1、UDC 62-272.5 DEUTSCHE NORM June 1981 Circular section torsion bar springs Calculation and design DIN 2091 Drehstabfedern mit rundem Querschnitt; Berechnung und Konstruktion As it is current practice in standards published by the International Organization for Standardization (ISO), the comma has bee
2、n used throughout as a decimal marker. Dimensions in mm 1 Other relevant standards and documents DIN DIN DIN DIN DIN 5481 Part 1 Internal and external serrations DIN 17 221 SAE J 498 b 13 Part 15 IS0 metric screw threads; basic allowances and tolerances for screw threads of 1 mm diameter and larger
3、76 Part 1 Runouts, undercuts for IS0 metric threads according to DIN 13 332 Part 1 Centre holes; 60, types R, A, B and C 332 Part 2 (Preliminary Standard) Centre holes; 60 with screw thread for shaft ends of electrical machines Hot-rolled steels for quenched and tempered springs; quality specificati
4、ons Involute toothings 2 Representation A I6 Figure 1 I ?- I Torsion bar spring with serrated clamping heads and centerings Mt max 1 Mt2 4- 8 Q) o m Mtl C O ._ 8 I- Torsion bar spring diagram I I $1 Twisting angle d - Continued on pages 2 to 10 Explanations on page 10 Solesale rightsof GermanStandar
5、ds(0IN-Normen) are with Beuth Verlag GmbH, Berlin30 05.82 DIN 2091 Engl. Price group 9 Sales No. O109 Page 2 DIN 2091 3 Symbols, terms, units d Bar diameter mm da Tip diameter mm df Root diameter of head profile mm G Shear modulus N/mm* h, Tooth depth mm i, Polar moment of inertia m m4 I Shank lengt
6、h, free torsion bar length mm Twisting angle Torsional moment G * d4 * 8 *TE lf 573 * 32 M,=W,.r = Overall length of torsion bar Equivalent length Elastic length Fillet length Head length Cylindrical portion of shank Torsional moment Torsional moment at commencement of stressing Number of stress rev
7、ersals Surface pressure Radius of curvature of fillet Strength after hardening and tempering Spring rate Polar section modulus Torsion work Number of teeth Slipping, shearing strain Creep loss Relaxation Ratio of root diameter of head profile to bar diameter Twisting angle (angular measure) Twisting
8、 angle (arc measure) Twisting angle at commencement of stressing Ratio of equivalent length to fillet length Shear stress Shear stress amplitude Mean stress Permissible shear stress Yielding point Continuous stroke strength Calculated nominal stress mm mm mm mm mm mm N.mm Torsion spring rate Mt t- 6
9、 R - N.mm N/mm2 mm - Work of elastic strain Mt B wt = 2 * 57,3 N P R Rln (9) M: * If 16 * MS * If wt = - 2-G*IP G-TE- Slippage Y= for the range covered by Hookes law: d-t) 2 * If * 57,3 N/mm2 N . mm/O m m3 N.mm - - % % (10) (11) 16 * M, Y= G-n.d3 (12) (13) O 7 y= - G Shear stress 16 * Mt 5= - TE - d
10、3 Bar diameter O V d=i/r_ 16 * Mt 4 Calculation equations Polar section modulus Fillet length TE; d3 16 w, = - Polar moment of inertia Head length 0,5 * df 104 and stroke stresses 0.1 . rH, are applicable as dynamic stress for torsion bar springs. Figure 6. N 1200 Im m2 1000 800 600 400 200 O O 200
11、400 600 800 NlmmZ 1200 Mean stress Zm _c Fatigue strength for finite life diagram for high-grade steel torsion bars in accordance with DIN 17 221 with ground surface shot-blasted with steel balls Head/bar ratio: 6 21.3 Degree of presetting: y = 0.02 Range of diameters: 10 to 60 mm DIN 2091 Page 7 Fi
12、gure 7. 1200 Nlrn m2 1000 800 6 O0 400 2 O0 O O 2 O0 400 600 8 O0 NImrn2 1200 Mean stress t, - Fatigue strength diagram for high-grade steel torsion bars in accordance with DIN 17 221 with ground surface shot-blasted with steel balls Head/bar ratio: 6 L 1.3 Degree of pre-setting: y = 0,02 Range of d
13、iameters: 10 to 60 mm 7.3 Surface pressure on the head of the torsion bar The permissible surface pressure on the heads of the torsion bars depends on several factors, in particular on the design and arrangement of the heads and of their companion pieces. It is advisable to have discussions with the
14、 manufacturer on this matter. 7.4 Relaxation and creep Relaxation in the case of torsion bars is a loss of torque at a constant angle of twist, whilst creep is an increase in the angle of twist at a constant torque, expressed in the form of a percentage from the initial state. Important factors in t
15、his respect are the applied stress, stress duration, steel grade, strength of hardening and tempering and degree of pre-setting, also the working temperature. The relaxation and creep values after a period of 48 hours are considered as characteristic values (see Figs 8 and 91, although the phenomeno
16、n is by no means fully terminated at this point in time (see Fig. IO). Page 8 DIN 2091 22 Yo 20 18 16 O O - 12 8 6 4 2 O Theoretical skin shear stress Z L Figure 8. Approximate values for the creep losses of torsion bars made from 50 CrV4 material in accordance with DIN 17 221 after a duration of st
17、ressing of 48 hours at room temperature, in function of the theoretical skin shear stress DIN 2091 Page 9 10 O z P al U E4 2 O 500 6 O0 700 8 O0 N lmm2 900 Theoretical skin shear stress T _c Figure 9. Approximate values for the relaxation of torsion bars made from 50 CrV 4 material in accordance wit
18、h DIN 17 221 after a duration of stressing of 48 hours at room temperature, in function of the theoretical skin shear stress Page 10 DIN 2091 Y x 0.2 IP O 48 100 200 h 3 O0 Duration of stressing t - Figure IO. General diagram of approximate values of relaxation yR and of creep loss YK in function of
19、 the duration of stressing Explanations Standard DIN 2091 which was withdrawn in 1973 and was entitled “Torsion bar spring; calculation, material, dimensioning“, July 1949 edition, is superseded by this standard (new edition), which has been adapted to the present state of the art. Apart from the ba
20、sic considerations required for the calculation of torsion bars, certain data and information which should be taken into account for the purpose of achieving a technically sound design have been included in the standard. Amongst these is the determination of the equivalent length, which results from
21、 the geometrical relationships existing at the transition from the shank of the torsion bar to the head. In the case of torsion bars which utilize the material to the fullest extent, and which are only stressed in one direction, pre-setting offers a good opportunity to reduce the stress on the criti
22、cally stessed skin zone. In the case of the design of dynamically stressed torsion bars, finite life fatigue strength diagrams and fatigue strength diagrams have been adopted for the first time, which also take account of the shank diameter for the material stress which may arise. The relaxation and creep diagrams are also a new feature, and they illustrate this effect on the material arising from the pretreatment, on the basis of extensive tests.
