3. Determine the actual gear ratio

4. Determine the optimal center distance from the condition of chain durability

Accept a = 1500 mm,then center distance in steps

5. Determine the number of chain links.

Accept l P = 126

6. Specify the center distance and P in steps:

7. Determine the actual center distance.

Take the final center distance, taking into account the elimination of the chain slack from its own weight

8. Determine the chain length.

9. Determine the diameters of the stars:

pitch circle

circumference of protrusions

d 1 = 11.1 mm- tab. 5P

hollow circles

Check calculation

10. Check the rotation frequency of the lower asterisk by the condition

n 1 ≤

Allowable speed

n 1 = 301.21 min -1< =398мин -1

condition is met.

11. Check the number of chain beats on the sprocket teeth according to the condition

U ≤ [U]

The estimated number of chain beats

Permissible number of strokes

U = 3.67< [U]=13,3

condition is respected.

12. Actual chain speed

13. Circuit power transmitted by a circuit.

14. Check the pressure in the hinges of the chain according to the condition

The area of ​​the projections of the hinge bearing surface

b 3 = 25.4 mm 2  - tab. 5P

  = 26 N / mm 2- tab. 7

P C = 15,67 N / mm 2< = 26 Н/мм 2 .

The calculated circuit is suitable for operation.

15. Check the strength of the chain by the ratio

S ≥ [S]

Chain preload

K f = 6.0  - for horizontal chains - takes into account sagging;

q = 5.5 kg / m  - weight of 1 m of the chain (Table 5P);

g = 9.81 m / s 2;

K D = 1,2  (see item 1).

Chain tension from centrifugal force, N

F P = 12700 daN = 127 kN  - breaking load of the chain, table. 5P.

Allowable safety factor for roller chains on the table. eight. [S] = 9.8

S = 51.3\u003e [S] = 9.8

The strength condition is satisfied.

16. Determine the force of the pressure circuit on the shaft.

K B = 1,15 - table.6.

Calculation of gears

Before proceeding to the calculation of gears, it is necessary to study the basic criteria for their performance / 1 / c 126 ... 128.

During the transmission of torque (Fig. 7a), in engagement, in addition to the normal force F n, a friction force F tr = F n ∙ f is applied, which is associated with sliding. Under the action of these forces, the tooth is in a complex stress state (Fig. 7, b).

Two main stresses have a decisive influence on its performance: contact stress σ H and bending stress σ F. For each tooth, these stresses vary in time over an intermittent, nebulized cycle (see Fig. 7, a). The duration of stress for one revolution of the wheel (t 1) is equal to the duration of the engagement of one tooth (t 2).

Variable stresses cause fatigue destruction of teeth: tooth breakage due to bending stresses (Fig. 8, a), chipping of the tooth surface from contact stresses (Fig. 8, b), wear is also associated with contact stresses and friction in engagement ( c) jamming and other damage to the surface of the teeth.

Fig. 8. Types of damage to the teeth

Calculation on contact strength is essential for closed (operating under heavy lubrication conditions) gears. The purpose of the calculation is to prevent fatigue chipping of the working surfaces of the teeth for a given service life. The bending calculation is essential for open gear teeth with high surface hardness. The purpose of the bending calculation is to prevent tooth breakage.

Pay attention to the determination of the forces acting in the gears and which are the initial for calculating the teeth, shafts and the selection of bearings. It should be remembered that the calculation of gears is performed on the design loads. These loads are greater than the nominal (theoretical) ones, since due to the deformation of the wheels, shafts, bearings, body parts and the inevitable errors in their manufacture and installation, additional dynamic loads occur. Design load

where T, F t - rated load (torque on the shaft and the circumferential force); K - coefficient of calculated load

K β - coefficient of concentration of the load, depends mainly on the asymmetry of the location of the wheels relative to the supports and the relative width of the wheel Ψ bd=, which affect the deformation of the parts and the misalignment of the tooth; K υ - coefficient of dynamic load, depends mainly on the peripheral speed and precision manufacturing gears; K β, K υ choose according to tables and graphs.

In the design calculation take approximately K = 1.1 ... 1.5. Smaller value is taken when working on materials (HB ≤ 350) with symmetric arrangement of wheels for indirect teeth.

Understand that choosing the right material for gears determines the size and cost of transmission. Steel is currently the main material for the manufacture of gears. Unless there are special requirements regarding the dimensions of the transfer, materials with average mechanical characteristics should be chosen, with a hardness of ≤ 350 NB (heat treatment normalization or improvement). This ensures perfect cutting of the teeth after heat treatment, high precision manufacturing and good workability of the teeth.

For uniform wear of the teeth and better workability, the hardness of the gear NB 1 is assigned more than the hardness of the wheel NB 2 on (20 ... 50) NB.

The choice of material, heat treatment and hardness. Table 9

Notes: l.  In gear gears, make steels gears and wheels to choose the same. At the same time, for gears whose dimensions do not impose high requirements, cheap brands of 40, 40X type steels should be used. 2.   For wheels of large-diameter open gears (D≥500 mm), use steel casting (35L, 40L, 45L, 40GL, heat treatment - normalization, improvement) together with forged gear made of steel of the corresponding brand.

The allowable contact stresses in the calculation of contact strength are determined separately for gear teeth [σ] H 1 and wheels [σ] H 2.

Mechanical characteristics of steel. Table 10

Notes: 1.In the column "Heat treatment" the following notation is used: H-normalization, Y-improvement, high-frequency hardening by high-frequency currents. 2. For cylindrical and bevel gears, connect smaller values ​​with zag, S zag.

[σ] H 1 = K HL 1 [σ] HO 1; [σ] H 2 = K HL 2 [σ] HO 2

where [σ] H 01, [σ] H 02 is the permissible contact stress corresponding to the limit of contact endurance at the number of cycles of voltage change N HO (Table 11); K HL - durability coefficient

K HL = ,

where N is the number of voltage cycles for the entire service life

N = 573ω h L h,

where ω is the angular velocity of the corresponding shaft, s -1; L h - service life of the drive, hours.

The definition of K HL taking into account the drive load curve is given in the literature / 2 / c 15 ... 16.

For normalized and improved wheels 1,0≤ K HL ≤2,6.

If N\u003e N HO, then take K HL = 1.

The value of the number of cycles N HO. Table 11

Cylindrical and bevel gears with straight and indirect teeth at HB 1cr -HB 2cp = 20 ... 50 are calculated by the smaller value [σ] H, i.e. on less strong teeth of gear pair.

Gears with indirect teeth with HB 1cr -HB 2cp ≥70 and wheel hardness ≤ 350 NB are calculated from the average allowable contact voltage

[σ] H = 0.45 ([σ] H 1 + [σ] H 2),

at the same time [σ] H must not exceed 1.23 [σ] H 2.

The allowable stress when calculating the bend is determined for the gear and wheels separately

[σ] F 1 = K FL 1 [σ] F 01; [σ] F 2 = K FL 2 [σ] F 02,

where [σ] F 0 is the allowable bending stress, which corresponds to the bending endurance limit with the number of stress change cycles N fo (Table 9); K fl - the coefficient of durability

K FL= ,

where N F 0 is the number of voltage change cycles corresponding to the fatigue limit. For all steels N fo = 4 ∙ 10 6. With a hardness of HB≤ 350.

1 ≤ K FL ≤ 2.08.

If N\u003e N F 0, take K fl = 1.

When designing a spur gear, follow the sequence below.

1. Select a material for gear and determine the allowable stress for the calculation of the contact endurance and bending.

2. Determine the transmission center distance a w, mm

a w = K a (u + 1) ,

where K a = 43 for helical and chevron gears;

K a = 49.5 for spur;

Ψ a= - the ratio of the width of the crown wheel;

Ψ a are taken from a number of standard numbers: 0.1; 0.15; 0.2; 0.25; 0.315; 0.4; 0.5; 0.63, depending on the position of the wheels relative to the supports: with a symmetrical arrangement of 0.4 ... 0.5; with asymmetrical 0.25 ... 0.4; with the console 0.2 ... 0.25.

u- gear ratio; T 2 - torque on the low-speed shaft of the gearbox, H ∙ m; [σ] H is the permissible contact stress; K n b - load concentration factor. For running teeth at constant load K H b = 1.

The resulting value of the axial spacing a w rounds to the nearest value from a series of normal linear dimensions (Table 1H).

3. Determine the engagement module m, mm

m ≥

where K m = 6,8 - for spur gears; K m = 5.8 - for helical and chevron;

d 2 = pitch diameter of the wheel, mm; b 2 = Ψ a ∙ a w is the width of the crown of the wheel, mm;

[σ] F is the allowable stress of bending of the wheel material with a less durable tooth, N / mm 2.

Determine the module of the link from the condition m = (0.01 ... 0.02) and choose its value from the standard number series of numbers (not less than previously calculated).

m, mm 1st row -1.0; 1.5; 2; 2.5; 3; four; five; 6; eight; ten

2nd row -I, 25; I, 75; 2.25; 2.75; 3.5; 4.5; 5.5; 7; 9

When choosing a module, the 1st ~ row is preferable. In power gears with HB≤ 350, take m\u003e 1 mm.

4. To determine the angle of inclination of the teeth β min for helical gear and chevron gears

β min = arcsin.

In helical gear take β = 8 ° ... 20 °; in chevron - β = 25 ° ... 40 °.

5. Determine the total number of gear teeth and wheels for spur gears Z ∑ = Z 1 + Z 2 =; for helical and chevron Z ∑ = Z 1 + Z 2 = .

The resulting value of Z ∑ is rounded to the nearest side to an integer.

6. To clarify the actual value of the angle of inclination of the tooth.

Accuracy of calculating the angle β to the fifth decimal place

7. Determine the number of gear teeth

The value of Z 1 is rounded to the nearest integer. From the condition of noise reduction and absence of tooth trimming, it is recommended: Z 1 ≥17.

When getting Z 1 ≤17, take Z 1 = 17, or design the cutting teeth with a positive tool offset. The method of calculating such gearing can be found in the literature: / 2 / c 21 ... 22.

8. Determine the number of teeth of the wheel.

Z 2 = Z ∑ -Z 1.

9. Determine the actual gear ratio u f and check its deviation Δu from the given u: u f =;

Δu = ≤ 4% .

10. Determine the actual center distance:

a w = -   for spur gears;

a w =   - for helical gears.

11. To determine the main geometrical parameters of the transmission according to the formulas given in table. 12.

Fig. 9. Geometric parameters of a cylindrical gear.

Accuracy of calculation of wheel diameters up to 0.01 mm. The width of the gear rims is rounded to a whole number by normal linear dimensions (Table 1 P).

Geometric parameters of gears. Table 12

Verification calculation

12. Check center distance:

13. Check the suitability of the wheel blanks (see Table 10).

14. Check the contact stresses σ H, N / mm 2:

σ H = K

where K = 436 for spur gears; K = 376 for helical and helical gears.

F t = is the external force in the mesh, N;

K N a is the coefficient taking into account the distribution of the load between the teeth; K H a = 1 - for spur gears; for helical gears, K N a is determined according to the graph in Figure 10, depending on the peripheral speed of the wheels v =, m / s and the degree of accuracy of the transmission (Table 13); K Hυ-dynamic load factor (tab. 14).

Fig. 10 Graph for determining the coefficient K H a according to the curves of the degree of accuracy

Underload of transmission is allowed (σ H<[σ] H) не более 15 %, перегрузка (σ H >[σ] H) up to 5%. If the condition is not met, increase the axle spacing a w, the width of the wheels or designate other wheel materials or other heat treatment, recalculate the allowable stresses and repeat the entire transfer calculation.

15. Check the bending stress of the gear teeth σ F 1 and wheel σ F 2, H / mm 2: σ F 2 = Y F 2 ∙ Y β ∙ K F a ∙ K Fβ K Fυ ≤ [σ] F 2;

σ F 1 = σ F 2 ∙ ≤ [σ] F 1,

where m is the gearing module, mm; b 2 - width of the gear rim of the wheel, mm; F t is the external force in the engagement, H; K F a = 1 for spur gears. For helical and chevron, depending on the degree of accuracy:

The values ​​of the coefficients K Hυ and K Fυ when HB 2 ≤350. Table 14

Note. The numerator provides data for spur in the denominator - for helical gears and wheels with circular teeth.

K Fβ = 1 - for running teeth; F u -to table 13; Y F 1 and Y F 2 the coefficients of the shape of the tooth are determined according to Table 15, depending on the number of gear teeth Z 1 and the wheel Z 2 for spur gears. For helical gears and chevron wheels - depending on the equivalent number of gear teeth Z υ 1 = and wheels Z υ 2 =; Y β = 1 - for spur gears; Y β = 1- for helical gears;

[σ] F 1 and [σ] F 2 - allowable stress gear and wheels, N / mm 2.

Tooth shape factors Y F 1 and Y F 2. Table 15

Note. The tooth shape factors Y F correspond to the tool offset factor x = 0.

If, in the test calculation, σ F is significantly less than [σ] F, then this is permissible, since the loading capacity of closed gears is limited by the contact strength.

The calculation of the parameters of the asterisk is made depending on the size, parameters of the drive chain, double-row 2PR-25.4-11340 GOST 13568-75.

An example of a drawing of an asterisk (Appendix 7). Chain Transfer Ratio i= 3, the chain pitch is 25.4 mm.

The diameter of the pitch circle of the asterisk leading

where t  - chain pitch;

z  1 - the number of teeth of the drive sprocket;

The diameter of the circle protrusions

The diameter of the circle of the hollows of an asterisk

,

where r=0,5025d  1 –0.05 is the radius of the depressions;

d  1 - the diameter of the roller chain (table 17) d 1 =15,88.

Diameter of groove

,h= 24.2 is the width of the chain plates,

  mm

Table 17

Circuit parameters

Note. in the designation of the chain, numeral 2 indicates a double-row chain; for a single-row chain, the value of A is the distance between the rows of chain rollers equal to 0.

Sprocket tooth width mm.

Sprocket width for double row mm.

Rim thickness mm.

Release diameter to facilitate mm sprocket.

The thickness of the disk mm.

Construction of the tooth profile of an asterisk (Fig. 53).

The coordinate of the radius of curvature mm.

Tooth radius in longitudinal section mm.

Tooth width mm.

Fig. 53. Star parameters:

a) front view; b) side view

Calculation of parameters of the V-belt pulley

Belt drives refer to gears with flexible coupling, through which it is possible to ensure the infinitely variable transmission ratio (Variator Appendix 15). An example of drawing a pulley for a V-belt transmission is given in Appendix 8.

The calculation of the parameters of the V-belt pulley is determined by the cross section of the GOST 1284-68 belt.

For the belt section 0, the calculated diameter of the pulley leading d  1 is determined from the standard range: 63, 71, 80, 90, 100, 112, 125, 140, 160, 180, 200, 224, 250. External pulley diameter = 125 mm.

Depending on the cross section of the belt (Table 18)

  = 125 + 2 × 2.5 = 130mm,

Choose a table. nineteen.

Table 18

Main dimensions of V-belts

Type of	Designation	Sizes of section	Amm 2	Lm	d  1min, mm	T  1, N × m
b	b  etc	h	y 0
Normal section	ABOUT		8,5		2,1		0,4...2,5		£ 30
A				2,8		0,56...4,0		15...60
B			10,5			0,8...6,3		50...150
AT			13,5	4,8		1,8...10		120...600
R				6,9		3,15...15		450...2400
D			23,5	8,3		4,5...18		1600...6000
E						6,3...18		³4000
Narrow	PP		8,5		2,0		0,63…3,55		£ 150
UA				2,8		0,8…4,5		90…140
Ub				3,5		1,25…8,0		300…2000
HC				4,8		2,0…8,0		³1500

Table 19

The parameters of the cross section of the belt and the size of the grooves of the pulley

Mm inner diameter accept d  in = 110 mm.

Pulley rim width:

where z  - number of belts (grooves);

e  - step between grooves;

f  - distance from rim edge.

Options e, f  are shown in fig. 54.

Rim thickness for V-belts.

Sample diameter mm.

Mm hub length, d- diameter of the hole of the hub pulley.

Fig. 54. The profile of the grooves of the pulleys

Bibliographic list

1. Enterprise Standard. Course and diploma design. General requirements for registration: a tutorial / T.I. Steam Room, N.V. Syreyshchikova, V.I. Guzeev, L.V. Vinokourov. - 4th ed., Pererab. and add. - Chelyabinsk: Publishing house of SUSU, 2008. - 56 p.

2. Modern engineering. Machine parts and design fundamentals: textbook / PN. Uchaev, S.G. Yemelyanov, E.V. Pavlov et al. - Moscow: Akademiya, 2008. - 352 p.

3. Anurev, V.I. Reference book of the designer-mechanical engineer: 3 t. / V.I. Anurev / ed. I.N. Zhestkova. –8th ed., Revised and add. - M .: Mashinostroenie, 2001. –T.1. –920с.; Т.2. - 912 s .; V.3. –864s

4. Lelikov, O.P. Fundamentals of calculation and design of parts and components of machines: lecture notes for the course “Machine parts” / О.P. Lelikov. - 2nd ed., Pererab. and additional. - M .: Mashinostroenie, 2004. - 440 p.

5. Dunaev, P.F. Designing units and parts of machines: a manual for engineering specialties of universities / PF. Dunayev, O.P. Lelikov. - M .: Academy, 2004. - 496 p.

6. Scheinblit, A.E. Course design of machine parts: study guide / A.E. Scheynblit. - Kaliningrad: High School, 2002. - 455 p.

7. Akhlyustina, V.V. Machine parts. Calculation of mechanical gears. Designing chain transmissions: a tutorial / V.V.Akhlyustina, E.R. Logunova. - Chelyabinsk: Publishing house, 2008. - 135 p.

8. Ustinovsky, E.P. Multivariate design of cylindrical gear, bevel and worm gears with the use of computers: a manual for course design / E.P. Ustinovsky, Yu.A. Shevtsov, Yu.K. Yashkov. - Chelyabinsk: CSTU, 1995. - 105 p.

9. Sokhrin, P.P. Technical documentation in course design for machine parts: guidelines. P.P. Sokhrin, E.P. Ustinovsky, Yu.A. Shevtsov / ed. P.P. Sohrina. - Chelyabinsk: Chelyabinsk State Technical University, 1994. - 73 p.

10. Akhlyustina, V.V. Metrology, standardization and certification: a tutorial / V.V.Akhlyustina, E.R. Logunova. –Chelyabinsk: Publishing house of SUSU, 2008. - 211 p.

Applications

Annex 1

Appendix 3

Appendix 5

Appendix 7

Appendix 8

1. Tolerance of the coaxiality of the sliding bearings pos. 6, 8, 0.04 mm.

2. The tolerance of parallelism of the guides of position 3, 0.05 mm.

3. Adjust the position of the slide position 1, to provide a screw pos.7.

4. Sliding bearings position 6.8 and rolling elements position 9, lubricate CIATIM 201 GOST 6267-74.

Appendix 11

Pusher to butt welding machine