - also take a negative sign. Figure 8. Internal gear 3 General terms concerning gear pairs 3.1 Gear pair A gear pair is a simple mechanism consisting of two gears the axes of which are in a defined position r
40、elative to each other so that the first gear transmits its rotation to the second gear by way of the teeth which come suc- cessively into engagement (see Section 3.8). Gears with circular (axially symmetrical) datum surfaces which are concentric with the gear axis effect a uniform transmission of ro
41、tary motion; gears with non-round or eccentric datum surfaces effect a transmission of the rotary motion which varies periodically. a) Figure 9. Gear pair a) Cylindrical gear pair b) Bevel gear pair 3.1.1 Gear and mating gear One of the two gears of a gear pair is arbitrarily desig- nated as the gea
42、r and the gear meshed with it as the mating gear. 3.1.2 Pinion (small gear) and wheel (large gear) The smaller of the two gears constituting a gear pair is designated as the pinion or small gear whilst the larger is termed the wheel or large gear. The smaller gear is denoted by the subscript 1 and t
43、he larger by the sub- script 2. With certain types of gear pairs the small gear and the large gear are given special names (e. g. worm and worm- wheel, see Sections 5.2.1 and 5.3). 3.1.3 Driving and driven gear The gear of a gear pair which drives the other is termed the driving gear. The gear which
44、 is driven by the other gear is the driven gear. The driving gear is denoted by the subscript a and the driven gear by the subscript b. 3.1.4 Multiple gear-pairing, gear train A gear train is a combination of two or more gear pairs which are activelv related to one another. Figure IO. Gear train 3.2
45、 Gear transmission A gear transmission is an assembly consisting of one or more gear pairs and the housing or frame (usually enclos- ing the gear pairs) which mounts the bearings for the stationary gear axes. In a gear transmission the magnitude and/or direction of the rotary motion and torque can b
46、e transformed in one or more stages. 3.2.1 Single-stage gear transmission A single-stage gear transmission contains a gear pair con- sisting of a gear and mating gear mounted in a housing (frame) together with the bearings for both gear axes. 3.2.2 Multi-stage gear transmission A multi-stage (two-st
47、age, three-stage etc.) gear trans- mission contains several (two, three etc.) gear pairs (gear trains) arranged successively in the direction in which the rotary motion is transmitted, and mounted in a common housing. 3.2.3 Fixed-axis gear transmission A fixed-axis gear transmission is a single-stag
48、e or multi- stage gear transmission in which all the rotatably mounted gear axes occupy non-varying positions. 3.2.4 Epicyclic or planetary gear transmission (gear train) An epicyclic or planetary gear transmission is one having at least three gears arranged in sequence in the effective direction, s
49、uch that the shafts of two of the gears are arranged coaxially whilst the third or intermediate gear (epicyclic or planet gear) is mounted on a rotating arm Page6 DIN868 (planet carrier) coaxial with the gear shaft and rotates with the arm. An epicyclic or planetary gear train thus consists gener- ally of the externally-toothed central gear (sun gear, central pinion), one (or more parallel-mounted) exter- nally-toothed planet gear(s) and the internal gear (usually non-rotatable) which is coaxial with the sun gear. In special cases an external gear may be used instead of the internal ge
